Processes and eﬀects of root-induced changes to …...Also, Prof. Andrew Bassom provided help in...

Processes and effects of root-induced changes to

soil hydraulic properties

Craig Anthony Scanlan

B. Agribusiness Hons

This thesis is presented for the degree of

Doctor of Philosophy of

The University of Western Australia

School of Earth and Environment

2009

Thesis Abstract

Root-induced changes to soil hydraulic properties (SHP) are an essential component in

understanding the hydrology of an ecosystem, and the resilience of these to climate change.

However, at present our capacity to predict how roots will modify SHP and the conse-

quences of this is limited because our knowledge of the processes and effects are highly

fragmented. Also, current models used to investigate the relationship between plants and

root-induced changes to SHP are based on empirical relationships which have limited ap-

plicability to the various and often contrasting ecosystems that occur. This thesis focuses

specifically on the quantifying the processes by which roots modify SHP and developing

models that can predict changes to these and the water balance.

Both increase and decreases in saturated hydraulic conductivity have been attributed

to the presence of roots. In general, decreases occur when the root system is relatively

young, and increases occur when the roots senesce and begin to decay, creating voids for

water flow. The evidence available suggests that the change in pore geometry created

by roots is the dominant process by which roots modify SHP because they are more

permanent and of a greater magnitude than changes to fluid properties or soil structure.

We first quantified the effects of wheat roots on SHP of a coarse sand with a laboratory

experiment where we measured changes in both SHP and the root system at 3, 5, 7 and

9 weeks after sowing (weeks). From sowing to 7 weeks the plants were in the vegetative

growth phase and Ks showed a declining trend: it decreased to 0.44 of its value by the

end of this period. However, at 9 weeks the wheat plants were in the reproductive growth

stage Ks had increased to 1.32 of its value prior to sowing. While the changes in Ks were

not significant, the trend was in agreement with observations. Changes in unsaturated

hydraulic conductivity occured in the range of 0 to -30 cm matric head.

Given the importance of root radius to changes in SHP we then characterised how

root radius frequency distribution is affected by soil texture and plant type. We collated a

database of reported root radius frequency distributions and fitted distribution functions

to these because the fitted parameters provide a basis for comparison and for calculating

statistical properties of the distribution. We found that the log-normal distribution func-

tion provided the best fit overall and the relationship between fitted parameters showed

iii

some organisation, allowing representative root types to be chosen that reflect the range

that occurs. We found the growth habit and growth media both had a significant effect

on the distribution mean.

To quantify root-induced changes to soil hydraulic conductivity and water retention

we developed a conceptual model based upon the capillary-bundle model. The central

assumption to our model was that the geometry of roots within pores can be simplified to

concentric cylinders, and this allowed us to derive scaling functions for flux, capillary rise

and volume in root-occupied pores as a function of the ratio of inner to outer cylinder radius

β. Overall, this model produced the same trends as those observed: both increases and

decreases were predicted depending on β, however this was sensitive to the connectivity

of pores with roots and soil texture.

While the conceptual model is a useful tool for predicting how roots modify SHP its

application is limited in water flow models as they usually require analytical functions that

describe the hydraulic conductivity and water retention function. We derived a model for

this purpose based upon the van Genuchten-Mualem formulation and the multi-domain

concept, treating the soil as a domain with and without roots. There is no reported data

that is suitable for parameterising the model, therefore we defined the parameter space for

those we introduced from published data and modelling analysis. Comparison of modelled

and observed changes in infiltration rate suggest that in real soils the increases are due to

a small number of vertically-orientated roots with very high connectivity.

In the final research chapter we implemented the analytical model in a water flow

model to examine how root-induced changes to SHP affect soil water storage and plant

uptake over the period of a year. Rainfall for Merredin, Western Australia was modelled

at high temporal resolution using seasonally variable parameters for inter- and intra storm

duration and storm intensity. We simulated 15 years of rainfall with a static root system

present in a sand, loam and clay and found that overall the effects of root-induced changes

were greatest in a clay: both water storage and uptake were significantly greater than soil

not modified by roots. The reason for this was the increase in hydraulic conductivity at

the soil surface resulting in less run-off.

The main message that can be drawn from this thesis is that root-induced changes to

iv

SHP are dynamic, and dependent upon the combination of soil texture, connectivity of

root-modified pores and the ratio of root radius to pore radius. Consequently, root-induced

changes to the water balance have the same dependencies.

The work in this thesis provides a significant first step towards improving our capacity

to predict how roots modify soil hydraulic properties. By defining the range for the param-

eters used to predict how the soil is modified by roots, we are able to make quantitative

assessments of how a property such as hydraulic conductivity will change for a realistic

circumstance. Also , for the first time we have measured changes in soil hydraulic prop-

erties and roots and have been able to establish why a rapid change from a root-induced

decrease to increase in Ks occurred. The link between physiological stage of the root

system, and the changes that are likely to occur has implications for understanding how

roots modify SHP: it may provide an effective tool for predicting when the switch from a

decrease to increase occurs.

Further work is required to test the validity of the assumptions we have made in our

models that predict changes to SHP. While we have endeavoured to define the parameter

space for those parameters that we have introduced, there is still some uncertainty about

the connectivity of root-modified pores. Also, the parameterisation of the soil domain

with roots is based upon work that measures ’fine’ roots only which may not provide a

true representation of the effect trees and perennial shrubs have on SHP. It is inevitable

that root-induced changes to SHP will affect the fate of solutes in the soil, and temporal

dynamics of root-induced changes to these may be particularly important for the timing

of nutrient and pesticide leaching.

v

Thesis Structure

This research conducted for this thesis has been presented in chapters 2 to 6 in the form

of scientific journal articles. Each of these chapters have been prepared as a complete

article, therefore there is some repitition in the introductions to these. It is likely that

some or all of the research chapters will be submitted for publication while this thesis is

being examined. Chapter 7 is a synthesis of this work, providing the major findings, their

implications and the outlook for research in this field of study.

vi

Acknowledgements

First, thank you to my wife Tasma for your unwavering support and belief, looking back

it was a momentous task to organise a wedding, renovate a house and finish a thesis at

the same time, but we did it. Thank you also to my family, friends and colleagues for

your encouragement to take the leap into a PhD. I would also like acknowledge my late

grandfather Bonnie, who inspired the fascination with earth and plants which has lead me

to this work.

A special thanks goes to Dr Gavan McGrath who was always willing to discuss problems

mathematical and technical, and most importantly to share a quiet beer. The daily trips

for coffee with Terry, Mat, Georgie, Michael, Henrick, Vanessa and Trudy were great fun

and a welcome break from a computer screen, and is one of the few things about student

life that I will miss.

There are a number of academics at UWA who have influenced my research. I have

enjoyed my frequent discussions with Em. Prof. Jim Quirk whose unstoppable enthusiasm

for science is inspiring. Also, Prof. Andrew Bassom provided help in simplifying the

mathematics in Chapter 3, and Prof. Zed Rengel and Dr. Andrew Rate helped me find

some direction in the early stages of my project.

I would also like to acknowledge the Grains Research and Development Corporation

and the Department of Agriculture and Food for their financial support.

Finally, I would like to thank my principal supervisor Prof. Christoph Hinz for his

guidance and encouragement. Christoph’s insistence to take a creative approach at the

beginning of my study, and ongoing support for pursuing each tangent as they emerged

has made the journey challenging yet extremely rewarding.

vii

DECLARATION FOR THESES CONTAINING

PUBLISHED WORK AND/OR WORK PREPARED FOR

PUBLICATION

This thesis contains work prepared for publication, some of which has been co-authored.

The bibliographic details of this work are indicated at the beginning of each chapter.

The University requires a declaration of the precise contributions of the student to the

published work and/or a statement of percent contribution by the student. This statement

is presented below and is signed by myself and my coordinating supervisor.

I contributed the majority of the work for all chapters which included experimental

design, model derivation, programming and implementation, analysis of results and writing

each chapter. My coordinating supervisor contributed ideas toward the problem definition

and structure for all chapters and toward model development for Chapters 4, 5 and 6.

Prof. Wolfgang Durner contributed ideas to the experimental design in Chapter 1 and Dr.

Sascha Iden provided assistance with the inverse modelling in the same chapter.

Mr. Craig Scanlan Prof. Christoph Hinz

Signature............................. Signature.............................

Candidate Coordinating Supervisor

ix

Contents

List of Tables vii

List of Figures ix

Chapter1 Introduction and Review 1

1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2. Importance of root-induced changes to soil hydraulic properties . . . . . . . 2

1.2.1. The hydrological feedback . . . . . . . . . . . . . . . . . . . . . . . . 2

1.2.2. Land-use change . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.3. Current modelling approaches . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4. Empirical relationships . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.5. Processes of root-induced changes to soil hydraulic properties . . . . . . . . 8

1.5.1. Pore-space geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

1.5.2. Fluid properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.5.3. Aggregation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.6. Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.7. Research Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.7.1. Objective 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

i

CONTENTS

1.7.2. Objective 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.7.3. Objective 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.7.4. Objective 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Chapter2 Wheat root-induced changes to hydraulic conductivity of a

sand 17

2.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.1. Experimental design . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

2.3.2. Plant growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.3.3. Multi-step outflow experiment . . . . . . . . . . . . . . . . . . . . . 23

2.3.4. Analysis of multi-step outflow data . . . . . . . . . . . . . . . . . . . 24

2.3.5. Plant measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.4.1. Saturated hydraulic conductivity . . . . . . . . . . . . . . . . . . . . 27

2.4.2. Root properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

2.4.3. Inverse analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

2.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

Chapter3 Using radius frequency distribution functions as a metric

for quantifying root systems 35

3.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

3.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.1. Data collection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3.2. Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.3. Calculation of root volume and surface area . . . . . . . . . . . . . . 39

ii

CONTENTS

3.4. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.4.1. Description of database . . . . . . . . . . . . . . . . . . . . . . . . . 51

3.4.2. Application of frequency distribution functions to database . . . . . 52

3.4.3. Regression analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

3.4.4. Statistical properties of root radius frequency distributions . . . . . 54

3.4.5. Root system volume and surface area . . . . . . . . . . . . . . . . . 57

3.4.6. Relevance of integral limits to root radius frequency distributions . . 58

3.4.7. Influence of botanical traits on derived parameters . . . . . . . . . . 60

3.4.8. Influence of methodology on derived parameters . . . . . . . . . . . 61

3.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

Chapter4 A conceptual model of root-induced changes to soil

hydraulic properties 65

4.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

4.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

4.3. Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3.1. Fluid behaviour in concentric cylinders . . . . . . . . . . . . . . . . . 68

4.3.2. Geometric features of root systems . . . . . . . . . . . . . . . . . . . 71

4.3.3. Geometric features of the soil . . . . . . . . . . . . . . . . . . . . . . 72

4.3.4. Modified capillary-bundle model . . . . . . . . . . . . . . . . . . . . 73

4.4. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

4.4.1. Saturated hydraulic conductivity . . . . . . . . . . . . . . . . . . . . 78

4.4.2. Unsaturated hydraulic conductivity . . . . . . . . . . . . . . . . . . 81

4.4.3. Water retention . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.4.4. Application of model to experimental data . . . . . . . . . . . . . . 82

4.5. Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.5.1. Comparison of model predicted and reported root-induced changes

to SHP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

4.5.2. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

iii

CONTENTS

Chapter5 A dynamic model of root-induced changes to soil hydraulic

conductivity and water retention 89

5.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

5.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

5.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.1. Model theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5.3.2. Scaling hydraulic properties . . . . . . . . . . . . . . . . . . . . . . . 92

5.3.3. Domain with roots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

5.3.4. Domain without roots present . . . . . . . . . . . . . . . . . . . . . . 95

5.3.5. Hydraulic functions of the modified soil . . . . . . . . . . . . . . . . 97

5.3.6. Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . 97

5.3.7. Parameter sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . 98

5.3.8. Application: Ponded infiltration . . . . . . . . . . . . . . . . . . . . 98


5.4.1. Parameter estimation for domain with roots . . . . . . . . . . . . . . 100

5.4.2. Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

5.4.3. Application: Ponded infiltration . . . . . . . . . . . . . . . . . . . . 106

5.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

Chapter6 The impact of root-induced changes to soil hydraulic

properties on the water balance 111

6.1. Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111

6.2. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112

6.3. Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.3.1. Rainfall modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.3.2. Water flow modelling . . . . . . . . . . . . . . . . . . . . . . . . . . 114


6.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

iv

CONTENTS

Chapter7 Synthesis and Outlook 123

7.1. Summary of chapters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

7.2. Conclusions and implications . . . . . . . . . . . . . . . . . . . . . . . . . . 126

7.3. Limitations and future work . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

Appendices 129

AppendixA Derivations for Chapter 4 131

A.1. Capillary rise in concentric cylinders . . . . . . . . . . . . . . . . . . . . . . 131

A.2. Derivation of dimensionless ratios . . . . . . . . . . . . . . . . . . . . . . . . 132

A.2.1. Capillary rise ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132

A.2.2. Flux ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133

A.2.3. Volume ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

A.3. Derivation of conductivity function . . . . . . . . . . . . . . . . . . . . . . . 134

AppendixB Compression data 137

AppendixC Parameter values used for one at a time sensitivity analysis 139

Bibliography 141

v

List of Tables

1.1. Summary of changes in hydraulic conductivity attributed to the activity of

root systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1. Composition of nutrient solution used to grow wheat in columns . . . . . . 23

2.2. Summary of changes to the root system and saturated hydraulic conduc-

tivity over the course of the experiment . . . . . . . . . . . . . . . . . . . . 28

3.1. Functions used to analyse root radius frequency distributions . . . . . . . . 42

3.2. Functions used to analyse higher moments of root radius frequency distri-

butions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.3. Botanical and methodological attributes and optimised parameters for the

log-normal distribution function for each observed root radius frequency

distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.1. Log-normal distribution parameters for 3 root types . . . . . . . . . . . . . 72

4.2. List of parameters used in the modified capillary-bundle model . . . . . . . 79

5.1. List of parameters for the analytical model . . . . . . . . . . . . . . . . . . 101

6.1. Parameter values used for Ks of root-modified domain and soil hydraulic

functions in the sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . 117

B.1. Change in van Genuchten α and Ks with compression . . . . . . . . . . . . 138

vii

List of Figures

2.1. Cross-sectional illustration of the column design used for the experiment . . 21

2.2. Apparatus used to raise the columns during the multi-step outflow experiment 22

2.3. An example of measured and simulated outflow and matric head from the

multi step outflow experiment . . . . . . . . . . . . . . . . . . . . . . . . . . 25

2.4. An example of optimised hydraulic conductivity and water retention func-

tions for a soil column prior to planting and after plant growth . . . . . . . 29

2.5. Summary of r2 of observed vs. predicted cumulative outflow and matric

potential for differing numbers of nodes . . . . . . . . . . . . . . . . . . . . 30

3.1. Graphical representation of conversion of an histogram to cumulative fre-

quency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.2. Comparison of observed data and fitted distribution functions for 4 examples 53

3.3. Summary of RMSE for each function used for regression analysis of root

radius frequency distributions . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.4. Optimised parameters for the log-normal CDF for each root radius fre-

quency distribution in the database . . . . . . . . . . . . . . . . . . . . . . . 55

3.5. Summary of the distribution mean, variance, skewness and kurtosis of the

root radius frequency distributions in our database . . . . . . . . . . . . . . 56

3.6. Summary of root surface area and volume calculated with Equations 3.5

and 3.6 respectively for the root radius distributions in our database . . . . 58

ix

LIST OF FIGURES

3.7. Percent error in root volume and surface area calculated using the mean

root radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

3.8. Relationship between error of root surface area and volume calculated using

the histogram-based method and the skewness of the root radius distribution 59

3.9. Summary of cumulative frequency, % of root surface area and % of root

volume from a continuous distribution at the physiological lower limit of

root radius . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.10. Root radius frequency distribution mean grouped by growth habit . . . . . 62

4.1. A conceptual cross-section of capillary rise in a cylinder and between con-

centric cylinders . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

4.2. The effect of the ratio of root radius to pore radius on change in capillary

rise, flux and volume in pores with roots present . . . . . . . . . . . . . . . 71

4.3. The interaction between soil texture, connectivity of root-modified pore

space and the ratio of root to pore radius on changes to saturated hydraulic

conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80

4.4. Comparison of cumulative frequency distributions of pore and root radius . 81

4.5. Effect of root type and connectivity of root-modified pore space on root-

induced changes to the unsaturated hydraulic conductivity function of a

sand . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

4.6. Interaction between the ratio of root radius to pore radius and soil texture

on root-induced changes to water retention . . . . . . . . . . . . . . . . . . 83

4.7. Comparison of observed and modelled root-induced changes to saturated

hydraulic conductivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

5.1. The ratio of van Genuchten (1980) α for soil in the compressed to original

state cα, and the ratio of saturated hydraulic conductivity for soil in the

compressed to original state cK . . . . . . . . . . . . . . . . . . . . . . . . . 96

5.2. Graphical illustration of the two root profiles used to investigate the effect

of root-induced changes to SHP on infiltration under ponded conditions . . 99

x

LIST OF FIGURES

5.3. Parameter values for the van Genuchten (1980) effective saturation function

for the domain with roots derived from root radius frequency distributions . 102

5.4. A comparison of the effective saturation functions for three representative

root distributions and three soil types . . . . . . . . . . . . . . . . . . . . . 102

5.5. A summary of the goodness of fit of the van Genuchten (1980) effective

saturation function to root radius frequency distributions . . . . . . . . . . 103

5.6. Modelled relationship between macroporosity and saturated hydraulic con-

ductivity of the soil domain with roots . . . . . . . . . . . . . . . . . . . . . 104

5.7. Sensitivity ofKsm predicted using Equation 6.6 to changes in model parameters105

5.8. Sensitivity of predicted changes to the hydraulic conductivity function to

changes in β, B1, and root length density. . . . . . . . . . . . . . . . . . . . 107

5.9. Sensitivity of predicted changes to the water retention function to changes

in soil texture, root length density and β. . . . . . . . . . . . . . . . . . . . 108

5.10. Effect of connectivity of root modified domain and vertical root distribution

on temporal infiltration rate . . . . . . . . . . . . . . . . . . . . . . . . . . . 109

6.1. Seasonal storm properties for Merredin . . . . . . . . . . . . . . . . . . . . . 115

6.2. Seasonal patterns of mean soil water storage for soil with and without root

modifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

6.3. Seasonal patterns of mean cumulative plant water uptake for soil with and

without root modifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119

6.4. Mean annual run-off as a fraction of rainfall for soils in their original state

and after root modification . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

6.5. An example of simulated changes in the water balance for a clay where the

root-modified soil has low connectivity . . . . . . . . . . . . . . . . . . . . . 121

xi

Chapter 1Introduction and Review

1.1 Introduction

Root-induced changes to soil hydraulic properties (SHP) are an essential component in

understanding how soils and plants interact, and the resilience of ecosystems to climate

change. These changes are particularly relevant to the soil-plant hydrological feedback

that occurs in arid areas, and the change in hydrology that results from a change in land

use such as a change of crop type, forestry or revegetation.

At present our capacity to predict how roots will modify SHP and the consequences of

this is limited because our knowledge of the processes and effects are highly fragmented.

Also, current models used to investigate this feedback are based on empirical relationships

which have limited applicability to the myriad of ecosystems that occur. To improve our

capacity to predict the effect of root induced changes on this feedback, models based upon

a clear understanding of the processes that cause these are required.

In general there is a lack of cohesion between the processes of root-induced changes

to SHP and the observed change in behaviour that results. Typically, work in this area

quantifies one or the other. For example, both decreases and increases in near- and

saturated hydraulic conductivity have been attributed to the growth and subsequent decay

of roots but no quantitative measure of roots was made (Meek et al., 1989, 1992; Murphy

et al., 1993). In some cases macropores created by roots have been measured, but without

a direct measurement of the roots that created them (McCallum et al., 2004; Meek et al.,

1

CHAPTER 1. INTRODUCTION AND REVIEW

1989; Rasse et al., 2000). Alternatively, root growth has been shown to cause zones of

compaction (Braunack and Freebairn, 1988; Bruand et al., 1996; Clemente et al., 2005)

and to affect aggregate stability (Ellsworth et al., 1991; Perfect et al., 1990) but the impact

of these on SHP was not measured. While there are reports that relate infiltration rate to

root mass (Barley, 1954; Petersson et al., 1987), they are insufficient to derive empirical

relationships or to make a quantitative assessment of the mechanisms causing change.

This thesis focuses specifically on the processes by which roots modify SHP and pre-

dicting the changes to these and the water balance. In this chapter we first establish the

importance of root-induced changes to SHP to the hydrology of an ecosystem, and discuss

current approaches to modelling this. We highlight the need for a process-based descrip-

tion of root-induced changes to SHP and then examine each of these processes in detail,

and identify the most important processes. Finally, we develop research objectives that

systematically address the work required to improve our capacity to predict root-induced

changes to SHP.

1.2 Importance of root-induced changes to soil hydraulic

properties

1.2.1 The hydrological feedback

Root-induced changes to soil hydraulic properties (SHP) are central to the hydrological

feedback between plants and soils. This feedback occurs when plant roots change soil to

an extent that the hydraulic properties of the soil have changed, leading to a change in

water available to the plant. This feedback may be positive or negative: positive in the

case where changes to soil hydraulic properties lead to an increase in the rate of plant

growth and therefore to further modification of the soil, or negative in the case where

root-induced changes decrease the amount of water available, leading to less growth and

modification of the soil until a steady-state is reached (Ehrenfeld et al., 2005).

The study of the occurrence and influence of the plant-soil hydrological feedback has

mostly focused on arid ecosystems. This feedback has been proved to be a critical fac-

tor in explaining how, and why patchy or banded vegetation occurs (Gilad et al., 2007;

2

1.3. CURRENT MODELLING APPROACHES

HilleRisLambers et al., 2001; Rietkerk et al., 2002; Saco et al., 2007; Ursino, 2007; von

Hardenberg et al., 2001). The underlying principle to this feedback in arid environments

is that infiltration rate is higher where plants are present and that the spatial arrangement

of vegetation and bare areas evolves as an optimal run-on - run-off system. There is a

considerable body of evidence that shows that infiltration rate is higher where vegetation

is present (Dunkerley, 2002; Greene, 2002; Rietkerk, 1998; Seyfried, 1991; Wilcox et al.,

2003), and the processes which cause this are believed to be principally the formation of

macropores by decayed roots, a greater fraction of aggregates and protection of the soil

surface from raindrop impact by leaf litter (Wilcox et al., 2003).

1.2.2 Land-use change

When a change in land use occurs, for example from annual crops to lucerne, or the

revegetation of earth covers for mine-site rehabilitation, dramatic changes in the water and

solute balance can occur. Where annual crops have been replaced with lucerne increases

in infiltration rate over the first 3 to 4 years of 200 to 400% have been observed, which is

attributed to the formation of macropores by the decaying lucerne taproot (Meek et al.,

1989, 1990, 1992; Mitchell et al., 1995; Rasse et al., 2000). While there is no evidence of

how these changes in SHP affected the water balance or crop growth, Kavdir et al. (2005)

found that decayed lucerne taproots contributed to nitrate leaching. This also appears

true for earth covers that are created over mine sites where increases in infiltration rate

have been observed over the first 2 to 3 years (Loch and Orange, 1997).

1.3 Current modelling approaches

To date modelling studies of the plant-soil hydrological feedback have employed relatively

simple empirical approaches to the interaction between plants and SHP. HilleRisLambers

et al. (2001) proposed a function based on empirical evidence (Rietkerk, 1998) where

infiltration rate has a positive though asymptotic relationship with vegetation density,

which has been used by others in the study of the influence of various forcing variables

on the evolution of spatial vegetation patterns (Ursino, 2007; Saco et al., 2007; Rietkerk

et al., 2002; Gilad et al., 2007). Similarly, the effect of precipitation rates on the spatial

3


organisation of vegetation was studied by including a feedback where run-off decreases as a

function of biomass density (von Hardenberg et al., 2001). Interactions between the plant-

soil feedback and the vegetation-precipitation feedback have been studied by implementing

the HilleRisLambers et al. (2001) model (Dekker et al., 2007), and interactions with the

vegetation-shading feedback were studied using weighted infiltration for bare and vegetated

areas (Baudena and Provenzale, 2008). All of these studies approach the influence of the

plant-soil feedback at a conceptual level: the generation of spatial patterns by the models

similar to those observed was qualitative evidence that the major processes had been

accounted for. However, there has been no analysis of the sensitivity of these predictions to

the parameterisation of the relationship between infiltration rate and vegetation density, or

indeed how these parameters change for different combinations of soil and vegetation types.

While these models have provided insight into how we can expect vegetation patterns to

change in response to different forcing variables, the reliance on an empirical function is a

weakness.

The widely used empirical relationships between infiltration rate and vegetation

density may have limited ecological scope

The use of a single empirical relationship between infiltration rate and vegetation

density can not accurately describe the temporal changes to infiltration rate caused by a

new or invading plant. For example, the relationship derived by HilleRisLambers et al.

(2001) is based upon data from soil-plant systems that are well established (Rietkerk,

1998), and application of this function makes the assumption that infiltration rate increases

instantaneously when plants are present. However, this is not the case: there is a time-lag

between the establishment of a new plant and an increase in infiltration rate (Deuchars

et al., 1999; Meek et al., 1989, 1992; Petersson et al., 1987; Loch and Orange, 1997;

Murphy et al., 1993). The time-lag reflects the lifespan and decay rate of the root systems

present (Eissenstat and Yanai, 1997; Gill and Jackson, 2000; Silver and Miya, 2001). The

spatial propagation of vegetation is likely to be highly sensitive to this time-lag, and the

exclusion of this is a major conceptual flaw of current approaches to modelling feedbacks.

The inclusion of a process-based prediction of root-induced changes to infiltration rate is

4

1.4. EMPIRICAL RELATIONSHIPS

required to improve modelled predictions of ecosystem response for different soil and plant

types and climatic conditions.

Process-based modelling of root-induced changes to SHP will provide a more

realistic analysis of the sensitivity of the hydrological feedback to different com-

binations of soil type, plant type and climatic conditions

1.4 Empirical relationships

The only empirical relationships we are aware of that relate root properties to any SHP

are for hydraulic conductivity in the near-saturated range. Prathapar et al. (1989) found

a positive linear relationship between hydraulic conductivity at 4 cm tension (K−4) and

root length density of senesced wheat and pasture. In this case, K−4 of the clay loam

was far more sensitive to root length density of wheat than pasture, which was attributed

to changes in pore structure created by tillage used in the wheat field. Alternatively,

Barley (1953) found a negative linear relationship between infiltration rate and root mass

in pasture that included annual and perennial plants in autumn, which he attributed to

roots blocking pore space. The most likely explanation of this difference in response is

the maturity of the roots present in the two studies. The roots of the plants studied

by Prathapar et al. (1989) would have been at various stages of decay creating voids for

water flow, while the roots of the annual plants in the pasture studied by Barley (1953)

would have been fully intact and blocking pore space. This explanation is supported by

Petersson et al. (1987) who found that infiltration rate was negatively related to root mass

where trees were less than 3 years old, but positively related where trees were 15 to 20

years old.

There are no clear empirical relationships between root-induced changes to Ks and

plant type or period of growth. Table 1.1 shows a summary of increases and decreases

in near- and saturated hydraulic conductivity that have calculated from measurements of

Ks prior to and after root growth. Comparison of the change in Ks and species, texture,

location and decay period do not show any clear trends. Of the reports in Table 1.1, only

Barley (1954) and Sedgley and Barley (1958) include a quantitative measure of the roots

5


present who reported that roots occupied 8.4% and 2.6% of the pore volume respectively.

There are no clear empirical relationships between root-induced changes to Ks

and different plant or soil types

6

1.4.EMPIR

ICALRELATIO

NSHIP

S

Table 1.1: Summary of changes in hydraulic conductivity attributed to the activity of root systems%change

Ks prior Control Species Treatment Ks af-ter

Texture Location Measurement Growingperiod*

Decayperiod*

Reference

Increases

654 4.9*10−2 Unplanted Lucerne 3.2*10−1 Silt loam Column Ks 3 18 Li and Ghodrati(1994)

635 4.9*10−2 Unplanted Corn 3.1*10−1 Silt loam Column 2 18 Li and Ghodrati(1994)

537 8.3*10−2 Bare fal-low

Lucerne RSM 4.5*10−1 Loam Field Ks 33 2 Kavdir et al. (2005)

400 3.8*10−2 Initialvalue

Lucerne Light traffic 1.5*10−1 Sandy loam Field IR 30 Meek et al. (1992)

397 2.2*10−2 Initialvale

Lucerne NT 8.6*10−2 Sandy loam Field IR 36 Meek et al. (1990)


Lucerne RSM 2.8*10−1 Loam Field Ks 33 4 Kavdir et al. (2005)

323 1.4*10−1 Initialvale

Wheat Direct drilling 4.4*10−1 Clay loam* Field Ks(0.5 hPa) 4.8 Suwardji and Eber-bach (1998)

230 2.5*10−3 Initialvalue*

Lucerne NT 5.9*10−3 Silty clay Field IR 41 Mitchell et al.(1995)

200 4.4*10−2 Initialvalue

Lucerne NT 8.7*10−2 Sandy loam Field IR 38 Meek et al. (1989)


Lucerne RSM 2.5*10−2 Loam Field Ks 24 Rasse et al. (2000)

118 1.2E+00 Initialvale

Corn Over plants inrow

1.4E+00 Clay loam Field IR 3 Prieksat et al.(1994)

Decreases

-33 1.9*10−1 Initialvalue

Corn 1.3*10−1 Sandy loam Column Ks 0.5 2 Barley (1953)

-41 2.3*10−1 Initialvale

Corn No till-Loose 1.3*10−1 Sandy loam Field IR 36 Meek et al. (1990)


Lucerne NT 2.2*10−2 Sandy loam Field IR 3.2 Meek et al. (1989)

-63 3.4*10−4 Unplanted Ryegrass 1.3*10−4 Sandy loam Column Ku(-30 hPa) 8 6 Sedgley and Barley(1958)

-72 4.4*10−3 Initialvale

Wheat Direct drilling 1.2*10−3 Clay loam* Field Ku(-4 hPa) 4.8 Suwardji and Eber-bach (1998)

-81 4.4*10−4 Unplanted Ryegrass 8.5E-05 Sandy loam Column Ku(-30 hPa) 8 Sedgley and Barley(1958)


Corn 2.1*10−2 Sandy loam Column Ks 0.5 Barley (1953)

RSM = roots and shoot mulch, IR = infiltration rate, Ks = saturated hydraulic conductivity (cm min−1, NT = no traffic* Growth and decay period are in months

7


1.5 Processes of root-induced changes to soil hydraulic prop-

erties

The processes by which roots modify SHP are numerous and we have grouped these as

changes to pore space geometry, aggregation and fluid properties. Roots change the geom-

etry of pore space by filling pore spaces, creating macropores when they decay, rearranging

soil particles and changing connectivity. In addition, the compounds released by roots col-

lectively known as root exudates play a role in the formation of aggregates and of the

physical properties of the soil solution. We now examine each of these in detail.

1.5.1 Pore-space geometry

Decreases in near- and saturated hydraulic conductivity have been attributed to the block-

ing of pore space by roots. Most decreases in Ks that have been reported are in agricultural

crops when they are relatively young. For example, in a cotton crop infiltration rate de-

creased by 40% after 67 days of growth (Meek et al., 1990), and infiltration rate in lucerne

decreased by 55% from 189 to 264 days after sowing Meek et al. (1989). Over three years

and three locations Murphy et al. (1993) found that hydraulic conductivity at -1 cm matric

potential in wheat crops decreased by 20 to 60 % from seeding to tillering, and that while

the same trend was observed at -4 cm matric potential the amount of change was far less.

The greatest decrease that has been reported occured when corn was grown in columns

of a synthetic sandy loam and Ks decreased by 90% (Barley, 1954). Decreases in Ks have

been found where 2 to 3 year old acacia trees were present, but an increase where 20 to

25 year old trees were present (Petersson et al., 1987).

Decreases in near- and saturated hydraulic conductivity have been observed when

the root system is relatively young

The longevity of root-induced decreases in hydraulic conductivity depends upon the

lifespan of the root and how long it takes to decay. For example, decreases in Ks due to

roots have been reported for wheat plants up to tillering (Murphy et al., 1993), and it

has been found that in spring wheat 17% of the roots produced during the period from

8

1.5. PROCESSES OF ROOT-INDUCED CHANGES TO SOIL . . .

emergence to stem elongation had decayed by stem elongatioin, and from elongation to

ripening 37% of roots produced had decayed (Swinnen et al., 1994). The increase in decay

rate observed by Swinnen et al. (1994) explains the change from a decrease to increase

in Ks observed at a similar stage by Murphy et al. (1993). The difffent time scales in

the switch from a decrease to increase in Ks where wheat (Murphy et al., 1993; Suwardji

and Eberbach, 1998) or trees (Petersson et al., 1987) are grown are partly attributable

to species and root diameter, but also temperature, latitude and the ratio of carbon to

nitrogen in the roots (Eissenstat and Yanai, 1997; Gill and Jackson, 2000; Silver and Miya,

2001).

The lifespan and rate of decay of a root system determines when a shift from an

decrease to an increase in Ks will occur

Increases in near- and saturated hydraulic conductivity have been frequently attributed

to the formation of macropores by decaying roots. The greatest increase that has been

reported occurred where lucerne was grown in columns of silt loam for 3 months before

being terminated and left to decay for 18 months, where Ks increased by a factor of 6.5 (Li

and Ghodrati, 1994). Most of the increases occur in lucerne crops; however, this reflects the

focus of the studies rather than a true comparison between species. The changes reported

by Li and Ghodrati (1994) are an interesting example: these plants were only grown for

2 to 3 months before being terminated, yet caused the greatest observed increase. This

may be because the roots were allowed to decay for 18 months, which would be sufficient

time for almost complete decay (Silver and Miya, 2001; van Noordwijk et al., 1994).

The macropores formed by decayed roots typically have a greater radius and connec-

tivity than matrix pore structure. Macropores left by decayed roots tend to be long and

tubular in comparison to pore space in the soil matrix (Jassogne et al., 2007; Tippkotter,

1983); however, their cross-sectional geometry is more likely to be annular than circular

because remnants of the decayed root may remain in the void (Barley, 1954). Macropores

formed by graminoids and lucerne have been observed up to 1 (Barley, 1954; Tippkotter,

1983) and 8 mm (McCallum et al., 2004; Meek et al., 1992) in diameter respectively, which

is relatively large compared to those in the soil matrix. Additionally, the connectivity (de-

9


fined as the reciprocal of tortuosity) of root induced macropores is greater than within

the soil matrix. For example, using the length / effective length conceptualisation of con-

nectivity Perret et al. (1999) found that macropores in a soil a long-term pasture had a

connectivity of 0.92 to 0.42, whereas Moldrup et al. (2001) found that the connectivity of

a range of soil textures was approximately 0.5 at saturation and decline rapidly as water

content decreased.

Pore space left by decaying roots has a greater connectivity than the soil matrix

and is likely to have an annular geometry

The evidence available suggests that roots tend to occupy the larger pores in the soil

matrix. For example, up to 65% (van Noordwijk et al., 1993) and 54 to 41% (North and

Nobel, 1997) of roots have been found to be occupying pores with a greater radius or

between cracks and aggregates (van Noordwijk et al., 1993). Stewart et al. (1999) found

that 11 to 26 % of the roots of native grasses were located within macropores, which was

5 to 15% more than if roots were located purely at random. Also, channels formed by

decaying roots are often recolonized by new roots (Rasse and Smucker, 1998; Wang et al.,

1986; Williams and Weil, 2004). However, Stewart et al. (1999) also found that 80% of

roots were located within 1.1 to 2.2 mm of a macropore which may reflect the higher

fertility of this soil (Pankhurst et al., 2002).

Roots tend to occupy the larger pores in the soil matrix

When roots grow into and expand within a pore whose initial radius is smaller that

the radius of the root a zone of compression is created around the root. The compression,

or increase in density, declines exponentially as distance from the root increases, and has

been shown to extend 1 to 2 mm from the surface of maize roots Bruand et al. (1996) and

at least 40 mm from the surface of a 27 year-old Eucalyptus grandis tree roots (Clemente

et al., 2005). Porosity near the root surface was reduced from 0.41 to 0.32 by maize roots

(Bruand et al., 1996) and to 0.15 to 0.25 adjacent to tree roots (Clemente et al., 2005). The

compression caused by roots is an important consideration because Ks has been shown to

decline linearly with compression (Assouline, 2006b; Zhang et al., 2006).

10

1.5. PROCESSES OF ROOT-INDUCED CHANGES TO SOIL . . .

Where roots expand within an initially smaller pore a zone of compression is

created around the root

1.5.2 Fluid properties

The compounds released by roots are collectively termed root exudates (Curl and Truelove,

1986) and these can change the fluid properties of soil water. Read and Gregory (1997)

found that root exudates of maize and lupin reduced surface tension from 72.5 (pure

water) to 48 mN m−1 when exudate concentration was 0.7 mg mL−1 which according to

the Young-Laplace equation will lead to a reduction in matric head and there is evidence

to support this. Using a synthetic analogue for root exudates at a concentration of 0.5 mg

mL−1 Read et al. (2003) found that soil water content was 0.02 cm3 cm−3 less between 2000

and 7000 cm matric head. Read and Gregory (1997) also found that exudates increased

viscosity from 1 (pure water) to 2.1 mPa s−1 at 0.7 mg L, and according to Poiseuille’s

law should lead to a decrease in hydraulic conductivity. Hallett et al. (2003) found that

sorptivity was lower in the rhizosphere than the bulk soil which suggests that a decrease

in hydraulic conductivity occurred. However, the change in surface tension and viscosity

were sensitive to concentration of the exudates (Read and Gregory, 1997) and the amount

of solid material in the exudates (Read et al., 1999), and the concentration of exudates at

the root surface were sensitive to growing conditions (Read and Gregory, 1997).

The concentration of root exudates declines exponentially as distance from the root

increases. Using a pulse labelling technique it has been shown that approximately 2/3 of

the exudate produced remains within 2 mm of the root surface (Kuzyakov et al., 2003;

Norton et al., 1990; Sauer et al., 2006), and that 4 days after the pulse of 14CO2 was

applied exudates diffused to 12 to 15 mm from the root surface (Kuzyakov et al., 2003;

Sauer et al., 2006), and to 20 mm from the root surface after 18 days of exposure to

14CO2 (Helal and Sauerbeck, 1983). However, movement of labelled C through hyphal

strands several cm from the root surface has also been observed (Norton et al., 1990) The

concentration of labelled C near the root surface is supported by evidence that bacteria

and carbon content are greater in the 1-3 mm of soil surrounding macropores (Pierret

11


et al., 1999; Pankhurst et al., 2002) than the bulk soil, and that rhizosphere sheath of corn

roots was 0.4 to 1.2 mm (Watt et al., 1994), all of which have some dependence upon root

exudates. However, the spatial distribution of exudates does not remain static as it is

readily depleted by sorption, oxidisation and microbial degradation (Inderjit and Weston,

2003).

The evidence of the longevity of root exudates is scarce. After 1 week Norton et al.

(1990) found that the labelled C concentration outside the rhizosphere decreased by 50%.

Over a growing season Swinnen et al. (1995) found that microbial respiration consumed

54 to 87 % of the rhizodeposit at tillering, and Warembourg and Paul (1977) found that

the season patternal in rhizosphere respiration in a native grassland was highly variable

and appeared to be related to water content.

Changes to fluid properties are mostly confined near to the root surface, and

there is paucity of information about how long this effect will last

1.5.3 Aggregation

The growth and activity of roots has been shown to affect the size and stability of soil

aggregates, and this can directly affect the water balance because infiltration rate is pos-

itively correlated with these measures (Lado et al., 2004b,a). Aggregates improve the

entry of water into the soil by protecting the soil surface from raindrop impact and ulti-

mately surface sealing, and aggregate stability has been shown to be a good predictor of

infiltration rate (Wood and Blackburn, 191).

Plant species has been shown to affect changes in aggregate stability throughout a

growing season. Ellsworth et al. (1991) found that wet aggregate stability was generally

lower under soybeans than corn and Perfect et al. (1990) found that it was greater under

lucerne and bromegrass than corn. The difference in wet aggregate stability where the

different species were grown was attributed to different root exudate release and wetting

and drying cycles; however, neither provided a comparison with soil without plants present.

To our knowledge only Rasse et al. (2000) has compared aggregate properties of soil with

and without roots present and found that the mean weight diameter of aggregates and Ks

12

1.6. SUMMARY

was significantly greater where lucerne roots were present.

Wetting and drying cycles can lead to both an increase and decrease in the fraction

of soil that is aggregates. In an aggregated soil, Degens (1997) found that overall wet-dry

cycles decreased the amount of stable aggregates > 0.25 mm. Contrary to this, Czarnes

et al. (2000) found that porosity increased for up to 5 wetting and drying cycles, both

with and without root exudate analogues. It is difficult to separate the effects of wet/dry

cycles from that of root exudates because they generally occur simultaneously and both

affect aggregation (Kavdir et al., 2005; Materechera et al., 1992; Rasse et al., 2000).

There is little data on how roots change the properties of aggregates in comparison

to a bare soil, and there is contradictory evidence as to whether root growth leads

to an increase or decrease in the fraction of soil that is present as aggregates

1.6 Summary

Root-induced changes to SHP can have a major effect on how an ecosystem functions.

These changes can lead to a hydrological feedback between plants and soils and contribute

the spatial arrangement of vegetation patches in arid areas. Root-induced changes can

also have a major effect when a change of land use occurs, leading to greater infiltration

and solute leaching.

Our ability to predict how plants will change SHP is limited. Current modelling

approaches use an empirical relationship between vegetation density and infiltration rate;

however, this relationship has limited scope and assumes an instantaneous increase when

vegetation is present and this is not the case. Our ability to predict what changes will

occur and their consequences can only be improved by a better understanding of the

processes and developing models based upon this.

We summarise that changes to pore geometry appear to be the dominant mechanism

for root-induced changes to SHP. First, the effects are more permanent: roots can block

pores or act as a macropore once decayed for periods of months to years, whereas changes

to fluid and aggregate properties are controlled by shorter term processes such as the

release and consumption of root exudates and wetting and drying cycles. Second, the

13


effects appear to be greater: changes to pore geometry have lead to changes in near- and

saturated hydraulic conductivity from -90 to 650 %. While fluid properties have been

shown to decrease water content by approximately 7 % this was for soil where the entire

soil solution was modified, when in reality this zone is confined to the zone near the root

surface.

1.7 Research Objectives

In the review we identified that the key to improving the prediction of the changes roots

cause to SHP is a better understanding of the processes, and that the dominant process is

changes to pore geometry. To address this we developed four sequential research objectives

which are addressed in this thesis.

1.7.1 Objective 1

Obtain experimental evidence of how roots modify the soil water retention and hydraulic

conductivity functions over the life-cycle of the plant

Both increases and decreases in near- and saturated hydraulic conductivity have been

attributed to the activity of roots; however, there are no reports that make a quantita-

tive link between geometric properties of the root system and changes in soil hydraulic

properties. Changes in water retention due to roots have also been reported but not in

conjunction with measurements of hydraulic conductivity. The aim of this work is to pro-

vide a holistic picture of how plant roots modify soil hydraulic properties, by measuring

the hydraulic conductivity and water retention functions of root-modified soils, and the

length and radius of the root system. We expect the effect of the roots on SHP to change

as the plant matures.

1.7.2 Objective 2

Collate quantitative information about root systems that can be used to predict how different

types will change soil hydraulic properties

Root length and root radius frequency distribution are the simplest quantitative mea-

sures of root system geometry, and appear to be the dominant factors that determine how

14

1.7. RESEARCH OBJECTIVES

much change roots can cause to soil hydraulic properties. However, there is no synthesis

of the reported data for different plant types. By collating reported data we expect to

be able to identify how different plant types, soil types and climatic conditions affect the

shape of the root radius frequency distribution.

1.7.3 Objective 3

To develop a conceptual model that will predict root-induced changes to soil water retention

and hydraulic conductivity based upon the geometric properties of the root system and

initial soil parameters

A model that predicts root-induced changes to SHP is required to investigate how these

changes affect the water balance using a water flow model. While empirical models that

relate infiltration rate to biomass exist, their application is constrained to the environments

they were derived from, and provide no insight into the temporal developments of root-

induced changes. A physically-based model is required for this purpose as provides a

clear test as to whether the physical principles included can explain the changes to SHP

that have been observed, and because it provides a clear link between the process of

root-induced changes to the outcomes of changes to the water balance.

1.7.4 Objective 4

To investigate how root-modified SHP change infiltration and redistribution of rainfall and

assess the potential impact of this on plant water uptake

While there is a body of evidence that shows that roots can modify SHP there has been

no work that investigates specifically how this affects soil water storage and plant water

uptake. By incorporating the conceptual model (Objective 3) into a water flow model

we expect to be able to quantify how root-induced changes affect storage and uptake for

different soil types.

15

Chapter 2Wheat root-induced changes to hydraulic

conductivity of a sand

C.A. Scanlan1, C. Hinz1, W. Durner2 and S. Iden2

1. School of Earth and Environment, The University of Western Australia, 35 Stirling

Highway, Crawley 6009, Australia

2. Institut fur Geookologie, Technische Universitat Carolo - Wilhelmina zu Braun-

schweig, Langer Kamp 19c, 38106 Braunschweig, Germany

2.1 Abstract

Root-induced changes to soil hydraulic properties occur across a range of soils and plant

species; however, there is a lack of quantitative evidence relating these changes to prop-

erties of root systems. We conducted a multi-step outflow experiment on soil columns

with wheat plants present at 3, 5, 7 and 9 weeks after sowing, and used a combination of

direct and inverse methods to determine the water retention and hydraulic conductivity

functions of these. The trend in root-induced changes was related to the physiological

development of the wheat plants; Ks decreased during the vegetative phase to 0.44 of its

value prior to sowing and increased to 1.3 of its value prior to sowing during the repro-

ductive phase. Root-induced changes to the hydraulic conductivity functions occurred in

the range of 0 to -30 cm matric head. While there was a lack of significance in change in

17

CHAPTER 2. WHEAT ROOT-INDUCED CHANGES TO HYDRAULIC . . .

Ks at the different sampling times the experimental method we developed provided proof

of concept, and provides justification for a large-scale study.

2.2 Introduction

Root induced changes to soil hydraulic properties (SHP) have been widely reported (Bar-

ley, 1954; Meek et al., 1990, 1989, 1992; Murphy et al., 1993; Petersson et al., 1987;

Prathapar et al., 1989; Sedgley and Barley, 1958; Suwardji and Eberbach, 1998; Yunusa

et al., 2002); however there is a lack of quantitative information relating root system prop-

erties to these. Most studies that attribute changes to SHP to roots make no reference to

a measurable property of the roots in question; there are only a few reports that relate

changes in saturated hydraulic conductivity (Ks) to root mass or length (Barley, 1953;

Petersson et al., 1987; Prathapar et al., 1989). Without quantitative information about

the above and below ground parts of the plants in question it is difficult to quantify the

processes that lead to root-induced changes to SHP. To improve our understanding of how

roots modify SHP and the implications of this an integrated study of soil and plants in

hydrology is required (Ahuja et al., 2006; Smucker and Hopmans, 2007).

Root-induced changes to SHP are dynamic and to an extent reflect the lifespan of the

plant. Different temporal patterns in changes to SHP have been shown where annuals,

perennials and trees are present. For example, where annual plants are dominant Ks

typically decreases during the vegetative growth stage then increases when the plants

mature, within a period less than 1 year (Barley, 1954; Meek et al., 1990; Murphy et al.,

1993; Prathapar et al., 1989; Suwardji and Eberbach, 1998). Increases in infiltration rate

where perennial forbs are present has been observed over a number of years (Meek et al.,

1989, 1992; Yunusa et al., 2002), which were attributed to the slow decay of woody and

/ or tap roots. In forestry systems increases in infiltration rate have been observed over

periods of 15 to 50 years (Deuchars et al., 1999; Johnson-Maynard et al., 2002). As with

annual plants, there is evidence that the effect of tree roots on SHP is determined by the

maturity of the root system. Infiltration rate has been shown to negatively related to

root mass in trees less than 3 years old, but positively in trees approximately 20 years old

(Petersson et al., 1987). The difference in temporal pattern is due to the differing root

18

2.3. METHODOLOGY

sizes and that large roots take longer to decay (Silver and Miya, 2001).

While root-induced changes to near- and saturated hydraulic conductivity are fre-

quently reported, this does not provide a complete picture of how the soil has been changed.

Knowledge of how the hydraulic conductivity and water retention function is required to

quantify how root induced changes affect the water balance. To date this has only been

reported by Kodesova et al. (2006); however their work did not focus on the before and

after root growth status of the soil, so any changes are impossible to quantify.

Based upon the evidence available, we hypothesised that changes in Ks can be ex-

plained by changes in root length density and radius. Here, we report a laboratory exper-

iment which was conducted with the aim of testing this hypothesis. To gain evidence of

how the behaviour of the soil would change, we used inverse modelling to determine both

the water retention and hydraulic conductivity functions of a soil modified by roots at a

sequence of physiological stages, and made root measurements each time we measured soil

hydraulic properties.

2.3 Methodology

2.3.1 Experimental design

To determine how wheat roots modify SHP of well-defined soil columns as the plants

progressed through their life-cycle we measured these properties at 4 time intervals after

sowing. The sampling times were 3, 5, 7 and 9 weeks after sowing, and three replicates were

measured at each time. At each sampling time, a multi-step outflow experiment (MSO)

was conducted on three columns that had been planted and on three control columns

without plants. Following the MSO the three planted columns that had been measured

were disassembled for visual analysis and to measure root properties. In total there were

15 columns, 12 planted with wheat (4 times of sampling * 3 replicates) and 3 control

columns which were not planted.

19


Soil

The soil used in the experiment had a high Ks, allowed homogeneous packing and did

not restrict plant growth. A soil with high Ks was favourable as changes in this would

be easier to detect. We used sand obtained from a commercial soil supplier that had no

visible aggregates or pieces of organic matter. Soil pH (6.4 CaCl2) posed no problems

for root growth (Tang et al., 2003); however, low extractable potassium and phosphorus

concentrations (2 and 15 mg kg−1 respectively) were growth-limiting (Moody and Bolland,

2001; Wong et al., 2001).

Column apparatus

The column apparatus was designed to allow the measurement of root-modified SHP in-

situ and to allow unimpeded root growth. We built a suction plate into the base of the

column to avoid poor contact to a suction plate when the column was placed on it, and

to be able to maintain similar water content profiles in all the columns while the plants

were growing in a glasshouse. It was important to maintain similar water content profiles

in the columns because we applied a nutrient solution and the spatial allocation of roots

is highly responsive to nutrient availability (Robinson, 1994). Apart from the built-in

suction plate, the other major design consideration was the length of the column. On one

hand the column needed to be long enough to avoid root matting at the bottom, and on

the other needed to be short enough to avoid non-unique parameterisation of the hydraulic

conductivity function (Hopmans et al., 2002). As a compromise between these conflicting

design requirements we chose a soil height of 45 cm.

Figure 2.1 shows the design of the columns which were constructed from commercially

available polyvinyl chloride plumbing materials. The columns were 50 cm high and had

an inside diameter of 10 cm. The suction plate was made by fitting an end cap to the

base of the column which had an outlet tube attached to its base and a perforated disc

to support the nylon membrane and soil. The nylon membranes (GE Osmonics Labstore,

Minnesota, USA, www.osmolabstore.com) were 90 µm thick, had an air entry point of 211

cm matric head and a mean saturated hydraulic conductivity of 2.54 x 10−4 cm min−1.

To minimize packing-induced heterogeneity the soil was dried and packed into the

20

2.3. METHODOLOGY

Figure 2.1: Cross-sectional illustration of the column design used for the experiment.Column height and diameter were 50 and 10 cm respectively, soil was packed 45 cm highand the tensiometer port was 25 cm from the base.

columns in 2 cm increments. The soil was dried to 0.01% gravimetric soil water content

and passed through a 0.2 cm sieve. A tool with an adjustable stopper was used to compact

each layer of soil to a bulk density of 1.6 g cm−3. To consolidate the packed soil we applied

two wetting and drying cycles to each column, where we saturated the columns with 0.01

M L−1 CaCl2 then drained them by applying -100 cm matric head at the botton for 24

hours.

The columns were watered with a nutrient solution while the plants were growing in

the glasshouse. Prior to planting 1 L of nutrient solution (Table 2.1) was applied to each

column. Following planting, and every 4 days after this 0.4 L of nutrient solution was

applied to each column. The nutrient solution has been formulated to ensure that plant

growth is not limited by nutrient supply in highly weathered soils (Rose et al., 2007). The

columns were placed on a bench and the outlet tubes in a reservoir 20 cm below the bench,

which ensured the entire column remained unsaturated during plant growth. A 1 cm layer

of polypropylene beads was added to the soil surface to minimize evaporation.

21


Figure 2.2: Apparatus used to raise the columns during the multi-step outflow experiment.Balances for weighing outflow are in the foreground and the data logger for the mini-tensiometer transducers is in the background

22

2.3. METHODOLOGY

Table 2.1: Composition of nutrient solution used to grow wheat in columns after Roseet al. (2007)

Compound Concentration (µM)

NH4NO3 2000KNO3 2000Ca(NO3)2 1000MgSO4.7H2O 200KH2PO4 200CaCl2 600FeNaEDTA 20H3BO3 10ZnSO4.7H2O 2MnSO4.H2O 2CuSO4.5H2O 0.5CoSO4.7H2O 0.5Na2MoO4.H2O 0.1

2.3.2 Plant growth

Wheat was chosen for this experiment because it is has an annual growth habit and

because it allowed us to compare our results with similar work which typically involves

wheat or a grass (e.g. Barley, 1954; Murphy et al., 1993). It was necessary to use an

annual plant to capture changes to SHP in a relatively short period of time. We sowed 10

spring wheat (Triticum aestivum L. cv. Wyalkatchem) seeds 2 cm deep and thinned the

emerged seedlings to 5 per column at 2 weeks.

The columns were located in a glasshouse at the University of Western Australia,

Crawley during September and October. During the 9 week growing period, the minimum,

mean and maximum temperature was 11, 21 and 30◦C respectively, and minimum, mean

and maximum relative humidity was 34, 62 and 77% respectively.

2.3.3 Multi-step outflow experiment

A multi-step outflow experiment (MSO) was conducted on the soil columns to determine

their water retention and hydraulic conductivity functions. We modified the usual MSO

method (Hopmans et al., 2002) by beginning the experiment with a saturated column

having water ponded 5 cm above the soil surface. At each time of sampling, the columns

23


were wet ‘from the bottom up’, by applying a positive head of water at the outlet tube at

the base of the column. We started with a saturated column to provide data that reflects

the hydraulic conductivity and water retention of the soil near- and at saturation. During

the MSO the column was drained by applying suction at the base in six increments, being

0, -10, -20, -40, -80 and -120 cm matric head each lasting 2 hours. Suction was applied by

a hanging water column and was changed by raising the columns using the stand shown

in Figure 2.2.

Figure 2.3 shows an example of cumulative outflow and matric potential data collected

from an MSO. The cumulative outflow from the base of the columns (outflow) was mea-

sured using automatically using electronic balances connected to a PC via serial cables,

and recorded using A&D software (www.aandd.jp/products/software/winct.html). Ma-

tric potential at the mid-point of the column (matric potential) (Hopmans et al., 2002)

was measured using UMS T5 mini-tensiometer transducers (Munich, Germany, www.ums-

muc.de) and was also recorded using a PC via a data logger. We used automated methods

to take these measurements because they were taken every minute for 12 hours for 3

columns.

2.3.4 Analysis of multi-step outflow data

Direct analysis

The Ks of the soil-membrane system in each column was measured directly from outflow

data from the first step of the MSO (no suction at base of column). As the pond of

water drained during this first step the column set-up was equivalent to a falling-head

permeameter (Marshall and Holmes, 1979), and as we assumed that the saturated water

content of the column did not change during this phase of the experiment, we calculatedKs

of the soil-membrane system from the calculated pond height at 1 minute intervals. TheKs

of the membrane only in each column was measured once the experiment was completed

and the soil was removed. Flux from the columns was measured while maintaining a

constant head of 15 to 20 cm using Marriotte bottles. As the Ks of the soil-membrane

system and membrane only were known, the Ks of the soil only was calculated using an

electrical resistance analogy (Marshall and Holmes, 1979, p 105). We express the change

24

2.3. METHODOLOGY

0 100 200 300 400 500 600 700

0

5

10

15

−40

−30

−20

−10

0

10

20

30

Cum

ulat

ive

outfl

ow (

cm)

Time (min)

Mat

ric h

ead

at m

idpo

int o

f col

umn

(cm

)

Observed outflowSimulated outflowObserved matric potentialSimulated matric potential

Figure 2.3: An example of measured and simulated outflow and matric potential from themulti-step outflow experiment. Data are from a column with plants present measured 7weeks after sowing

25


in Ks as relative Ks which is the Ks of a column at any sample time divided by its value

prior to sowing, because the variability of Ks between the individual columns may be

greater than the changes caused by root growth.

Inverse analysis

Inverse analysis of the data from each of the MSO experiments was conducted using a

model with free-form hydraulic functions (Iden and Durner, 2007). This model solves

water flow in one dimension by numerical solution of Richards’ equation, using water re-

tention and hydraulic conductivity functions that are spline interpolations of nodes. For

the inverse analysis, the model optimised the node locations for the water retention and

hydraulic conductivity functions by minimising the weighted sum of squares using the

shuffled-complex-evolution algorithm (Iden and Durner, 2007). The objective function

included cumulative outflow (at the base) and matric potential at the mid-point of the

column. We used a model with free-form hydraulic functions to avoid error caused by

assumptions about the shape of the retention and hydraulic conductivity functions and

by coupling these with common parameters (Iden and Durner, 2007; Nielsen and Luck-

ner, 1992). Avoiding shape restrictions was particularly important in this experiment as

roots can cause significant changes in pore structure (Barley, 1954; Jassogne et al., 2007;

Udawatta et al., 2008).

We initialised the water flow model used for the inverse analysis based upon information

from preliminary work on the soil material. The saturated water content θs and air entry

point were determined using the hanging water column method (Dane and Hopmans,

2002) and were 0.33 (cm3 cm−3) and -10 cm matric head respectively and Ks was 7.7 cm

min−1. An inverse analysis was conducted on each MSO data set with 1, 2, 3, 4 and 5

nodes in the water retention and hydraulic conductivity functions.

2.3.5 Plant measurements

Root mass, volume and length were measured following the MSO at each time of sampling.

When the columns were disassembled, the soil was washed from the roots using a hose

over a 0.2 cm aperture sieve, and the roots were stored overnight at 4◦C. Root length was

26

2.4. RESULTS

measured using WinRhizo software (Arsenault et al., 1995) (Canada, www.regent.qc.ca/),

which converts grey-scale digital images of washed roots into black and white, and cal-

culates length from the number of pixels in a skeletonized version of the black and white

image (Bauhus and Messier, 1999). For each column, root length density was calculated

by dividing root length L (cm) by soil volume Vs (cm3), root volume Vr (cm3) was de-

termined by water displacement, and root mass m (g) was measured after drying for 48

hours at 70◦C. We also recorded the growth stage of the plants at each time of sampling

(Zadoks et al., 1974).

We also calculated properties of the root system from our measurements; root tissue

density ρr (g cm−3):

ρr =m

Vr(2.1)

Mean root radius r (cm) as:

r =

(

Vr

Lπ

)0.5

(2.2)

And specific root length Sr (cm g−1) as:

Sr =L

m(2.3)

2.4 Results

2.4.1 Saturated hydraulic conductivity

After the wheat had been sown Ks was not significantly different (p<0.05) at the different

sampling times; however, there was a decreasing trend up to week 7 and an increasing trend

after this (Table 2.2). The switch from a decreasing to increasing trend corresponded to

the shift from the vegetative to reproductive growth stage in the wheat plants.

The Ks of the columns measured prior to sowing had a log-normal distribution. We

fitted the log-normal distribution (Weisstein, 2008b) to the cumulative frequency of these

values and found that the parameters for the mean µ and standard deviation σ were -2.85

and 0.72 respectively, and the mean of this distribution (Weisstein, 2008a) was 0.07 cm

min−1.

27


Table 2.2: Summary of changes to the root system and saturated hydraulic conductivityover the course of the experiment. For each row different superscripts indicate significantdifference (p<0.05) using Tukey multiple comparison. Number of replicates was 3.

Weeks after sowing 3 5 7 9

Mean root length den-sity (cm cm−3)

2.03a 9.37bc 11.7cd 13.73d

Mean root mass (g percolumn)

0.42a 1.94b 3.15c 2.86bc

Mean root volume (cm3

per column)5.23a 25.67bc 39.67cd 43.33d

Mean root tissue den-sity (g cm−3)

0.08a 0.08a 0.09a 0.07a

Mean root radius (cm) 0.015a 0.015a 0.017a 0.016a

Mean specific rootlength (cm g−1)

54056a 54413a 37657a 50705a

Mean relative Ks 1.06a 0.62a 0.44a 1.32a

Zadoks et al. (1974)growth stage

15 to 23 32 to 45 59 71

Growth stage descrip-tion

Seedlings totillering

Stem elon-gation tobooting

Ear emer-gencecomplete

Kernel wa-ter ripe

2.4.2 Root properties

Multiple comparison analysis using the Tukey method of root properties at the four sam-

pling times showed significant (p<0.05) changes in the root system (Table 2.2). The

properties that we measured; root length density, mass and volume, were all significantly

different at 3 and 5 weeks, and at 3 and 9 weeks. The root properties that we calculated;

root tissue density, mean root radius and specific root length, were not significantly dif-

ferent at any time. There were no significant relationships between any root property and

relative Ks.

Visual analysis of the soil after the columns were disassembled did not show any

accumulation of roots along the soil-column interface or at the base of the column. Visual

analysis of cross sections of soil showed a relatively even distribution of roots (not shown);

however, root length density appeared to highest near the soil surface and lowest at the

base of the column.

28

2.4. RESULTS

0 10 20 30 40−4

−3

−2

−1

0

1

2

log 1

0 H

yd. c

ondu

ctiv

ity (

cm m

in−1)

−Matric head (cm)

Before plantingAfter plant growth

0 10 20 30 400.0

0.1

0.2

0.3

0.4

Wat

er c

onte

nt (

cm3 c

m−3

)

−Matric head (cm)

Figure 2.4: Optimised hydraulic conductivity and water retention functions for a columnwith plants present measured 7 weeks after sowing (same column as Figure 2.3). Shadedareas show the 95% confidence region.

2.4.3 Inverse analysis

We compared the optimised hydraulic conductivity functions of each column that was

planted from measurements taken immediately prior to the experiment to those taken

when it was measured (at 3, 5, 7 or 9 weeks) and found that root induced changes occurred

within the 0 to -30 cm matric head range. An example of this is shown in Figure 2.4 where

the hydraulic conductivity functions of the column before and after plant growth are most

different at saturation and begin to converge at -20 cm matric head. Assuming that pores

are cylindrical, the Young-Laplace equation (e.g. Warrick, 2003) can be used to calculate

pore radius from capillary rise (matric potential). The range in matric head where changes

were observed was 0 to -20 cm, which relates to pore radii greater than or equal to 0.0075

cm (75 µm). It appears that roots had little impact on pores with a radius less than 75 µm,

as the overlaying of confidence intervals at matric head less than -20 cm matric head was a

common feature of the optimised functions. Comparison of the optimised water retention

functions showed no consistent change due to the growth of roots (not shown). The broad

confidence intervals for the optimised hydraulic conductivity and water retention functions

shown in Figure 2.4 were a common feature results from the inverse modelling.

29


0.96

0.98

1.00

1 Node 2 Nodes 3 Nodes 4 Nodes 5 Nodes

r2 out

flow

(cm

)

0.96

0.98

1.00

r2 mat

ric p

oten

tial (

cm)

1 Node 2 Nodes 3 Nodes 4 Nodes 5 Nodes

Figure 2.5: Summary of r2 of observed vs. predicted cumulative outflow and matricpotential for differing numbers of nodes in the water retention and hydraulic conductivityfunctions

Overall, the optimised hydraulic functions provided a good prediction of outflow and

matric potential, and this was not greatly affected by the number of nodes in the functions

(Figure 2.5). For example, the median r2 of observed vs. predicted outflow for all the

columns was 0.997 when one node was used, and 0.998 for two to five nodes; however,

the 25th percentile was much lower when one or two nodes was used. Interestingly, the

median r2 of observed vs. predicted matric potential was 0.99 for one node and 0.98 for

two or more. Also, increasing the number of nodes to greater than 2 did not result in a

consistent change in shape in the hydraulic conductivity function (not shown).

2.5 Discussion

The lack of statistical significance of changes in Ks for the different times of sampling

means that we can not make conclusions regarding our hypothesis, and we attribute this

to the variability of Ks of the columns and due to a low number of replicates. Based upon

the log-normal distribution of the initial Ks of the soil columns, analysis of variance on

synthetic data showed that at least 10, 25, 40 and 50 columns would have been required

30

2.5. DISCUSSION

to detect significant (p<0.05) changes in Ks of -50, -40, -30 and -20%. Such large numbers

of columns create logistical problems for the MSO which is conducted over long periods,

where the availability of apparatus will limit the amount of columns that can be measured

at a particular growth stage; however, this is feasible for Ks measurements on course

textured soils which can be obtained relatively quickly.

The trend in relative Ks that we observed is the same as reported by Murphy et al.

(1993). In their study, Murphy et al. (1993) found that in general near-saturated hydraulic

conductivity decreased from sowing to tillering, then began to increase again. They at-

tributed the decrease to roots blocking macropores and the increase to the formation of

macropores that are well connected to the surface by dying and decaying roots. While our

study was designed to test the hypothesis that changes in Ks can be related to changes in

soil properties, the lack of significance between root measurements at weeks 7 and 9 weeks

especially means that we can not provide evidence of why this switch from a decrease to

an increase occurs. However, the agreement in between the changes in Ks between our

work here and elsewhere (e.g. Barley, 1954; Murphy et al., 1993) provides justification for

a highly replicated column experiment (20 to 50) of root induced changes to soil hydraulic

conductivity.

The timing of root-induced changes to Ks is in part controlled by the physiological

stage of the plant. Broadly, these stages can be grouped as emergence, vegetative and

reproductive growth (Setter and Carlton, 2000), and rate of development through these is

governed by genetics, air temperature and nutrient and water availability (McMaster et al.,

1992). Importantly, root growth and branching is also regulated by the physiological stage

of the plant (Klepper et al., 1984). For example, new seminal roots are only produced for

the first 60 degree days1, whereas new roots are produced at the main stem from 60 to

420 degree days (Klepper et al., 1984) which roughly corresponds to the vegetative phase

(McMaster et al., 1992). Root mass increases exponentially until approximately the end

of the vegetative phase (Gregory et al., 1978; Gregory and Eastham, 1996) and it is during

this phase that we and others (Barley, 1954; Murphy et al., 1993) have observed a decrease

in Ks in the range of 40 to 60%. There is less certainty about the timing of the switch

1Degree days is calculated on a daily time step and is the average daily temperature minus a basetemperature

31


from a decrease to increase in Ks due to shrinking and / or decaying roots because root

life span is highly dependent on factors such as soil moisture, temperature and nutrient

availability (Eissenstat and Yanai, 1997; Hooker et al., 2000). For example, 70% of roots

of perennial ryegrass had a life-span of greater than 36 days when the temperature was

15◦C, but only 16% remained when the temperature was 27◦C (Forbes et al., 1997).

It is likely that the effect of roots on the shape of the hydraulic conductivity function

is dependent upon the interaction between the type of root system and soil texture. In

our experiment the results suggest that roots only affected pores with a radius greater

than 75 µm, which is a similar range to those reported for roots, for example Costa et al.

(2001) found that 90 to 99% of roots have a diameter greater than this. Using a sand in

our experiment may have made changes to the hydraulic conductivity and water retention

functions more difficult to detect because of the similarity of the pore size distribution to

the root diameter frequency distribution.

The broad confidence intervals of the optimised hydraulic functions is most likely due

to vertical variability in Ks of the columns. Heterogeneity in the hydraulic properties of

a soil column can lead to problems identifying unique hydraulic functions using inverse

modelling (Durner et al., 2008). The vertical distribution of wheat roots is typically

exponential (Zuo et al., 2004), so it is likely that root-induced changes to the soil profile

were not uniform. Also, the model only considers one fluid (water) whereas in reality

there are two: air must also flow through the soil matrix. At high matric potentials

air permeability is reduced and this can cause an error in the prediction of hydraulic

conductivity (Schultze et al., 1999). The error due to reduced air permeability may have

been magnified by our experimental design, as the soil was in the near-saturated range for

most of the MSO and the long columns increased the pore volume that air had to move

into.

The use of columns for this type of study may have introduced wall effects on the

observed behaviour. Greater flow can occur between the soil and column wall than in

the soil matrix because the pore spaces that are created along the wall are greater (e.g

Gao et al., 2006). We did not observe a mat of roots on the outside of the soil when the

columns were disassembled at any sampling time: if this were occurring in our columns

32

2.6. CONCLUSION

it is reasonable that is was a constant effect and did not have a bearing on the trend we

observed.

2.6 Conclusion

The results from our study show the same trend as observed elsewhere; a decrease in

Ks occurs during the vegetative stage and an increase in the reproductive growth stage

of wheat. Based upon the range of Ks in the columns before sowing, and on the level

of change in Ks observed, we recommend that similar studies use at least 10 columns

per treatment to detect a significant change of -50%, and at least 50 columns to detect

a significant change of -20%. The trends we observe provide justification for further

experimental analysis of root-induced changes to SHP but on a much larger scale.

The optimised soil hydraulic functions show root induced changes in the hydraulic

conductivity function in the range of 0 to -30 cm matric head. The broad confidence

intervals around these optimised functions are most likely due to a non-uniformly modified

soil profile and variable hydraulic conductivity near saturation due two-phase flow effects

of air entrapment and movement at and near saturation.

33

Chapter 3Using radius frequency distribution

functions as a metric for quantifying root

systems

C.A. Scanlan1 and C. Hinz1



3.1 Abstract

Root radius frequency distributions have been measured to quantify the effect of plant,

environment and methodology on root systems; however, to date the results of such studies

have not been synthesised. We propose that frequency distribution functions can be used

as a metric to describe root systems because (1) statistical properties of the frequency

distribution can be determined, (2) the parameters for these can be used as a means of

comparison, and (3) the analytical expressions can be easily incorporated into models

that are dependent upon root geometry. We collated a database of 96 root radii frequency

distributions and botanical and methodology traits for each measurement. We fitted the

exponential, Rayleigh, normal, log-normal, logistic and Weibull cumulative distribution

functions to each distribution in our database. We found that the log-normal function

35

CHAPTER 3. USING RADIUS FREQUENCY DISTRIBUTION . . .

provided the best fit to these distributions and that none of the distribution functions was

better or worse suited to particular shapes. We derived analytical expressions for root

surface and volume and found that overall they provide a more accurate method than

calculating these from the mean root radius or a histogram of root radii. We also found

that growth habit and growth media had a significant effect on the distribution mean.

3.2 Introduction

Root radius frequency distributions have been measured to provide detailed information

about how root systems differ or adapt to the soil environment. They have been used as

a measure; to characterise root morphology (Eissenstat, 1991; Mooney, 2002; Pregitzer

et al., 1997, 2002; Torssell et al., 1968), to relate root morphology to ion uptake (Keller

et al., 2003; Ryser and Lambers, 1995; Sullivan et al., 2000), to quantify the influence of

tillage system (Pagliai and De Nobili, 1993; Qin et al., 2004), genotype (Costa et al., 2002)

or soil water content (Kuchenbuch et al., 2006) on root radius, to examine interactions

between root radius and colonization by mycorrhizal fungi (Reinhardt and Miller, 1990)

and to examine the sensitivity of measured radius to methodology (Bouma et al., 2000;

Pierret et al., 2005; Zobel, 2003). However, to our knowledge there has been no synthesis

of how properties of the root system, their growing environment or methodology affect the

statistical properties of the radius frequency distributions.

The methods used to measure root radii frequency distributions can be broadly divided

into manual and automated. The most commonly used manual method is to measure root

length using the line-intersect method (Newman, 1966; Tennant, 1975) and diameter using

an enlarged photographic image (e.g. Pallant et al., 1993) or an ocular microscope (e.g.

Reinhardt and Miller, 1990). In general, automated methods involve capturing a digital

image of a sample of roots with a camera or flat-bed scanner, and measuring length

and diameter from a processed binary image. There are two main approaches to digital

image analysis (Zobel, 2003): where root diameter is measured from the binary image

and length is measured from a single-pixel width skeleton version of the binary image

(Lebowitz, 1988), or where length and diameter are measured from the perimeter and

area of the binary image (Kaspar and Ewing, 1997; Pan and Bolton, 1991).

36

3.3. METHODS

The results from both manual and automated methods of measuring root systems are

typically reported as histograms of root length in prescribed radius classes (e.g. Costa

et al., 2002), because both methods treat the root system as individual segments of equal

radius. The shape of the histogram reflects morphological properties of the root system

(Sullivan et al., 2000) and frequency distribution functions can be fitted to these to derive

parameters that reflect the shape of the distribution (Anderson et al., 2007).

We propose that cumulative frequency distribution functions can be used as a metric

for describing root systems. The parameters for these provide a basis for comparison

and can be used to calculate statistical properties of the frequency distribution, such as

the mean, variance, skewness and kurtosis (Weisstein, 2008a). In addition, closed-form

expressions of frequency distribution functions can be readily incorporated into analytical

models of nutrient (e.g. Claassen and Barber, 1977) or water uptake (e.g. Hainsworth

and Aylmore, 1986), allowing properties of the root system such as morphology to be

incorporated which can not by assuming the root is a single cylinder of average radius.

To investigate our proposal, we collated a database of root radii frequency distribu-

tions from the literature and fitted 6 cumulative frequency distribution functions to each

distribution in our database with two specific aims. First, to determine which cumula-

tive distribution functions provided the best fit to our database and second, if particular

functions provided a better fit to certain shapes of radii frequency distribution. We also

examined whether plant type, environmental conditions had an effect on the shape of the

distributions.

3.3 Methods

3.3.1 Data collection

We compiled a database of root radii frequency distributions for individual plants as well

as information about the botanical properties of each plant and the methods used extract

and measure the roots. Where data was presented graphically we measured individual

points and then converted those measurements to the appropriate scale. The growth

habit, duration and botanical classification were sourced from the USDA Plants Database

37


050

100

150

200

0.0

to 0

.1

0.1

to 0

.2

0.2

to 0

.3

0.3

to 0

.4

0.4

to 0

.5

0.5

to 0

.6

0.7

to 0

.8

0.8

to 0

.9

0.9

to 1

.0 >1

Root radius classes (mm)

Roo

t len

gth

(m)

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

Fre

quen

cy

Figure 3.1: Graphical representation of the conversion of an histogram to cumulativefrequency. The histogram of root length for each radius class is for Maize (LRS) fromCosta et al. (2002) and was converted to a cumulative frequency by summing the frequencyin each radius class.

(USDA, 2008), which uses the Cronquist (1981) classification system. We assumed that the

whole root system was recovered and not stained for measurement unless stated otherwise.

In most cases root frequency distributions were presented as frequency histograms. We

converted the histograms to cumulative frequency distributions by relating the cumulative

frequency at each root radius category to the upper limit of that category (Figure 3.1). We

assumed that all the radius classes observed were reported, and that the distributions were

not truncated at the upper limit of observed radius. However, we acknowledge that the

application of a continuous distribution function has limitations as root radius approaches

zero, as there is a physiological lower limit to root radius (Dittmer, 1949; Fusseder, 1984)

and we examine the practical implications of this discrepancy below.

3.3.2 Regression analysis

We fitted six cumulative distribution functions to each root radii frequency distribution in

our database. These included two one-parameter functions; the exponential and Rayleigh

distributions, and four two-parameter functions; the normal, log-normal, logistic and

Weibull distributions (Tables 3.1 and 3.2). The parameters for these functions were opti-

38

3.3. METHODS

mised by minimizing the residual sum of squares using the Gauss-Newton algorithm with

the nls function in R (R Development Core Team, 2006), which also provides the stan-

dard error of optimised parameter values. We used the root-mean square error (RMSE) to

express how well the distribution with optimized parameters matched the measured; how-

ever, because we needed to compare the performance of functions with differing number

of parameters p we used:

RMSE =

n∑

i=1

(f (ri)− yi)2

n− p

0.5

(3.1)

Where f(ri) is the calculated frequency at radius ri, yi is the observed frequency and n is

the number of points in the measured frequency distribution (Amacher et al., 1988).

The mean, variance, skewness and kurtosis of each distribution were calculated from

the optimised parameters of the distribution functions (Tables 3.1 and 3.2). For clarity,

we prefix these attributes with distribution. We calculated all four properties for the

log-normal and Weibull distributions which are non-symmetrical, and only the distribu-

tion mean and variance for the remainder of the distribution functions because they are

symmetrical and their distribution skewness and kurtosis are a constant.

3.3.3 Calculation of root volume and surface area

The optimised parameter values were used to calculate root volume and surface area using

analytical expressions. We derived these expressions by assuming that roots have a circular

cross-section of radius r (cm) and that the root system can be described using a probability

density function of root radius per cm of root f(r) (cm−1). Our approach utilises the raw

moments (Weisstein, 2008c) of the distribution, where the nth moment Mn is:

Mn =

∫ ∞

0rnf (r) dr (3.2)

39


For any distribution function root surface area Aa (cm2 cm−1) can be expressed as:

Aa = 2πM1 (3.3)

And root system volume V a (cm3 cm−1) can be expressed as:

V a = πM2 (3.4)

Analytical solutions for the first two moments are possible for all the distribution

functions we used. For example the surface area of a root system described with the

log-normal distribution function (Weisstein, 2008b) is:

Aa = 2πeµln+σ2ln/2 (3.5)

And the volume can be expressed as:

V a = πe2(µln+σ2ln) (3.6)

To date root volume and surface area have been calculated using the mean root ra-

dius or from a histogram of root radii and we determined the error induced using these

methods by comparison with analytically-derived results. The mean radius is calculated

from measurements of root segments of equal length and root volume V m (cm3 cm−1)

and surface area Am (cm2 cm−1) are calculated by assuming the root is a cylinder (Evans,

1977). Root volume and surface area are calculated from a histogram by considering the

root system as a number of cylinders of varying radius and length (Boot and Mensink,

1990; Ryser and Lambers, 1995), where the length of a cylinder for radius category i is its

frequency f(i) and the radius ri (cm) is the mean of the upper and lower radius limit of

that category. Surface area calculated directly from the histogram Ah (cm2 cm−1) is:

Ah =m∑

i=1

f(i)2πri (3.7)

Where m is the number of root radius categories.

40

3.3. METHODS

Similarly, volume calculated directly from the histogram V h (cm3 cm−1) is:

V h =n∑

i=1

f(i)πr2i (3.8)

To assess the error ε (%) caused by calculating root volume and surface area using

the mean radius or from the histogram, we calculated the difference from the analytically

derived results:

ε(X) = 100Xc −Xa

Xa(3.9)

Where X can be V or A, and c can be m or h.

We assessed the error in calculating root volume and surface area from the mean root

radius or a histogram of root radius using modelled root radius distributions. This was

necessary because the individual measurements of root radius are required to calculate

the mean root radius, and the data we collected had already been summarised in the

form of histograms or frequency distributions. We used the log-normal parameters we

derived for each of the distributions in our database to create sets of individual root radius

measurements by generating 1000 equally-distributed random probabilities and calculated

the corresponding radius using the inverse of the log-normal distribution function.

41

CHAPTER

3.USIN

GRADIU

SFREQUENCY

DISTRIB

UTIO

N...

Table 3.1: Functions used to analyse root radius frequency distributions

No. of params Fr Distribution mean / M1 Distribution variance M2

Exponential 1 1− e−λr 1λ λ−2

Rayleigh 1 1− e−r2

2s2 s√

π/2 4−π2 s2

Normal 2 12

[

1 + erf(

r−µn

σn

√2

)]

µn σ2n

Log-normal 2 12

[

1 + erf(

ln(r)−µln

σln

√2

)]

eµln+σ2/2 eσ2ln+2µln

(

eσ2ln − 1

)

e2(µln+σ2ln)

Logistic 2 11+e−(r−m)/b m 1

3π2b2

Weibull 2 1− e−(r/β)α βΓ(

1 + α−1)

β2[

Γ (1 + 2α−1)− Γ2(

1 + α−1)]

a All functions from Weisstein (2008d)

42

3.3.METHODS

Table 3.2: Functions used to analyse higher moments of root radius frequency distributions

Distribution skewness Distribution kurtosis

Log-normal√

eσ2ln − 1

(

2 + eσ2ln

)

e4σ2ln + 2e3σ

2ln + 3e2σ

2ln − 6

Weibull2Γ3(1+α−1)−3Γ(a+α−1)Γ(1+2α−1)

[Γ(1+2α−1)−Γ2(1+α−1)]3/2+ ... f(α)

[Γ(1+2α−1)−Γ2(1+α−1)]2

Γ(1+3α−1)[Γ(1+2α−1)−Γ2(1+α−1)]3/2

a Γ is the gamma function

bf(α) = −6Γ4(1 + α−1) + 12Γ2(1 + α−1)Γ(1 + 2α−1)− 3Γ2(1 + 2α−1)− 4Γ(1 + α−1)Γ(1 + 3α−1) + Γ(1 + 4α−1)

c All functions from Weisstein (2008d)

43

CHAPTER

3.USIN

GRADIU

SFREQUENCY

DISTRIB

UTIO

N...

Table 3.3: Botanical and methodological attributes and optimised parameters

for the log-normal distribution function for each observed root radius frequency

distribution

Index Common Name Growth

Habit

Growth

Dura-

tion

Class Section Growth

Media

Media Desc. Stained Man /

Auto

No.

Classes

µln σln

Pregitzer et al. (2002)

1 Balsam poplar* Tree Perennial Magnoliopsida Section Field Organic Y Manual 10 -4.94 0.56

2 White spruce* Tree Perennial Pinopsida Section Field Organic Y Manual 10 -4.54 0.51

3 Slash pine* Tree Perennial Pinopsida Section Field Sand Y Manual 10 -4.52 0.46

4 White oak* Tree Perennial Magnoliopsida Section Field Clay loam Y Manual 10 -4.97 0.64

5 Sugar maple* Tree Perennial Magnoliopsida Section Field Sandy loam Y Manual 10 -4.46 0.3

6 Red pine* Tree Perennial Pinopsida Section Field na Y Manual 10 -4.44 0.41

7 Tulip tree* Tree Perennial Magnoliopsida Section Field Sandy loam Y Manual 10 -3.39 0.27

8 Oneseed Juniper* Tree Perennial Pinopsida Section Field Sandy loam Y Manual 10 -3.92 0.2

9 Twoneedle Pinyon* Tree Perennial Pinopsida Section Field Sandy loam Y Manual 10 -3.93 0.23

Pregitzer et al. (1997)

10 Sugar maple Tree Perennial Magnoliopsida Section Field Sandy loam N Manual 5 -4.38 0.14

11 White Ash Tree Perennial Magnoliopsida Section Field Sandy loam N Manual 5 -3.97 0.45

12 Downy yellow violet Forb/Herb Perennial Magnoliopsida Section Field Sandy loam N Manual 4 -4.13 0.76

13 Broad-lead waterleaf Forb/Herb Perennial Magnoliopsida Section Field Sandy loam N Manual 4 -3.74 1.23

Pallant et al. (1993)

14 Corn Graminoid Annual Liliopsida All Field Silt loam Y Manual 11 -5.04 0.64

Continued on Next Page. . .

44

3.3.METHODS

Table 3.3 – Continued


Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln



Zobel et al. (2007)

17 Cacao Tree Perennial Magnoliopsida All Pots Vemiculite N Automated 24 -5.06 0.89




Ryser and Lambers (1995)

21 Tor-grass* Graminoid Perennial Liliopsida All Pots Sand N Manual 40 -5.41 0.48




25 Orchard grass* Graminoid Perennial Liliopsida All Pots Sand N Manual 40 -5.45 0.57




Zobel (2003)

29 Switchgrass Graminoid Perennial Liliopsida All Pots Soil N Automated 30 -4.95 0.7

30 Mixed pasture Mixed Mixed Mixed All Field Soil N Automated 24 -4.97 0.86

Pierret et al. (2005)


45

CHAPTER

3.USIN

GRADIU

SFREQUENCY

DISTRIB

UTIO

N...



Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln

31 Canola Forb/Herb Annual Magnoliopsida All Field Sandy loam N Automated 19 -4.37 0.6



Reinhardt and Miller (1990)

34 Pasture Graminoid Perennial Liliopsida Section Field Silt loam Y Manual 4 -5.25 0.59

35 Prarie Mixed Mixed Mixed Section Field Silt loam Y Manual 4 -5.03 0.54

Sullivan et al. (2000)

36 K. B. Blacksburg Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.39 1.08

37 K. B. Barzan Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.52 1.04

38 K. B. Conni Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.43 1.01

39 K. B. Dawn Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.55 1.09

40 K. B. Eclipse Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.53 1.07

41 K. B. Gnome Graminoid Perennial Liliopsida Section Pots Sand N Automated 5 -5.51 0.98

Peng et al. (2005)

42 Purple Elsholtzia* Forb/Herb Annual Magnoliopsida All Solution Solution N Automated 6 -4.64 0.7

43 Shiny Elsholtzia Forb/Herb Annual Magnoliopsida All Solution Solution N Automated 6 -4.8 0.84

Eissenstat (1991)

44 Mandarin Tree Perennial Magnoliopsida Section Field Sand N Manual 13 -3.33 0.23

45 Orange Tree Perennial Magnoliopsida Section Field Sand N Manual 13 -3.48 0.17

Bouma et al. (2000)


46

3.3.METHODS



Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln

46 Common Cordgrass* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -5.15 0.96

47 Common Cordgrass* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -5.14 0.85

48 Seaside Alkaligrass* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -5.61 1.26

49 Seaside Alkaligrass* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -5.86 1.48

50 Sea Couch* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -5.03 0.65

51 Sea Couch* Graminoid Perennial Liliopsida All Solution Solution Y Automated 5 -4.76 0.55

Torssell et al. (1968)

52 Townsville stylo Forb/Herb Perennial Magnoliopsida All Pots Clay loam N Manual 7 -5.06 0.51

Blouin et al. (2007)

53 Erect Brome Graminoid Perennial Liliopsida All na Soil Y Automated 9 -5.24 0.98

Costa et al. (2002)

54 MaizeLRS Graminoid Annual Liliopsida All Pots Sand Y Automated 10 -5.18 1.01

55 MaizeLNS Graminoid Annual Liliopsida All Pots Sand Y Automated 10 -5.13 1

56 MaizeP3905 Graminoid Annual Liliopsida All Pots Sand Y Automated 10 -5 0.91

Qin et al. (2004)

57 Winter wheat Runal Graminoid Annual Liliopsida All Field Silt loam Y Automated 20 -3.5 0.43

58 Winter wheat Runal Graminoid Annual Liliopsida All Field Silt loam Y Automated 20 -3.51 0.43

Pagliai and De Nobili (1993)

59 Summer grape* Vine Perennial Magnoliopsida All Field Clay loam N Automated 4 -4.03 0.85

60 Summer grape* Vine Perennial Magnoliopsida All Field Clay loam N Automated 4 -4.06 0.83


47

CHAPTER

3.USIN

GRADIU

SFREQUENCY

DISTRIB

UTIO

N...



Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln

Miller (1981)

61 Maize (Seneca) Graminoid Annual Liliopsida All Solution Solution N Manual 17 -4.98 0.31

Costa et al. (2001)

62 Barley Graminoid Annual Liliopsida Section Pots Sandy loam* Y Automated 10 -5.23 0.93

63 Wheat Graminoid Annual Liliopsida Section Pots Sandy loam* Y Automated 10 -5.25 1.03

64 Maize Graminoid Annual Liliopsida Section Pots Sandy loam* Y Automated 10 -4.88 0.83

65 Soybean Forb/Herb Annual Magnoliopsida Section Pots Sandy loam* Y Automated 10 -4.17 0.37

Kuchenbuch et al. (2006)

66 Maize Graminoid Annual Liliopsida All Pots Loamy sand Y Automated 13 -4.3 0.68

Keller et al. (2003)

67 Basket willow* Tree Perennial Magnoliopsida All Field Clay Y Automated 16 -5.5 1.24











48

3.3.METHODS



Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln






82 Maize Graminoid Annual Liliopsida All Field Clay Y Automated 16 -4.71 0.94







89 Alpine Pennycress* Forb/Herb Perennial Magnoliopsida All Field Clay Y Automated 16 -5.16 0.95




Mooney (2002)

93 Mixed conifer forest Tree Perennial Pinopsida All Field na na Automated 10 -4 1.1

94 Mixed conifer forest Tree Perennial Pinopsida All Field na na Automated 10 -4.95 0.82




49

CHAPTER

3.USIN

GRADIU

SFREQUENCY

DISTRIB

UTIO

N...



Habit

Growth

Dura-

tion


Media


Auto

No.

Classes

µln σln

a b

* = Estimated from information availableK.B. = Kentucky Bluegrass

50

3.4. RESULTS AND DISCUSSION

3.4 Results and discussion

3.4.1 Description of database

Our database of 96 root radius frequency distributions contained 22 separate studies and

included a diverse range of plant types and methodologies (Table 3.3). The growth habits

of plants in the database included trees, forbs / herbs (forbs), graminoids and vines. All of

these plants were from the Spermophyta (seed plants) superdivision, and from either the

Coniferphyta (conifers) or Magnoliophyta (flowering plants) division. The classes of these

plants were either Liliopsida (eg. maize, wheat, Kentucky bluegrass), Magnoliopsida (eg.

willow, cocoa, soybean) or Pinopsida (eg. pine, spruce and juniper trees). The majority

(58) of the distributions we collected were from plants grown in field conditions, 28 were

grown in pots, 9 in nutrient solution and one not stated. The majority of the roots were

measured using computer-based methods using commercial software such as WinRhizo

(48) or MacRhizo (2) (www.regent.qc.ca/), Delta-T Scan (www.delta-t.co.uk/)(6) or free-

ware programs (4). The remainder were measured manually using the line intersect method

(Newman, 1966; Tennant, 1975), an ocular microscope or an enlarged photographic image.

There was some organisation between botanical and methodological factors in the

database. The Kruskal-Wallis test showed a significant (p<0.05) relationship between

growth media and growth habit. Roots that were measured from plants grown in field con-

ditions were mostly trees, while plants grown in pots or solution were mostly graminoids.

Similarly, there was a significant (p<0.05) relationship between growth media and stain-

ing: roots from plants grown in field conditions were mostly stained for measurement,

while those grown in pots were not. Growth habit and duration were both significantly

different for class and order; however, this is to be expected as the classification system

used used to define these is based upon the structure and physiological characteristics of

plants (Cronquist, 1981).

Almost all of the research we collated focused on fine roots; however, the definition

of fine roots was inconsistent amongst the articles. For example, Pregitzer et al. (1997)

defined fine roots as those having a branching order greater than two, while others defined

a maximum radius of 0.05 cm (Costa et al., 2001; Reinhardt and Miller, 1990), 0.07 cm

51


(Kuchenbuch et al., 2006) or 0.1 cm (Eissenstat, 1991), and others simply as ‘fibrous’

(Sullivan et al., 2000) or ‘fine’ (Pregitzer et al., 2002) roots. However, these values are

lower than the range of radius limits for fine roots reported by Gill and Jackson (2000),

which reinforces their point that the definition of fine roots is inconsistent in the literature

and not a useful discriminator for comparison. In our database 64 of the reported root

radius frequency distributions had a maximum radius less than or equal to 0.1 cm, though

the maximum was 0.6 cm which is similar to the range in the database of Gill and Jackson

(2000). Higher order roots of trees can have radii in the range of 1 to 5 cm (Clemente

et al., 2005; Danjon et al., 1999; Resh et al., 2003); however, these are not included in

the data we have collected. Therefore our findings must be viewed in the context of ‘fine’

roots rather than the entire root system.

3.4.2 Application of frequency distribution functions to database

3.4.3 Regression analysis

The log-normal distribution provided the best fit to our database of root radii frequency

distributions. Figure 3.2 shows some examples of distributions from the database and

the best fit to these for each of the functions. These examples show that the log-normal

distribution function is the most flexible and best suited to the range of shapes observed,

and this is reflected in the range of RMSE calculated for each function when they were

compared to the observed data (Figure 3.3). The log-normal distribution function had

the lowest median RMSE (0.02) and the narrowest inter-quartile range (0.0094 to 0.027).

The Weibull, normal and logistic (also two parameter functions) had similar inter-quartile

ranges, though the Weibull function produced a slightly lower median RMSE. The Rayleigh

and exponential (one parameter) had a higher median RMSE and greater inter-quartile

range, reflecting their lower flexibility due to having one shape parameter only. The only

similar work we are aware of showed that a bi-modal log-normal distribution function

provided the best fit to bi-modal radius frequency distributions (Anderson et al., 2007).

There was some organisation of the relationship between fitted parameters (parame-

ter space) for the log-normal distribution (Figure 3.4). There was a moderate negative

correlation between µln and σln (r = -0.48) indicating that the parameter space is rela-

52


0.00 0.01 0.02 0.03 0.04 0.05

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

freq

uenc

y

Root radius (cm)

Observed: Table 1.2 Index = 17Log−normal RMSE = 0.015Weibull RMSE = 0.019Normal RMSE = 0.049Logistic RMSE = 0.045Rayleigh RMSE = 0.067Exponential RMSE = 0.023

a

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

freq

uenc

y

Root radius (cm)


b

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

freq

uenc

y

Root radius (cm)


c

0.00 0.02 0.04 0.06 0.08 0.10

0.0

0.2

0.4

0.6

0.8

1.0

Cum

ulat

ive

freq

uenc

y

Root radius (cm)


d

Figure 3.2: Comparison of observed data and fitted distribution functions for 4 examplesfrom Table 3.3. Note the different x axis scales.

53


Log−normal Weibull Normal Logistic Rayleigh Exponential

0.00

0.05

0.10

0.15

0.20

0.25

RM

SE

Two parameters One parameter

Figure 3.3: Summary of RMSE for each function used for regression analysis of root radiusfrequency distributions

tively well defined. However, as indicated by the density plots in Figure 3.4 the optimised

parameters themselves are not normally distributed, which needs to be considered in a

sensitivity analysis using the parameter space. The mean µln and σln were -4.7 and 0.75

respectively. There was a strong correlation between the standard error of µ (µe) and the

standard error of σ (σe) (r = 0.97) showing that as would be expected, for distributions

where the log-normal distribution function did not provide a good fit the parameters µ and

σ needed to be varied greatly to decrease the residual sum of squares, and as evidence of

this there were positive correlations between RMSE and µe and σe of r = 0.38 and r = 0.53

respectively. There were no strong correlations between the number of observations n and

any of the parameters described here.

3.4.4 Statistical properties of root radius frequency distributions

Figure 3.5 shows a summary of the statistical attributes of the root radius frequency

distributions in our database. The median distribution mean was 1 x 10−2 cm and the

25th and 75th percentile were 8.3 x 10−3 and 1.6 x 10−2 cm respectively. The 25th and 75th

percentile of distribution variance was 3.6 x 10−5 and 1.8 x 10−4 respectively, and there

was also a moderate correlation between distribution mean and variance (r=0.57) (data

54


−6.0 −5.5 −5.0 −4.5 −4.0 −3.5 −3.0

0.0

0.4

0.8

Den

sity

−6.0 −5.5 −5.0 −4.5 −4.0 −3.5 −3.0

0.0

0.5

1.0

1.5

2.0

µln

σ ln

Error bars are standard error

0.0 0.5 1.0 1.5

0.0

0.5

1.0

1.5

2.0

Density

Figure 3.4: Optimised parameters for the log-normal CDF for each root radius frequencydistribution in the database. The red, green, cyan and blue circles correspond to Figure3.2 a, b, c and d respectively

55


0.00

00.

005

0.01

00.

015

0.02

00.

025

0.03

0M

ean

(cm

)

0e+

001e

−04

2e−

043e

−04

4e−

045e

−04

Var

ianc

e

02

46

810

Ske

wne

ss

050

100

150

Kur

tosi

s

Figure 3.5: Summary of the distribution mean, variance, skewness and kurtosis of the rootradius frequency distributions in our database calculated from the optimised log-normalparameters

not shown). All the distributions in our database had positive distribution skewness (tail

elongated to the right) and kurtosis (distribution shows a strong peak at the mean), which

partly explains why the two non-symmetrical (log-normal and Weibull) functions provided

the best fit to the database, and distribution skewness and kurtosis were highly correlated

(r = 0.89). The relationship between distribution skewness and kurtosis may reflect the

branching behaviour of root systems. For example, a herringbone branching system (e.g.

Dunbabin et al., 2003) is characterised by a taproot and first order laterals only so its

radius distribution is likely to have a long tail because the largest roots (tap root) make

up a small part of the total length, and the remainder of the roots are of the same order,

leading to a peakiness at the mean of the distribution. In contrast, the dichotomous

branching system (e.g. Dunbabin et al., 2003) can have several orders of branching, and

is therefore likely to have a wider range of root radii, leading to a frequency distribution

that has a relatively shorter tail and a lower peak at the mean.

We found no evidence that any of the distributions were better or worse suited to

different shape types, as indicated by distribution mean, variance, skewness and kurtosis.

For all distributions except the Rayleigh there was a positive trend between RMSE and

56


distribution mean; however, the correlations were weak, which for example were r= 0.35,

0.38, 0.43 and 0.42 for the log-normal, Weibull, normal and logistic CDF respectively. This

trend may be an artefact of the data as when the distribution mean is small less points

occur in the steep part of the curve than when it is large, and there is less potential for

error between fitted and observed. There were no obvious relationships between RMSE

and the other distribution attributes.

The overall goodness of fit of the log-normal CDF and lack of systematic error asso-

ciated with distribution shapes are sound evidence this distribution is a reliable proxy to

represent root systems mathematically. While in principle it would preferable to derive the

distribution mean, variance, skewness and kurtosis directly from data, where data is only

available as a frequency distribution the results are are highly sensitive to the smoothness

of the data and deriving these attributes from a fitted function provides a more reliable

estimate (Skaggs and Shouse, 2002). In addition, deriving these attributes from a fitted

function provides a consistent method that can be applied to a broad range of root types

as demonstrated by fitting distribution functions to our database.

3.4.5 Root system volume and surface area

Figure 3.6 shows a summary of root surface area and volume calculated using Equations

3.5 and 3.6 for the root radius distributions in our database. The median root surface

area was 0.06 cm2 cm−1 and the 25th and 75th percentile was 0.05 and 0.1 cm2 cm−1

respectively. This range is very similar to the range in the database collated by Jackson

et al. (1997), where over a number of biomes the mean surface area ranged from 0.07

to 0.18 cm2 cm−1, which were for tundra and tropical evergreen forest respectively. The

median root volume was 0.0005 cm3 cm−1 and the 25th and 75th percentile was 0.0004 and

0.0013 cm3 cm−1 respectively, which is similar to the range of 0.0002 to 0.0008 cm3 cm−1

which was calculated by Ryser and Lambers (1995) using a method similar to Equation

3.8. However, a range of 0.003 to 0.004 cm3 cm−1 was calculated by Eissenstat (1991)

using root cross-sectional area, which are an order of magnitude greater and is perhaps an

example of the sensitivity of the calculated ratio to the initial measurement.

Figure 3.7 shows that the error induced by calculating root volume from the mean root

57


0.00

000.

0010

0.00

200.

0030

Roo

t vol

ume

(cm3 c

m−1

)

0.00

0.05

0.10

0.15

0.20

Roo

t sur

face

are

a (c

m2 cm

−1)

Figure 3.6: Summary of root surface area and volume calculated with Equations 3.5 and3.6 respectively for the root radius distributions in our database

radius is sensitive to the distribution skewness. This is to be expected because the mean

of the individual root radius measurements and the distribution mean are the same when

the distribution is perfectly symmetrical; however, the difference between these increases

as the distribution becomes increasingly asymmetrical. Figure 3.5 shows that 75% of the

distributions in our database had a skewness greater than 2, meaning that significant error

would almost always be induced using this method.

The error due to histogram-based calculations of root volume and surface area was

most sensitive to the number of categories in the histogram (Figure 3.8). These results

suggest that for root distribution data at least 15 categories are required to reduce the

error to less than 10%. However, the range of error was also sensitive to the number of

modelled root radius measurements where the range in error decreaes as the number of

modelled points increases (data not shown).

3.4.6 Relevance of integral limits to root radius frequency distributions

The use of raw or central moments to analyse a distribution is based on the assumption

the distribution is being integrated from r=0 to ∞; however, in reality root radius does

not conform to this assumption. The upper limit of r=∞ does not pose a problem for the

58


0 2 4 6 8 10

−10

0−

60−

40−

200

20

Skewness

% e

rror

Root volumeRoot surface area

Figure 3.7: Percent error in root volume and surface area calculated using the meanroot radius. Data is for modelled root radius measurements based upon the log-normalparameters derived for the distributions in Table 3.3

5 10 15 20 25 30

−15

−5

05

1015

20

Number of bins in histogram

% e

rror

in r

oot v

olum

e

a

5 10 15 20 25 30

−15

−5

05

1015

20

Number of bins in histogram

% e

rror

in s

urfa

ce a

rea

b

Figure 3.8: Effect of the number of categories in the histogram on the error in calculatingroot volume (a) and surface area (b) from the histogram using Equations 3.7 and 3.8.Heavy line is the mean error and thin lines are the 95% confidence intervals. Data arefor modelled root radius measurements based upon the log-normal parameters derived forthe distributions in Table 3.3

59


application of distribution functions to root radii data if all measured data are reported,

and as stated above we assume this was the case for the studies we have used. However,

the lower limit of 0 does pose a problem: there is a physiological lower limit to the radius

of roots which should result in a truncation of the distribution near to r=0. While this

is a theoretical flaw of analysing root radius data with the equations here, the practical

implications are insignificant.

Figure 3.9 shows a summary of the potential error in calculating cumulative frequency

(a), surface area (b) and volume (c) assuming a lower limit of 0. For this analysis we

assumed that the physiological lower limit of root radius was 3.5 x 10−4 cm (Dittmer, 1949;

Fusseder, 1984) and calculated the cumulative frequency, surface area and volume at that

point using the parameters derived for each distribution in our database. The median

cumulative frequency, % of surface area below the physiological limit and % of volume

below the physiological limit were 1.28 x 10−5, 2.57 x 10−5% 1.67 x 10−7% respectively.

Clearly, these values are very small and are an insignificant source of error in comparison

to up to 40% error in calculated root length that can occur due to the grayscale threshold

(Bouma et al., 2000) or image resolution (Zobel, 2003) for automated analysis and up to

45 % error in length due to washing methods (Amato and Pardo, 1994). Therefore, for

the types of extraction and measurement methodology used in our database, analysis of

root radius distribution data with the equations here is appropriate.

3.4.7 Influence of botanical traits on derived parameters

Analysis of variance showed that growth habit was the only botanical trait that had a

significant (p<0.05) effect on the distribution mean. The median distribution mean was

highest in vines, followed by trees, forbs, graminoids then mixed (Figure 3.10), which were

2.5 x 10−2, 1.2 x 10−2, 1.2 x 10−2, 8.6 x 10−3 and 8.8 x 10−3 cm respectively. This is

a similar range to that found by (Jackson et al., 1997), where the mean radius of fine

roots for trees, shrubs and grasses in their database was 2.9 x 10−2, 2.2 x 10−2 and 1.1 x

10−2 cm respectively. The distribution mean was higher in annual than perennial plants,

though mixes of these were similar to perennials (not shown). The distribution mean for

roots from Liliopsida and mixed classes of plants had a similar and notably lower median

60


0e+

001e

−04

2e−

043e

−04

4e−

045e

−04

6e−

047e

−04

Cum

ulat

ive

freq

uenc

y at

phy

siol

ogic

al li

mit

(a)

0.00

00.

002

0.00

40.

006

0.00

80.

010

% o

f dis

trib

utio

n su

rfac

e ar

ea b

elow

phy

siol

ogic

al li

mit

(b)

0.0e

+00

5.0e

−06

1.0e

−05

1.5e

−05

% o

f dis

trib

utio

n vo

lum

e be

low

phy

siol

ogic

al li

mit (c)

Figure 3.9: Summary of cumulative frequency (a), % of root surface area (b) and % of rootvolume (c) from a continuous distribution at the physiological lower limit of root radius

than Magnoliopsida and Pinopsida plants (not shown). There was no clear trend between

any botanical properties and distribution variance.

The influence of root length density on the shape of the root radii frequency distribu-

tions was not clear which was in part due to the limited data available. Only 31 of the

frequency distributions we found also reported root length density and 30 of these were

less than 2.5 cm cm−3. This range of root length density is relatively small to what has

been observed in crops (de Willigen and van Noordwijk, 1987) and temperate grasslands

(Jackson et al., 1997) but similar to that found in natural forests (Jackson et al., 1997).

There was no relationship between root length density and the distribution mean or vari-

ance; however, we can not make conclusions about whether or not this is a physiological

property due to the limited data set.

3.4.8 Influence of methodology on derived parameters

Only one methodological trait had a significant effect on the shape of the radii frequency

distribution: the distribution mean was significantly different (p<0.05) for the different

growth media. The median distribution mean of roots grown in field conditions was 1.3

x 10−2 cm, higher than those grown in pots and solution which were 7.8 x 10−3 and 8.5

61


0.00

0.01

0.02

0.03

0.04

Vine Tree

Forb

/ Her

b

Gram

inoid

Mixe

d

Dis

trib

utio

n m

ean

(cm

)

n = 2 n = 36 n = 13 n = 43 n = 2

Figure 3.10: Root radius frequency distribution mean grouped by growth habit

x 10−3 cm respectively. There were clear trends that were not significantly different: the

distribution variance of roots measured using automated methods had a greater median

and inter-quartile range than those measured manually, and the distribution variance of

roots that were stained showed a much greater inter-quartile range than those that were

not. There was no significant interaction between growth media and growth habit for

either the distribution mean or variance.

The lower distribution mean and greater range of distribution variances for roots mea-

sured automatically compared to those measured manually highlights a major method-

ological problem in root research: the extraction and measurement of fine roots. The

difference between the measurement methods in our database is undoubtably due to the

improved detection of fine roots using high resolution images and sophisticated software.

However, there can also be considerable differences in the outcome from digital analysis

due to subtle differences in methodology. For example, root length calculated by image

analysis software can be greatly reduced if the roots are not stained, especially for fine

roots (Bouma et al., 2000; Costa et al., 2001). Also, the most commonly used commercial

software can not detect 10% changes in root radius when it is less than 6 x 10−3 cm (Zobel

and Zobel, 2008). In the context of our database, it was impossible to compare the effect

of digital parameters because they were not well reported, and the description of the root

62

3.5. CONCLUSION

methodology was generally incomplete.

There was evidence that soil type and depth affected the shape of the root radii fre-

quency distributions. Soil texture had a significant (p<0.05) effect on the distribution

mean; however, there was no logical trend across textural types except that sand was

much lower than the finer textures. In contrast, the distribution variance was not sig-

nificantly affected by soil texture, but the the median and inter quartile range for the

clay and clay loam were greater than the silty loam, sandy loam, loamy sand and sand.

Also, when outlier data were removed the linear regression showed a significant (p<0.05)

positive relationship between the distribution mean and soil depth. An increasing trend

in mean root radius has also been observed in trees (Lopez et al., 2001; Kizito et al., 2006)

and crop plants (Keller et al., 2003).

3.5 Conclusion

The log-normal distribution function is a suitable proxy for describing root radii frequency

distributions. We found that compared to 5 other distribution functions, the log-normal

had the lowest range of RMSE when fitted to a database of observed root radius distri-

butions, and found no evidence that this function was better or worse suited to particular

shapes. We derived analytical expressions for root surface area and volume using the 1st

and 2nd raw moments respectively of the distribution functions. We compared root surface

area and volume calculated from the analytical expressions to that calculated from mean

root radius or from a histogram of root radii and found that the analytical expressions

provide greater accuracy.

The use of a radius distribution function to describe root systems assumes that the

lower limit of root radius is 0 where in reality there is a physiological lower limit. Our

analysis showed that this assumption leads to errors of less than 0.01% for root volume

and surface area calculated using the expressions we derived, meaning that they are valid

method.

Analysis of the effect of botanical and methodological factors revealed two significant

(p<0.05) effects: growth media and growth habit both had a significant effect on the

distribution mean, however there was no interaction between these. We also found a

63


significant relationship between growth habit and growth media, where trees were most

likely to be grown in field conditions and graminoids were most likely to be grown in pots.

64

Chapter 4A conceptual model of root-induced

changes to soil hydraulic properties




4.1 Abstract

Root-induced changes to soil hydraulic properties (SHP) can lead to complex hydrological

interactions between plants and soil. We developed a conceptual model based on the

capillary-bundle approach that describes how roots change soil hydraulic conductivity and

water retention. The central assumption of our model is that the geometry of roots within

pore space can be simplified to concentric cylinders, which allows us to model capillary

rise, flux and volume within root-occupied pores based upon physical principles only. The

model requires values for the root radius frequency distribution, root length density, van

Genuchten (1980) shape parameters for the soil, the ratio of root to pore radius for root-

occupied pores and the connectivity of pores with and without roots. Modelled changes

to saturated hydraulic conductivity (Ks) were sensitive to the ratio of root radius to pore

radius, the connectivity of root-modified pores, and soil texture. Changes to Ks increased

as soil texture became finer and as the connectivity of root-modified pores increased. The

65

CHAPTER 4. A CONCEPTUAL MODEL OF ROOT-INDUCED . . .

unsaturated hydraulic conductivity and water retention functions became increasingly bi-

modal in appearance as the difference between the frequency distribution of root and pore

radii increased. Our model predicted both increases and decreases in Ks due to changes

in the ratio of root radius to pore radius. The greatest change occurred in near- and

saturated conditions which is in agreement with observations. Comparison of predicted

and observed changes show that they are similar; however, the lack of data that provides

a thorough test of the model highlights the need for further research that examines the

processes by which roots modify SHP.

4.2 Introduction

Soil moisture plays a central role in the interactions between soils and vegetation, espe-

cially in arid conditions (Porporato and Rodriguez-Iturbe, 2002). It in-part controls water

uptake by vegetation, infiltration of rainfall, and evaporative losses (Hillel, 1998); however,

soil-vegetation interactions have an added layer of complexity: plant roots can modify soil

hydraulic properties (SHP) (e.g. Barley, 1954; Li and Ghodrati, 1994; Meek et al., 1990).

Root induced changes to SHP can have a major impact on the spatial distribution of soil

moisture (e.g. Devitt and Smith, 2002; Dunkerley, 2002; Seyfried, 1991), where for example

a feedback can occur between vegetation density and infiltration rate (Gilad et al., 2007;

HilleRisLambers et al., 2001; Rietkerk et al., 2002; Saco et al., 2007; Ursino, 2007; von

Hardenberg et al., 2001).

While modelling provides a powerful tool for investigating these complex systems, this

approach is limited by a lack of processed-based description of root-induced changes to

SHP. An empirical relationship between vegetation density and infiltration rate shown

by HilleRisLambers et al. (2001) has been employed in a number of studies of spatial

vegetation patterns (Gilad et al., 2007; HilleRisLambers et al., 2001; Rietkerk et al., 2002;

Saco et al., 2007; Ursino, 2007; von Hardenberg et al., 2001). However, this relationship

can not be applied universally because the changes caused by roots are likely to reflect the

diameter and morphology of the root systems and the initial condition of the soil. Also, this

empirical approach assumes an instantaneous increase in infiltration rate where vegetation

is present, but there is ample evidence that root-induced changes to SHP is a dynamic

66

4.2. INTRODUCTION

process in which both decreases and increases in hydraulic conductivity occurs (e.g. Barley,

1954; Petersson et al., 1987). Decreases in infiltration rate have been observed where

cereals, lucerne and trees are present when the plant is relatively young, and increases

only occur when roots begin to senesce and decay (Barley, 1954; Meek et al., 1989, 1992;

Murphy et al., 1993; Petersson et al., 1987). To improve our capacity to predict the timing

and extent of changes to SHP a model based upon mechanisms is required.

Roots modify SHP by a number of mechanisms: the creation of macropores by decaying

roots (Rachman et al., 2004a; Rasse et al., 2000; Yunusa et al., 2002; Mitchell et al., 1995;

Meek et al., 1989, 1992; van Noordwijk et al., 1991; Petersson et al., 1987; Barley, 1954),

blocking pores (Barley, 1953, 1954; Sedgley and Barley, 1958; Suwardji and Eberbach,

1998; Gish and Jury, 1982; Meek et al., 1990), changes to aggregate properties due to

wetting and drying, physical enmeshment or compounds released by roots (Reid and Goss,

1982; Pojasok and Kay, 1990; Haynes and Beare, 1997; Tisdall and Oades, 1979; Monroe

and Kladivko, 1987; Morel et al., 1991), modification of surface tension of soil particles by

compounds released by roots (Read et al., 2003; Read and Gregory, 1997), compression

of soil due to root expansion (Clemente et al., 2005; Bruand et al., 1996; Braunack and

Freebairn, 1988; Dexter, 1987a), and physical re-arrangement of soil particles during root

growth (Barley, 1954; Blevins et al., 1970; Whiteley, 1989). In Chapter 1 we identified

that blocking pore space and creation of macropores as the dominant mechanisms of root-

induced changes to SHP, which do so by changing pore geometry (e.g Jassogne et al., 2007;

Nye, 1994; Tippkotter, 1983; van Noordwijk et al., 1993).

Roots modify the geometry of the pore space by re-arranging soil particles and by the

occupation of pore space. Macropores created by decayed roots of grasses have been found

to be in tubular in appearance (Barley, 1954; Jassogne et al., 2007; Tippkotter, 1983), and

provide a less tortuous pathway than the soil matrix (Perret et al., 1999). Between 54

and 65% of roots are within pores that have greater radius (North and Nobel, 1997; van

Noordwijk et al., 1993) suggesting an anular geometry (Nye, 1994). These observations

about the geometry of roots and pore space lead us to hypothesise that root-induced

changes to SHP can be explained by the change of fluid behaviour caused by the presence

of a root within a pore and the connectivity of root-modified pores relative to the soil

67


matrix.

In this chapter we detail a conceptual model of root-induced changes to hydraulic con-

ductivity and water retention. The central assumption of this model is that the geometry

of roots within pore space can be simplified to concentric cylinders, and we model capil-

lary pressure and flux within these based upon physical principles only. First we show the

development of the model, second we assess the sensitivity of modelled hydraulic conduc-

tivity and water retention to the parameters we have included, third we compare modelled

changes in saturated hydraulic conductivity (Ks) to the experimental data from Chapter

3, and finally discuss the predictions of the model in the context of reported root-induced

changes to SHP.

4.3 Methodology

Our conceptual model of root-induced changes to soil hydraulic properties is based upon

a modification of the capillary-bundle model (Childs and Collis-George, 1950; Marshall,

1958; Millington and Quirk, 1959). We consider roots as solid cylinders that lie concentri-

cally within larger cylinders that represent pore space (Figure 4.1), and this allows us to

investigate a priori how roots modify soil hydraulic properties based upon fluid behaviour

within concentric cylinders.

In this section we first describe how we calculate capillary rise, water flux and volume

between concentric cylinders, and relate this to an empty cylinder. Next we show how

the frequency distribution of root radii is used to modify the pore size distribution of a

soil initially containing no roots, where we assume that roots grow into the existing pore

network but can change the radius and connectivity of the pores they occupy. Finally

we present a model that combines these two aspects to predict the water retention and

hydraulic conductivity of the root-modified soil.

4.3.1 Fluid behaviour in concentric cylinders

The calculation of capillary rise within concentric cylinders is based upon the same as-

sumptions used for capillary rise in a cylinder (Figure 4.1a), where the height of capillary

rise can be calculated as a balance of the upward and downward forces acting on the liquid

68

4.3. METHODOLOGY

Figure 4.1: A conceptual cross-section of capillary rise in a cylinder (a) and betweenconcentric cylinders (b) where r1 and r2 are the radius of the inner and outer cylinderrespectively, and hc and ha is the capillary rise within a cylinder and concentric cylindersrespectively.

(Marshall and Holmes, 1979). In concentric cylinders (Figure 4.1b) we assume the upward

force is the product of the radius of the inner r1 (cm) and outer r2 (cm) cylinder respec-

tively, surface tension γ (g cm s−2 cm−1) and wetting angle Θ. The downward force is the

product of capillary rise h (cm), r1, r2, density of the liquid ρ (g cm−3) and gravitational

acceleration g (cm s−2). We derived capillary rise between concentric cylinders ha (cm)

by equating the upward forces of the inner plus the outer cylinder to the downward forces

of the outer minus the inner cylinder which simplified to:

ha =λ

r2 − r1(4.1)

Where λ = 2γ cosΘρg (cm2). For complete derivation of Equation 4.1 refer to Appendix A.

The average velocity qa (cm s−1) between concentric cylinders (Cutlip and Shacham,

69


1999; Wantanabe and Flury, 2008) is:

qa =ρg (H2 −H1)

8ηL

[

r21 + r22 −r22 − r21

ln (r2/r1)

]

(4.2)

Where H1 and H2 denote pressure head at either end of the concentric cylinders (cm

H2O), L denotes length of the cylinders (cm) and η denotes dynamic viscosity (g cm−1

s−1).

The volume within concentric cylinders wa (cm3) is the volume of the outer cylinder

minus the inner cylinder and simplifies to:

wa = lπ(

r22 − r21)

(4.3)

We now derive dimensionless expressions to assess how r1 changes capillary rise, flux

and volume within concentric cylinders compared to a cylinder of radius r2 (for complete

derivations see Appendix A). Equations 4.1, 4.2 and 4.3 represent a cylinder of radius r2

when r1=0.

The ratio δh (-) of capillary rise within concentric cylinders ha (r1, r2) to capillary rise

within a single cylinder ha (r1 = 0, r2) was derived using Equation 4.1:

δh =ha (r1, r2)

ha (r1 = 0, r2)=

1

1− β(4.4)

Where:

β =r1r2

(r1 ≤ r2) (4.5)

Similarly we derived the ratio δq (-) of flux within concentric cylinders qa (r1, r2) to

flux within a single cylinder qa (r1 = 0, r2) using Equation 4.2:

δq =qa (r1, r2)

qa (r1 = 0, r2)= 1 + β2 − 1− β2

ln (1/β)(4.6)

And finally the ratio δw (-) of volume within concentric cylinders wa (r1, r2) to volume

70

4.3. METHODOLOGY

within a single cylinder wa (r1 = 0, r2) was derived using Equation 4.3:

δw =wa (r1, r2)

wa (r1 = 0, r2)= 1− β2 (4.7)

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

05

1015

20

δ q a

nd δ w

δ hβ

δwδq

δh

Figure 4.2: The effect of the ratio of root radius to pore radius β on change in capillaryrise δh, flux δq and volume δw in pores with roots present

These dimensionless ratios are functions of β only and illustrate the effect of the radius

of the inner cylinder relative to the radius of the outer cylinder on capillary rise, flux and

volume in root-occupied pores. Figure 4.2 shows that δh increases rapidly where β > 0.8,

and the steepest decrease in δq occurs at low values of β, meaning that even a root of a

very small radius relative to the pore greatly reduces the flow rate in comparison to an

unoccupied pore.

4.3.2 Geometric features of root systems

The two geometric features of root systems we included in the model are root length

density D (cm cm−3) and the root radius frequency distribution. In Chapter 3 we showed

71


Table 4.1: Log-normal distribution parameters for 3 root types

Type µ σ

1 -5.5 12 -4.75 0.753 -4.0 0.5

that the log-normal frequency distribution (Weisstein, 2008b) provided the best fit to

our database of measured frequency distributions. Additionally, we found a moderate

correlation between the parameters for this function (Figure 3.4), which allowed us to

constrain the parameter space to the 3 representative points shown in Table 4.1. The

cumulative frequency of root radius FR(r) is expressed as:

FR(r) =1

2

[

1 + erf

(

ln(r)− µ

σ√2

)]

(4.8)

Where µ and σ are the mean and standard deviation respectively.

4.3.3 Geometric features of the soil

Our model requires the initial pore radii frequency distribution of a soil which was derived

from the van Genuchten (1980) effective saturation function Se(h)(-):

Se(h) =θ − θrθs − θr

= (1 + (αh)n)−m (4.9)

Where θ (cm3 cm−3) is water content, θs (cm3 cm−3) and θr (cm3 cm−3) are saturated

and residual water content respectively, α (cm−1) and n (-) are shape parameters and

m = 1− 1/n (van Genuchten, 1980).

Matric head h (cm) is related to pore radius using the Young-Laplace equation (e.g.

Warrick, 2003):

h =λ

r(4.10)

By substituting h in Equation 4.9 with the right-hand side of Equation 4.10 we ex-

72

4.3. METHODOLOGY

pressed the cumulative frequency of pore radii FP (r) as:

FP (r) =

[

1 +

(

αλ

r

)n]−m

(4.11)

We derived Equation 4.11 from the van Genuchten (1980) effective saturation function

because the parameter space for α and n is relatively well defined and structured, based

on the large database first used by Carsel and Parrish (1988), which allowed us to choose

parameters that represent a realistic range of soils.

4.3.4 Modified capillary-bundle model

The capillary-bundle model conceptualises the soil pore volume as a series of bundles

of cylindrical tubes (e.g. Childs and Collis-George, 1950; Marshall, 1958; Millington and

Quirk, 1959). The total volume and radii of the cylinders in each bundle is derived from

the water retention function where matric head is related to pore radius using Equation

4.10. There are two implicit assumptions to this model, first that flux and matric head

are a function of pore radius only, and second that no flux occurs through pores that are

drained in unsaturated conditions.

The model we describe here differs from the conventional capillary-bundle model in that

some of the pore cylinders in a bundle may be occupied by roots, which we conceptualise

as two separate sets of bundles of cylindrical tubes, one with roots present and one without

which are denoted as R and P respectively. The radius distribution was segmented into

m logarithmically spaced radius classes ri (cm). We assumed that pore cylinders were

orientated vertically and that where pores were occupied by roots, the roots occupied the

entire length of the cylinder, and that the total number of pores and total pore volume

did not change. In the following we describe how we calculate the number, volume and

radius of cylinders with and without roots present.

Initial soil properties

The frequency of pore volume in each radius class fPi is calculated from FP (r):

fPi = FP (ri)− FP (ri −∆r) (4.12)

73


The volume of cylindrical pores in each radius class vPi (cm3 cm−3) is:

vPi = fPi (θs − θr) (4.13)

The number of cylindrical pores in each radius class nPi (-) is given by:

nPi =

vPi φ

Lπr2i(4.14)

Where φ is soil volume (cm3).

Pores with roots

We calculate the number and volume of pore cylinders in each radius class for the set

of bundles with roots present by assuming that the radius of pores with roots present

conforms to that of the root. The frequency of root length in each radius class fRi is found

by integrating the log-normal probability density function over the range of each radius

class:

fRi = FR(ri)− FR(ri −∆r) (4.15)

Where µ and σ are the mean and the standard deviation respectively (Weisstein, 2008b).

Therefore the number of cylindrical roots in each radius class nRi (-) is:

nRi = fR

i

Dφ

L(4.16)

And the total number of cylindrical pores in the soil volume NR (-) is:

NR =m∑

i=1

nRi (4.17)

The volumetric fraction of roots in each radius class vRi (cm3 cm−3) is:

vRi =nRi Lπr

2i

φ(4.18)

74

4.3. METHODOLOGY

Therefore the total fraction of root volume V (cm3 cm−3) is :

V R =m∑

i=1

vRi (4.19)

Pores without roots

We now determine the number and volume of pore cylinders in each radius class for the

set of bundles without roots present. We assume that the likelihood of pores in any radius

class being occupied by roots is determined by the frequency of volume of that class,

therefore the number of pores in each radius class occupied by roots pRi (-) is:

pRi = NRfPi (4.20)

And the number of cylindrical pores in each radius class that are not occupied by roots

is:

pPi = nPi − pRi (4.21)

While Equations 4.20 and 4.21 satisfy our assumption that the total number of pores

do not change, they do not necessarily satisfy our assumption that total pore volume does

not change. This is because total root volume may be different to the total volume of the

pores occupied by roots, and we describe this difference as the compensation volumetric

fraction C (cm3 cm−3). To maintain our constant volume assumption the total volume

of the pores without roots changes according to the compensation volume leading to a

change in pore volume and radius for the different classes. We begin quantifying this by

calculating the volume occupied by pores allocated to roots ai (cm3 cm−3):

ai =pRi Lπr

2i

φ(4.22)

Therefore the total volumetric fraction allocated to roots A (cm3 cm−3) is :

A =m∑

i=1

ai (4.23)

75


The volume of roots without pores ui (cm3 cm−3) is:

ui = vPi − ai (4.24)

Therefore the total volumetric fraction without roots U (cm3 cm−3) is

U =m∑

i=1

ui (4.25)

The compensation fraction C is:

C = V R −A (4.26)

This introduces a physical limitation to the model, as it is unlikely that in reality pores

without roots would increase in volume where V is less than A. Mean root radius lies

between 0.005 and 0.05 cm (Chapter 3) whereas mean pore radii of soils is between 0.001

and 0.01 cm (Kosugi, 1997), therefore this situation would only occur where the effects of

fine roots are modelled for a coarse sand.

We make the simplifying assumption that pores without roots will be compressed

according to their frequency of volume, therefore the compensation fraction of each radius

class ci (cm3 cm−3) is:

ci = CuiU

(4.27)

After compensation the volume of pores without roots in each class si (cm3 cm−3) is:

si = ui − ci (4.28)

The volume of each of cylindrical pores without roots ti (cm3) is:

ti =φsi

pPi(4.29)

76

4.3. METHODOLOGY

Therefore the radius of each of cylindrical pores without roots is zi (cm) is:

zi =

(

tiLπ

)1/2

(4.30)

Calculation of hydraulic properties of the soil-root system

The hydraulic properties of the soil-root system are found by treating soil with and without

roots present as separate components. Calculation of hydraulic conductivity for pore

space without roots (Equation 4.32) and with roots present (Equation 4.35) is based on

the function summarized by Jury et al. (1991), and we have included parameters for the

connectivity of pores without τP and with τR roots present. We define pore connectivity

as the ratio of sample length L (cm) to capillary length Lc (cm) (e.g. Jury et al., 1991):

τX =L

LXc

(4.31)

Where X can be the capillary length of pores with R or without P roots.

Hydraulic conductivity for each pore radius class without roots present KPi (cm s−1)

is:

KPi = τP

ρg

8ηsiz

2i (4.32)

Matric head for each pore radius class without roots present hPi (cm) is:

hPi =λ

si(4.33)

Volume for each pore radius class without roots present wPi (cm3 cm−3) is:

wPi = si (4.34)

Hydraulic conductivity for each pore radius class with roots present KRi (cm s−1) is:

KRi = τR

ρg

8ηvRi r

2i δq (4.35)

77


Matric head for each pore radius class with roots present hRi (cm) is:

hRi =λ

riδh (4.36)

Volume for each pore radius class with roots present wRi is (cm3 cm−3):

wRi = vRi δw (4.37)

The hydraulic conductivity of the root modified soil at a given matric head KM (h) is

the sum of hydraulic conductivity of pore space with and without roots present:

KM (h) =

j∑

i=m

KPj +

k∑

i=m

KRk (4.38)

Similarly the water content of the root modified soil at a given matric head θM (h) is the

sum of the water content of soil with and without roots present:

θM (h) = θr +

j∑

i=m

wPj +

k∑

i=m

wRk (4.39)

Where j and k are the radius class where hP and hR are equal to h.

4.4 Results

4.4.1 Saturated hydraulic conductivity

TheKs of the initial soil and the root modified pore space determined whether roots caused

an increase or decrease in Ks. To demonstrate this in Figure 4.3 we show an analysis of

the interactive effects between parameters that determine Ks of the root modified pore

space, which include the connectivity of pores with roots τR, the ratio of root radius to

pore radius β and root length density, and soil texture (initial Ks) on changes in Ks of the

root-modified soil. For the sand where the the initial Ks was high (0.056 cm s−1), when

τR was 0.01 roots always caused a decrease in Ks, as Ks of root modified pore space only

ranged from 0.00002 to 0.0088 cm s−1 when β was 0.9 and 0.3 respectively. In contrast,

78

4.4. RESULTS

Table 4.2: List of parameters used in the modified capillary-bundle modelParameter Description

Model inputs

h Capillary rise or matric head (cm)δh Scalar for capillary rise in concentric cylinders (-)β Ratio of root radius to pore radius (-)δq Scalar for flux in concentric cylinders (-)δw Scalar for volume in concentric cylinders (-)µ Parameter for log-normal frequency distribution functionσ Parameter for log-normal frequency distribution functionθs Saturated water content (cm3 cm−3)θr Residual water content (cm3 cm−3)α Shape parameter for effective saturation function (cm−1)n Shape parameter for effective saturation function(-)τR, τP Connectivity of pores with and without roots respectively (-)Model outputs

KRi ,KP

i Hydraulic conductivity of pores with and without roots respectively of radius i (cm s−1)hRi ,h

Pi Matric head of pores with and without roots respectively of radius i (cm)

wRi ,w

Pi Volumetric fraction of pores with and without roots respectively of radius i (cm3 cm−3)

KM (h) Hydraulic conductivity of the root modified soil (cm s−1)θM (h) Volumetric water content of the root modified soil (cm3 cm−3)Constants used in derivation

r Root or pore radius (cm)r1,r2 Radius of inner and outer cylinder respectively (cm)γ Surface tension (g cm s−2 cm−1)Θ Wetting angleρ Fluid density (g cm−3)g Gravitational acceleration (cm s−2)ha Capillary rise between concentric cylinders (cm)qa Flux through concentric cylinders (cm)wa Volume within concentric cylinders (cm)λ Product of constants in Young-Laplace equation (cm2)H2,H1 Pressure head at either end of the concentric cylinders (cm)L Length of cylinder (cm)η Dynamic viscosity (g cm−1 s−1)φ Soil volume (cm3)

79


Root length density (cm cm−3)

% C

hang

e in

K s

−500

50100150

0 5 10 15

Sand

τR =

1

0 5 10 15

Loam

τR =

1

0 5 10 15

Clay

τR =

1

Sand

τR =

0.1

LoamτR

= 0

.1

−50050100150

Clay

τR =

0.1

−500

50100150

SandτR

= 0

.01

Loam

τR =

0.0

1

Clay

τR =

0.0

1

β = 0.3β = 0.5β = 0.7β = 0.9

Figure 4.3: The interaction between soil texture (Carsel and Parrish, 1988), connectivity ofroot-modified pore space τP , and the ratio of root to pore radius β on changes to saturatedhydraulic conductivityKs, where the roots are Type 3 (Table 4.1) and connectivity of poreswithout roots τP was 0.01 (Jury et al., 1991)

in the clay the initial Ks was 0.0065 cm s−1 and where τR was 1 roots always caused an

increase in Ks, as Ks of root modified pore space ranged from 0.002 to 0.8833 cm s−1

when β was 0.9 and 0.3 respectively.

The range of change in Ks predicted by our model was most sensitive to τR. The

connectivity of real soils is in the range of 0.001 to 0.1 (Jury et al., 1991; Wantanabe

and Flury, 2008) and as there is evidence that the connectivity of root modified pores is

greater (Perret et al., 1999) we assessed the effect of roots for τR in the range of 0.01 to 1.

As shown in Figure 4.3 when τR was 0.01, 0.1 and 1 the range of predicted changes were

-54 to 6%, -51 to 395%, and 19 to 4480%. For all combinations of soil texture and τR the

% change in Ks was linearly related to root length density.

80

4.4. RESULTS

−6 −5 −4 −3 −2 −1 0

0.0

0.2

0.4

0.6

0.8

1.0

FP

log10 [Pore radius (cm)]

ClayLoamSand

(a)

−6 −5 −4 −3 −2 −1 0

0.0

0.2

0.4

0.6

0.8

1.0

FR

log10 [Root radius (cm)]

Type 1Type 2Type 3

(b)

Figure 4.4: Comparison of cumulative frequency distributions of pore and root radius for(a) sand, loam and clay (Carsel and Parrish, 1988) and (b) for root types 1, 2 and 3 inTable 4.1. Pore radius was calculated using Equation 4.10

4.4.2 Unsaturated hydraulic conductivity

The unsaturated hydraulic conductivity functions predicted by our model tended to have

a bi-modal appearance due to the differing radii frequency distributions of soils and roots

(Figure 4.4). For the parameter range we used, type 2 and 3 roots mostly had root

radii 0.003 cm while the pore radii of loam and clay were mostly below this. The radius

frequency distribution of type 3 roots and sand were similar. Figure 4.5 illustrates how

root type and τR can influence the shape of the hydraulic conductivity functions of root

modified soils. Root types 1, 2 and 3 lead to changes in the hydraulic conductivity function

at matric head of -6 to -3160, -1000 and -100 cm head respectively and the differing ranges

reflect the shape of the root radii distributions. The connectivity of root modified pores

determined the extent of the change in the unsaturated hydraulic conductivity function

induced by roots (Figure 4.5). In the examples shown here, the change in hydraulic

conductivity at -30 cm head is 6.2 x 10−4, 8.6 x 10−3 and 8.9 x 10−2 cm s−1 when τR

is 0.01, 0.1 and 1 respectively. As β decreased (δh decreased) the range affected by roots

shifted to higher matric head (data not shown).

81


log10 [−Matric head (cm)]log 1

0 [H

ydra

ulic

con

duct

ivity

(cm

sec−1

)]

−8

−6

−4

1.0 1.5 2.0 2.5 3.0

τR = 0.01

1.0 1.5 2.0 2.5 3.0

τR = 0.1

1.0 1.5 2.0 2.5 3.0

τR = 1No rootsRoot type 1Root type 2Root type 3

Figure 4.5: Effect of root type (Table 4.1) and connectivity of root-modified pore spaceτR on root-induced changes to the unsaturated hydraulic conductivity function of a sand(Carsel and Parrish, 1988), where τP = 0.01 (Jury et al., 1991), β = 0.9 and D = 15 cmcm−3

4.4.3 Water retention

Our model predicts that roots modify the water retention function in two ways: by reduc-

ing the saturated water content and / or by changing the shape of the retention function

(Figure 4.6). Type 3 roots with a root length density of 15 cm cm−3 reduced saturated

water content of all soils by approximately 1, 2, 3 and 5 % when β was 0.3, 0.5, 0.7 and 0.9

respectively. Type 1 and 2 roots had far less effect and reduced saturated water content

by less than 2 % when β was 0.9. A change of shape only occurred in the clay, where

water content was reduced by approximately 6% at matric head less than -6 cm head. This

change in shape became greater as β decreased because as the voids being created by the

’shrinking’ root became larger and the capillary pressure decreased (Figure 4.2). Overall,

these changes are small in relation to those predicted for near- and saturated hydraulic

conductivity.

4.4.4 Application of model to experimental data

Figure 4.7 shows a comparison changes in Ks observed in the experiment in Chapter 2 and

those predicted by the model described here. While the variability of the experimental

82

4.4. RESULTS

log10 [−Matric head (cm)]

Vol

umet

ric w

ater

con

tent

(cm3 c

m−3

)

0.1

0.2

0.3

0.4

0.5 1.0 1.5 2.0 2.5

Sand

0.5 1.0 1.5 2.0 2.5

Loam

0.5 1.0 1.5 2.0 2.5

Clay

No rootsWith roots β = 0.3

With roots β = 0.5

With roots β = 0.7

With roots β = 0.9

Figure 4.6: Interaction between the ratio of root radius to pore radius β and soil texture(Carsel and Parrish, 1988) on root-induced changes to the water retention function, whereroot type is 3 (Table 4.1), τP = 0.01 (Jury et al., 1991) and D = 15 cm cm−3

data makes it difficult to make conclusive statements about the model, it does provide a

useful qualitative comparison.

The trend in change in Ks predicted by our model is similar to that observed. In the

experiment when root length density was 9.4 and 11.7 cm cm−3 Ks decreased by 41 and

58% respectively, and our model predicts a decrease to -21 and -26% respectively when β

is 0.9. During this period the wheat plants were at the stem elongation to ear emergence

phenological stage and it is likely only a small fraction of roots had begun to decay (van

Noordwijk et al., 1994), therefore a β of 0.9 is reasonable. The under-prediction of the

decrease in Ks may be due to separation of pores with and without roots in our model,

where roots only affect the connectivity of pores they occupy. In real soils, roots may also

decrease the connectivity of the soil volume by creating capillary breaks between sections

of soil. The increase in Ks observed when root length density was 13.7 cm cm−3 occurred

when the wheat plants were begining to mature. Our model predicts a similar increase

to the observed when β is between 0.7 and 0.9, which is a realistic range as roots in our

experiment would have been decreasing in radius due to translocation of carbon from roots

to the seed (Gebbing et al., 1998) and due to root senescence and decay (Liljeroth, 1995;

van Noordwijk et al., 1994).

83


This comparison highlights the need for experimental data to test the validity of the

assumptions in our model. At present there are no reports of root induced changes to SHP

that include measurements of root length density and the root radii frequency distribution.

While β could only be measured directly by thin section or tomographic analysis we believe

it may also be estimated from temporal changes in the root radii frequency distribution.

2 4 6 8 10 12 14

−50

050

100

Mean root length density (cm cm−3)

% c

hang

e in

sat

urat

ed h

ydra

ulic

con

duct

ivity

β = 0.5β = 0.7β = 0.9Observed (Chapter 2)

*Error bars are standard error

Figure 4.7: Comparison of changes to saturated hydraulic conductivity reported in Chapter2 and those using the model described here. Soil parameters were from Chapter 2: θr=0.02,θs=0.32, α=0.05 and n=3.1, root parameters were for wheat roots from Qin et al. (2004),τR = 0.1 and τP =0.01 (Jury et al., 1991)

4.5 Discussion

4.5.1 Comparison of model predicted and reported root-induced changes

to SHP

The critical effect of the ratio of root radius to pore radius β in our model on the affect

of roots on Ks is supported by the evidence available. For example, Barley (1954) found

that the growth of corn roots reduced Ks by 80% and following decay, which is analogous

84

4.5. DISCUSSION

to a decrease in β, the reduction in Ks was 33%. Similarly, Murphy et al. (1993) found

a consistent decrease in Ks in wheat from sowing to tillering and a consistent increase in

Ks from tillering to maturity. The decrease in Ks was attribued to roots blocking pores

and the increase to the creation of voids by decaying roots. More generally, root-induced

decreases in Ks have been reported where the root system is relatively young (Meek et al.,

1989, 1990; Suwardji and Eberbach, 1998) where the majority of roots would be fully

intact, and increases have been reported where roots have begun senescence and or decay

(Kavdir et al., 2005; Li and Ghodrati, 1994; Meek et al., 1990, 1992; Mitchell et al., 1995;

Prieksat et al., 1994; Rasse et al., 2000; Suwardji and Eberbach, 1998).

The degree of change in Ks predicted by our model is highly sensitive to the combina-

tion of root type, connectivity of root-modified pores and β, which is supported by field

observations. For example, increases in Ks where cereal plants have been grown appear

positively related to the period of time that root decay has occurred (Li and Ghodrati,

1994; Prieksat et al., 1994; Suwardji and Eberbach, 1998), presumably because the average

root radius decreases as the root decays (Henry and Deacon, 1981), which is equivalent to

decrease in β. In field conditions increases in Ks where cereal plants are grown (e.g. Priek-

sat et al., 1994; Suwardji and Eberbach, 1998) are typically much less than where lucerne

has been grown (e.g. Kavdir et al., 2005; Meek et al., 1990) (Table 1.1). The most likely

explanation for this is a combination of greater connectivity and radius of the pathway

provided by the decayed lucerne root. Lucerne has a herringbone branching behaviour

(e.g. Dunbabin et al., 2003) which is characterised by a taproot and first order lateral

branches only, whereas cereals have several main roots with a vertical growth habit and

many orders of branching (e.g. Hackett and Bartlett, 1971), creating a network of pores

that are less connected in the vertical direction (Tippkotter, 1983), and in addition at 5

cm below the crown lucerne roots have a radius of 0.38 to 0.5 cm (Johnson et al., 1998),

approximately four times the maximum radius observed in cereals such as corn (Pallant

et al., 1993).

While our model assumes a constant connectivity ratio for all matric head this may

not be the case (Resurreccion et al., 2008). Apparent bi-modal hydraulic conductivity

functions (Kodesova et al., 2006; Mohanty, 1999) may not only be a result of a bi-modal

85


pore size distribution, but also due to matric head-dependent connectivity. For example,

the pore network created by the decay of tap-rooted plants like lucerne may have a very

high connectivity in the vertical direction as larger roots tend to form long tubular channels

(Barley, 1954; Jassogne et al., 2007); however, the channels formed by the decay of large

roots are likely to drain at matric head in the near-saturated range (Sedgley and Barley,

1958). At matric head where the larger root channels have drained, the pore network

created by lateral roots is likely to have a much lower connectivity in the vertical direction

as finer roots tend to form channels with greater curvature (Barley, 1954).

While our model provides insight into how root-modified pore geometry changes the

hydraulic behaviour of a soil, its conceptual basis (the capillary bundle model) and the

assumptions we have made about root-pore geometry may limit its ability to predict

absolute changes in real soils: particularly in unsaturated hydraulic conductivity. The

capillary-bundle model assumes that flux is determined by pore radius only and that

pores completely empty when their equivalent capillary pressure is applied, whereas in

real soils pores do not completely empty in unsaturated conditions, rather the matric

head determines the thickness of the water film on the solid surface and therefore the

conductivity (Jury et al., 1991). This physical discrepancy between the model assumption

and behaviour of real soils is a major limitation of our model. However, the effect of roots

on pore geometry is unknown therefore we cannot quantify if, or how much our model

predictions will diverge from the behaviour of real soils.

Our assumption that a root within a pore can be represented as concentric cylinders

also needs further investigation. This assumption is core to calculating the volume-pressure

and conductivity-pressure relationship of root modified pore space; however, when roots

decay they become fragmented (Barley, 1954), and in unsaturated conditions move to

one side of the pore (Nye, 1994; van Noordwijk et al., 1993; North and Nobel, 1997), or

may be oval in shape rather than circular (Rachman et al., 2005; Udawatta et al., 2008)

resulting in different geometry to our assumption. Also, our assumption of symmetry may

lead to an over-prediction of the decrease in saturated hydraulic conductivity caused by

roots at low values of β, or for fine roots which are more likely to be in contact with the

pore wall to access water or nutrients. To assess the error induced by our assumption

86

4.6. CONCLUSIONS

further research is needed, which involves numerical solution of the capillary rise and flux

within asymmetric arrangements of cylinders that represent roots and pores. This work

goes beyond the scope of this chapter.

4.5.2 Outlook

Research is needed to bridge the knowledge gap of how roots modify the physical properties

of soils and how these changes are reflected in soil hydraulic properties. The research re-

quired to bridge this gap reflects the assumptions we made when constructing our model.

Specifically, the interaction of root and pore radius, the relationship between root ra-

dius and root-induced pore connectivity, pore root geometry and the effect of pore-root

asymmetry on the volume-pressure and pressure-conductivity relationships need further

attention. This research is vital to improving our understanding and capacity to predict

root-induced changes to SHP.

4.6 Conclusions

Overall our model reproduces the trends that have been observed in root modification of

SHP, which are that the greatest effects occur in near- and saturated hydraulic conductiv-

ity, and that there is little effect in the water retention function. Specifically, predicted Ks

was sensitive to changes in β which relates to root shrinkage and / or decay. Our model

predicted either an increase or decrease in Ks in response to β which agrees with observed

increases or decreases in Ks due to the growth or decay of root systems respectively. Pre-

dicted changes to Ks were also sensitive to the connectivity of root-modified pore space

and this is supported by differing levels of change in infiltration reported of for fibrous

and tap-rooted plants.

Our work has raised areas that need further research to improve our understanding

of how roots modify SHP. From a modelling perspective, the sensitivity of capillary rise

and flux to the non-concentric placement of a root within a pore needs to be determined.

This is especially important for quantifying how roots modify water flow in unsaturated

conditions, when roots are likely to be pulled to pore walls by capillary forces. The connec-

tivity of root-modified pore space for different root radii and architectural arrangements

87


also needs to be determined, and is especially important information for predicting the

interaction between plant species and soil type on Ks. From experimental perspective,

it is imperative that root length and radius frequency distribution are quantified in bio-

hydrology studies. This information is vital to improve our knowledge of how roots modify

SHP at both a system and process level.

88

Chapter 5A dynamic model of root-induced changes

to soil hydraulic conductivity and water

retention




5.1 Abstract

Soil-plant simulation models provide a powerful tool for investigating the complex systems

that emerge when plants modify the hydraulic conductivity and water retention behaviour

of the soil they occupy. Richards equation-based models require the parameterisation of

the hydraulic conductivity and water retention functions, which has not been addressed for

root-modified soils. We derived a model based upon the van Genuchten-Mualem model,

conceptualising the soil as having a domain with and without roots present. We assumed

that the pore size distribution of the domain with roots was determined by the root system,

and defined the parameter space for the effective saturation function of the domain with

roots from root radius frequency data. As there was insufficient data to parameterise our

model we used reported data to make estimates of the parameters we introduced. The

89

CHAPTER 5. A DYNAMIC MODEL OF ROOT-INDUCED CHANGES . . .

conductivity, matric head and volume of the domain with roots was scaled according the

ratio of root radius to pore radius. Sensitivity analysis showed that saturated hydraulic

conductivity of the root modified soil was most sensitive to the ratio of root radius to

pore radius and the volume per unit length of root. The shape of the root-modified water

retention and hydraulic conductivity function was most sensitive to the ratio of root to pore

radius, the connectivity of the domain with roots and root length density. Comparison of

results from simulated and actual infiltration experiments in root-modified soils suggests

that the increases observed are due to a small number of vertical roots creating macropores

that have a very high connectivity.

5.2 Introduction

Root-induced changes to soil hydraulic properties (SHP) are dynamic and reflect the

activity of the root system present. Seasonal patterns have been shown for annual plants,

where saturated hydraulic conductivity decreases when the roots are growing rapidly, then

increases as the roots begin to decay (Bormann and Klaasen, 2008; Murphy et al., 1993;

Suwardji and Eberbach, 1998). There is also evidence that an initial decrease occurs where

perennial plants are present followed by an increase as roots senesce and decay (Meek et al.,

1989; Petersson et al., 1987). Such decreases are attributed to roots blocking pores and

the increases to the creation of macropores as the root decays (e.g. Barley, 1954; Meek

et al., 1992; Murphy et al., 1993). The greatest changes have been observed in near- and

saturated hydraulic conductivity (Murphy et al., 1993; Sedgley and Barley, 1958; Suwardji

and Eberbach, 1998), which is an important consideration as these properties dominate

infiltration and solute flux (Hillel, 1998). The changes to SHP by roots leads to a complex

hydrological system where plants have the capacity to modify the infiltration and storage

of water which their growth depends upon (Porporato and Rodriguez-Iturbe, 2002).

Modelling provides a powerful tool for investigating and furthering our understanding

of these complex systems as it allows to relatively easily examine how individual factors

affect the overall system. However, reliable model predictions are heavily dependent on

the model capturing the main interactions between plants and soil and being accurately

parameterised. At present soil-plant models consider soil hydraulic properties to be static

90

5.3. METHODS

(e.g. Connolly et al., 2002; Simunek et al., 2005; Vanclooster et al., 1995) despite evidence

that this is not always the case (e.g Bormann and Klaasen, 2008; Meek et al., 1992; Murphy

et al., 1993), which may lead to erroneous predictions about plant growth or water and

solute fluxes.

Soil-plant models usually operate by coupling models of soil water flow and plant

growth, linked by root growth and water uptake (e.g. Connolly et al., 2002; Vanclooster

et al., 1995). The most common approach to modelling water flow is the numerical solution

of Richards equation which usually requires parametric functions that describe the water

retention and hydraulic conductivity functions (e.g. Connolly et al., 2002; Simunek et al.,

2005; Vanclooster et al., 1995). While there is some evidence of root induced changes to

these functions (Kodesova et al., 2006; Mohanty, 1999) it is insufficient to derive empirical

relationships.

In this paper we address the need for a quantitative description of root-induced changes

to soil hydraulic conductivity and water retention by deriving an analytical model based

on the van Genuchten (1980) model and root radius frequency distributions. This work

builds on Chapter 4 using the scaling functions that relate changes in capillary rise, flux

and volume of a root-occupied pore to the ratio of root radius to pore radius. However,

it is different in that the functions are derived by modifying existing functions for water

retention and hydraulic conductivity, rather than being based solely on physical behaviour

of fluids in cylinders. First we derive the model, and second, as there is insufficient data

to parameterise our model we draw on reported data to make estimates of the parameters

we introduce, third we demonstrate the changes predicted by the model and finally we

implement the analytical model in a water flow model to examine the effects of root-

induced changes under ponded conditions.

5.3 Methods

5.3.1 Model theory

We introduce the effect of roots on soil hydraulic conductivity and water retention by

considering the pore volume as being comprised of two separate domains: a pore space

91


domain with and a pore space domain without roots which are denoted as 1 and 2 respec-

tively. Parameters for the soil in its original state and after root modification are denoted

as o and m respectively. The water retention and hydraulic conductivity of the entire soil

is assumed to be a sum of the two domains (e.g. Mohanty et al., 1997; Ross and Smettem,

1993). We assume that equilibration of water content between the two domains is instan-

taneous and that matric potential-induced changes to soil structure do not occur. The

effective saturation function Sei (h) for each domain i is based on van Genuchten (1980):

Sei (h) =

θi − θriθsi − θri

= [1 + (αi|h|)ni ]−mi (5.1)

Where θsi (cm3 cm−3) and θri (cm3 cm−3) are saturated and residual water content respec-

tively, αi (cm−1) and ni (-) are shape parameters, mi = 1 − 1/ni and h is matric head

(cm).

The unsaturated hydraulic conductivity function K(h) is based on van Genuchten-

Mualem model (van Genuchten, 1980):

Ki(h) = Ksi (S

ei )

li [1− (1− (Sei )

1mi )mi ]2 (5.2)

where Ksi (cm min−1) and li (-) are saturated hydraulic conductivity and a tortuosity

parameter respectively.

While the model described here is similar in structure to other multi-domain models

(Durner, 1994; Mohanty et al., 1997; Priesack and Durner, 2006; Ross and Smettem, 1993;

Smettem and Kirkby, 1990) it differs conceptually as the fraction occupied by each domain

and shape parameters for these are dynamic, and change in response to the root system

present. In the following we explain the theoretical basis of our approach to modification

of pore space by roots.

5.3.2 Scaling hydraulic properties

Flux, capillary rise and volume within a pore where a root is present were scaled according

the ratio of root radius to pore radius β. The first main assumption of this model is that

the geometry of roots within pores can be simplified to concentric cylinders, and based

92

5.3. METHODS

upon this we have previously derived dimensionless expressions of the change in these

properties as a function of β only (Chapter 4). In all 3 cases when β=0 (ie. no root

present) the scalar equals one, and we assume that this is the case for the domain without

roots. The hydraulic conductivity of a pore with a root present relative to the pore only

δK is:

δKi =

1 β = 0

1 + β2 − 1−β2

ln 1β

β > 0

(5.3)

The capillary rise within a pore with a root present relative to the pore only δh is:

δhi =1

1− β(5.4)

The volume of a pore with a root present relative to the pore only δv is:

δvi = 1− β2 (5.5)

5.3.3 Domain with roots

The second main assumption of this model is that the radius frequency distribution of pores

in the root-modified domain is determined by that of the root system. We use Equation

5.1 to describe the effective saturation function of the domain with roots, assuming that

pore radius r (cm) is related to matric head h (cm) using the Young-Laplace equation

(e.g. Warrick, 2003):

h =2γcosΘ

rρg(5.6)

Where γ is surface tension (g cm s−2 cm−1), Θ is wetting angle (we assume 0), ρ is

fluid density (g cm−3) and g is gravitational acceleration (cm s−2).

We also assume that the residual water content of the domain with roots θr1 equals zero

and that the saturated volume of the domain with roots θs1 is determined by the volume

of root per unit length of root θM (cm3 cm−1) and root length density D (cm cm−3):

θs1 = θMD (5.7)

93


The shape parameters α1 and n1 relate to the pore network created by the root system

after complete decay has occurred and capillary pressure is due to the pore radius only

hp. However, while roots remain intact capillary pressure in root-occupied pores will be

changed and we express hp (cm) as:

hp =h

δh(5.8)

The third main assumption of this model is that roots also modify the soil by com-

pression. When roots expand radially within a pore that was initially smaller than the

root, a zone of compression is created near the root surface (Braunack and Freebairn,

1988; Bruand et al., 1996; Clemente et al., 2005; Dexter, 1987a). However, there is a

physiological limit to the pressure that root cells can exert on the soil around them (e.g.

Dexter, 1987b; Misra et al., 1986), which may not be great enough to cause compression

of all pores.

We simplify the interaction between pore and root radius by considering the com-

pressed volume εc (cm3 cm−3) to be the difference between root volume and pore volume

of the original soil of radius greater than an arbitrary limit rc (cm), which is calculated

from their effective saturation functions and simplifies to:

εc = max{

0, θs1

[

− (1 + (α1hc)n1)−m1 + (1 + (α2hc)

n2)−m2

]}

(5.9)

Where hc (cm) is the matric head that relates to rc using Equation 5.6.

Changes in pore size distribution near roots and to the water retention function fol-

lowing compression suggests that rc is in the range of 0.00025 to 0.0025 cm . Guidi et al.

(1985) found aggregates around roots had more pores with a radius less than 0.00025

cm and less pores greater than this in aggregates from the bulk soil. Similarly, Blevins

et al. (1970) found that soil near to roots had more pores between 0.001 and 0.0025 cm

radius and less pores greater than 0.0025 cm radius than soil 0.2 cm from the root surface.

Comparison of water retention curves before and after compression shows that volumetric

water content is only affected by compression at matric potential < 60 hPa (Stange and

Horn, 2005) and < 300 hPa (Zhang et al., 2006), which according to Equation 5.6 corre-

sponds to a radius less than 0.0005 and 0.0016 cm respectively. For the remainder of this

94

5.3. METHODS

paper we assume rc is 0.001 cm.

We assume that the volume gained by the root system when it compresses soil has

the same pore size distribution as the roots create, therefore the total volumetric fraction

occupied by the domain with roots V1 (cm3 cm−3) is:

V1 = εc + θs1 (5.10)

We calculate saturated hydraulic conductivity of the domain with roots Ks1 as a func-

tion of the volumetric fraction of macropores φm (cm3 cm−3) (Germann and Beven, 1981)

which we define as root modified pore space that remains saturated at matric head greater

than or equal to -10 cm:

Ks1 = B1φ

N1m (5.11)

Where B1 (cm min−1) and N1 (-) are empirically derived parameters.

5.3.4 Domain without roots present

We assume that roots modify the domain without roots present via compression only,

which leads to a change in pore size distribution (Assouline, 2006b,a). We used empirically-

derived relationships to model how compression changes the hydraulic conductivity and

water retention functions of the domain without roots. Changes in saturated hydraulic

conductivity and the van Genuchten (1980) shape parameter α are expressed as a function

of relative porosity εr (-), which we define as the ratio of pore volume before to that after

compression:

εr = 1− εcθs − θMD

(5.12)

Figure 5.1 a and b show the relationship between εr and cα and cK respectively using

data summarized in Appendix B, where cα is the ratio of van Genuchten (1980) α after

compression to that before, and cK is the ratio of saturated hydraulic conductivity after

compression to that before. There was no relationship between εr and the van Genuchten

95


0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

εr

c α

0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

εr

c K

Figure 5.1: The ratio of van Genuchten (1980) α for soil in the compressed to originalstate cα (a), and the ratio of saturated hydraulic conductivity for soil in the compressedto original state cK (b), both plotted against relative porosity ǫr. Points are data inAppendix B and lines are the best fit using Equation 5.13.

(1980) n parameter. For both sets of data we calculated cx (-) as:

cx = axεr + bx (5.13)

Where x can be α or K.

The optimised values for aα and bα were 3.08 and -2.08 respectively, and the optimised

values for aK and bK were 3.47 and -2.47 respectively. The parameters were optimised

with the constraint ax + bx = 1 as cx must equal one when εr equals one.

The van Genuchten (1980) shape parameter α for the domain without roots α2 is:

α2 = αocα (5.14)

Where αo is the value for the original soil before roots were introduced.

Similarly, saturated hydraulic conductivity of the domain without rootsKs2 (cm min−1)

is:

Ks2 = KocK (5.15)

Where Ko is the saturated hydraulic conductivity of the original soil (cm min−1).

96

5.3. METHODS

The volume of the domain without roots V2 (cm3 cm−3) is:

V2 = θso − V1 (5.16)

5.3.5 Hydraulic functions of the modified soil

The effective saturation function is found by combining Equations 5.1, 5.5 and 5.8:

Sei (h) = δvi

[

(

1 +

(

αih

δhi

)ni)−mi

]

(5.17)

The water retention function for the root-modified soil θm(h) is:

θm(h) = θro +2

∑

i=1

ViSi(h) (5.18)

And the hydraulic conductivity function Km(h) is:

Km(h) =2

∑

i=1

Ksi δ

ki Si(h)

li[

1−(

1− Si(h)1

mi

)mi]2

(5.19)

5.3.6 Parameter estimation

While the parameter space for the van Genuchten (1980) parameters α and n for soils is

well defined (e.g. Carsel and Parrish, 1988; Rawls et al., 1982), it has not been defined for

the root modified domain. Recalling that we assume that the pore size distribution of the

domain with roots is determined by the root radii frequency distribution, we determined

α1, n1 and θM for each root radius frequency distribution in our database from Chapter

3. Each distribution was converted to an effective saturation function (Equation 5.1) by

converting root radius to matric potential using Equation 5.6, and by calculating cumu-

lative volume. The parameters were optimised by minimizing the residual sum of squares

using the Gauss-Newton algorithm in the nls function in R (R Development Core Team,

2006), and the initial value for θM was calculated using the parameters derived for each

distribution in the database in Chapter 3 as:

θM = πe2(µ+σ2) (5.20)

97


Where µ and σ are parameters for the log-normal distribution function (Weisstein, 2008b).

As with the shape parameters for the domain with roots present, the parameter space

for the saturated hydraulic conductivity of the domain with roots Ks1 has not been inves-

tigated. The macropore volume has proven to be a good predictor of saturated hydraulic

conductivity (Germann and Beven, 1981; Timlin et al., 1999), and we investigated this re-

lationship for the domain with roots using the modified capillary bundle model developed

in Chapter 4. We define macropore volume as the difference between volumetric water

content at saturation and at -10hPa. This model requires parameters for the log-normal

frequency distribution of root radius we which obtained from our database in Chapter

3. The model also requires a value for the connectivity of root-modified pores τR, where

connectivity is defined as the ratio of flow path length to sample length (e.g. Vervoort and

Cattle, 2003). For the τR we used a range of 0.001 to 0.1 which is the range observed for

soils (Jury et al., 1991; Wantanabe and Flury, 2008), for root length density up to 15 cm

cm−3 (de Willigen and van Noordwijk, 1987).

5.3.7 Parameter sensitivity analysis

We used two approaches to investigate the sensitivity of root-induced changes to soil

hydraulic properties to parameter values. First we conducted a one at a time sensitivity

analysis which provides an efficient screening method for determining the most influential

parameters, but it must be interpreted within the context of the initial parameter values,

from which the change in Ksm and parameter value are calculated (Hamby, 1994). The

initial parameter values and the range for each is shown in Appendix C. Second, we

investigated how a factorial of parameters affected the shape of the hydraulic conductivity

and water retention functions and presented these graphically.

5.3.8 Application: Ponded infiltration

We simulated the effects of root-modified SHP on ponded infiltration by implementing the

model described here in WAVE (Javaux and Vanclooster, 2006). One-dimensional water

flow was simulated by numerical solution of Richards equation:

98

5.3. METHODS

0 5 10 15 20

100

8060

4020

0

Soi

l dep

th (

cm)

Root length density (cm cm−3)

Exponential profileConstant profile

Figure 5.2: Graphical illustration of the two root profiles used to investigate the effectof root-induced changes to SHP on infiltration under ponded conditions. The total rootlength per soil surface area was 200 cm cm−2 for both profiles

∂θ

∂t=

∂

∂z

[

K(h)

(

∂h

∂z+ 1

)]

− S (5.21)

Where θ is volumetric water content (cm3 cm−3), t is time (min), z is depth (cm), h is

matric head (cm), S (cm3 cm−3 min−1) is a sink term for plant water uptake, and K(h)

(cm min−1) is the unsaturated hydraulic conductivity function:

We incorporated our model intoWAVE by substituting it for the existing van-Genuchten-

Mualem formulation, and the only other change made to the model was the the differential

moisture capacity function:

dθ

dh=

(

1− β2) θR + εc(1 + (α1h)

n1)m1m1 (α1h (1− β))n1

n1/h

(1 + (α1h (1 + β))n1)m1

−θs − θr − θR − εc(1 + (αch)

n2)m2m2 (αch)

n2n2/h

1 + (αch)n2

(5.22)

The modified water flow model was used to investigate how vertical root distribution

and connectivity of the domain with roots affected temporal infiltration rate. The sim-

ulated soil profile was a loam (Carsel and Parrish, 1988) one metre deep, β was 0.3 and

parameters for the domain with roots were for root type 3 in Figure 5.3. The initial soil

99


moisture profile was determined by a linear gradient of -200 and -100 cm matric head

at the top and bottom of the soil profile respectively. Water was ponded above the soil

surface at a height of 1 cm for the length of the simulations and free drainage occurred

at the bottom of the profile. We assumed that root length per unit soil surface area was

200 cm cm−2 (de Willigen and van Noordwijk, 1987) and distributed this vertically with

either the exponential or constant distributions shown in Figure 5.2.


5.4.1 Parameter estimation for domain with roots

Shape parameters

Figure 5.3 shows the values for α1, n1 , and θM derived from the root radii frequency

distributions. The 25th, 50th and 75th percentile for α1 was 0.14, 0.22 and 0.33 cm−1

respectively, which is an order of magnitude greater than generally observed for soils (e.g.

Carsel and Parrish, 1988). The 25th, 50th and 75th percentile for n1 was 2.8, 3.1 and 3.8

respectively was generally two to three times the range of n values for soils (e.g. Carsel

and Parrish, 1988). The 25th, 50th and 75th percentile for θM was 0.0004, 0.0006 and

0.0022 cm3 cm−1 respectively. In our model, root length density and θM determine the

saturated water content of the domain with roots, which for a root length density of 15

cm cm3 cm−1 corresponds to 1, 2 and 8 % of the saturated water content of a sandy loam

(Carsel and Parrish, 1988).

We chose 3 representative points in Figure 5.3 for further comparison with soils, and

the corresponding effective saturation functions are compared to those typical of a sand,

loam and silty clay (Carsel and Parrish, 1988) in Figure 5.4. All three examples from

the root parameters are completely drained at a matric potential of -100 cm matric head,

whereas for the soils only the sand is completely drained at this pressure. Additionally,

the root-derived effective saturation functions have a steeper gradient than soils indicating

a narrower pore size distribution.

Overall, the van Genuchten (1980) effective saturation function provided a good de-

scription of calculated cumulative root volume. The inter-quartile range of RMSE for

100


Table 5.1: List of parameters for the analytical model

Parameter Description

Model inputs

h Matric head (cm)α1 van Genuchten (1980) shape parameter for soil domain with roots (cm−1)n1 van Genuchten (1980) shape parameter for soil domain with roots (-)D Root length density (cm cm−3)θM Root volume per cm root (cm3 cm−1)β Ratio of root radius to pore radius (-)rc Pore radius compression limit (cm)Ks

o Saturated hydraulic conductivity of original soilθro Residual water content of original soil (cm3 cm−3)θso Saturated water content of original soil (cm3 cm−3)αo van Genuchten (1980) shape parameter of original soil (cm−1)no van Genuchten (1980) shape parameter of original soil (-)B1 Empirical parameter for calculating Ks

1 (cm min−1)N1 Empirical parameter for calculating Ks

1 (-)Model outputs

θm(h) Water retention function of root-modified soilKm(h) Hydraulic conductivity function of root-modified soilParameters used in derivation

δK Conductivity scalar for domain with roots (-)δh Matric potential scalar for domain with roots(-)δv Volume scalar for domain with roots (-)hp Matric potential determined by pore only (cm)εc Pore volume compressed by roots (cm3 cm−3)Vi Volume of domain (cm3 cm−3)Ks

i Saturated hydraulic conductivity of domain (cm min−1)φm Macropore volume of domain with roots (cm3 cm−3)εr Relative porosity of soil domain without roots present (-)γ Surface tension (g cm s−2 cm−1)Θ Wetting angleρ Fluid density (g cm−3)g Gravitational acceleration (cm s−2)

101


0.0 0.2 0.4 0.6 0.8 1.0

02

46

810

12

n1

(−)

α1 (cm−1)

1

2 3

a

0.0 0.2 0.4 0.6 0.8 1.00.

000

0.00

50.

010

0.01

50.

020

θM (

cm3 c

m−1

)

α1 (cm−1)

1 2

3

b

Figure 5.3: Parameter values for the van Genuchten (1980) effective saturation functionfor the domain with roots derived from the root radius frequency distributions in thedatabase from Chapter 3. Points 1, 2 and 3 are parameters for representative root typeswhich are implented in Figure 5.4.

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

Effe

ctiv

e S

atur

atio

n


Point 1 α=0.12, n=6.02Point 2 α=0.22, n=2.80Point 3 α=0.78, n=2.44

(a)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

0.0

0.2

0.4

0.6

0.8

1.0

Effe

ctiv

e S

atur

atio

n


Sand α=0.145, n=2.68Loam α=0.036, n=1.56Silty Clay α=0.005, n=1.09

(b)

Figure 5.4: A comparison of the effective saturation functions for three representativeroot distributions and three soil types. The parameters for three representative rootdistributions are shown in Figure 5.3 which are implemented using Equation 5.1 in (a).

102


0.00

000

0.00

005

0.00

010

0.00

015

0.00

020

RM

SE

(cm

3 cm

−1)

a

0.0000 0.0005 0.0010 0.0015 0.0020

0.00

000.

0005

0.00

100.

0015

0.00

20

Analytical derived θM (cm3 cm−1)

Fitt

ed θM

(cm

3 cm

−1)

b

Figure 5.5: A summary of the goodness of fit of the van Genuchten (1980) effective sat-uration function to root radius frequency distributions. Figure a shows the RMSE forcumulative root volume calculated from root radius frequency distributions and that fit-ted using Equation 5.1. Figure b shows a comparison of root volume per length of rootθM obtained using Equation 5.20 and by fitting. Line is 1:1.

fitted vs. calculated cumulative volume in the 96 root radius frequency distributions in

our database from Chapter 3 was 0.000014 to 0.000066 cm3 cm−1 (Figure 5.5a). To put

this error into context, as stated above the inter-quartile range of θM was 0.0004 to 0.0022

cm3 cm−1. The fitted and analytically-derived θM (Figure 5.5b) were similar which is

evidence that the parameter optimisation process has not resulted in unrealistic values.

Saturated hydraulic conductivity

Figure 5.6 shows the relationship between macroporosity and saturated hydraulic conduc-

tivity of the domain with roots modelled using the modified capillary bundle model in

Chapter 4. We fitted Equation 5.11 to the results for each level of τR and the optimised

parameters for data where τR was 0.001, 0.01 and 0.1 were B1 6.5, 65 and 652 respectively,

and N1 1.36 for all levels. The optimised parameters provided a reasonable description of

the results: for each level the r2 was 0.74. The relationship found by Germann and Beven

(1981) suggests that range of τR we used is similar to real soils (Figure 5.6).

The only work reported that provides a comparison to our modelling analysis of the

relationship between macroporosity and saturated hydraulic conductivity is the data by

103


0.00 0.01 0.02 0.03 0.04 0.05 0.06

0.0

0.1

0.2

0.3

0.4

Ks 1

(cm

min−1

)

φm (cm3 cm−3)

τR=0.001τR=0.01τR=0.1Germann and Beven (1981)

Figure 5.6: Modelled relationship between macroporosity and saturated hydraulic conduc-tivity of the soil domain with roots. Points shown are for τr = 0.001 •, 0.01 •, and 0.1 •.Lines are the best fit to points of the same colour using Equation 5.11.

Burger (1922, 1927, 1929, 1932, 1937, 1940) summarised by Germann and Beven (1981).

Burger (1922) measured macroporosity by placing 10 cm long intact saturated soil cores

on a free-draining sand bed and measuring the loss of mass after 24 hours, and average

infiltration rate from the time taken for the pond of water to infiltrate. While our defi-

nition of macroporosity is similar to that measured by Burger (1922), there is insufficient

detail to determine saturated hydraulic conductivity from the average infiltration rate.

Therefore, we can not make conclusive statements about the accuracy of the relationships

we derived between Ks1 and φm, only that based upon the range of connectivity that

has been observed (Jury et al., 1991; Wantanabe and Flury, 2008) and the relationship

summarized by Germann and Beven (1981) the values we derived for B1 and N1 seem a

reasonable estimate. Quantifying the relationship between Ks1 and φm is an important

step in predicting how roots modify SHP and requires further field investigation.

104


−100 0 100 200 300

−10

00

100

200

300

% change in parameter

% c

hang

e in

sat

urat

ed h

ydra

ulic

con

duct

ivity

of r

oot−

mod

ified

soi

l Root length densityθM

α1

n1

βB1

θs

θr

α2

n2

Ksat

Figure 5.7: Sensitivity ofKsm predicted using Equation 6.6 to changes in model parameters.

Results are from a one at a time sensitivity analysis and the initial parameter values andrange for each in the analysis are given in Appendix C

5.4.2 Sensitivity Analysis

The results from the parameter sensitivity analysis show that for the initial parameters we

chose, saturated hydraulic conductivity of the root-modified soil Ksm is most sensitive to

changes to θM and β (Figure 5.7). This is to be expected because these parameters directly

affect the saturated hydraulic conductivity of the domain with roots. Interestingly, Ksm

was sensitive to decreases in the shape parameters α1, n1 and n2, because this leads to

a reduction in the the compressed volume (Equation 5.9) which contributes to the pore

volume of the domain with roots.

Root induced changes to unsaturated hydraulic conductivity were sensitive to β and

B1, though only occurred at matric head greater than -10 cm. The root-modified hydraulic

conductivity functions of a loam (Figure 5.8) show that increases occurred when B1 was

652 and β was less than or equal to 0.7. For all other combinations of B1 and β hydraulic

conductivity decreased at matric head greater than -3 cm, and increased at matric head

105


occurred between approximately -3 and -10 cm matric head.

While there is no data that allows a direct comparison, in general the evidence available

agrees with the predictions of our model. To our knowledge, root-induced changes to

hydraulic conductivity have only been observed at matric head of -4 cm and greater

(Murphy et al., 1993; Prathapar et al., 1989; Suwardji and Eberbach, 1998); however,

conductivity at matric head less than this is rarely measured in similar work. The critical

effect of β in determining whether roots cause an increase or decrease in saturated hydraulic

conductivity is supported by our results in Chapter 2 and other reports Barley (1954);

Murphy et al. (1993). However, it is not possible to draw comparisons about the effect

of B1 and connectivity of the domain with roots in real soils because this has not been

investigated

Overall, the water retention function was relatively insensitive to root-induced changes

to the soil. For the examples shown in Figure 5.9 saturated water content was reduced

by 5.5, 5.5 and 6.2% in the sand loam and clay respectively when root length density was

15 and β was 0.9. The other notable feature of these examples is the shift of the curve

towards lower matric potential in the sand, which occurs because root modification of the

soil led to a higher proportion of pores that have an equivalent matric head between -6

and -100 cm. The degree of change in saturated water content, which is relatively small

compared to near-saturated hydraulic conductivity is in agreement with field observations

(Fuentes et al., 2004) and our results from Chapter 2.

5.4.3 Application: Ponded infiltration

Figure 5.10 shows a comparison of temporal infiltration rate in a loam with and without

root modifications to SHP. All simulations had infiltration rate greater than 0.5 cm min−1

at the beginning of the experiment and declined rapidly to a near- or steady state rate;

however, the final rate was affected by B1 and root profile. For example, at 300 minutes

the infiltration rate of the soil without root modification was 0.018 cm min−1, and where

B1 was 6.5 the infiltration rate for the exponential and linear root profiles were about the

same, and where B1 was 65, infiltration rate was 145 and 163% greater for the exponential

and linear root profiles respectively. However, where B1 was 652, infiltration rate was

106



Hyd

raul

ic c

ondu

ctiv

ity (

cm m

in−1)

0.0

0.5

1.0

0.5 1.0 1.5

β = 0.3

B1

= 6

0.5 1.0 1.5

β = 0.5

B1

= 6

0.5 1.0 1.5

β = 0.7

B1

= 6

0.5 1.0 1.5

β = 0.9B

1 =

6

β = 0.3

B1

= 6

5

β = 0.5

B1

= 6

5

β = 0.7

B1

= 6

5

0.0

0.5

1.0

β = 0.9

B1

= 6

5

0.0

0.5

1.0

β = 0.3

B1

= 6

52

β = 0.5

B1

= 6

52

β = 0.7

B1

= 6

52

β = 0.9

B1

= 6

52

RLD = 0RLD = 5RLD = 10RLD = 15

Figure 5.8: Sensitivity of predicted changes to the hydraulic conductivity function tochanges in β, B1, and root length density. Results are for a loam and Type 3 roots

107



Wat

er c

onte

nt (

cm3 c

m−3

)

0.1

0.2

0.3

0.4

0.5 1.0 1.5

Sand

β =

0.9

0.5 1.0 1.5

Loam

β =

0.9

0.5 1.0 1.5

Clay

β =

0.9

Sand

β =

0.7

Loam

β =

0.7

0.1

0.2

0.3

0.4Clay

β =

0.7

0.1

0.2

0.3

0.4Sand

β =

0.5

Loam

β =

0.5

Clay

β =

0.5

Sand

β =

0.3

Loam

β =

0.3

0.1

0.2

0.3

0.4

Clay

β =

0.3 RLD = 0

RLD = 5RLD = 10RLD = 15

Figure 5.9: Sensitivity of predicted changes to the water retention function to changes insoil texture, root length density and β. Results are for Type 3 roots

108


0 50 100 150 200 250 300

0.00

0.10

0.20

B1 = 6.5a

No root modificationRoots: exponential profileRoots: linear profile

0 50 100 150 200 250 300

0.00

0.10

0.20

Sur

face

infil

trat

ion

rate

(cm

min−1

)

B1 = 65b

0 50 100 150 200 250 300

0.00

0.10

0.20

Time (minutes)

B1 = 652c

Figure 5.10: Effect of connectivity of root modified domain and vertical root distributionon temporal infiltration rate

147 and 736% greater for the exponential and linear root profiles respectively: the higher

infiltration rate with the linear profile was due to a combination of higher root length

density below 25 cm depth (Figure 5.2 and high connectivity.

The predicted changes in infiltration rate due to root modifications of SHP when B1

is 65 and 652 are similar to those observed for grasses and lucerne. In separate studies,

Meek et al. (1989) found that infiltration rate in lucerne crops increased 200% over 2.6

years, and 400% over 3 years (Meek et al., 1990), and the increase was attributed to the

decay of taproots and the formation of macropores. Infiltration rate in a ten year-old

grass hedge was approximately 670 % greater than in adjacent soybean and corn crops

(Rachman et al., 2004b), which was attributed to greater macroporosity in the grass

109


hedge (Rachman et al., 2004a). However, there are two important differences between

field-measured infiltration and the simulations presented here. First, in field conditions

infiltration capacity reflects saturated flow, capillary flow and lateral divergence (Reynolds

et al., 2002), while in the simulations no lateral divergence occurs. This may be particularly

important where decayed lateral roots increase conductivity in a direction away from the

infiltrometer. Second, the vertical root distribution of cereals and grasses (Jackson et al.,

1996; Zuo et al., 2004) and lucerne (Abdul-Jabbar et al., 1982; Luo et al., 1995) is generally

exponential, yet the simulated changes are greatest for the constant profile. This suggests

that the vertical roots of these plants which only make up a small proportion of total root

length have a very high connectivity (τR), perhaps greater than 0.1 which is the highest

value we have used here.

5.5 Conclusion

The van Genuchten (1980) effective saturation function provides a good description of the

pore size distribution created by roots. The shape the effective saturation functions of the

soil domain with roots is similar to those typically derived for sand.

We introduced new parameters for our model, and had to draw upon reported values or

modelling to define parameter ranges. We derived a relationship between macro-porosity

and saturated hydraulic conductivity of the domain with roots, and while our estimates

seem reasonable there is a need to make measurements of this relationship in field con-

ditions. We introduced a parameter that describes the minimum pore size that can be

compressed by roots and the evidence available suggests this is approximately 0.001 cm.

Comparison of simulated and observed infiltration rate under ponded conditions sug-

gests that continuity of root-induced changes down the soil profile is important for changes

to behaviour of the soil profile in saturated conditions. It also highlights the need for fur-

ther investigation into how root architecture influences the connectivity of fluid flow.

110

Chapter 6The impact of root-induced changes to soil

hydraulic properties on the water balance




6.1 Abstract

While there is a body of evidence that show roots can modify soil hydraulic properties

there has been no work that addresses how these changes affect the overall water balance.

We used a water flow model that includes root-induced changes to the soil hydraulic

conductivity and water retention functions to investigate this. We simulated soil water

flow and plant water uptake for a sand, loam and clay using 15 years of modelled rainfall

for Merredin, Western Australia. Our results show that the effects of roots was greatest in

the clay, both water uptake and storage in the top 100 cm of soil were significantly greater

in root-modified compared to unmodified soil. This was because root-induced changes in

near- and saturated hydraulic conductivity were greatest in the clay, which reduced the

amount of run-off.

111

CHAPTER 6. THE IMPACT OF ROOT-INDUCED CHANGES TO SOIL . . .

6.2 Introduction

Despite the extensive evidence that shows that roots can modify soil hydraulic properties

(SHP) (e.g. Messing et al., 1997; Meek et al., 1992; Murphy et al., 1993; Petersson et al.,

1987), to our knowledge there are no reports that specifically address how these changes

affect the water balance. Major root-induced changes to SHP tend to occur when a change

in land use occurs, such as a change from lucerne to annual crops (Meek et al., 1990), in

crop establishment methods (Fuentes et al., 2004; Murphy et al., 1993), the revegetation

of mine-site earth covers (Loch and Orange, 1997) or in forest establishment (Deuchars

et al., 1999; Johnson-Maynard et al., 2002). Knowledge of if, and how the water balance

changes under the new land use is necessary to predict the growth or resilience of the

vegetation, and any external environmental effects such as run-off and drainage.

While there are no specific reports that examine whether root-induced changes to SHP

lead to changes in the water balance, there are many reports of changes to factors that

contribute to this. For example, increases in infiltration rate have been widely reported

(e.g. Deuchars et al., 1999; Meek et al., 1989; Murphy et al., 1993; Petersson et al., 1987)

which can lead to a reduction in run-off (Hillel, 1998), and therefore a greater fraction

of rain entering the soil. Root induced changes to the soil can also affect the spatial

distribution of infiltration: dye tracer studies have shown that both live and decayed roots

act as a path preferential flow paths (Nobles et al., 2004), leading to deeper infiltration

(Archer et al., 2002; Devitt and Smith, 2002). Other reports have shown that root induced

changes can lead to an increase in macro-porosity (Johnson-Maynard et al., 2002; Meek

et al., 1989; Rasse et al., 2000) and saturated water content (Rachman et al., 2004a).

The evidence available suggests that soil texture will play a critical role in the change

in the water balance that occurs. In Chapters 4 and 5 we showed that the same root

system has a different impact on a sand, loam and clay, especially for saturated hydraulic

conductivity where the relative increase is far greater for a clay than a sand. Other

modelling studies have shown that soil texture plays a critical role in determining the

type of vegetation that dominates, because it determines the spatial distribution of water

through infiltration and the temporal availability of this (Fernandes-Illescas et al., 2001),

and root-induced changes to SHP will add another dimension to this.

112

6.3. METHODS

The aim of the work reported in this chapter is to quantify how root-induced changes to

SHP affect the water balance where vegetation has been established. As these changes are

most obvious when a land use change occurs we compare the before and after situations,

where the before state is a soil without roots present, and the after state is where the

vegetation and SHP properties are at a steady-state. We investigated the influence of soil

texture and the connectivity of the root-modified soil domain on root-induced changes,

which reflects changes in soil structure. Also, to examine effects on the water balance

under a realistic scenario, we simulated water flow and plant growth with seasonally-

variable rainfall and evaporation.

6.3 Methods

A sensitivity analysis of seasonal changes to soil- and plant water uptake dynamics to root-

induced changes to SHP was implemented using a Monte Carlo type of analysis. Soil-water

flow and plant water uptake were simulated for a period of one year for a factorial of three

soil types and three levels of connectivity of the soil domain with roots (connectivity),

using 15 realisations of stochastically generated rainfall.

6.3.1 Rainfall modelling

Rainfall was modelled as a series of independent storm events using a combination of a

seasonal model of storm properties (Hipsey et al., 2003) and the bounded random cascade

model (Menabde and Sivapalan, 2000). Hipsey et al. (2003) showed that the mean time

between storms tb (days), storm duration tr (hours) and storm intensity si (mm hour−1)

exhibited clear seasonal variation that can be expressed as a function of time t (days) as:

x(t) = ax cos(bxt+ cx) + dx (6.1)

Where x can be tb, tr or is and the over bar denotes the mean of a frequency distribution,

and ax, bx, cx and dx are empirically derived parameters for each storm property.

Rainfall was modelled in two steps. First, we assume that all 3 storm properties are

independent and have an exponential frequency distribution (Hipsey et al., 2003; Robinson

113


and Sivapalan, 1997), and we take a random sample from the inverse function of this

distribution:

x(t, χ) = x(t) logχ (6.2)

Where χ is a uniformly distributed random number.

By applying Equation 6.2 to each storm property a time series of individual storms of

an average intensity is created, which have one storm period and the storm depth R(t)

(mm) is:

R(t) = tr(t)si(t) (6.3)

The next step was to disaggregate each storm event using the bounded random cascade

method (Menabde and Sivapalan, 2000) to produce more realistic within-storm patterns

in intensity. This method successively breaks up each storm period into equally-spaced

periods to achieve the desired temporal resolution while maintaining R(t). For example,

in the first disaggregation the storm period is divided into two equally spaced periods,

and R(t) is partitioned between the storm periods using the weightings w1 and w2, where

each weighting wi is:

wi =yi

y1 + y2(6.4)

Where y1 and y2 are random numbers that were drawn from a gamma distribution.

Rainfall and pan evaporation were modelled for Merredin which is located in the south-

west of Western Australia (Figure 6.1a). The climate is Mediterranean with the majority

of rain falling from June to August, and with a mean annual (22 years) rainfall and pan

evaporation of 305 and 2280 mm respectively (Department of Agriculture and Food WA,

2009). The values for ax, bx, cx and dx were calculated using a regression model based

upon latitude and longitude (McGrath and Hinz, 2009) and the resulting storm parameters

tb(t), tr(t) and is(t) are shown in Figure 6.1b.

6.3.2 Water flow modelling

Soil-water flow and plant water uptake were simulated using the one-dimensional model

described in Chapter 5. In brief, we modified the water flow model WAVE (Javaux and

Vanclooster, 2006) to include an analytical function that describes root-induced changes

114

6.3. METHODS

110 115 120 125

−36

−34

−32

−30

−28

Latit

ude

Longitude

a

Indian Ocean

Perth

Merredin

1 61 121 181 241 301 361

02

46

810

12

01

23

45

6

Day of year

Inte

r−st

orm

dur

atio

n (d

ays)

and

sto

rm d

urat

ion

(hou

rs)

Sto

rm in

tens

ity (

mm

/h)

and

eva

pora

tion

(mm

/day

)b

Inter−storm durationStorm durationStorm intensityEvaporation

Figure 6.1: Geographical location of Merredin (a) and seasonal storm properties used togenerate synthetic rainfall (b).

to soil water retention and hydraulic conductivity, which assumes that the hydraulic con-

ductivity and water content of the root-modified soil is the sum of the soil domains with

and without roots. The governing equation for water flow was:

∂θ

∂t=

∂

∂z

[

K(h)

(

∂h

∂z+ 1

)]

− S (6.5)

Where θ is volumetric water content (cm3 cm−3), t is time (min), z is depth (cm),

h is matric head (cm), S (cm3 cm−3 min−1) is the sum of root water uptake from the

various soil layer sz (cm3 cm−3 min−1), and K(h) (cm min−1) is the unsaturated hydraulic

conductivity function:

K(h) =2

∑

i=1

Ks(i)δk(i)Sei (h)

li[

1−(

1− Sei (h)

1mi

)mi]2

(6.6)

Where Sei (h) is the effective saturation function for the soil domain i:

Sei (h) = δv

[

(

1 +

(

αih

δh

)ni)−mi

]

(6.7)

Where αi, ni and mi are shape parameters (van Genuchten, 1980) for the two soil domains,

where the domain with and without roots are denoted as 1 and 2 respectively.

Root water uptake for each soil layer sz (cm3 cm−3 min−1) was modelled by calculating

115


the potential uptake from each depth according potential evapotranspiration T (cm min−1)

and a root length weighting, then reducing this according to hz (van Genuchten, 1987):

sz =Lz

LaT

1

1 +(

hzh50

)p1 (6.8)

Where Lz (cm cm−2) and La (cm cm−2) are root length at depth z and and total root

length per unit surface area respectively, h50 is the pressure head where uptake is reduced

by half and p1 is an empirically derived constant.

We assumed that the properties of the root system remained constant for the length

of the simulation. The shape parameters for the soil domain with roots, α1, n1 and θm

were 0.56, 2.8 and 0.00320 respectively (Figure 5.4, Type 3) and β was 0.5. Total root

length per unit surface area was 250 cm m−2 (de Willigen and van Noordwijk, 1987) and

this was distributed vertically according to the probability density function of root depth

distribution:

Lz = La

∫ zi

zi−∆z−kz

∗

log(k)dz∗ (6.9)

Where k has an empirically derived value of 0.96 (Jackson et al., 1996).

The modelled soil profiles were uniform in texture and 300 cm in depth. The three

textural types used in the analysis were a sand, loam and clay (Carsel and Parrish, 1988),

and the parameters for connectivity are those derived for low, medium and high connec-

tivity in Chapter 5 (Table 6.3.2). We discretised the soil profile into 1, 2, 5 and 10 cm

layers from 0 to 50, 50 to 100, 100 to 200 and 200 to 300 cm soil depth respectively.

The initial soil moisture profile was defined by a linear gradient between 200 and 500 cm

matric head at the top and lower boundary respectively, and free drainage occurred at the

lower boundary. We assumed that appart from root-induced changes to the soil they were

structurally stable and that surface crusting did not occur.


Our results show that root-induced changes to soil hydraulic properties had the greatest

effect on plant water uptake (uptake) and soil water storage in the top 100 cm of soil

116


Table 6.1: Parameter values used for Ks of root-modified domain and soil hydraulic func-tions in the sensitivity analysis

Parameters for Ks of root-modified domainB N

Low connectivity 6.5 1.36Medium connectivity 65 1.36High connectivity 652 1.36

Soil parametersθs θr α n

Sand 0.43 0.045 0.145 2.68Loam 0.43 0.078 0.036 1.25Clay 0.38 0.068 0.08 1.09

(storage) in clay: both were significantly greater in the after state for most of the year.

Figures 6.2 and 6.3 show a summary of seasonal patterns in storage and uptake for the

before and after state, and as would be expected, there was a clear link between these.

Storage in the clay was approximately 25%, and signficantly (p>0.05) greater after 76 days

for all levels of connectivity and uptake reflects this, where for all levels of connectivity

was significantly greater after day 32 and cumulative uptake was approximately double by

day 365 (data not shown). Storage in the loam was significantly greater in the after state

from day 155 to 181 for medium and high connectivity; however, this did not translate

into greater uptake.

The physical explanation for these changes in uptake and storage is the hydraulic

conductivity at and near-saturation of soils in their before and after state. For example,

when comparing saturated hydraulic conductivity (Ks) of the soils in the after to before

state, sand decreased by 28% and loam and clay increased by 89 and 557% respectively.

For the clay, this had a major impact on the amount of rain lost as run-off (Figure 6.4).

In its original state, 0.51 of annual rainfall was lost as run-off, and after root modifications

was 0.2, 0.07 and 0.1 for low, medium and high connectivity respectively. A different trend

occurred in the loam, where root-induced changes increased run-off when connectivity was

low, and decreased when connectivity was medium or high. No run-off occurred for the

sand in either state.

Figure 6.5 shows an example of the seasonal dynamics of uptake and cumulative run-

off and drainage for a clay in the before and after state where connectivity is low. This

117


Day of year

Mea

n st

ored

wat

er in

top

100

cm o

f soi

l

5

10

15

20

25

100 200 300

1

2Low connectivity

Cla

y

100 200 300

1

2Medium connectivity

Cla

y

100 200 300

1

2High connectivity

Cla

y

5

10

15

20

25

1

2

Low connectivity

Loam

1

2

Medium connectivity

Loam

1

2

High connectivityLo

am

5

10

15

20

25

12

Low connectivity

San

d

12

Medium connectivityS

and

1

2

High connectivity

San

d

Root−modified soilUnmodified soil

Figure 6.2: Seasonal patterns of mean soil water storage for soil with and without rootmodifications. Thick lines are the mean for 15 years and thin lines are 5 and 95% confidenceintervals.

118


Day of year

Mea

n cu

mul

ativ

e w

ater

upt

ake

(cm

)

0.05

0.10

0.15

0.20

100 200 300

1

2

Low connectivity

Cla

y

100 200 300

1

2

Medium connectivity

Cla

y

100 200 300

1

2

High connectivityC

lay

0.05

0.10

0.15

0.20

1

2

Low connectivity

Loam

1

2

Medium connectivity

Loam

1

2

High connectivity

Loam

0.05

0.10

0.15

0.20

1

2

Low connectivity

San

d

1

2

Medium connectivity

San

d1

2

High connectivity

San

d

Root−modified soilUnmodified soil

Figure 6.3: Seasonal patterns of mean cumulative plant water uptake for soil with andwithout root modifications. Thick lines are the mean for 15 years and thin lines are 5 and95% confidence intervals.

119


Loam Clay

0.0

0.1

0.2

0.3

0.4

0.5

Mea

n ru

noff

as a

frac

tion

of a

nnua

l rai

nfal

l

Unmodified soil

Modified soil − low connectivity

Modified soil − med connectivity

Modified soil − high connectivity

Figure 6.4: Mean annual run-off as a fraction of rainfall for soils in their original stateand after root modification for three levels of connectivity of the soil domain with rootspresent

example is typical of the results from our analysis, where large rainfall events tend to lead

to run-off in the before state, and increase in storage for soil in the after state. In terms

of the vegetation, the net results is greater water uptake due to greater water availability.

The dependence upon soil type is an important consideration: it suggests that large

shifts in the water balance due to physical modification of the soil by roots are only possible

on fine textured soils. However, the effect of this shift on plant growth or off-site effects

such as run-off and drainage is likely to be sensitive to the combination of soil texture,

plant type and rainfall distribution (Fernandes-Illescas et al., 2001).

While the work reported here is a valuable first step in understanding the impact of

root-induced changes on the overall hydrological cycle, we acknowledge that the assump-

tions we made limit the conclusions we can draw about real systems. In particular, our

assumption of a steady-state root system does not account for the seasonal dynamics of

root growth and decay (Deans and Ford, 1986; van Noordwijk et al., 1994) and there-

fore changes in soil hydraulic properties (Murphy et al., 1993; Bormann and Klaasen,

2008). Our assumption of a spatially uniform root and soil profiles contrasts to the spatial

variability in root growth (e.g. Persson, 1980; Robinson, 1994) and soil properties (e.g.

120


Day of year

Dai

ly r

ainf

all (

cm)

1 16 31 46 61 76 91 121 151 181 211 241 271 301 331 361

0.0

0.5

1.0

1.5

2.0

2.5

3.0

a

1 16 31 46 61 76 91 121 151 181 211 241 271 301 331 361

05

1015

2025

30

Day of year

Cum

ulat

ive

upta

ke (

cm)

or

stor

age

in r

oot−

zone

(cm

)

b

Storage − unmodified soilStorage − root modified soilUptake − unmodified soilUptake − root modified soil

1 16 31 46 61 76 91 121 151 181 211 241 271 301 331 361

05

1015

Day of year

Cum

ulat

ive

runo

ff (c

m)

or

roo

t−zo

ne d

rain

age

(cm

)

c

Runoff − unmodified soilRunoff − root modified soilDrainage − unmodified soilDrainage − root modified soil

Figure 6.5: An example of simulated changes in the water balance for a clay where theroot-modified soil has low connectivity

121


Jury et al., 1987; Nielsen et al., 1973) that occur. Also, we assume that the soil is struc-

turally stable, whereas in reality surface sealing can occur during rainfall which leads to a

reduction in infiltration rate.

These discrepancies between our model assumptions and the complexities of the hy-

drological cycle in field conditions highlight areas that require further research. From

a modelling perspective, two logical steps are required to improve our understanding of

how root-induced changes affect the water balance and plant growth. First, to include

the dynamics of root growth and decay, and above ground growth which will lead to sea-

sonal changes in soil hydraulic properties and potential water uptake. This will provide

a process-based approach to modelling the soil-plant hydrological feedback. Second, is to

ascertain the role of spatially variable root and soil properties, which is a dominant feature

of the run-on - run-off systems of managed and natural landscapes in arid areas. From

an experimental perspective, field evidence is required of how the water balance changes

after a system reaches a new steady-state to provide evidence that in parallel with further

modelling.

6.5 Conclusion

Both soil-water storage and uptake were significantly greater in the clay after root modi-

fications after day 76, with total uptake being double that in the before state for all levels

of connectivity. This occurred because Ks of the surface 10 cm of the clay after root

modification was approximately 10 times greater than before, resulting in mean annual

run-off being reduced by 60%.

The results suggest that root-induced changes to the water balance will be greatest

in fine-textured soils; however, this is likely to be sensitive to the combination of soil

texture, plant type and rainfall distribution. Further work is required to determine the

effect seasonally dynamic root growth and decay, and the spatial distribution of roots and

soil properties have on root-induced changes to the water balance.

122

Chapter 7Synthesis and Outlook

7.1 Summary of chapters

The research presented in this thesis was motivated by the need for a quantitative under-

standing of the processes and effects of root-induced changes to soil hydraulic properties.

This need arises because plants can cause significant changes to SHP and ultimately in

the hydrology of an ecosystem. In arid environments, root induced changes to SHP can

lead to a feedback loop between soils and plants, where root growth and decay improve

the capacity of the soil to store water, which leads to further plant (and root) growth.

At present, the sensitivity of these systems to changes in environmental conditions is as-

sessed using models that rely on an empirical relationship between vegetation density and

infiltration rate. However, this relationship is not adequate for assessing the effects of

root-induced changes to SHP in ecosystems that differ from where it has been derived.

Major changes in hydrology also occur where a land use change occurs, for example from

an annual to a perennial crop, or the revegetation of mine-site earth covers. To improve

our capacity to predict the fate of vegetation, water balance and off-site impacts in these

situations, process-based models were required.

We began this research with a review of the processes and effects of root-induced

changes to SHP. The main theme that emerged from this work was the lack of cohesion

between the processes and outcomes of root-induced changes, and this is reflected in the

reliance on an empirical function that relates infiltration rate to vegetation density. We

123

CHAPTER 7. SYNTHESIS AND OUTLOOK

also identified that the dominant process of root-induced changes is the change to pore

geometry created by roots.

To begin to bridge the gap between observations of processes and outcomes of root-

induced changes to SHP we conducted an experiment where we measured the hydraulic

conductivity and water retention functions of a soil modified by wheat, and root length

and mass at 3, 5, 7 and 9 weeks after sowing (weeks). We found that saturated hydraulic

conductivity (Ks) showed a declining trend up until 7 weeks while the wheat plants were

in the vegetative growth stage, then increased at 9 weeks when the plants were in the veg-

etative growth stage. While there were no significant changes in Ks at different sampling

times, or betweenKs and root properties, the trend we observed is in agreement with other

reports. We also observed root-induced changes in unsaturated hydraulic conductivity at

matric head greater than -30 cm. The trends in changes to hydraulic conductivity and

root properties provide justification for a much larger column study: to detect changes in

Ks from 20 to 50% we recommend 50 or 10 columns per treatment respectively.

To improve our capacity to predict root-induced changes to SHP we first needed to

characterise how root radii changes for different plant species and soil texture. We used

root radii frequency distributions to describe root systems because they reflect the mor-

phology of the root system and can be described using distribution functions, and the

parameters for these provide a basis for comparison and calculating statistical properties

of the distribution. We collated a database of 96 observed root radius frequency distribu-

tions and found that the distribution mean was significantly different (p<0.05) for different

growth habits and different growth media. We compared the performance of a number of

distribution functions for describing the observed root radii frequency distributions and

found that overall the log-normal distribution was the most suitable. An advantage of

using the log-normal distribution function is that there is some organisation within the

parameter space which means a small number of representative root ’types‘ within this

can be used to represent the range that occurs.

In Chapter 4 we developed a conceptual model that described root-induced changes

to the soil water retention and hydraulic conductivity function based upon the length and

radius frequency distribution of the root system. This model was based upon the capillary

124

7.1. SUMMARY OF CHAPTERS

bundle concept which simplifies the soil to a series of bundles of cylinders of equal radius.

The central assumption of our model was that the geometry of roots within pores can be

simplified to concentric cylinders, and the root-modified soil was described as a series of

bundles with and without roots present. For the bundles with roots present, we derived

scaling functions for flux, capillary rise and volume that were a function of the ratio of root

radius to the radius of the pores they occupy β, which is a proxy for root decay. Modelled

changes to saturated hydraulic conductivity (Ks) were sensitive to the ratio of root radius

to pore radius, the connectivity of root-modified pores, and soil texture. Changes to

Ks increased as soil texture became finer and as the connectivity of root-modified pores

increased. Overall our model produced similar changes to what has been observed: root-

induced changes to Ks can switch from a decrease to an increase depending upon β and

the greatest effect was in near- and saturated hydraulic conductivity.

While the modified capillary bundle model provides a simple approach to investigating

the effects of roots on soil hydraulic properties, its application in water flow models is

limited. The most common approach to modelling water flow is the numerical solution of

Richards equation which usually requires parametric functions that describe the water re-

tention and hydraulic conductivity functions; however, these do not exist for root-modified

soils. To meet this need, we derived a model based upon the van Genuchten-Mualem for-

mulation and the multi-domain concept, conceptualising the soil as a domain with and

without roots. This model differs from other multi-domain models in that it is dynamic:

the properties of both domains change depending upon the shape parameters that describe

the domain with roots and root length density. The shape parameters for the domain with

roots were derived by fitting the van Genuchten effective saturation function to each of the

root radius frequency distributions in the database from Chapter 3, and flux, capillary rise

and volume of the domain with roots was scaled according to β using the functions derived

for the modified capillary bundle model. As with observations and the conceptual model,

root-induced changes were greatest in near- and saturated hydraulic conductivity. Sensi-

tivity analysis showed that predicted changes to Ks were most sensitive to the volume per

unit length of root and β. Comparison of hydraulic conductivity functions revealed that

changes to hydraulic conductivity at matric head greater than -10 cm were most sensitive

125


to β and the connectivity of the domain with roots. We ended this chapter with modelled

infiltration experiments, investigating the effect of different root profiles and connectivity

of the domain with roots. Comparison with observed changes in infiltration rate suggest

that in real soils the increases are due to a small number of vertically-orientated roots

with very high connectivity.

The results from our modelled infiltration experiments suggested that root-induced

changes could lead to major changes in soil water storage and plant water uptake, there-

fore we investigated this with year-long simulations using modelled seasonal rainfall for

Merredin, Western Australia for a sand, loam and clay. Overall, our results show that

root-induced changes to soil hydraulic properties had the greatest effect on plant water

uptake (uptake) and soil water storage in the top 100 cm of soil (storage) in clay: both

were significantly (p<0.05) greater than in the unmodified soil. This occurred because

Ks of the surface 10 cm of the clay after root modification was approximately 10 times

greater than before, resulting in mean annual run-off being reduced by 60%.

7.2 Conclusions and implications

The work in this thesis provides a significant first step towards improving our capacity to

predict how roots modify soil hydraulic properties. By defining processes and the range

for the parameters used to predict how the soil is modified by roots, we are able to make

quantitative assessments of how a property such as hydraulic conductivity will change for

a realistic circumstance. Also, the simplification of the geometry of roots in pore space to

concentric cylinders proved to be a critical component of predicting the effects of roots on

flux, capillary rise and volume of root occupied pores. The analytical model we derived

can be readily incorporated into any water flow model that simulates water flow with

Richards equation, which provides a powerful tool for assessing when, and by how much

root-induced changes affect soil water storage, uptake and drainage.

The main message that can be drawn from this thesis is that root-induced changes

to SHP are significant processes that need to be explicitly considered during changes of

land use or soil management. For the first time, this thesis provides us with a framework

for quantifying these changes and it is consistent with current approaches to modelling

126

7.3. LIMITATIONS AND FUTURE WORK

soil-water flow.

This thesis has improved our understanding of the processes of how roots modify SHP.

We identified that changes to pore geometry are the dominant process by which roots lead

to changes in SHP because the effects are more permanent and are of a greater magnitude.

This is supported by the capacity of the modified capillary bundle to produce the same

trends as those observed, which is based upon changes to pore geometry only. Subsequent

modelling analysis shows that β and the connectivity of root-modified pores are the most

important geometric change that roots cause.

For the first time, we have measured changes in soil hydraulic properties and roots and

have been able to establish why a rapid change from a root-induced decrease to increase

in Ks occurred. The link between physiological stage of the root system, and the changes

that are likely to occur has implications for understanding how roots modify SHP: it may

provide an effective tool for predicting when the switch from a decrease to increase occurs.

The capacity to predict dynamic changes to SHP has implications for modelling the

hydrological feedback between plants and soils. The ability to include the relative rates of

root growth and decay through β and root length density will allow for a more realistic

temporal evolution to changes to SHP, which has implications for water infiltration, storage

and uptake.

7.3 Limitations and future work

Experimental work is required to test the validity of the assumptions we have made in our

models that predict changes to SHP. While we have endeavoured to define the parameter

space for those parameters that we have introduced, there is still some uncertainty about

the connectivity of root-modified pores in particular.

The parameterisation of the soil domain with roots is based upon work that measures

’fine’ roots only. The root systems measured in this work were often cut from larger roots,

which has significant implications for predicting changes to SHP. Our modelling analysis

showed that larger roots have a greater effect therefore it is reasonable that the large

roots not measured in these root studies will affect SHP. The multi-domain structure of

analytical model is ideally suited to including large roots as a separate domain.

127


We expect further insights into how root-induced changes affect the water balance

by shifting from one- to two dimensional analysis. The evolution of spatial patterns of

vegetation is often modelled using a two-dimensional surface, and we hypothesise that

the patterns that emerge under dynamic SHP will differ from those when the empirical

approach is used because of the time-lag before an increase in Ks occurs and because of

the seasonality of root growth and decay.

It is inevitable that root-induced changes to soil hydraulic properties will affect the fate

of solutes in the soil. This may be particularly important for soil nutrients and modelling

investigation of the dynamics of plant and root growth, nutrient uptake and changes to

SHP is warranted.

128

Appendices

129

Appendix ADerivations for Chapter 4

A.1 Capillary rise in concentric cylinders

The equilibrium between upward and downward forces on liquid within a cylinder can be

described as:

2πrγcosΘ = πr2hρg (A.1)

where γ is surface tension (g cm s−2 cm−1), Θ is wetting angle, r is the radius of

the cylinder (cm), h is the height of capillary rise (cm), ρ is density (g cm−3) and g is

gravitational acceleration g (cm s−2).

For concentric cylinders we assume that the upward force is the sum of the surface

tension at the circumference of the inner and outer cylinders and that the downward force

is the mass of liquid held by the outer cylinder minus the mass of liquid that has been

displaced by the inner cylinder and is expressed as:

2πr1γcosΘ+ 2πr2γcosΘ = πr22hρg − πr21hρg (A.2)

Where r1 and r2 are the radius of the inner and outer cylinder respectively.

Which simplifies to:

2π (r1 + r2) γcosΘ = πρgh(

r22 − r21)

(A.3)

131

APPENDIX A. DERIVATIONS FOR CHAPTER 4

Solving for h:

h =2 (r1 + r2) γcosΘ

ρg(

r22 − r21) (A.4)

Seperating constants:

h =2γcosΘ

ρg

r1 + r2r22 − r21

(A.5)

Simplifes to:

h =2γcosΘ

ρg (r2 − r1)(A.6)

A.2 Derivation of dimensionless ratios

A.2.1 Capillary rise ratio

Capillary rise within concentric cylinders h can be expressed as:

h =2γcosΘ

ρg (r2 − r1)(A.7)

First we separate constants:

h =2γcosΘ

ρg

1

(r2 − r1)(A.8)

Then represent constants as a:

h =a

r2 − r1(A.9)

We then define the ratio of the inner to outer cylinder radius β:

β =r1r2

(A.10)

Substitute Equation A.10 into Equation A.9:

h =a

r2 − βr2(A.11)

132

A.2. DERIVATION OF DIMENSIONLESS RATIOS

h =a

r2 (1− β)(A.12)

h =a

r2

1

1− β(A.13)

Eliminating constants leaves the ratio δh:

δh =1

1− β(A.14)

A.2.2 Flux ratio

The average velocity q between concentric cylinders Cutlip and Shacham (1999):

q =∆p

8ηl

[

r21 + r22 −r22 − r21

log (r2/r1)

]

(A.15)

Where η is dynamic viscosity g cm−1 s−1.

Represent constants as a:

q = a

[

r21 + r22 −r22 − r21

log (r2/r1)

]

(A.16)

From A.10 we know that:

r1 = βr2 (A.17)


q = a

[

β2r22 + r22 −r22 − β2r22

log (r2/βr2)

]

(A.18)


q = a

[

r22(

1 + β2)

− r22(

1− β2)

log (1/β)

]

(A.19)

Separate constants:

q = ar22

[

1 + β2 − 1− β2

log (1/β)

]

(A.20)

133


Eliminating constants leaves the ratio δq:

δq = 1 + β2 − 1− β2

log (1/β)(A.21)

A.2.3 Volume ratio

The volume within concentric cylinders with an inner and outer cylinders radius of r1 and

r2 respectively w can be expressed as:

w = lπr22 − lπr21 (A.22)


w = lπ(

r22 − r21)

(A.23)


w = lπ(

r22 − β2r22)

(A.24)


w = lπr22(

1− β2)

(A.25)

Eliminating constants leaves the ratio δw:

δw = 1− β2 (A.26)

A.3 Derivation of conductivity function

The derivation of the hydraulic conductivity function follows that of Jury et al. (1991,

page 90), however our final derivation differs as we express hydraulic conductivity K as a

function of volume rather than matric potential h. We have included the full derivation

for clarity.

The volume flow rate Q[

cm3sec−1]

through a single cylinder of length L and radius

134

A.3. DERIVATION OF CONDUCTIVITY FUNCTION

R can be calculated using Poiseuille’s Law:

Q =πR4ρg

8η

∆H

Lc(A.27)

Where ∆H is the difference in pressure head (cm) and Lc is the length of the cylinder.

The total flux through a bundle of cylinders Qt is the sum of flux through m radius

classes:

Qt =πρg

8η

∆H

Lc

m∑

j=1

NjR4j (A.28)

Where Nj is the number of cylinders in each radius class.

The rate of flux Jw is flux volume divided by cross-sectional area:

Jw =Qt

A(A.29)

The number of cylinders per cross-sectional area n is:

nj =Nj

Aj(A.30)

Therefore the rate of flux through a bundle of cylinders can be expressed as:

Jw =πρg

8η

∆H

Lc

m∑

j=1

njR4j (A.31)

The number of cylinders per cross-sectional area n can also be expressed as:

nj =θjπr2j

(A.32)

By substituting Equation A.32 into A.33 and simplifying:

Jw =ρg

8η

∆H

Lc

m∑

j=1

θjR2j (A.33)

We need to express the rate of flow as hydraulic conductivity K rather than Jw. From

135


Darcy’s Law we know that:

Jw = −Ks∆H

∆z(A.34)

Where Ks is saturated hydraulic conductivity.

We can re-write flux in the capillary bundle in the form of Darcy’s Law:

Jw = −

ρg

8η

m∑

j=1

θjR2j

∆H

∆z

L

Lc(A.35)

Where ∆z = 0-L therefore:

L

∆z= −1 (A.36)

Connectivity τ is expressed as:

τ =L

Lc(A.37)

Therefore, Ks of the capillary bundle can be expressed as:

Ks =τρg

8η

m∑

j=1

θjR2j (A.38)

136

Appendix BCompression data

137

APPENDIX B. COMPRESSION DATA

Table B.1: Change in van Genuchten α and Ks with compressionPorosity(cm3

cm−3)

α Ks (cm

min−1)

relporosity

rel a rel ks

Zhang et al. (2006) Heyang 0-5 0.52 3.221 0.088 1.00 1.00 1.000-5 0.48 0.405 0.075 0.93 0.13 0.850-5 0.40 0.125 0.016 0.82 0.31 0.2210-15 0.51 2.552 0.074 1.00 1.00 1.0010-15 0.45 0.992 0.047 0.88 0.39 0.6410-15 0.38 0.134 0.006 0.83 0.14 0.13

Mizhi 0-5 0.51 0.089 0.056 1.00 1.00 1.000-5 0.45 0.08 0.037 0.89 0.90 0.660-5 0.39 0.074 0.021 0.87 0.93 0.5610-15 0.49 0.095 0.069 1.00 1.00 1.0010-15 0.45 0.082 0.031 0.90 0.86 0.4510-15 0.36 0.071 0.019 0.81 0.87 0.62

Laliberte et al. (1966) Columbia sandyloam

0.55 0.008 0.080 1.00 1.00 1.00

0.52 0.007 0.052 0.95 0.83 0.650.48 0.006 0.026 0.87 0.69 0.330.47 0.005 0.021 0.84 0.59 0.260.45 0.013 0.80 0.17

Touchet silt loam 0.51 0.005 0.023 1.00 1.00 1.000.49 0.004 0.018 0.95 0.82 0.810.46 0.003 0.011 0.90 0.66 0.470.43 0.008 0.85 0.370.41 0.006 0.79 0.26

Unconsolidatedsand

0.45 0.001 4.527 1.00 1.00 1.00

0.44 0.001 4.039 0.98 0.99 0.890.43 0.001 3.691 0.96 0.99 0.820.42 3.369 0.94 0.740.40 2.959 0.90 0.65

Reicovsky et al. (1980) Barnes loam 0.63 0.034 0.179 1.00 1.00 1.000.55 0.014 0.064 0.89 0.42 0.360.50 0.011 0.022 0.80 0.33 0.120.40 0.004 0.002 0.64 0.13 0.01

Smith and Woolhiser(1979)

Pouder fine sand 0.53 0.086 0.394 1.00 1.00 1.00

0.49 0.254 0.92 0.650.44 0.065 0.186 0.84 0.76 0.47

Stange and Horn (2005) Ab 0.62 0.03 1.00 1.00Ab 0.60 0.03 0.98 1.00Ab 0.58 0.03 0.93 0.89Ab 0.57 0.02 0.92 0.79Ab 0.49 0.01 0.80 0.21Ap 0.63 0.02 1.00 1.00Ap 0.62 0.03 0.98 1.24Ap 0.61 0.02 0.97 1.14Ap 0.60 0.02 0.96 1.14Ap 0.60 0.02 0.96 1.10Ap 0.58 0.02 0.92 0.86HPAp 0.48 0.13 1.00 1.00HPAp 0.45 0.07 0.95 0.57HPAp 0.41 0.05 0.86 0.35HPAp 0.33 0.04 0.69 0.30HPAp 0.31 0.03 0.65 0.25HPAxh 0.44 0.39 1.00 1.00HPAxh 0.39 0.09 0.90 0.23HPAxh 0.38 0.08 0.86 0.20HPAxh 0.36 0.06 0.82 0.16HPAxh 0.34 0.05 0.78 0.13HPAxh 0.33 0.05 0.76 0.12HPAxh 0.32 0.03 0.74 0.09HPBCv 0.49 0.07 1.00 1.00HPBCv 0.46 0.04 0.95 0.62HPBCv 0.42 0.03 0.85 0.42HPBCv 0.39 0.02 0.81 0.30HPBCv 0.38 0.02 0.77 0.26DGAb 0.55 0.01 1.00 1.00DGAb 0.54 0.01 1.00 1.00DGAb 0.52 0.01 0.96 0.89DGAb 0.52 0.01 0.96 1.00

138

Appendix CParameter values used for one at a time

sensitivity analysis

139

APPENDIX

C.PARAMETER

VALUESUSED

FOR

ONE

AT

ATIM

E...

Parameter Reference value Lower limit Upper Limit Reference

α1 0.139 0.06 3.98 Database in Chapter 3n1 5.8 2.15 10.57θm 0.0022 0.00012 0.009

Root length density 15 0 25 de Willigen and van Noordwijk (1987)

β 0.5 0.3 0.9 Chapter 4

B1 65 6.5 652 Defined here

αo 0.036 0.005 0.145 Carsel and Parrish (1988)no 1.56 1.09 2.68θro 0.078 0.034 0.1θso 0.43 0.36 0.46Ks

o 0.0173 0.0003 0.495

140

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