Modelled and measured stand transpiration and canopy

conductance of an Australian native forest

Rhys Whitley1,2,3, Melanie Zeppel1,2,Belinda Medlyn4, Derek Eamus1,2

U T SUniversity of Technology, Sydney Institute for Water and Environmental

Resource Management

1Institute for Water and Environmental Resource Management, University of Technology Sydney2Department of Environmental Sciences, University of Technology Sydney

3Department of Physics and Advanced Materials, University of Technology Sydney4Department of Biological Sciences, Macquarie University

Talk Outline

A new method of estimating stand transpiration (Ec) as an alternative to Penman-Monteith (PM) equation

Comparing against the PM and an Artificial Neural Network (ANN)

Spatial variability of responses between ecosystems

Future Work

)/1(

)(

ca

apnc GG

DGCGRE

Methods of Modelling Transpiration

)()()( 321 fDfRfGG SMaxcc

)()(ˆ)( 321 fDfRfEE SMaxcc

Penman-Monteith Equation and Jarvis-Stewart Model.1. Needs measurements of Gc

2. Circular, Complex and Time Consuming

Directly expressed in the Jarvis-Stewart Model.1. Measurements in Ec

2. Retains Mechanistic value as Ec = GcD

Artificial Neural NetworkUsed as a statistical benchmark for the Jarvis models.

Defines an input map based onRS, D and

Defines a prediction map based on a linear regression between Ec and (RS, D and

1.0

x1

x2

xn

SOFM Network

Linear Mapping Network

Gives a prediction that indicates the ‘best’ possible fit given our data

Paringa Site: Liverpool Plains

0.8 ≤ LAI ≤ 1.2

Rainfall: ~ 600 mm

Shallow sandy soil with exposed sandstone

SpeciesDensity

(stems ha-1)

Basal area

(m2 ha-1)

Callitris glaucophylla

212.2 5.9

Eucalyptus crebra

42.2 14.5

SYDNEY

PARINGA

Methods of Collection

Greenspan sap flowsensors

4 sensors per tree 7 trees per species

2 species

Transpiration

Solar Radiation

Vapour Pressure Deficit

Soil MoistureContent

Weather station 100 m from tree stand

Theta probes at 10, 40 & 50 cm

Scaling to Stand Water Use

Stand water use is ….. sap velocity of the stand x sapwood area of the stand

Mean sap velocity for each species

Sapwood area of the stand estimated using the DBH vs. sapwood area relationship for each species

1 Jan 1 Feb 1 Jul 1 Aug 1 Sep

0200400600800

100012001400

0123456789

1 Jan 1 Feb 1 Jul 1 Aug 1 Sep56789

101112131415

020406080100120140160180200

1 Jan 1 Feb 1 Jul 1 Aug 1 Sep

0.00.51.01.52.02.53.0

S

ola

r R

adia

tio

n

(W m

-2)

RS D

Vap

ou

r Pressu

reD

eficit (kPa)

So

il M

ois

ture

Co

nte

nt

(mm

3 mm

-3) R

ainfall (m

m)

Sta

nd

Tra

nsp

irat

ion

(mm

d-1)

Ec

Measurement Time Series

Model Functional Dependencies

)exp()(ˆ 232 DkDkDf

)exp()( 22 DkDf

f1(RS )RS1000

1000 k1RS k1

f3()0

wC w1

, W,W C, C

Dependence of Gc and Ec onchanging solar radiation

Dependence of Gc on changingvapour pressure deficit

Dependence of Gc and Ec onchanging soil moisture content

Dependence of Ec on changingvapour pressure deficit

Parameterising the Model

0

200

400

600

800

1000

1200

1400

0:00:00 4:00:00 8:00:00 12:00:00 16:00:00 20:00:00

Sola

r R

ad

iati

on

RS (

Wm

-2)Filter the data set by removing….

a) Precipitation events

b) Hours where solar radiation is < 0i.e. between 0800-1600 hrs

Boundary Line Analysis

Quantile Regression

Heuristic Search Algorithms

We need to find the most likely values for the seasonal

response parameters

We need to use data that shows non-limiting response to Ec and Gc!

Monte-Carlo Markov-ChainMethods

Methods of finding parameter values that are close to maximum

likelihood

Functional Relationships

0 200 400 600 800 1000 1200 1400

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.0

0.2

0.4

0.6

0.8

1.0

Solar Radiation (W m-2)

Sta

nd

Tra

nsp

irat

ion

(m

m h

r-1)

Vapour Pressure Deficit (kPa)

Soil Moisture Content (mm3 mm-3)

Ec/

Ec

max

Jarv

is-S

tew

art

Mo

de

l:

for

Ec

Jarv

is-S

tew

art

Mo

de

l:

for

Gc:

0 200 400 600 800 1000 1200 1400

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0 1 2 3 4 5 6 7 8 9 10 11 12 13 140.0

0.2

0.4

0.6

0.8

1.0

Solar Radiation (W m-2)

Can

op

y C

on

du

ctan

ce (

mm

hr-1

)

Vapour Pressure Deficit (kPa)

Soil Moisture Content (mm3 mm-3)

Gc/

Gc

max

1 Jan 2 Jan 3 Jan 4 Jan 5 Jan 6 Jan 7 Jan

0.00

0.05

0.10

0.15

0.20

5 Feb 6 Feb 7 Feb 8 Feb 9 Feb 10 Feb 11 Feb 12 Feb

0.00

0.05

0.10

0.15

0.20

0.25

14 Jul 15 Jul 16 Jul 17 Jul 18 Jul 19 Jul 20 Jul 21 Jul

0.00

0.05

0.10

0.15

0.20

9 Sep 10 Sep 11 Sep 12 Sep 13 Sep 14 Sep 15 Sep 16 Sep

0.00

0.05

0.10

0.15

0.20

0.25

Sta

nd

Tra

ns

pir

ati

on

(m

m h

r-1)

Sapflow PM Jarvis ANN

Summer Winter

Residuals and Correlation

0 50 100 150 200 250 300 350-3

-2

-1

0

1

2

3

4

0 50 100 150 200 250 300 350

-4 -3 -2 -1 0 1 2 3 40

10

20

30

40

50

60

70

80

90

100

110

120

Penman-Monteith Ec

Fre

qu

ency

Standard Deviation

Jarvis-Stewart Ec

-4 -3 -2 -1 0 1 2 3 4

Standard Deviation

Sta

nd

ard

Dev

iati

on

Time (Hrs)

Time (Hrs)

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.00 0.05 0.10 0.15 0.20 0.25 0.30

0.00

0.05

0.10

0.15

0.20

0.25

0.30

JS-m

od

el T

ran

spir

atio

n (

mm

hr-1

)

R2 = 0.87slope = 0.86

PM

T

ran

spir

atio

n (

mm

hr-1

) R2 = 0.86slope = 0.79

AN

N T

ran

spir

atio

n (

mm

hr-1

)

Sapflow Transpiration (mm hr-1)

R2 = 0.86 slope = 0.85

Optimisation Results

Modified Jarvis Model (Ec ) Traditional Jarvis Model (Gc )

refmax (mm hr-1) 0.2667 (0.0054) 0.00821mm s-1 (0.00012)

k1 (W m-2) 200.38 (39.67) 257.99 (47.76)

k2 (kPa) 1.08 (0.02) - -

k3 (kPa) 0.44 (0.04) 0.39 (0.01)

θW (mm3mm-3) 7.0* - 7.14 (0.12)

θC (mm3mm-3) 11.84 (0.10) 11.49 (0.07)

MeasuredModified

Jarvis ModelPenman-Monteith ANN

Ec total (mm) 110.52 84.03 74.91 110.70

μEc (mm hr-1) 0.051 0.039 0.040 0.052

R2 - 0.87 0.86 0.86

RMSE (mm hr-1) - 0.028 0.030 0.021

Results Summary

Regions where the Jarvis model has been parameterised

Japanese Conifer

Amazonian Pasture& Rainforest

Australian Eucalypt1. Dolman et al. 19912. Wright et al. 19953. Sommer et al. 20024. Harris et al. 2004

1. Whitley et al. 2007

1. Komatsu et al. 2006

European Conifer and Poplar

1. Stewart 19882. Gash et al. 19893. Granier & Loustau 19944. Zhang et al. 19975. Bosveld & Bouten 2001

0 1 2 3 4 5 6 7

0 5 10 15 20 25 30 35 40

0 200 400 600 800 10000.0

0.2

0.4

0.6

0.8

1.0

Vapour Pressure Deficit (kPa)

Whitley et al. 2007 Komatsu et al. 2006 Harris et al. 2004 Sommer et al. 2002 Zhang et al. 1997 Wright et al. 1995 Granier and Loustau 1994 Dolman et al. 1991

Specific Humidity Deficit (g kg-1)

Ec

/ Ec

max

Solar Radiation (W m-2)

Spatial Variability of Parameters

Application of literature models

Measured Granier & Loustau 1994 Sommer et al. 2002

Ec total (mm) 110.52 1045.00 37.45

μEc (mm s-1) 0.051 0.489 0.018

RMSE (mm s-1) - 0.952 0.056

Models from Granier & Loustau 1994 and Sommer et al. 2002 were tested with our data and compared against our model

0 250 500 750 1000 1250 1500 1750 2000 2250 25000.00

0.04

0.08

0.12

0.16

0.20

0.24

0.28

0

1

2

3

4

5

6

Hours

Measured Ec Granier & Loustau 1994 Sommer et al. 2002

Sta

nd

Tra

nsp

irat

ion

(m

m h

r-1)

Current and Future Work

Traditional

Jarvis Model

ModifiedJarvis Model

ParameterEstimation

Nonparametric

Analysis

Bayesian Analysis

Acknowledgements

Many thanks to Gab Abramowitz for lending his code and his help with SOLO.

and

the lab team at UTS for the data

Thank you foryour time

Extra Slides

Genetic Algorithms

min2

(Optimum Solution)

• Are adaptive heuristic search algorithms based on natural selection and evolution.

• Powerful: Discovers optimum solutions rapidly for difficult high-dimensional problems.– e.g. 7 dimensional

parameter space.

• Searches this entire parameters space for the global minimum - optimum value.

DataResult

Optimum SolutionsTest

2min

2>2min

Set population of random solutions

Evaluation

Cross-mix solutions

Randomly select

solutionsMutate

Example: Genetic Algorithm Process

Bayesian Parameter Estimation

• Solve Bayes Theorem for the Jarvis model

N

i i

iiN

ii

Nki

M

kkk

i

kikik

fyIXP

IP

IP

IXPIPIXP

2

2

1

12/

1

1

)(

2

1exp)2(),|(

)|(

)|(

),|()|(),|(

Uniform Prior

Gaussian Likelihood

Spatial Variability of ParametersForest Type Species References

European Conifer

Japanese Conifer

Pinus sylvestris

Pinus nigra var. maritimaPteridiura aquilinura (L.) KuhnPinus pinaster Ait.Pteridium aquilineMolinia coerulePseudotsuga menziesii (Mirb.) Franco

Cryptomeria japonica

Stewart 1988

Gash et al. 1989Granier and Loustau 1994Bosveld and Bouten 2001

Komatsu et al. 2006

European Poplar Populus trichocarpa Populus tacamahaca

Zhang et al. 1997

Amazonian Rainforest Piptadenia suaveolensLicania micranthaBocoa viridifloraNaucleopsis glabra

Dolman et al. 1991Harris et al. 2004

Amazonian Pasture Brachiaria decumbensBrachiaria humidicolaZea maysVigna unguiculataManihot esculenta

Wright et al. 1995Sommer et al. 2002

Australian Eucalypt Eucalyptus crebraCallitris glaucophylla

Whitley et al. 2007

Artificial Neural Network

• Uses a Self-Organising Feature Map (SOFM) and Self-Organising Linear Output Map (SOLO).

• SOFM trains and maps the input space.

• SOLO maps inputs into outputs using piecewise linear regression.

• Used as a statistical benchmark for the Jarvis models.

Input Classification Map

Architecture of SOLO

1.0

x1

x2

xn

SOFM Network

Linear Mapping Network

vji

wji

I/O Prediction Map

0

10

n

ijiijj vxvz

zj

Setup of Models

f1(RS )RS1000

1000 k1RS k1

f3()0

wC w1

, W,W C, C

)exp()(ˆ 232 DkDkDf )exp()( 22 DkDf

f1(RS )RS1000

1000 k1RS k1

f3()0

wC w1

, W,W C, C

Jarvis-Stewart Model

For Gc:

Jarvis-Stewart Model

For Ec: