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WATER EROSION: EROSIVITY AND ERODIBILITY

(In Encyclopedia of Environmental Management. Taylor & Francis, New York.,

Published online: 29 May 2013: 980-990)

P.I.A. Kinnell, Institute of Applied Ecology, University of Canberra, Australia.

ABSTRACT

Conceptually, rainfall erosivity is the capacity of rain to produce erosion where as soil

erodibility is the susceptibility of the soil to be eroded. However, no absolute numerical

values can be determined for them because rainfall erosion results from various forms of

erosion (splash erosion, sheet erosion, rill erosion, interrill erosion) that are driven by

different forces. Originally, the terms erosivity and erodibility were associated with the

rainfall factor (R) and the soil factor (K) in the Universal Soil Loss Equation where the event

erosivity factor was given by the product of the kinetic energy of the storm (E) and the

maximum 30-minute rainfall intensity (I30). Soil loss at the scale at which the USLE applies

results from the discharge of sediment with runoff but, because the USLE does not include

any direct consideration of runoff in the event erosivity factor, it is not good at accounting for

event soil loss at some geographic locations. Erodibility values have units of soil loss per unit

of the erosivity index and cannot be used with erosivity indices other than the one that was

associated in their determination. Some models ignore this fact and so ignore certain

fundamental rules that should apply to the modelling of water erosion. So called processed

based models attempt to account for the effects of the various forms of erosion and do

consider the effect of runoff on erosivity associated with each form. Particles travel across the

soil surface at virtual velocities that vary from the velocity of the flow to near zero. Little

regard is given to this fact in the determination of soil erodibility values.

Keywords: Soil loss, splash erosion, sheet erosion, rill erosion, interrill erosion, rainfall kinetic energy,

runoff, sediment composition.

Revised 8 Jan 2011

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WATER EROSION: EROSIVITY AND ERODIBILITY

(In Encyclopedia of Environmental Management. Taylor & Francis, New York.,

Published online: 29 May 2013: 980-990)

INTRODUCTION

Conceptually, rainfall erosivity is the capacity of rain to produce erosion where as soil

erodibility is the susceptibility of the soil to be eroded. Historically, the terms erosivity and

erodibility were originally associated with the R and K factors in the Universal Soil Loss

Equation (USLE),

A = R K L S C P (1)

where A is the long term (eg 20 years) annual average soil loss per unit area from sheet and

rill erosion, R is the rainfall (erosivity) factor defined as the average annual value of the

product of the total storm kinetic energy (E) and the maximum 30-minute intensity (I30, twice

the maximum amount of rain that falls in any 30 minute period during a storm), K is the soil

(erodibility) factor, L is the slope length factor, S is the slope gradient factor, C is the crop

(vegetation) and crop management factor, and P is the conservation support practice factor

(Wischmeier and Smith, 1978). Numerically, soil erodibilty is the mass of soil eroded per

unit of the erosive index. This means that numerical values of K can only be used when R is

as it was originally defined, the average annual value of the product of E and I30.

The USLE was designed to predict sheet and rill erosion from field sized areas and only R

and K have units. The L, S, C and P factors each have values of 1.0 for the so called “unit”

plot, a bare fallow area 22.1 m long on a 9 % slope with cultivation up and down the slope.

Consequently, the soil loss for the “unit” plot (A1) is given by

A1 = R K (2)

and, for any other situation,

A = A1 L S C P (3)

Although traditionally K is calculated by dividing A1 by R, basically K can be perceived as

the regression coefficient in the direct relationship between event soil loss on the unit plot

(A1e) and EI30.

To reduce the need to run long term experiments to determine K values for soils where K is

unknown, Wischmeier (1971) developed a nomograph for determining K from soil properties

for soils with less that 70 % silt in the USA. Alternatively, K values in customary US units

for soils where the nomograph can be used may be obtained using

K = (2.1 X11.14

10-4

(12 – X2 ) + 3.25 (X3 – 2) + 2.5 (X4 – 3)) / 100 (4)

where X1 is % silt multiplied by 100 – % clay, X2 is % organic matter, X3 is the soil structure

code used in the US soil classification, and X4 is the profile permeability code. A number of

other equations have been developed for soils at various geographic locations (eg. El-Swaify

and Dangler , 1976; Young and Mutchler, 1976; Loch et al, 1998; Zhang et al., 2008) but Eq.

4 is frequently used outside the USA without being validated for the soils involved.

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The two staged mathematical approach shown by Eqs 2 and 3 results from the fact that the

USLE is an empirically based model. It was developed in the 1960s and 1970s from more

than 10,000 plot years of data. Mathematically, the Revised Universal Soil Loss Equation

(RUSLE, Renard et al (1997)) uses Eqs. 2 and 3 in the same way as the USLE but changes

were made to how some of the factors in the model are calculated. Originally, in the USLE,

the events used to calculate R were restricted to those that produced more than 12.5 mm of

rain or at least 6.25 mm of rain in 15 min. That rule was abandoned in the RUSLE when R

values were calculated for the western part of the USA because it was argued that the rule

had no appreciable effect on R values. Yu (1999) noted that changing the threshold to zero

increased the R factor by 5 % in the tropical region of Australia.

VARIANTS OF THE UNIVERSAL SOIL LOSS EQUATION

Eq.2 operates on the assumption that a direct linear relationship exists between event erosion

(Ae) and EI30. Although this assumption is appropriate at some geographic locations, it is not

appropriate at others (Fig. 1). Soil measured as a loss from the plots used to develop the

USLE was discharged in runoff. When runoff occurs, the amount of soil discharged (Qs) in

the runoff can be considered to be the product of the amount of water discharged (Qw) and the

sediment concentration (cs), the amount of soil per unit quantity of water,

Qs = Qw c (5)

It follows from Eq. 5 that, in the USLE, the sediment concentration is directly proportional to

EI30 divided by runoff amount. However, it has been observed (Kinnell, 2010) that the

sediment concentration for an event at some geographic locations is correlated to the product

of the kinetic energy per unit quantity of rain and I30 (Fig. 2). This results in an event

erosivity index (Re) that is given by

Re = QRe EI30 (6)

where QRe is the runoff ratio (runoff amount divided by rainfall amount) for the event. This

index is more effective in accounting for event soil losses at some locations where that EI30

index does not work well (Fig. 3).

A number of other event erosivity indices have been proposed. Williams (1975)

proposed a modification of the USLE to predict event sediment yield (SYe),

SYe = 11.8 (qe qp)0.56

K L S Ce Pe (7)

where qe is the volume of runoff (m3) for the event, qp is the peak flow rate (m

3/s), K, L, and

S are standard USLE factors, and Ce and Pe are event C and P factors. This model is

commonly known as the Modified Universal Soil Loss Equation (MUSLE). In APEX

(Williams et al, 2008),

SYe = Xe K L S Ce Pe [RKOF] (8)

Xe is selected from

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Xe = EI30 (9a)

Xe = 1.586 (qeqpe)0.56

DA0.12

(9b)

Xe = 0.65 EI30 + 0.45 (qeqpe)0.33

(9c)

Xe = 2.5 (qeqpe)0.5

(9d)

Xe = 0.79 (qeqpe)0.65

DA0.009

(9e)

Xe = b5 qeb6

qpeb7

DAb8

(9f)

where DA is drainage area expressed in ha, b6 – b8 are user selected coefficients (Williams et

al, 2008), and RKOF is the coarse fragment factor as defined by Simanton et al. (1984).

However, Eqs. 7 and 8 with 9b – 9f all use USLE K factor values and not ones that are

associated with the different erosivity indices used and so do not conform with the

mathematical modeling rules upon which the USLE model is based. Consequently, the

MUSLE and APEX models are not valid variations of the USLE. In addition, any model that

uses event erosivity index values that are calculated using runoff from a vegetated area or any

area that is not cultivated up and down the slope will violate the mathematical rules if it uses

USLE C and P factor values.

Mathematical models like the USLE and its derivatives are largely designed to aid

management decisions and operate at a level where spatial and temporal variations in the

various forms of erosion (splash erosion, sheet erosion, rill erosion, interrill erosion) are not

considered in any appreciable detail. However, rill erosion is driven by flow energy while

sheet and interrill erosion are associated more closely with rainfall kinetic energy. In order to

better account for this, Onstad and Foster (1975) used the equation

Re = 0.5EI30 + 0.5α(qe qp)0.333

(10)

Eq. 10 indicates that the sediment concentration for an event (ce) in the data set considered by

Onstad and Foster (1975) is given by

ce = 0.5[EI30/qe] + 0.5[α( qp)0.333

/qe0.666

] (11)

The value of α in Eq. 10 was set so that the long-term average value of Re produced by Eq.

10 was the same as the long-term average value produced when Re = EI30. Given that K is, by

definition, the amount soil loss per unit of R when Re = EI30, this enabled Eq. 10 to be used

with USLE K values to predict soil loss from bare fallow areas. Although Williams et al.

(1984a, b) indicated that Onstad and Foster (1975) was the source of Eq. 9c, there is no

provision in APEX to do the same.

Bagarello et al. (2010) observed that

Re = (QRe EI30)β (12)

with β > 1.0 applied to soil losses from a number of simultaneously operating plots of

different length (λ) established at the experimental station of Sparacia, Sicily. Subsequent

analysis (Bagarello et al. (in review)) established that β > 1.0 appeared to be the result of an

interaction between event runoff (Qe) and slope length (λ) on sediment concentration so that

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Re = QRe EI30 Qe0.0207λ

(13)

when λ is in metres.

Arguably, from a physical viewpoint, since slope length and gradient influence the erosive

stress, they can be considered to be factors that influence erosivity but the USLE model is not

designed to model the physical processes themselves. It is designed to predict rainfall erosion

based on climate, soil, topography, crops and management factors. Normally, in the USLE

model, the effect of slope length on soil loss is expressed through the L factor but in the case

of Eq. 13, L would remain at 1.0 irrespective of variations in slope length. The positive effect

of runoff on sediment concentration may have been associated with the fact that the data were

collected on a 15 % slope. Rainfall erosion on much lower slope gradients is not associated

with as high an erosion stress from runoff as likely to have been the case at the Sparacia site.

In fact, the RUSLE makes provision for the cushioning effect of water depth on the energy of

raindrop impact on low slopes.

RAINFALL KINETIC ENERGY

Data on storm rainfall kinetic energy is not measured at many geographic locations and often,

kinetic energy values are obtained indirectly. If data on storm rainfall intensities are available

then it is common for storm kinetic energies to be estimated from rainfall kinetic energy –

intensity relationships. These relationships are based on raindrop size data collected during

rainfall events at a geographic location assumed to have rainfall characteristics that are

consistent with those at the geographic location of interest. Various techniques have been

employed to do this and these have generated rainfall intensity – kinetic relationships which

are often used at locations which lie outside the climatic zones where the measurements were

originally made. In the USLE, the relationship recommended between the kinetic energy per

unit quantity of rain (e) and rainfall intensity (I) for the USA is expressed by

e = 916 + 331log10 I , for I < 3in/h (14a)

e = 1074 , for I ≥ 3in/h (14b)

where e is in units of ft-ton/acre/in, and I is in in/h, following analysis of drop size data

collected by Laws and Parsons (1943). In the RUSLE, Eq. 14 is replaced by

e = 1099 (1 - 0.72 exp[- 1.27I]) (15)

whose metric equivalent is

em = 0.29 (1 - 0.72 exp[0.05Im]) (16)

where em has units of MJ/ha/mm and Im has units of mm/h. Eqs. 15 and 16 use the

mathematical form proposed by Kinnell (1981, 1987). Yu (1999) observed that replacing Eq.

13 by Eq. 14 reduced the R factor by about 10 % in the tropical region of Australia. A

number of other mathematical equations have been reviewed by van Dijk et al. (2002). Some

of these produce negative values of rainfall kinetic energy at low rainfall intensities. Eq. 16

produces a response curve that increases non-linearly from low values at low intensities with

em values remaining close to 0.29 MJ/ha/mm for intensities beyond 75 – 100 mm/h.

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However, short term values measured during rainstorms vary greatly about the values

produced by Eq. 16 or any other rainfall intensity – e relationship. Also, although Eqs. 15 and

16 were developed for use in the USA, they have been used in other parts of the world

without validation. In many cases, that results in erroneous values. In effect, storm kinetic

energies calculated from rainfall intensity – kinetic energy relationships produce numerical

values that are biased towards high intensity rainfall at the expense of low intensity rainfall.

In many geographic locations, there is a lack of rainfall intensity data so that it is not possible

to determine storm kinetic energies using rainfall kinetic energy – intensity relationships.

Event or daily rainfall amounts are more commonly recorded. One approach that has been

used in a number of geographic areas such as Canada (Bullock et al., 1989), Finland

(Rekolainen and Posch, 1993; Posch and Rekolainen,1993), Italy (Bagarello and D’Asaro,

1994), and Australia (Yu and Rosewell, 1996) considers that EI30 is related to a power of

event rainfall amount, (Xp)

EI30 = a1Xpb1

(17)

where a1 and b1 are empirical constants. The value of a1 may show seasonal variation

(Richardson et al., 1983; Posch and Rekolainen,1993). Given that, in the context of the

criteria associated with the USLE/RUSLE model, daily rainfall provides a reasonable proxy

for storm rainfall amount (Hoyes et al., 2005), Eq. 17 using daily rainfall amount provides a

practical approach to extending observed EI30 values to areas where appropriate rainfall

intensity data are lacking.

MORE PROCESS BASED MODELS

Although the USLE/RUSLE is the most widely used method of predicting soil losses from

the land worldwide, rainfall erosion results from various forms of erosion (splash erosion,

sheet erosion, rill erosion, interrill erosion) that are driven by different forces so that there is

no absolute measure of either rainfall erosivity or soil erodibility. Consequently, more

process based models have been developed in order to predict the contributions of the various

forms of erosion more directly. Often, the forms vary in a topographic sequence with splash

erosion dominating erosion at the upper end of a slope, sheet erosion further down before

areas of rill and interrill erosion. Particles detached at the top of the slope may be transported

by a number of different transport mechanisms before being finally discharged from the

eroding area. The Water Erosion Prediction Program in the USA generated the WEPP model,

a more process based model than the USLE/RUSLE designed to model the spatial

contributions of rill and interrill erosion in agricultural landscapes (Flanagan and Nearing,

1995). Flow Shear stress (τ) is used as the erosivity factor in rill erosion model,

Dr = kr (τ - τc) ( 1 – qsr / Tr) , τ > τc (18)

where Dr is rill detachment, kr is the rill erodibility factor, τc is the critical shear stress that

has to be exceeded before detachment occurs, qsr is the sediment load in the flow, and Tcr is

the sediment load at the transport limit. For erosion to occur, particles must be plucked from

within the soil surface where they are held by cohesion and inter-particle friction.

Detachment is the term used to refer to this process. For detachment in rills to occur, the flow

must have shear stress that exceeds τc. Also, for erosion to occur, detached particles must be

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transported away from the site of detachment. Flows are known to have a limited capacity to

transport soil material and that limit is represented by Tr in Eq. 18. Consequently, the term 1

– qsr / Tr causes Dr = 0 when the sediment load in the rill equals the transport limit. As a

result, Dr may vary along the length of a rill. Interrill erosion contributes to qsr so that rill

erosion may be completely suppressed if the discharge of sediment from the interrill areas is

high enough.

Originally, the erosivity factor in the WEPP interrill model was assumed to be the square of

rainfall intensity (I) so that basically

Di = ki I2 (19)

where Di is interrill detachment and ki is the interrill soil erodibility factor. A series of rainfall

simulation experiments (Elliot et al, 1989) was undertaken to determine ki values for soils in

the USA. Subsequent analysis (Kinnell, 1993) of the data generated by these experiments

established that it was more appropriate to use

Di = kiq qi I (20)

where qi is the runoff rate from the interrill area, and kiq is the interrill erodibility factor. The

ki values determined using Eq. 19 cannot be used in Eq. 20 (Kinnell, 1993).

Di is determined using data on the amounts of soil material discharged from interrill areas.

The use of the term “detachment” in relation to Di is not absolutely correct because the

transport processes involved in moving soil material over interrill areas are not 100 %

efficient. Also, detachment varies with raindrop size and velocity but, in using Eq.20, that

effect is ignored. However, provision is made in WEPP to take account of differences in drop

size distribution associated with different rainfall simulators in experiments designed to

determine values of kiq.

Eqs. 18 and 20 provide the basic equations that enable WEPP to model the contributions of

rill and interrill erosion to soil loss more directly than when USLE/RUSLE model is used but,

in WEPP, the spatial distribution of rill and interrill areas needs to be well defined. WEPP

was originally designed to operate in situations where ridge tillage is used. With ridge tillage,

interrill erosion is well defined as being on the ridge slopes and rill erosion in the furrows. In

other situations, the distributions of rill and interrill areas is more difficult to specify. In

rangelands, broad areas of surface water flow occur more commonly than rills so that splash

and sheet erosion dominate. An alternative to the WEPP cropland interrill erosion model,

Dss = kss I1.05

qss 0.59

(21)

where DSS “detachment” associated with splash and sheet erosion, kss is the erodibility factor

and qss is the runoff rate from the associated eroding surface, has been developed for use in

rangelands (Wei et al.,2009).

EUROSEM is another erosion model that is more process based than the USLE/RUSLE. In

EUROSEM, detachment by raindrop impact (Dr) is modeled using

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kD

Dr = _____

KE exp (-zh) (22)

ρs

were kD is an index of detachability that is determined experimentally, ρs is particle density,

KE is the rainfall kinetic energy of the raindrops impacting the ground, z is a factor that

varies with soil texture, and h is the mean depth of the water layer on the soil surface.

Detachment by flow is modeled using

Df = β w vs (CT – C) (23)

where β is an index of detachability, w is flow width, vs is particle settling velocity, C is the

sediment concentration, and CT is the sediment concentration at the transport capacity of the

flow.

The coefficients used in Eq. 22 result from measurement of soil material transported by

splash under ponded conditions in the experiments of Torri et al. (1987) where increases in

water depth were observed to reduce splash erosion. The effect of water depth on splash

erosion results from (a) dissipation of raindrop energy in the water layer and (b) the effect of

water depth on splash trajectories. Considering that splash does not transport 100 % of the

material detached by raindrops impacting water, Eq. 22 does not actually model detachment.

Also, erosion by rain-impacted flows where sediment is transported by rolling, saltation and

suspension in the flow is the real focus of Eq. 22 and the effect of flow depth on erosion by

rain-impacted flows is quite different to its effect on splash erosion (Kinnell, 2005).

As a general rule, the values of soil erodibility factors have to be determined experimentally

although there are cases where they are predicted from soil properties. In areas where

detachment results from raindrop impact, erodibility is affected by modification of the soil

surface generated by the impacts. Raindrop impacts on surfaces not covered by water may

break soil aggregates and generate surface crusts which affect soil erodibility. In areas where

soil crusts occur, particles are held more tightly within the soil surface than in areas that are

not crusted and this reduces detachment. With splash erosion, loose particles sit and wait on

the soil surface between drop impacts. The transport efficiency of splash increases with slope

gradient but, over time, a layer of loose particles builds up on the soil surface and energy has

to be expended in moving them before detachment can occur. Consequently, this layer

provides a degree of protection against detachment. When raindrops impact a soil surface

covered by water, the protection provided by loose particles sitting on the surface is in

addition to that provided as the result of the dissipation of raindrop energy in the water layer.

Although splash erosion may dominate erosion for considerable periods during a rainfall

event, rain-impacted flows are usually more important in moving soil material across the soil

surface because the transport mechanisms in rain-impacted flows are much more efficient

than splash transport. In rain-impacted flows, particles move across the soil surface by

rolling, saltation and in complete suspension. Shallow low velocity flows often do not have

the capacity to cause particles to move by rolling and saltation by themselves but rolling and

saltation can be stimulated to occur when raindrops impact the soil surface through the flow.

Under these circumstances, each rolling or saltation event is of limited duration and is

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associated with individual raindrop impacts. Fig.4 illustrates how raindrop and flow factors

influence the detachment and transport processes associated with the erosion of fine particles,

silt and sand by rainfall. Particles moving by raindrop induced rolling and saltation move

across the surface at rates that depend on raindrop size, impact frequency, particle size and

density and the velocity of the flow. Consequently, depending on the rain and flow

conditions, particles in rain impacted flows travel across the surface at virtual velocities that

vary from near zero to the velocity of the flow. In effect, particles are winnowed from the soil

surface at various rates. Large gravel particles may not move at all and so, over time, soils

that have high gravel contents may become highly resistant to erosion through the formation

of erosion “pavements”. Particles moving by raindrop induced rolling and saltation sit on the

soil surface between drop impacts and so provide a degree of protection against detachment

as described in the case of splash erosion. As a result, soil resistance to erosion may vary

considerably during a rainfall event. If H is the degree of protection provided by the loose

material, then all the material discharged from the soil surface comes from the layer of loose

material when H = 1.0. Consequently, it follows from Eq. 20 that, for any given rainfall

event,

Di = (kiq.U (1 – H) + H kiq.P) qi I (24)

where kiq.U is the interrill erodibility factor when no loose material exists on the surface and

kiq.P is the soil erodibility factor when loose material completely protects the soil surface from

detachment. As noted earlier, detachment of soil particles from a cohesive surface varies with

cohesion and interparticle friction so that factors such as the development of surface crusts

can cause kiq.U to vary with time. The soil erodibility term in Eq. 24 is kiq.U (1 – H) + H kiq.P

and values of kiq obtained in rainfall simulator experiments like those undertaken by Elliott et

al (1989) lie between kiq.U and kiq.P. Where exactly they do lie is unknown because H is

unknown.

THE EFFECT OF PARTICLE TRAVEL RATES ON

SEDIMENT COMPOSITION AND ERODIBILITY

As noted above, erodibilities have units of soil loss per unit of the erosivity index used in the

model that is being considered in the analysis of the data. Factors such as cohesion, particle

size and aggregates stability have been observed to influence these erodibilities. Data on the

physical and chemical nature of the soil involved may, in some cases, be used to predict

erodibility but often little attention is given to the composition of the sediment discharged in

experiments undertaken to determine erodibility.

The composition of the soil transported from an eroding area by rain-impacted flow during an

experiment tends to be finer than the original soil (eg. Meyer et al., 1980; Miller and

Baharuddin, 1987; Palis et al, 1990; Parsons et al., 2006) and particle travel rate is one of the

factors influencing sediment composition. Fast moving particles detached at the top of an

eroding area arrive at the downstream boundary well before slow moving particles detached

at the same place at the same time. Consequently, once sediment transport in rain-impacted

flow starts, the fine material dominates the early discharge of sediment but the composition

of the sediment becomes coarser with time as the more of the slower moving particles reach

to downstream boundary. If the particles are stable, then at the steady state, the composition

of the sediment discharge must be the same both physically and chemically as the original

soil. This is demonstrated by the results of laboratory experiments on erosion of sand by rain-

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impacted flows by undertaken by Walker et al (1978). In these experiments, 3 m long sloping

beds of sand were eroded for 1 hour by rain-impacted flows generated by artificial rain at

three rainfall intensities (45, 100 and 150 mm/h). The data shown in Fig. 5 were generated by

rain made up of a single drop size (2.7 mm) falling on rain generated flows over beds of sand

with 2 different slope gradients (5 %, 0.5 %). The least erosive situation is the case where 45

mm/h rain fell when the slope gradient was 0.5 %. The most erosive situation is the case

where 150 mm/h rain fell when the gradient was 5 %. The enrichment factor is the ratio of

the proportion of the material in the sediment discharge to the proportion in the original

material. In all cases, the discharge of sediment was dominated by fine material at 2 minutes

and, in some cases, coarse material at 1 hour (Fig. 5). In the most erosive situation (150 mm/h

rain falling on 5 %.slope ), the sediment composition at 1 hour was close to the composition

for the steady state, the composition that occurs when the enrichment factor for all particles

sizes equals 1.0. Sediment composition generated by the rain impacted flows varies with the

intensity of the rain, the slope gradient, slope length and time because particles of different

size and density travel at different rates. The differential rate of transport of particles in rain-

impacted flows has consequences with respect to erodibility because the actual area

contributing to the soil loss does not stabilize until the slowest moving particles detached at

the farthest point from downslope boundary at the start of the rainfall event are discharged.

This fact is seldom considered when experiments are undertaken to determine erodibility.

Eq. 24 is essentially targeted at situations where raindrop induced saltation controls sediment

discharge in situations like that illustrated in Fig. 6A. Particles of silt and sand may travel

over the soil surface in more than one mode before being discharged. For example, as may be

perceived from Fig. 6B, they may leave the point of detachment traveling in splash (ST), then

move further downslope by raindrop induced saltation (RIS) and finally by flow driven

saltation (FDS) as flow energy increases down the slope. Transitions between raindrop

induced saltation and flow driven saltation may vary in time and space during a rainfall event

and will depend on the intensity of the rain, the infiltration characteristics of the soil, the

length of the slope and the slope gradient. The effect of the transition can have an appreciable

effect on both soil loss and the composition of the sediment discharged. Fig. 7B shows

modeled flow velocities at the brink (discharge boundary) of planar bare soil surfaces of

various length on a 9 % slope resulting from the rainfall event shown in Fig. 7A. Fig. 8 shows

the loss of materials of various size and density from those bare soil surfaces when a

mechanistic model of erosion by rain-impacted flow was used by Kinnell (2009). For the

surfaces up 15 m in length, particles larger than 0.1 mm in size traveled over the whole length

by raindrop induced saltation. Under these conditions more of the 0.11 mm sand was lost

during the event that 0.46 mm coal. On the 20 m long area, 0.46 mm coal which had been

traveling slower than 0.11 sand on shorter areas, traveled for a short period of time by flow

driven saltation during the high intensity bursts of rain and, as a result, more of the 0.46 mm

coal was lost than the 0.11 mm sand. On areas 25 m long and more, flow driven saltation also

contributed to the discharge of 0.11 mm sand but the amount lost was always less than the

amount of 0.46 mm coal. Little regard is given to the effect of temporal and spatial changes

in transport mechanism when experiments are undertaken to determine values for soil

erodibility factors in sheet and interrill erosion areas even though these changes may have a

major impact on the amount of soil lost from an area.

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CONCLUSION

Although conceptually, rainfall erosivity is the capacity of rain to produce erosion where as

soil erodibility is the susceptibility of the soil to be eroded, the factors controlling the erosive

stress applied to the soil surface and the factors influencing the resistance of the soil to them

vary in time and space in complex ways. In all existing predictive models of rainfall erosion,

numerous simplifications and assumptions have to be made for practical reasons and, as a

result, these models do not have the capacity to deal with such complexity. Consequently,

erosivity and erodibility values are specific to the model in which they are parameterised and

to the scale that the model operates within.

REFERENCES

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American Society of Agricultural Engineers 1994, 37 , 785–791.

Bargarello, V. Di Stefano; C., Ferro, V., Kinnell, P.I.A, Pampalone, V.; Porto, P.; Todisco, V.

Predicting soil loss on moderate slopes using an empirical model for sediment concentration.

In review. Hydrological Processes 2010.

Bullock, P.R.; de Jong, E.; and Kiss, J.J... An assessment of rainfall erosion potential in

southern Saskatcheuian , from daily rainfall records. Canadian Agricultural Engineering

1987, 29, 109-115

Elliot, W.J.; Liebenow, A.M.; Laflen, J.M.; Kohl, K.D. A compendium of soil

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14

Figure Captions

Figure 1. The relationships between event erosion (Ae) and EI30 obtained on bare fallow plots

in the USA: (A) Plot 5 Experiment 3 at Holly Springs, MS and (B) Plot 5 Experiment 1 at

Morris, MN. Eff(ln) is the Nash–Sutcliffe (1970) efficiency factor for logarithmic transforms

of the data.

Figure 2. The relationship between event sedment concentration (ce) and the product of I30

and the kinetic energy per unit quantity of rain (E / re) for Plot 5 Experiment 1 at Morris, MN.

Figure 3. The relationship between event erosion and the product of event runoff ratio (QRe)

and EI30 for Plot 5 Experiment 1 at Morris, MN.

Figure 4. Schematic of how variations raindrop kinetic energy and flow shear stress affect the

detachment and transport of silt, sand and fine particles during rainfall erosion. Ec is the

critical raindrop kinetic energy required to cause raindrop detachment (RD). Its variation

during rain with no runoff signifies changes in resistance to detachment caused by, for

example, the development of a soil crust. Its variation with flow shear stress signifies the

cushioning effect of increasing water depths. τc(bound) is the critical shear stress required to

cause flow detachment (FD). τc(loose) is the critical shear stress required to cause flow driven

saltation (FDS). FS is continuous suspension in the flow. RIS is raindrop induced saltation.

ST is splash transport.

Figure 5. Enrichment factor curves at for sediment discharged at 2 minutes and 60 minutes

when beds of sand were eroded by rain impacted flows in experiments undertaken by Walker

et al (1978) using 2.7 mm raindrops. (Extracted from Figure 3 of Walker et al (1978)).

Figure 6. Schematic representation of how detachment and transport processes associated

with rainfall erosion may vary spatially on planar inclined bare soil surfaces.

Figure 7. Brink (downstream boundary) flow velocities (B) for bare soil of various lengths

inclined at 9 % produced by the rainfall-runoff model described by Moore and Kinnell (1987)

and the rainfall intensities recorded during a rainfall event at the Ginninderra Experiment

Station, Canberra, Australia (A).

Figure 8. Amounts of coal, sand and fine particles discharged for the rainfall and runoff

conditions shown in Figure 7 when a mechanistic model of erosion by rain-impacted flow

was used by Kinnell (2009).

15

0.01

0.1

1

10

100

0.01 0.1 1 10 100observed event soil loss (t/ha)

soil loss estimated by R

e = EI 30 (t/ha)

1 : 1

Eff(ln) = 0.592

1

2

3

4

Ae = 0.0302 EI30 5 6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

45

46

Figure 1 47

48

49

50

0.01

0.1

1

10

100

0.01 0.1 1 10 100

observed event soil loss (t/ha)

soil loss estimited by R

e = EI 30 (t/ha)

1 : 1

Eff(ln) = 0.007

Ae = 0.0203 EI30

A

B

16

1

2

0.01

0.1

1

10

0.01 0.1 1 10

observed event sediment concentration (t/ha/mm)

estimated sedim

ent concentration (t/ha/m

m)

Eff(ln) = 0.303

1 : 1

3 4

5

Figure 2 6

7

ce = 0.0839 I30 (E / re)

17

1

0.01

0.1

1

10

100

0.01 0.1 1 10 100

observed event soil loss (t/ha)

estimated soil loss (t/ha)

Eff(ln) = 0.835

1 : 1

2 3

4

5

Figure 3. 6

7

Ae = 0.0839 QRe EI30

18

RAIN WITH

NO RUNOFF

RAIN WITH

RUNOFF

Fine Particles

RD-FS

Silt & Sand

RD-RIS

Silt & Sand

RD-FDS

Clay, Silt & Sand

RD-ST

Clay, Silt & Sand

FD-FDS,FS

NO EROSION E < Ec, τ < τc (bound)

A B

0

Ec Ec

0 τc (bound) τc (loose)

Raindrop

Energy (E)

Flow Shear Stress (τ) RAIN WITH

NO RUNOFF

1

3

5

7

9

11

13

15

17

19

21

23

25

27

29

31

33

35

37

39

41

43

45

46

47

48

49

Figure 4 50

51

19

1

2

3

4

5

6

7

8

9

10

11 12

13

14

Figure 5 15

16

17

18

19

20

20

1

2

3

4

5

6 7

8

Figure 6 9

10

11

12

13

14

RD - ST

RD – ST

RD – RIS

RD – RIS

RD - ST

RD – ST

RD – RIS

RD – RIS

RD – FDS

A B

RD - ST

RD – ST

RD – RIS

RD – RIS

RD – FDS

RD – FDS

FD – FDS

C

Flow

21

0

25

50

75

100

125

150

0 20 40 60 80 100 120 140

time (mins)

rainfall intensity (mm/h)

0

50

100

150

200

250

0 20 40 60 80 100 120 140

time (mins)

brink velocity (mm/s)

2 m5 m10 m15 m20 m25 m30 m

9% slope

critical for FDS of coal

1

2

3

4

A 5

6

7

8

9

10

11

12

13

Figure 7A 14

15

16

17

18

19

20

21

22

23

24

25

B 26

27

28

29

30

31

32

33

34

35

36

37

38

39

40

41

42

43

44

Figure 7. 45

46

22

1

2

0

5000

10000

15000

20000

25000

0 5 10 15 20 25 30 35

plot length (m)

coal and sand discharged

during event (g/m

)

0

500

1000

1500

2000

fine sedim

ent discharged

during event (g/m

)

coal p=0.11 p=0.2 p=0.46 p=0.9 fine

3 4

Figure 8 5

6

7

8

9

10