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HYDROLOGICAL PROCESSES

Hydrol. Process. 19, 851–854 (2005)

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/hyp.5816

INVITED COMMENTARY

Why the universal soil loss equation and the revised

version of it do not predict event erosion well

P. I. A. Kinnell*

School of Resource, Environmental

and Heritage Sciences, University

of Canberra, Canberra ACT

2601 Australia

*Correspondence to:

P. I. A. Kinnell, School of

Resource, Environmental and

Heritage Sciences, University of

Canberra, Canberra ACT 2601,

Australia.

E-mail:

peter.kinnell@canberra.edu.au

Introduction

The universal soil loss equation (USLE; Wischmeier and Smith,

1978) and its revised version (RUSLE; Renard et al., 1997) were

developed to predict the long-term average annual erosion A from

field-sized areas from six factors: R the rainfall-runoff (erosivity)

factor, K the soil (erodibility) factor, L the slope length factor, S

the slope gradient factor, C the crop and management factor and P

the conservation support practice factor. The USLE/RUSLE model

is often represented by the equation

A = RKLSCP(1)

where R is the average annual sum of the event rainfall-runoff

(erosivity) factor when this factor is given by the product of the

kinetic energy of the rainstorm E and the maximum 30 min rainfall

intensity I30, L = S = C = P = 1·0 when the area is bare fallow on

a 9% slope that is 22·13 m long with cultivation up and down the

slope, and K is the average annual soil loss per unit of R when

L = S = C = P = 1·0.

Although the USLE/RUSLE model was not designed to predict

event erosion, it can be suggested that erosion for a rainfall event

Aeis given by

Ae= EI30KeLSCePe

(2)

where the subscript ‘e’ indicates parameter values that vary between

rainfall events. For a bare fallow plot with cultivation up and

down the slope, Ce= Pe= 1·0. Also, Keis, in the case of the USLE,

considered not to vary with time, so that Ke= K. As a result, the

relationship between Aeand EI30can be expected to be to be given

by

Ae= bEI30

(3)

a linear equation that passes though the origin with b being a

coefficient. This expectation is not achieved in, for example, the case

of a bare fallow plot at Morris, MN (Figure 1), which is part of the

USLE/RUSLE database.

The Runoff Problem

One problem with the USLE/RUSLE model is that there is no direct

consideration of runoff even though erosion depends on sediment

Received 01 November 2004

Accepted 18 November 2004

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P. I. A. KINNELL

0.01

0.01

0.1

1

10

100

0.1110100

observed soil loss (t/ha)

predicted soil loss (t/ha)

Re = EI30

Zln = 0.084

Figure 1. Relationship between observed and predicted event soil loss for plot 10 (bare fallow) in experiment 1 at Morris, MN, when

predicted loss is bRe, where Reis EI30. The line shows where observed and predicted values are equal. Zlnis the Nash and Sutcliffe

(1970) efficiency factor for logarithmic transforms of the data. A value of zero indicates that the model is no better at predicting

the observed data than using the mean

being discharged with flow qs, which varies with

runoff qwand sediment concentration cs:

qs= qwcs

(4)

Given a capacity to determine runoff, and the

fact that sediment concentration is, at the plot

scale, dependent on the rate of expenditure of rain-

fall kinetic energy, it follows that csvaries with the

kinetic energy level of a rainstorm (kinetic energy

per unit quantity of rain) and some measure of

rainfall intensity. Assuming that I30is an appro-

priate measure of the intensity (Kinnell and Risse,

1998), the sediment concentration for an event cse

is given by

cse=kEI30

Be

(5)

where Beis rainfall amount for the event and k is

a coefficient, so that

qs=kqwEI30

Be

(6)

As shown in Figure 2, this approach results in an

increased capacity to predict event loss on the bare

fallow at Morris, MN.

Failure of the USLE/RUSLE model to include

direct consideration of runoff leads to systematic

errors in the prediction of event erosion.

0.01

0.1

1

10

100

0.010.11 10100

observed soil loss (t/ha)

predicted soil loss (t/ha)

Re = qw EI30/Be

Zln = 0.878

Figure 2. Relationship between observed and predicted event soil

loss for plot 10 (bare fallow) in experiment 1 at Morris, MN,

when predicted loss is kRewhere Re= qwEI30/Be

The USLE/RUSLE Model Structure Problem

Although the USLE/RUSLE model is described

by Equation (1), it operates in a two-stage way.

Because the L, S, C and P factors are ratios with

respect to the bare fallow cultivation up and down

the slope condition on a 9% 22·13 m slope, the

USLE/RUSLE model operates as

A1= RK(6a)

A = A1LSCP(6b)

Thus, Equation (2) operates as

A1e= KeEI30

(7a)

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Hydrol. Process. 19, 851–854 (2005)

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INVITED COMMENTARY

Ae= A1eLSCePe

(7b)

Although Equation (7a) can be replaced by an

equation that predicts A1e better, that in itself

does not mean that event erosion will then be pre-

dicted on a cropped area more reliably by the

combination of that equation and Equation (7b).

The problem with Equation (7b) is that it oper-

ates on the assumption that erosion occurs on

the vegetated area whenever erosion occurs on

the bare fallow area, and that is not true. This

is well illustrated by Figure 3, where A1e values

were measured on an adjacent bare fallow plot

and used with Equation (7b) to predict event losses

on a cropped plot. The approach results in signifi-

cant amounts of erosion being predicted for many

events that did not produce erosion on the vege-

tated plot.

The Impact on Predicting Long-Term

Erosion

It has been observed that the USLE/RUSLE over-

predicts low annual average erosion and under-

predicts high average erosion (Risse et al., 1993;

Rapp et al., 2001). It follows from Figures 1, 2

and 3 that the failure to consider runoff explic-

itly in the model is a factor in producing such

errors. Erosion is a hydrologically driven process

and runoff is a factor that is considered explicitly

in more process-based models like WEPP (Nearing

0.01

0.0001 0.001

observed event soil loss + 0.0001 (t/acre)

0.1

1

10

100

0.01 0.11 10100

predicted event soil loss (t/acre)

Figure 3. Relationship between event soil losses predicted by

multiplying event soil losses from a nearby bare fallow plot by

RUSLE-period soil loss ratios (fortnightly C factor values) and

event soil losses observed for conventional corn at Clarinda, IA,

plus 0·0001 tons acre−1to enable predicted losses to be displayed

when observed losses are zero

et al., 1989) and EUROSEM (Morgan et al., 1998).

However, if, for example, direct consideration of

runoff is used to enhance the prediction of event

soil loss and, in recognition of the problem associ-

ated with Equation (7b), runoff from the vegetated

area in determining event erosivity for the veg-

etated area is used rather than for bare fallow,

then values for the crop and management effect

and the conservation practice factor differ from

the Ceand Pevalues (Kinnell, 2003). However, if

erosion is considered on an average annual basis,

then Equation (6b) applies if R is not EI30and K is

determined with respect to that fact. For example,

consider the case of the event erosivity index used

in the USLE-M (Kinnell and Risse, 1998—which

is numerically the same as the product of runoff,

kinetic energy level and I30considered in Figure 2)

the annual average erosivity for the bare fallow

cultivation up and down the slope condition is

given by

n

?

RUM1=

i=1

QR1iEI30i

Y

(8)

where QR1i is the runoff ratio for the bare fallow

cultivation up and down the slope condition for

event i, n is the number of rainfall events that

occurred in Y years and the erodibility index is

given by

KUM=

A1

RUM1

(9)

This results in

A1= RUM1KUM

(10)

and so

A = RUM1KUMLSCP(11)

This is because the product of erosivity and erodi-

bility factors is directed at predicting A1no matter

what parameters are involved in determining the

event erosivity index, and, on an average annual

basis, erosion on a vegetated area will occur when

C > 0. Consequently, the condition that A > 0 will

occur when A1> 0 will be met. Also, the condi-

tion that erosion occurs on both bare and vegetated

areas will almost certainly be met on a yearly basis

in most locations, so that

AA= RUM1·AKUMLSCAPA

(12)

Copyright 2005 John Wiley & Sons, Ltd.

853

Hydrol. Process. 19, 851–854 (2005)

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P. I. A. KINNELL

where AA is the soil loss for a given year, CA

and PAare the C and P factors, and RUM1·Athe

sum of the product of QR1i and EI30i, for that

year, respectively. RUM1·Ais given by Equation (8)

when Y = 1 and n is the number of events in a

given year. Equation (12) provides an approach

that reduces the tendency for overprediction of low

annual erosion and underprediction of high annual

erosion.

Although including the runoff as an indepen-

dent factor in modelling erosion can be shown to

improve the accuracy of the USLE/RUSLE, the

prediction of erosion then requires runoff to be

predicted with an acceptable degree of accuracy.

There are a number of procedures for predict-

ing runoff, and the USDA curve number method

(USDA, 1972) is used in water quality models like

AGNPS (Young et al., 1987) and SWAT (Arnold

et al., 1998). However, it has been argued (Nearing,

2000) that the level of accuracy by which runoff

can be predicted is not sufficient for models like the

USLE-M to replace the USLE/RUSLE. Although

the matter of runoff prediction may be a matter for

debate, the fact remains that the failure to consider

runoff as a primary factor in the USLE/RUSLE

model is a factor in causing the USLE/RUSLE

to produce systematic errors in the prediction of

event erosion, which in turn leads to systematic

errors in predicting average annual soil loss.

References

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