A probabilistic approach for predicting rainfall soil erosion losses in semiarid areas

Ž .Catena 40 2000 403–420www.elsevier.comrlocatercatena

A probabilistic approach for predicting rainfall soilerosion losses in semiarid areas

C.M. Mannaerts a,), D. Gabriels b,1

a DiÕision of Water Resources and EnÕironmental Studies, International Institute of Aerospace SurÕeys andEarth Sciences ITC, PO Box 6, 7500 AA Enschede, Netherlands

b Department of Soil Management and Soil Care, Faculty of Applied Biological and Agricultural Sciences,UniÕersity of Gent, Coupure Links 653, B-9000 Gent, Belgium and Fund for Scientific Research,

Flanders, Netherlands

Received 24 September 1999; received in revised form 8 February 2000; accepted 9 February 2000

Abstract

The implementation of soil and water conservation structures in semiarid areas, usually poses adifficult design problem. This is, in large part, due to the high variability of rainfall and the hugepotential impact of extreme hydrologic events on structures and on the landscape in general.Magnitudes of runoff and soil loss or sedimentation rates in those environments are better notassessed by conventional modelling techniques, which tend to average out event magnitude andrecurrence variability in time and space. A probability-based approach is proposed here to analyseand predict rainfall erosion losses. The maximum annual storm and its associated erosivity is usedas a core element in the assessment of annual interrill and rill erosion rates. Frequency andcumulative soil loss distributions are obtained by combining verified annual and maximum dailyrainfall frequency distributions with a proposed erosion algorithm. This stochastic representationof erosion permits to evaluate soil losses for the maximum annual storm, as well as annual erosionrates as a function of recurrence interval. The proposed method was verified with a short series ofmeasured soil loss data in Cape Verde. The physical basis underlying the prediction algorithm andmethod in general, could be sustained by experimental data and field survey evidence. The methodseems applicable to arid and semiarid ecosystems with a high seasonal concentration of precipita-tion and with rainfall limited to only a few major storm events. q 2000 Elsevier Science B.V. Allrights reserved.

Keywords: Soil erosion; Extreme events; Probability distributions; Semiarid; Volcanic soils

) Corresponding author. Tel.: q31-53-487-42-10; fax: q31-53-487-4336.Ž . Ž .E-mail addresses: [email protected] C.M. Mannaerts , [email protected] D. Gabriels .

1 Tel.: q32-9-264-60-50; fax: q32-9-264-52-47.

0341-8162r00r$ - see front matter q2000 Elsevier Science B.V. All rights reserved.Ž .PII: S0341-8162 00 00089-8

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1. Introduction

Many commonly used soil loss prediction methods use statistical averaging tech-Ž .niques McCuen and Snyder, 1986 to obtain annual soil loss values for a given set of

environmental conditions. The mean is generally used to express the prevailing ornormal value of soil loss that can be expected annually. Prediction of mean annualvalues is useful and permitted in areas where annual rainfall tends to follow a normalprobability distribution. In arid and semiarid zones, annual rainfall distributions typicallyshow a pronounced skew and correspond better to lognormal, extreme value or Pearson

Ž .Type III probability density functions FAO, 1981 . As a consequence, averagingtechniques, based on normal event probability, are of limited value for describingrainfall recurrences in semiarid areas. In contrast to temperate regions, semiarid ecosys-tems are also more impacted by extreme events, such as severe storms, floods and

Ž .droughts Ven Te Chow et al., 1988 . The magnitude of hydrological events is inverselyrelated to its recurrence interval. The soil and water conservationist is usually moreinterested in flood or erosion damage caused by large events then the hazard containedin the more numerous smaller hydrological events. From a practical standpoint ofsedimentation engineering however, knowledge of both peak erosion rates and annualtotals of soil loss or sediment yields is necessary. They are required for the design ofterraces, check dam volumes and reservoir dead storage. The relative contributions oflarge and small storms to total annual soil loss must therefore be evaluated . Adding aprobability of recurrence to erosion events can therefore be considered essential forsuccessful erosion assessment in semiarid zones.

In semiarid regions, the general paucity of experimental runoff or erosion data, can bein part explained by the limited number of events. Soil productivity decline due toerosion and sedimentation problems are, however, important in those areas, as shown by

Ž .multiple sources Hudson, 1971; Roose, 1975; Ziemer et al., 1990 . Rainfall data areusually more commonly available in both time and space. The concept of usinglong-term climate data for a stochastic representation of hydrologic phenomena is wellknown. Rainfall vs. runoff and flood forecasting, based on statistical frequency analysis,

Ž . Žhas long been described ECAFE, 1966 and put into hydrologic practice Maidment,.1993 . The use of probability techniques in soil erosion studies is relatively limited. It

Žwas, to a certain extent, overshadowed by the USLE framework Wischmeier and Smith,.1978 , which dominated soil erosion assessment until recently. Only a few researchers,

Ž . Ž . Ž .i.e., Istok and Boersma, 1986 , Mills et al. 1986 and more recently Mannaerts 1992 ,Ž . Ž . Ž .Flanagan and Nearing 1995 , Hession et al. 1996 and Baffaut et al. 1998 applied the

probability concept to assess soil loss. Most authors used the concept to analysecumulative soil losses under fairly normally distributed rainfall or runoff event occur-rence. The principle may well prove to be most convenient in more arid regions, where

Ž .statistical averaging McCuen and Snyder, 1986 can be ‘‘a priori’’ excluded, because ofthe bias in representing the main distribution parameters. In this study, the extreme valuetheory was used to account for lognormality and a skewed event frequency distributionof rainfall and erosion phenomena. In fact, the statistical distribution parameters of therainfall series are used to generate a soil loss probability distribution. By doing so, the

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Fig. 1. Location map of the Cape Verde Islands and study area.

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Table 1Experimental site and plot characteristics used in the study

aSite Lithology Soil taxonomy No. of Slope Slope length Plot surface conditions Bare soilb w x w x w xplots % m %

Achada das Vacas MV1 basanite Lithic 2 7 5 natural vegetation 84Camborhid 2 14 5 bare, gravels 75

Achada das Vacas MV2 basanite Lithic 2 7 5 natural vegetation 72Torriorthent 2 14 5 bare, gravels 65

Achada San Felipe SF3 alkaline Ustertic 2 3 5 natural vegetation 86Ž .basalt Haplargid – – – stoney basalt –

aSee Rittmann, 1963.b Ž . Ž .Experimental plot operation MV1 and MV2 from 1981 to 1986 , SF3 from 1981 to 1983 .

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experimental soil erosion data gap, so common in semiarid regions, can to a certainextent be overcome, resulting in a better prediction of erosion rates.

2. Study area and data

Experimental rainfall, soil and erosion data for this study originate from the CapeVerde islands, a mountainous archipelago of volcanic origin, located 500 km west of the

Ž .African west coast in the Central-east Atlantic Fig. 1 . The Achada das Vacas–SanFelipe study site is located in Santiago island, 8 km north of Praia, the capital of CapeVerde. Geographical coordinates of the study location are 14859X N and 23845X W, withelevations ranging from 200 to 250 m asl. The experimental plots were located on a

Ž .south facing dissected basalt plateau slope gradient: 0.1–3% , of tertiary Miocene–Ž .Pliocene origin Machado, 1967 . Soils are derived from an alkaline basalt–basanite

volcanic rock series and can be classified, according to the USDA soil taxonomyŽ .USDA, 1975 in the Torriorthent, Haplargid, Camborthid and Torrifluvent great groups,depending on their geomorphologic position in the landscape and underlying bedrock.Soils are usually quite shallow, loamy to clayey and skeletal with important presence ofcoarse fragments in the profile, as well as on the surface. The importance of stone coverand rock fragments on the generation of runoff and erosion has been shown by various

Ž .authors Poesen et al., 1990 . The study area, including the experimental runoff plots,Ž .can be typed as semiarid rangeland Scetagri, 1981 , representing undisturbed soil

Ž .surfaces. With natural vegetation species such as, e.g., Faidherbia albida almost absentat the end of the seventies, the study site was reforested in the period from 1980 to 1984,with mainly Prosopis, Acacia and other drought resistant tree species. Water harvesting

Ž .techniques were used to provide rainfall runoff to the plantations Mannaerts, 1985 . Theclimate of the study area is distinctly semiarid according to conventional climate

Ž .classification systems such as Koppen or Thornthwaite Landon,1984 . Mean annual¨rainfall, air temperature and relative humidity are respectively 256 mm, 23.18C and69%. Rainfall in the study area and Cape Verde in general, is governed by the seasonalmovements of the Mid-Atlantic Intertropical Convergence Zone, and is entirely concen-

Table 2Soil properties and erodibility parameters used in study a

b b c d dw xSiter Percentages % Soil texture Coarse OM BD K K Kd US SIb y3 y1w x w x w xplot fragments % kg m kg kJClay Silt Sand

w x%3MV1 19.9 47.4 32.6 Loam 21.0 2.1 1.21=10 0.61 0.31 0.0413MV2 37.8 40.4 21.8 Clay loam 28.5 2.3 1.30=10 0.42 0.21 0.0283SF3 68.5 25.3 6.2 Clay 15.0 2.3 1.04=10 0.50 0.07 0.010

aAnalytical properties derived from 0 to 10 cm topsoil horizon.b Meaning of abreviations: Coarse fragments in % dry weight; OM: organic matter; BD: bulk density.cK : detachability index as soil loss per unit rainfall kinetic energy, derived from rainfall simulationd

Ž .Morgan, 1986 .d Ž .Wischmeier nomogram soil erodibility or K-factor index in US US tonracre per unit R-US and SI

Ž .metric units tonrha per MJrha mmrh .


trated in a summer monsoon period from August to October. From December to July,the climate is dry, with total rainfall seldom exceeding 10 mm in this whole dry seasonperiod. Long-term rainfall data for this study were obtained from meteorologic datasources in the Cape Verde. Runoff and combined interrill–rill soil loss data was

2 Ž .collected from 1980 to 1986 on 10 small 20-m runoff plots Mannaerts, 1984, 1992 onthree soil sites in Achada das Vacas–San Felipe area. Experimental site and soilanalytical data of the study area are summarized in Tables 1 and 2.

3. Methods

3.1. OÕerÕiew

The following procedure was adopted to obtain a probabilistic estimate of rainfallŽerosion losses from rainfall and soil data. From the long-term rainfall data records i.e.,

.40 years , the annual maximum 24-h rainfall and annual totals, were analysed in termsof their frequencies. Theoretical probability distributions were fitted to measured dataand their goodness-of-fit was evaluated. Erosivity values were then computed from the

Žrainfall data, using storm and annual erosivity–rainfall regression relationships Man-.naerts and Gabriels, 2000 . Soil loss of the annual maximum 24-h storms were

computed as the rainfall erosivity times soil erodibility, adjusted by a soil loss ratio toaccount for surface coarse fragments. Although feasible at this stage, no adjustment forslope gradient and length was made. Annual soil losses were then derived, adopting alogarithmic relationship between annual maximum storm and annual erosivity. Soil lossfrequency distributions for the maximum annual storms and annual totals were then

Žgenerated using rank plotting techniques with unbiased plotting positions Cunnane,.1978 . Theoretical soil loss distributions were derived by the method of the moments

Ž .Maidment, 1993 and the goodness-of-fit evaluated using confidence limits. Finally, theprobabilistic erosion estimates were compared to a short experimental field erosion data

Ž .set 1980–1986 , in order to verify the proposed modelling concept.

3.2. Probability and recurrence of rainfall in Cape Verde

The rainfall climate in Cape Verde tends to follow the regional weather regime of theWest African Sahel. Similar extreme fluctuations in summer monsoonal activity as well

Table 3Annual rainfall statistics for some stations in Santiago island, Cape Verde

a aLocation Elevation N years Median Mean SD CV Skew Kurtosisw x w x w x w x w xm asl mm mm mm %

Praia 67 40 172.4 203.3 145.4 71.5 0.68 2.63Trindade 210 40 206.2 256.3 182.6 71.2 0.86 2.96San Jorge 317 31 395.0 433.5 236.0 53.8 0.78 3.18

aSD: standard deviation in millimeters; CV: coefficient of variation in percent.


Ž .as drought frequencies are observed Babau, 1983; Demaree and Nicholis, 1990 .´Ž .Annual rainfall variability was analysed using representative time series 1945–1984 of

Ž .Praia and Trindade stations and San Jorge dos Orgaos 1965–1996 . The annualstatistics and variability indices are summarized in Table 3 for these stations, located atdifferent elevations in Santiago island.

The median values are significantly lower than the mean. The very high standardŽ . Ž .deviations SD and coefficients of variation CV% , the pronounced positive skewness

Ž .and platykurtic shape of the distribution kurtosis value-3 clearly illustrate the aridityof the rainfall regime in Cape Verde. The distribution of rainfall throughout the year was

Ž . Ž .evaluated using the Precipitation Concentration Index PCI Oliver, 1980 . The PCI of arainfall year can be derived from monthly rainfall data using Eq. 1,

122pÝ i

is1PCIs100 1Ž .212

pÝ iž /is1

with, p being the monthly precipitation in millimeters. PCI values theoretically rangei

from 8.3 for a complete uniform distribution of monthly rainfall to a theoretical value of100, when the entire annual rainfall is concentrated in one month. It is an appropriatemeasure to analyse and compare seasonality and temporal concentration of rainfall, dueto its emphasis on the relative distribution of rainfall irrespective of the total rainfall

Ž .received Michiels et al., 1992 . The PCI of the average rainfall year for the study area,was derived from the 40-year series, and amounted to respectively 28.3 and 27.9 forPraia and Trindade stations, indicating a very strong seasonal concentration of rainfallŽ .Michiels and Gabriels, 1996 . PCI values computed, on an annual basis, from the

Ž .measured 1980–1986 rainfall data set in the study area, varied from 30.0 1980 to 55.3Ž .1984 . A very strong temporal concentration of rainfall, to an almost entire concentra-

Žtion of rainfall in a few isolated large events i.e., the 1984 year with P s256 mm andan.P s180 mm can be concluded from these data. A particular feature of rainfall in24max

the Cape Verde is the very limited number of rainfall days per year and the very highproportion of rainfall contained in the maximum annual storm. Long-term averagenumber of rainfall days per year amount to respectively 18.7 and 20.9 days for the

Ž . Ž .Trindade Mannaerts, 1984 and Praia locations Babau, 1983 . From these totals,Žrespectively 64.2% and 74.8% represent days with low non-erosive rainfall P-10

.mm . In Fig. 2, cumulative annual rainfall is shown as a function of number of rainfallŽ .days. The 40-year daily record 1945–1984 of Trindade station was used for this

purpose. Fig. 2 represents the long-term average contributions of the major rain eventsto the annual rainfall total and can be interpreted as follows: the maximum annual stormprovides on average 26.7% of the annual rainfall total, whereas 52.7% of annual rainfallis supplied in only 3 rainfall days and so on. From Fig. 2, it is clear that the majoramount of annual fresh water supply in Cape Verde, and also the gross erosion damage,is due to only a few large rainfall events.

The probability and recurrence of these large rainfall events was analysed usingstatistical frequency analysis. The lognormal, the log-Pearson type III or the Gumbel


Fig. 2. Relationship between annual rainfall and contributions of daily events, ranked in decreasing order ofŽrainfall amount, based on long-term average values of Trindade station Ns40 years, 1945–1984, number of

.rainfall dayss748 .

extreme value distribution are potential distributions for analysing the rainfall frequen-cies in arid zones. In the case of soil and water conservation, where typical design returnperiods range from 5 to 50 years, there is usually little difference between the results

Ž .obtained by the different methods ECAFE, 1966 . Therefore, in view of the good fit ofrainfall frequencies in Cape Verde to the extreme value theory, the Gumbel probabilitydistribution was used to analyse recurrence intervals of rainfall. According to the

Ž .extreme value theory, the probability f x of a rainfall event not exceeding a givenxŽ .value x, is given by Eq. 2

f x sexpŽyexp a Ž xyj .. 2Ž . Ž .x

where a and j are the statistical distribution parameters derived from the n observedvalues. a represents the second moment parameter and j the mode or most frequentlyobserved value of the distribution. Distribution parameters were estimated from the

Ž .observed data series using the method of moments Maidment, 1993 . Frequency of


non-exceedance was calculated, by ranking the rainfall series in increasing order. TheŽ .empirical frequency was estimated using the Gringorten formula Eq. 3 or

iy0.4p s 3Ž .i nq0.12

where p is the empirical non-exceedance frequency of the ith event, and n the totali

number of events during the period.This formula can be recommended for deriving unbiased plotting positions for

Ž .extreme event distribution plots Cunnane, 1978 . Plotting of empirical frequencies in aŽ .linear ordinate against the reduced Gumbel variate y in Eq. 4 yields a straight line ini

case of good fit,

y syln yln 1yq 4Ž . Ž .Ž .i i

where y represents the value of the reduced Gumbel variate of the ith event, and q thei i

exceedance probability of the ith event. For an easier comparison, however, the eventŽ .recurrence interval, i.e., the return period T Eq. 5 was used here to representr

Ž .probability Baffaut et al., 1998 . The return period of an event is related to theŽ .non-exceedance probability f x byx

1T s 5Ž .r 1y f xŽ .x

3.3. An algorithm for deriÕing annual soil losses from the maximum annual storm

Based on a series of erosion plot measurements and field observations during andafter major storm events in Cape Verde in the period 1980–1986, we assumed that theannual erosion could theoretically be modelled using a logarithmic representation as

Asa 1q ln x 6Ž . Ž .Ž .in which A is the annual soil loss, a is a typical soil loss value for the respective rainfall

Ž .year, and x is the causal factor of the rainfall erosion process usually represented byŽ .the erosivity of rainfall. Eq. 6 suggests that the gross erosion damage a is caused by

Ž .one storm period i.e., the extreme or annual maximum 24-h storm , and that other stormŽ .events contribute relatively less to the total annual erosion A . Whereas these sec-

ondary storms may occur before the maximum annual storm event, this maximumannual rainfall will further deplete and void the surface from available erosion products,deposit them at the toe of the slope or deliver sediment to the drainage system.Secondary storms occurring after the annual maximum event will add relatively less tothe overall erosion damage. The physical background of the logarithmic form of theequation can be additionally substantiated by considering the differences in transportcapacity and erosive power between the smaller and the extreme storm events. Duringsmaller secondary rainfall events, eroded materials may travel only a short distance

Ž .before a decrease in flow velocity i.e., transport capacity of runoff causes deposition.Subsequent storm events are needed to mobilize or remobilise the sediment andtransport it to the toe of the slope or the drainage system. If we consider erosion ‘‘sensustricto’’ as soil losses deposited at the toe of slopes and field boundaries or sedimentdelivered to the channel drainage system, we may conclude that these smaller events


have substantially less erosive power. The extreme rainfall events will generally createlarge amounts of overland flow and runoff during considerable time periods permittingall entrainable sediment to easily reach the lower field boundaries and channel system.Eq. 6 above was further elaborated and transformed into Eq. 7, which permits annualrainfall erosion losses to be predicted from the maximum annual storm estimate and the

Ž . Ž .respective annual maximum 24-h storm EI and annual erosivity R by:24max

2 RyEI24 maxA sa 1q ln 7Ž .an 24max ž /ž /R

w 2 xin which A is the annual soil loss expressed in kgrm , a is the annualan 24maxw 2 x w 2maximum 24-h storm soil loss also in kgrm , R is the annual erosivity in kJ mmrm

x w 2 xh , EI the annual maximum 24-h storm erosivity value in kJ mmrm h .24max

Individual storm rainfall erosivity values were obtained from locally establishedŽ .regression relationships between erosivity expressed as energy–intensity or EI and30

Ž .rainfall amount and storm duration as predictor variables Mannaerts, 1992 . Annualerosivity was obtained as the sum of storm erosivity of all erosive rainfall events in acalendar year. Erosive rainfall is defined here as a storm event with a rainfall amountlarger than 10 mm. For a separate and detailed analysis of rainfall erosivity in Cape

Ž .Verde, we refer to Mannaerts and Gabriels, 2000 . Eq. 7 was derived by regressingexperimental storm period and annual soil loss figures to erosivity values using themodel function Eq. 6. When deriving the logarithmic term of Eq. 7, care had to be takento ensure a physically correct representation of reality in the extreme case when onlyone storm occurs during a year and annual erosivity R would equal EI . In that case,24max

Ž .the logarithmic term should asymptotically approximate zero or the ln 1 ™0. The termŽŽ . .ln 2 RyEI rR fulfils the requirement of approaching zero when EI ap-24max 24max

proaches R and fitted the experimental data set. With known values for soil erodibility,and soil loss ratios for weighing the effects of the local topography, surface cover andstructural conservation practices, the erosion extrapolation algorithm should finallybecome:

2 RyEI24 maxA sEI 1q ln K SLR 8Ž .an 24max ž /ž /R

w 2 xin which A is the annual soil loss expressed in kgrm , EI is the annualan 24maxw 2 xmaximum 24-h storm erosivity in kJ mmrm h , R is the annual rainfall erosivity in

w 2 x w xkJ mmrm h , K the soil erodibility or susceptibility to entrainment in kg hrkJ mm ,SLR is soil loss ratios for topographic, surface cover and soil management effects. Eq. 8theoretically permits to evaluate annual soil loss rates, based on erosion factor estima-

Ž .tions only. We can refer to Renard et al., 1993 for determination of soil loss ratios.

3.4. Plotting soil loss frequency distributions

By combining the rainfall data series with the erosion algorithm, time series of annualsoil loss totals were obtained. The statistical frequency analysis and plotting of thevalues was identical to the procedure described earlier for analysing rainfall frequencies.Exceedance frequencies of soil losses were calculated, by ranking the soil loss series inincreasing order. The empirical frequency was estimated using the Gringorten formula


Ž .Cunnane, 1978 , yielding the non-exceedance probabilities and return periods. Good-ness-of-fit was analysed using confidence intervals. Computation of confidence intervalsrequires estimation of the standard error or variance. For the Gumbel distribution withthe two parameters estimated by the method of moments as done in this study, the

Ž .variance of the pth quantile is given by Maidment, 1993

a 2 1.11q0.52 y q0.61 y2Ž .i iVar x s 9Ž . Ž .p n

Ž Ž ..for a sample of size n and y syln yln p , the Gumbel reduced variate with p thei i i

non-exceedance probability and a representing the second moment parameter of thedistribution, which can be estimated, from the sample variance s2 by

's 6as 10Ž .

p

We considered a fit to be acceptable if measured or simulated data fell within thespecified upper and lower confidence intervals of the theoretical distribution. Some

Fig. 3. Empirical and theoretical frequency distribution of annual maximum 24-h rainfall amounts of TrindadeŽ .station, Santiago Island, Cape Verde 1945–1984 series .


tolerance was given to the very low non-exceedance probabilities or return periods,representing very low to almost zero rainfall and soil losses and therefore of limitedimportance.

4. Results and discussion

4.1. Rainfall and soil loss frequency distributions

Fig. 3 shows a Gumbel distribution for the annual series of maximum daily rainfalls,derived using the method of moments, and fitted to the empirical maximum 24-h rainfalldepths for Trindade station, located near the study area. The 40-year data period

Ž .contained one missing value 1977 and one extreme outlier value with almost zero

Fig. 4. Simulated annual soil loss and theoretical Gumbel soil loss distribution for a lithic Camborthid soil,using the 1945–1984 Trindade rainfall series and soil data from MV1 site, Achada das Vacas.


Ž .rainfall P s1 mm in 1972 . Distribution parameters were determined discarding thean

missing value. As can be derived from Fig. 3, the extreme value theory can be applied toanalyse recurrences of the large rainfall events in Cape Verde, because all data pointsare within the confidence intervals.

By combining the Trindade rainfall series with the erosivity extrapolation algorithmŽ . Ž .Eq. 8 and the site and soil data Tables 1 and 2 , frequency distributions of annual soillosses, were generated for the Camborthid, Torriorthent and Haplargid soils. In order tobe comparable with observed erosion rates, simulated soil losses were adjusted for bare

Ž .soil percentage using data from the experimental plots Table 1 , and applying theŽRUSLE model time invariant option algorithms for estimating rangeland SLR’s Renard

.et al., 1993 . Figs. 4 and 5 show the annual soil loss frequency distribution of the lithicCamborthid soil, rank plotted as a function of the reduced Gumbel variate and as afunction of recurrence interval. The latter depiction of a statistical soil loss distributionyields an easier interpretation of soil losses. Experimental determination of the Gumbel

Ž .distribution parameters a and mode j from the generated stochastic annual soil lossseries permitted to evaluate typical soil loss probabilities for the other soils in the study

Fig. 5. Frequency distribution of annual soil loss of a lithic Camborthid soil using the 1945–1984 Trindaderainfall series and soil data from MV1 site.

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Table 4Annual soil loss probabilities and frequency statistics for the soils in the study areaa

bProbability of Return period Soil type Lithic Camborthid Lithic Torriorthent Ustertic HaplargidŽ .non-exc f x in years, Tx r Characteristic Soil loss in Soil loss in Soil loss in

w x w x w xvalue, quantile tonrha year tonrha year tonrha yearb0.37 1.58 Mode 7.8 4.3 2.5

Ž .0.50 2 Median 50% 10.3 5.5 3.10.80 5 20% 17.8 9.2 5.30.90 10 10% 22.8 11.6 6.70.96 25 4% 29.1 14.7 8.40.98 50 2% 33.8 17.0 9.80.99 100 1% 38.4 19.3 11.1

a Ž . Ž .Simulated annual soil loss from natural bare soil surface, slope length 22.4 m and slope gradient 9% .b Ž . Ž .Ustertic Haplargid soil loss estimates unreliable, due to very poor correspondence of nomogram soil erodibility K-factor in Table 2 , used for simulation Eq. 7

of soil loss probabilities, with plot observations and field erosion evidence for this soil.


area. Annual soil loss statistics for the Camborthid, Torriorthent and Haplargid soils aresummarized in Table 4, representing annual erosion rates, which can be expected on

Ž .natural undisturbed soil surfaces e.g., rangelands . Because no topographic factoradjustment could be made, soil losses from Table 4 can be considered to be deliveredfrom standard Wischmeier erosion plot topographic conditions, i.e., slope length 22.4 m,and slope gradient 9% or an LS-factor equal to unity.

4.2. Validation of model predictions with experimental plot soil loss data

The proposed erosion algorithms for deriving annual soil losses from storm-basedŽ .estimates Eqs. 7 and 8 were tested on an available 1981–1986 soil loss series from

Ž .experimental field plots in Achada das Vacas Mannaerts, 1992 , constituting in total 54plot-year data. Fig. 6 shows a scatter diagram of predicted vs. measured annual soil

Ž .losses. At first, we validated the extrapolation algorithm Eq. 7 . Predicted values were

Fig. 6. Comparison of simulated vs. measured annual soil loss for the experimental plots in Achada das Vacas,Ž .Santiago Island, Cape Verde data from 1981–1986 .


obtained by extrapolating measured maximum annual storm soil loss to an annualerosion rate using Eq. 7. The linear regression fit and coefficient of determinationŽ 2 .R s0.90 suggest validity of the erosivity extrapolation algorithm in this climatic and

Ž .soil environment. In the second instance, soil loss equation Eq. 8 was verifiedincluding estimators of erosion factors in the prediction. Soil erodibility was determined

Ž .using the nomogram method Table 2 , and topographic factor and surface coverŽ .adjustment was done using RUSLE model procedures Renard et al., 1993 . From the

scatter diagram in Fig. 6, it can easily be seen that the use of non-calibrated functionsfor erosion factors is very tentative and cannot be recommended. As an example, the

Ž .K-factor value of the Haplargid soil, Ks0.07 US-units Table 2 , compared far too lowto field evidence and consequently induces a large underestimation of simulated soil lossŽ .Fig. 6 . The use of the nomogram method for determining the erodibility of this clayey

Ž .volcanic soil should therefore be rejected Tables 2 and 4 . Prediction of soil loss for theŽ .steeper slope range 14% plots of the Camborthid soil with Eq. 8 was also not

successful, as shown in Fig. 6. Differences in depression storage and soil surfaceroughness among the plots, partly explain the anomalous behaviour of soil loss vs. slope

Ž .gradient on the MV1 site Mannaerts, 1992 . Impacts of depression storage and surfaceŽroughness on the mechanics of soil erosion have clearly been shown Chi-Hua Hang and

.Bradford, 1990 . Detailed predictor data at the individual plot scale to quantitativelyexplain these effects were not available.

5. Conclusions

Use of statistical mean or average values of rainfall and runoff, for calculating soillosses, can introduce serious bias in the evaluation of erosion rates in tropical semiaridregions like the Cape Verde Islands. Due to the high variability of rainfall occurrence insuch areas, large overestimations of erosion arise during dry years, when little to almostno soil loss is observed. Conversely, in wet years, underestimations from 200% to 500%may well arise, because extremely large events usually occur then, with major impactson the soil environment and landscape in general. These erroneous soil erosion evalua-tions can be avoided through the use of probability techniques. The Gumbel extremevalue distribution with parameters estimated using the method of moments fits well torainfall event recurrence in Cape Verde. This simple two-parameter distribution permitsto capture the non-normality of recurrence frequencies of hydrologic and associatedsurface erosion phenomena, encountered in those semiarid areas. The combination ofrainfall frequency analysis with a soil loss equation permits to analyze the range of soilloss magnitudes, which can be expected, on a storm or annual basis. Annual soil losssimulations using the probability technique in combination with the erosivity extrapola-

Žtion algorithm compared well with measured plot soil loss data from a 6-year 1981–.1986 monitoring period on the Achada das Vacas site in Santiago Island. It can be

noted that significant prediction errors occur in some cases, when non-calibratedfunctions for erosion factors are used. Bearing in mind this calibration requirement andin the light of the overall result, we think that the probability approach may be valid inother dry tropical areas, where extreme rainfall events contribute significantly to the


annual rainfall budget and, consequently, are the major source of soil loss. With a smallsoil loss data set available, or otherwise locally verified soil loss functions for soilerodibility, slope and cover effects, the method could be used as a planning tool forimproved design and implementation of soil and water conservation works in semiaridzones.

Acknowledgements

The authors acknowledge the Ministry of Agriculture, Forest Service and the InstituteŽ .of Agricultural Research INIDA of Cape Verde for providing ancillary precipitation

data.

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A probabilistic approach for predicting rainfall soil erosion losses in semiarid areas

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