SOIL ERODIBILITY ESTIMATION METHODS

1. Introduction

The intensification of soil erosion consequences in depletion of the top fertile soil

from agricultural land and the sedimentation in rivers and reservoirs. The rate of

erosion from the land surface depends mainly on the erosive power of the rainfall

event and the erodibility of the The susceptibility of surface soil to different

erosive agents (water and wind) is highly dependent on the physical

characteristics of the parent soil and the erosive power of the agents. The

strength of the raindrop splashes and depth of the surface runoff occurring from

precipitation determines the detachability of the individual soil aggregate and

bulk transport of the detached soil particles. The detachability of the soil

aggregate from the parent soil depends on the strength of how the individual soil

particles are bound together. The stronger the particles are bound together, the

less will be the susceptibility to erosion. The soil susceptibility to erosion is

expressed in terms of soil erodibility factor which can be defined as the rate of

soil loss per rainfall erosion index (MJ/mm)-1. Soil erodibility can be assessed by

any of the three established methods namely, the direct measurement on a

natural runoff plot, the rainfall simulation studies, and the predictive

relationships.

The direct measurement on a natural plot method and the rainfall simulation

methods need standardized field experimental plots. The method gives a reliable

erodibility factor, however it is costly and time consuming. The predictive

relationship approach is relatively the easier method to use, but the result is less

accurate as compared to the runoff plot and the rainfall simulation methods

(Römkens 1985).The predictive approaches are based on the soil physical,

chemical and mineralogical properties. Wischmeier et al. (1971) soil erodibility

nomograph is the most commonly used predictive method.

Different attempts were being made to establish the erodiblity factor

relationships with different soil properties. Oslon 1963, Ei_Swaify 1976, Young

1977, Williams 1984, Shiriza 1984, Sharpley 1990, Fryrear 1994, Chen 1995,

Zhang 2002 are among the common investigations conducted on the soil

erodibility estimation equations. The investigations suggested certain empirical

relations which can give soil erodibility value using certain data sets. However

adaptation of the research results of the investigations to other places still

remain a big challenge due to the area specific nature of empirical models or the

insufficiency of input data to make necessary adjustment for the specific

situations of the area under consideration.Likewise, very few investigations were

done so far for the specific situation of the soils in Ethiopia (Daba et al. 2002, J.S

Griffiths et al. 1989).

The limitation of the availability of the appropriate soil erodibility factor

estimation method is the main bottleneck for prediction of a reliable sediment

yield. Therefore there is a need to asses the existing soil erodibility estimation

methods with respect to data availability. Moreover, devising an alternative

approach for the erodibility estimation with a more simplified input parameter is

helpful to save money and time that could be expend on the intensive field data

collection. Hence, in this research the most commonly used soil erodibility

equation had been assessed, and suggested as a reference for the derivation of

the alternative soil erodibility factor estimation formula. The derived alternative

soil erodibility estimation method had been evaluated for the scope of it’s

applicability for the different soil characteristics.

2. Materials and methods

Data availability and reliability are the primary issue that should be considered

for the analysis of soil erodibility factor. The reliability on prediction of the

erodibility factor depends on the quality of the available input data. In this

research, the FAO/UNESCO-1998 world soil maps database and the soil map of

Upper Awash River basin in Ethiopia had been considered as source of available

soil data.

Food and Agriculture organization of the United Nations (FAO) had been

preparing and updating the world soil data base at different spatial scales. In

1990, a map of world soil resource was completed at a scale of 1:25,000,000

(FAO/EC/ISRIC, 2003).In 1998 the update version of the soil map was adopted as

world soil database. It was from the 1998 world soil data base that, the soil and

terrain map of the different parts of the content had been made available. The

Digital Soil and Terrain Database of North East Africa (SEA) that includes Ethiopia

was prepared separately and it has been available on purchase of the CD-ROM

containing all soil and terrain information of the area. The FAO soil map of the

Upper Awash basin is shown on figure 4.1.

Awash River basin in Ethiopia had been selected as a study area to analyze the

soil erodibility factor. Digital soil map of the area had been obtained from Federal

Ministry of Water Resources of Ethiopia. The study area has 10,540km2 with 80%

agriculture, 2.25% Urban, and the remaining 17.75% covered by different forests

and pasture land. The land slope varies from 0.7% to 16.5% with an undulating

topography at the far upstream part and uniform lowland in middle and

downstream parts. The area experiences heavy rainy seasons in months of July

and August with mean total annual rainfall of 1000mm. Different soil types exist

in the Upper Awash River basin. The major soil types of Awash is indicated on the

following figure 4.1

Figure 4.1 Soil map of the Upper Awash River basin and sampling locations

The physical properties of the soils in Upper Awash River basin had been

extracted from FAO/UNESCO world soil database. The corresponding soil

properties for each soil type are indicated on table 4.1.

Table 4.1 Soil properties extracted from FAO/UNESCO soil database

To verify the reliability of the FAO soil world data base characteristics, field data

on soil physical properties had been collected for major soils of the study area.

The major and dominant soils are five soil types and for each soil type sampling

had been done from 60cmx60cm pit with 100cm depth (figure 1.5).Five sampling

pits had been dug on the dominant soil types.

Figure 2.4 Soil sampling pit under excavation

The soil samples from each pit had been collected at two depth profiles, 0-30cm

and 30-100cm. The samples from each pit were analyzed in laboratory by

hydrometer method. The temperature correction, percent sand, percent silt and

percent clay computation had been done based on the Milford, 1997 laboratory

guideline procedures. The following are description of equations used for the

analysis of samples.

60cm

100cm 60cm

Soil moisture correction

Determination of weight of dry soil

The weight of the dry soil is determined by multiplying the air dry weight

by the

moisture correction factor (MCF)

Correcting hydrometer reading

To correct the hydrometer reading for the temperature, add 0.36 gram/liter for

every 1 degree Cent grade above 20 degree cent grade temperature; subtract

0.36gram/liter for every 1 degree C below 20 degrees cent grade temperature.

For temperature above 20 degree C

For the temperature below 20 degrees Cent grade

Determination of percent sand, silt and clay

Based on the laboratory analysis procedure and the application of the above

mentioned equations, the percent sand, silt and clay had been determined. The

computation result is shown on table 4.2 and figure 4.2.

Table 4.2 Hydrometer method of soil texture analysis data table

Sample ID PT1 Pt2 PT3 PT4 PT5Weight of dry sample (g) 50 50 50 50 5040-sec hydrometer reading (g/1) 16 19 18 16 16

Temperature 14 13 16 24 15

Corrected 40-sec reading (g/1) 18.16 21.52 19.44 14.56 17.82-hour hydrometer reading (g/1) 9 11 11 10 12

Temperature 16 14 19 23 19Corrected 2-hour reading (g/1) 10.44 13.16 11.36 8.92 12.36

Percent clay 20.88 26.32 22.72 17.84 24.72Percent silt 15.44 16.72 16.16 11.28 10.88

%Sand 63.68 56.96 61.12 70.88 64.4

Textural class name  SCL  SCL  SCL  SL  SL

Soil type LeptosolsHaplic Xerosols

Vitric Cambisol

Chromic luvisols

Dystric Nitosols

*** Remark:The temperature for sample analysis of PT4 is high because the laboratory analysis was conducted in afternoon time when the water from the pipeline was hot.

SCL=Sandy clay loam

SL=Sandy loam

The analysis result from the field data and the FAO soil database characteristics

had been compared and the result is indicated on the following figure (figure 4.2)

Figure 4.2 Comparison of the FAO/UNESCO soil properties with on field measured

Leptosols

0

10

20

30

40

50

60

70

%Sand %Silt %Clay

soil texture

fracti

on

% FAO soil(texture SCL)cal soil(texture SCL)

Haplic xerosols

0

10

20

30

40

50

60

%Sand %Silt %Clay

soil texture

fracti

on

% FAO soil(texture SCL)cal soil(texture SCL)

Vitric cambisols

0

20

40

60

80

%Sand %Silt %Claysoil texture

FAO soil(texture C)

cal soil(texture SCL)

Chromic luvisols

0

20

40

60

80

%Sand %Silt %Clay

soil texture

fracti

on

% FAO soil(texture SL)

cal soil(texture SL)

Dystric Nitosols

0

10

20

30

40

50

60

70

%Sand %Silt %Clay

soil texture

fra

cti

on

%

FAO soil(texture C)cal soil(texture SL)

From figure 4.2, it can be observed that for the most dominant soils

(Leptosols,Haplic Xerosols and Chromic Luvisols),the properties of the soils

extracted from FAO/UNESCO soil database is similar to the properties of the soils

analyzed from field data. The similarity and variation of the soil texture class had

been compared between the FAO/UNESCO soil properties and the on field

measured soil properties. The soil texture class was found to be sandy clay loam

(SCL) for Leptosols and Haplic Xerosols for both FAO soil characteristics and the

on field measured soil characteristics. Similarly, for the Chromic Luvisols, the soil

texture is sandy loam (SL) in both cases. Nevertheless, for Vitric cambisols and

Dystric Nitisols, there is significant variability in sand proportion which is the main

reason for the variability of the soil texture class as well. The significant variation

in sand proportion could be due to the location of the soil at low land area. In low

land areas, there is more chance of deposition and as a result the soil properties

remain variable from time to time. In such a situation, a representative sampling

should be made from a deeper depths and more sampling pits. In overall

conclusion on the reliability of the FAO/UNESCO soil properties, the available soil

characteristics data can be confidently applied, as it was proved during field data

collection and analysis.

2. Result and discussion

Review of existing soil erodibility estimation method

The attempt to establish equations for the determination of soil erodibility factor

started as early as the 1950’s.Since that time different empirical relations had

been established. Different investigators suggested different approaches for the

estimation of soil erodibility factor.

Wischmeier et al., 1971 developed the most widely used soil erodibility

nomograph (figure 3.1). The nomograph was developed from the 20 years field

data observed on 22.1m length, 1.83m width and 9% field plot in USA. For the

applicability of the nomograph, five soil parameters are required. The soil

parameters required to read the nomograph are the percent modified silt(0.002-

0.1m m),the percent modified sand(0.1-2mm),the percent organic carbon

matter(OM) and classes for structure(S) and permeability(P).An algebraic relation

was proposed to represent the nomograph for the cases where silt fraction

doesn’t exceed 70%.

Figure 3.1 Wischmeier et al. Soil erodibility estimation nomograph

msilt =Percent silt content (0.002mm-0.05mm)

mvfs = Percent of fine sand(0.05mm-0.10mm)

mc = Percent of clay(less than 0.002mm)

OrgC = Percent Organic carbon content

Csoilstr = Soil structure Code used in soil classification

Cperm = Soil Permeability class

Shirazi and Boersma, 1984 developed an empirical equation based on a natural

plot and simulated rainfall data from global data. In the analysis, soils with less

1 - very fine granular2 – Fine granular3 – Coarse granular4 – blocky,platey or massive

6 - very slow5 - slow4 - slow to medium3 - medium2 - med to rapid1 - rapid

than 10% of rock fragments were considered. The erodibility equation was

related to the mean geometric particle diameter.

Where fi is the primary particle size fraction in percent and mi is the arithmetic

mean of the particle size limits of that size.

William’s 1984 proposed general erodibility equation using soil texture and

organic carbon content as an input variable.

Where

fcsand = Factor that gives low soil erodibility factor for soils with high coarse sand

contents.

fcl-si = Factor that gives low soil erodibility factor for soils with high clay to silt

ratio.

forg = Factor that reduces soil erodibility for soils with high organic carbonic

content.

fhisand = Factor that reduces erodibility for soils with high sand content.

Selection and application of the equations should be done wisely so that a

reasonable erodibility value can be predicted. There had been few researches

conducted to evaluate the applicability of the different erodibility equation under

different conditions. The K.L Zhang et al. 2008 and R.Wawer et al., 2005 had

evaluated the degree of applicability of the most popular equation with respect to

the on field measured erosion data. The investigation revealed that the

Wischmeier et al., the William’s et al. and the Shirazi et al. erodibility equations

over estimated the erodibility values. From the result, it was observed that the

three methods had shown different range of errors. The Zhang et al. revealed

Shirazi and Boarsma equation had shown least error and William’s equation had

shown intermediate error. The Wischmeier et al. equation had shown largest

error as compared to the two methods. Similarly, the investigation by R.Wawer

also indicated the better performance of the William’s method as compared to

the Wischmeier et al.erodibility estimation equation, although both method

overestimated the result.

The review of the two research result indicates the direct application of the

erodibility estimation methods provides an over estimated values which can

significantly influence the soil loss rate or the sediment out flow from a

watershed. The over estimation of the methods could probably due to the many

soil parameters incorporated in the equation. The more the parameters are

considered, the more the error duplicates during data collection and analysis.

Moreover, soil parameters like the organic carbon content is difficult to accurately

measure and as a result large error can be introduced in to the equations.

The most popular soil organic measurement is by the soil burning method. The

method assumes that the loss due to the burning is the organic carbon content.

In soils having significant clay composition, the result is expected to be too

erroneous. The burning method is a very approximate method which varies in

accuracy depending on the clay content of the soil (Eleanor et al., 2008). The

better performance of the shirazi and Boarsma equation which is independent of

the organic carbon content can justify this comment.

In Shirazi and Boarsma equation, the geometric grain size which is a function of

particle size fraction and particle size limit may be too sensitive to small

discrepancies as it was represented by an exponential function (equation 3.2.2).

The small discrepancies in the data on particle size fraction and particle size limit

can lead to large error term. To avoid such discrepancies a detailed investigation

on the particle size information is required which needs many representative soil

sample data and accurate laboratory analysis.

The William’s erodibility equation input requirements can be extracted from

FAO/UNESCO soil data base. In the absence of the on field measured soil

properties, the FAO data base parameters are the possible alternative sources of

obtaining the soil properties that are required in William’s equation. However, the

demand for the more soil input parameters remain major challenge for erodibility

estimation.Therefore, assessing the possibility of alternative approach to

minimize the number of input data set requirement and easily measurable soil

parameters is mandatory. The formulation of an alternative soil erodibility

estimation approach is described in the proceeding chapter.

An alternative soil erodibility estimation approach

The texture of a soil plays a fundamental role in susceptibility of soil to erosion.

The texture of soils can be expressed in terms of the percent sand, silt and clay

proportion. On the basis of the discussion made under section 3.4, the respective

soil erodibility(K) factors had been computed from the William’s

equation(equation 3.6) for the Upper Awash basin. The computed K values and

the major soil texture ratios are indicated on figure 4.3.The right hand side y-axis

describes the different soil texture fractions (silt/sand, silt/clay and silt/ (sand and

clay)) while the left hand side y-axis describes the soil erodibility factor value

computed from William’s equation (Kwl).The x-axis represents the different FAO

soil numbering as denoted on table 4.1.

Figure 4.3 William’s erodibility(KWL) result for Awash River Basin

To investigate the possibility of formulating alternative soil erodibility estimation

equation using the soil textures, partial correlation had been done with respect to

Kwl, percent silt to percent clay ratio, percent silt to percent sand ratio, percent

silt to total percent of sand and clay. For the correlation analysis, two cases were

considered; case for Awash River basin soil and the case for FOA/UNESCO world

soil data.

Table 4.3 Correlation coefficient(r) of soil erodibility factor with respect particle

size

Ratio of soil distribution Awash Basin data FAO/UNESCO soil data

%Silt to % clay 0.77 0.54

%silt to % sand 0.72 0.78

%silt to % sand and % 0.88 0.82

clay

Percent silt to total percent clay and percent sand ratio reflects highest

correlation as compared to the remaining elements for both the cases.

Nevertheless, the correlation for the remaining two elements are still significant

since r value is greater than 0.5. Sand dominated soils are less susceptible to

erodibility, because they have low runoff potential. Clay soils are similarly less

susceptible to erodibility due to their strong binding effect of individual

aggregates. Thus, it can be concluded that soil erodibilty is inversely proportional

to the percentage sand and percentage clay. In contrary, the presence of high silt

proportion in the soil increases the susceptibility of the soil to erosive agent.

Based on the correlation result of the different soils considered and the result

summarized on table 4.3, percent silt to total percent clay and percent sand ratio

had been considered for the formulation of the alternative soil erodibility

estimation method.

A non linear regression equation had been fitted to the data of the study area.

Percent silt to total percent sand and percent clay ratio had been considered as

explanatory variable. The model fitted to a non linear power function with a form

of;

Evaluation of the ERFAC equation on Awash Basin soil data

The derived ERFAC equation had been applied for computation of the soil

erodibility values for the different soils in the study area. The result of the

computation was plotted on figure 4.4 as shown below. The x-axis represents the

dominant soil types in the study area while the Y-axis is the value of the

erodibility factor calculated by William´s method and the newly proposed

equation. The secondary Y-axis indicates the absolute relative errors.

Figure 4.4 Comparative analysis relative and relative errors for individual soil

types

The fitted model had been evaluated for its performance based on the statistical

indicators such as Pearson’s correlation coefficient(r), coefficient of determination

(R2), Nash-Sutcliffe efficiency (NSE), Percent bias (PBIAS), Relative mean square

error (RMSE) and individual absolute relative errors (RE). The following table

indicates the summary of the model performance evaluation indicators

Table 4.4 Statistical indicators of the newly proposed erodibility equation

Indicator description Indicator valuesR 0.88R2 0.75NSE 0.68PBIAS -0.14%RMSE 0.0046Individual relative errors -10% to 15%

Figure 4.5 Comparison of erodibility factor estimated by ERFAC and William´s

method

The statistical indicators described above shows a good model performance.

Nevertheless, the R2 and NSE are not as such significant, the relative errors

between the Kwl and the newly proposed equation (ERFAC) is very low. The

errors had been estimated to be less than 10% for most soils.

Beside the statistical indicators used for the empirical model evaluation, the

spatial pattern of the soil erodibility map by the both methods had been

analyzed. Soil erodibility map from the William´s equation and the newly

proposed ERFAC equation had been produced in GIS (figure 4.6).The erodibility

maps had been produced in such away that the total erodibility factor values

were divided in to four equal parts; low, medium, high and very high erodiblity

factors. The total range of the erodibility values are divided in to four equal parts

so that the first lower range can be assigned low, the second range can be

assigned medium. Similarly the third range is assigned high erodibility and fourth

and the maximum values of the range considered as very high erodibility

potential. Figure 4.6a shows soil erodibility factor obtained from Williams

equation (Kwl) and figure 4.6b shows erodibility map from the newly proposed

erodibility factor estimation method (ERFAC).In a similar way as the statistical

method shown above, the two maps are able to depict almost similar information

on the spatial variability of the soil erodibility. Areas occupied by the leptosols are

identical on both maps. The leptosols areas fall under high erodibility range.

However the areas identified as medium erodibility potential using Kwl method

fall under high erodibility potential in the case of the newly proposed method

(ERFAC).

(a) (b)

Figure 4.6 Spatial pattern of soil erodibility distribution in Awash Basin

Evaluation of the ERFAC equation on FAO world soil data

The applicability of the new proposed soil erodibility factor estimation method

(ERFAC) had been evaluated on the world soil map database. During the

validation step, soils which were used to establish the ERFAC equation had been

excluded. The ERFAC equation was applied to calculate the soil erodibility factor

and compare the results with erodibility factor calculated using William’s

equation. A total of 104 different FAO/UNESCO soils had been considered for the

analysis. The result of the ERFAC and William’s equation had been compared

based on the computation results from the respective equations (Eqn 3.6) & (Eqn

50

Kwl

0.105 - 0 .150(L ow )0.15 0 - 0 .195(M ed iu m)0.195 - 0 .239(H ig h)0.239 - 0 .284(V er y H ig h)

Kwl

0.105 - 0 .150(L ow )0.15 0 - 0 .195(M ed iu m)0.195 - 0 .239(H ig h)0.239 - 0 .284(V er y H ig h)

ERFAC0.102 - 0.1350.135 - 0.1690.169 - 0.2030.203 - 0.236

ERFAC0.102 - 0.1350.135 - 0.1690.169 - 0.2030.203 - 0.236

50 (Low) (Medium) (High) (Very high)

(Low)

(Medium)(High)

(Very high)843995

4.7). The results are summarized in to three groups based on their relative errors

observed during the computation. Group 1 are soils which show absolute relative

error less than 10%, Group 2 are soils which show absolute relative error less

than 20%, and Group 3 are all soils considered except 1 soils whose absolute

relative error exceeded 60%. The grouping of the soil is represented as shown on

figure 4.7 and figure 4.8.The list of soils in each soil groups is attached on Annex

A.

Figure 4.7 Chart indicating the pattern of grouping the different soil groups

The percentage of soils falling in group 1 comprises of 40% of the total soils

considered in the evaluation; while the percentage of soils in group 2 account for

80%.The remaining 20% of the soils show a relative errors between 20% to 60%

except for Gleyic podzols which its error is found to be 90%.The statistical

indicators (R2 and NSE) had been computed.

Table 4.5 Summary result of statistical indicators as compared to William’s

equation

Indicator Group 1 Group 2 Group 3

R2 0.90 0.71 0.73

NSE 0.92 0.64 0.57

Group 3RE<60%

Group 1RE<10%

Group 2RE<20%

Figure 4.8a Comparison of Williams equation and new proposed equation based soil erodibility factors for soils of group 1

Figure 4.8b Comparison of Williams equation and new proposed equation based soil erodibility factors for soils group 2

Figure 4.8c Comparison of Williams equation and new proposed equation based soil erodibility factors for all FAO soils

3. Conclusions and recommendations

The literature review of the soil erobility estimation equation assessment

revealed that the existing and popular erodibility factor estimation equations

over predicts the erobility factor as compared to on field observed erodibility

values. Neverthless,the erodibility factor predicted by Shirazi et al.1984, equation

is shows less relative errors as compared to Wischmeier eta al. equation and

Williams equation. The William’ equation had shown intermediate relative errors.

The input soil data required by the Shirazi et al. equation is the main draw back

for its applicability on data limited areas like Upper Awash basin in Ethiopia. In

contrary, the availability of the FAO/UNESCO-1998 soil data base is advantageous

as it contains soil physical properties required by the William’s equation. Hence,

the William’s equation is more preferable for its applicability on data limited

areas.

The over estimation of the erodibility factor by the Wischmeier et al.equation and

William’s equation could probably due to the many soil parameters incorporated

in the equation. The more the parameters are considered, the more the error

duplicates during data collection and analysis. Moreover, soil parameters like the

organic carbon content is difficult to accurately measure and as a result large

error can be introduced in to the equations. The most popular soil organic

measurement is by the soil burning method. The method assumes that the loss

due to the burning is the organic carbon content. In soils having significant clay

composition, the result is expected to be too erroneous. The burning method is a

very approximate method which varies in accuracy depending on the clay

content of the soil (Eleanor et al., 2008). The better the performance of the

shirazi and Boarsma equation which is independent of the organic carbon content

can justify this comment.

The Pearson’s correlation analysis had shown that the soil erobility factor is more

correlated with the percent silt to percent sand and percent clay ratio. This

indicates that soil erodibility is directly proportional to the percent silt and

inversely proportional to percent clay and percent sand. Higher clay content

indicates the strong binding property of the soil particles to resist easy

detachability. Sand dominant soils have a higher soil infiltration rate which

results less runoff potential to erode the soil particles.

The derived erodibility equation (ERFAC) had been evaluated for its applicability

on different soil characteristics. On the evaluation of its applicability, three soil

groups had been identified based on their absolute relative errors.40% of the

world soil types had shown absolute relative errors of less than 10%.Majority of

the soils in the group are characterized by less clay content with less than 30%

clay fraction. The textural classes of such soils range from silt loam to sand

textures. For the second group of soil which account for about 80% of the total

soil considered in the evaluation, the absolute relative errors between the

William’s erodibility estimation method and the ERFAC equation had been

computed to be less than 20%.Such soils extend to soils with clay proportion of

20% to 40% which increased the textural range from slit clay to sandy soil

textures. The third soil group had shown absolute relative errors of less than

60%.The analysis and evaluation of the applicability of the ERFAC equation

confirms that a reasonable and an acceptable soil erodibility factor can be

predicted by the equation.

The ERFAC equation performed well for soils with less clay contents having soil

texture from silty clay to sandy soils. For 80% of the world soil, the RE between

the William’s equation and the ERFAC equation had been estimated to be less

than 20%.The advantage of the ERFAC equation is that less soil parameters are

required as compared to the existing equations. Moreover, the input parameters

can be easily obtained in laboratory through dry and wet sieve analysis

techniques. The free availability of the FAO/UNESCO world soil database

characteristics is another advantage to apply the equation for preliminary

analysis of soil erosion.

Therefore, ERFAC is an alternative soil erodibility prediction equation that

simplifies the cost and time to be invested to collect huge data sets from field

works. Additionally there is less error propagation from the input data sets,

because it is based on few and easily measurable soil characteristics.