an evaluation of a fragmentation fractal dimension technique to determine soil erodibility

$: An evaluation of a fragmentation fractal dimension technique to determine soil erodibility$
Ž .Geoderma 90 1999 87–98

An evaluation of a fragmentation fractal dimensiontechnique to determine soil erodibility

M. Martınez-Mena a,), L.K. Deeks b, A.G. Williams b´a Department of Soil and Water ConserÕation, CEBAS-CSIC, P.O. Box 4195, E30080 Murcia,

Spainb Department of Geographical Sciences, UniÕersity of Plymouth, Drake Circus,

Plymouth, PL4 8AA, UK

Received 15 December 1997; accepted 23 September 1998

Abstract

The fragmentation fractal dimension, D , was used to characterise aggregate-size distribution,f

as an index of soil erodibility, of five soils with contrasting properties from semiarid andtemperate areas. The D was the slope of the regression of aggregate number vs. log of aggregatef

diameterrdiameter of the largest aggregates using scale-variant bulk density and assuming aconstant shape for all the aggregates sizes. Six aggregate sizes, ranging from 0.25 to 16 mm, were

Ž . y3obtained for each soil. Aggregate bulk density ABD ranged from 1.21 to 1.81 mg m fory3 Žsemiarid soils and from 0.83 to 1.55 mg m for temperate soils. Significant correlations from

.rsy0.72 to rsy0.98, p-0.05 between ABD and size indicated scale-variance in ABD. Df

values ranged from 2.92 to 3.25 for semiarid and from 2.15 to 2.24 for temperate soils. ResultsŽ . Žfrom aggregate stability test using a laboratory rainfall simulator and soil loss rates from erosion

.plots for each soil were compared with D to assess the suitability of D as an erodibility index.f f

Values of D equal to or less than 2.24 were associated with stable soil, with a predominantfŽ .percentage of large aggregates 43% to 53% of aggregates 8–16 mm , and negligible soil loss

rates. In contrast, D values greater than or equal to 2.84 were associated with a less stable soil,fŽ .with a low percentage of large aggregates size 7% to 16% of aggregates 8–16 mm , and notable

soil loss rates. The values of D in describing mass-size distribution were found to be a useful andf

effective index to discriminate soil erodibility in the range of soil included in this study. q 1999Elsevier Science B.V. All rights reserved.

Keywords: fragmentation fractal dimension; soil erodibility; aggregate-size distribution; aggregatestability; soil erosion

) Corresponding author. Tel.: q34-68-215717; Fax: q34-68-266613; E-mail:[email protected]

0016-7061r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0016-7061 98 00097-4

( )M. Martınez-Mena et al.rGeoderma 90 1999 87–98´88

1. Introduction

Soil erodibility can be defined as the susceptibility of aggregates to beingdetached and transported. The severity of the water erosion depends upon thequantity of material which has been detached and the capacity of the flow totransport it. The importance of the size of the detached fragments in controlling

Žthe magnitude of erosion has been observed by several authors Proffit et al.,.1991; Le Bissonnais, 1996 . Larger aggregates are more likely to be broken

down by raindrops than smaller aggregates, and finer material is more likely toform part of the suspended sediment in overland flow than coarser material.Erosion is thus, limited not simply by the rate at which raindrops detachsediment but by the rate at which they detach sediment of a size that overland

Ž .flow is able to transport Parsons et al., 1991 . Due to the fact that soil erosion isdominated by the breakdown of soil into aggregates rather than primary particlesŽ .Alberts et al., 1980; Slattery and Burt, 1997 , aggregate-size distribution can beused as an indicator of the potential erodibility of the soil. The greater thepercentage of small aggregates, the more susceptible the soil will be to erosionby overland flow.

Ž .Several authors Van Bavel, 1949; Mazurak, 1950; Gardner, 1956 have usedŽ .a single parameter such as geometric mean diameter GMD , derived from the

log-normal distribution function, as an index to characterise aggregate-sizedistribution and furthermore to characterise soil structure. However, the log-nor-mal function is based on the assumption that the probability of failure ofaggregates is scale-invariant and this assumption may not be valid for soilaggregate fragmentation because larger aggregates are more likely to fragment

Ž .more easily than smaller aggregates Rasiah et al., 1997 .Recent advances in fractal theory have introduced a scaling parameter, the

fragmentation fractal dimension, D , to characterise size-distribution of frag-f

mented soil. The value of D is equal to the absolute value of the power term DfŽ .yDin the relation: N sk x where N is the cumulative number of objects) x ) x

greater than x, and k is a constant equal to N at xs1. Experimentally,) xŽ .yDN sk x is difficult to use because of the tedium involved in measuring) x

Ž .N Logdson et al., 1996 . Instead N is calculated from aggregate mass data) x

assuming a constant shape for all aggregate sizes. D has been predominatelyf

used as an indicator of fragmentation caused by different tillage operations or asŽa result of a different cropping strategy Perfect and Kay, 1991; Rasiah et al.,

.1992; Eghball et al., 1993; Perfect and Blevins, 1997; Rasiah et al., 1997 .These studies have also confirmed the suitability of D as an indicator of changef

Ž .in aggregate size, and according to the results from Rasiah et al. 1997 , D wasf

a better indicator of the changes in dry and wet aggregate-size distribution thanparameters such as GMD or alpha parameter of the function of Rosin and

Ž .Rammler 1933 .

( )M. Martınez-Mena et al.rGeoderma 90 1999 87–98´ 89

In this paper we assess the use of D as an index of soil erodibility in a rangef

of soils from semiarid and temperate areas.

2. Material and methods

Soil samples were collected from five field sites with contrasting soil andŽ .climatic properties Table 1 . Three of the soils were collected from a semiarid

Mediterranean area in Southeast Spain and the other two samples were obtainedfrom a temperate area in Southwest England. The soils from the semiarid area

Ž .are poorly developed, calcareous 50% CaCO and have a low organic carbon3Ž .content 0.8–2.5% . Fine materials are predominant in the Abanilla and Color

Ž .samples, while coarse material is predominant in the Cemen sample Table 1 .In comparison the soils from the temperate area are well-developed and hadorganic carbon contents between 3% to 4%. The Debathe sample has a moderatestructure in the upper 0.40–0.60 m of the soil profile and possess good drainagecharacteristics, while the Rowden sample has a sub-angular blocky coarsestructure in the upper 0.0–0.25 m and poor drainage characteristics.

Ž .Soil samples were collected from the soil surface 0–0.1 m , taking care toensure minimum disturbance to the aggregates. Samples from the semiarid areawere taken from experimental plots that were instrumented to determine erosionrates. Aggregates were collected from four randomly chosen areas for each site.The samples from the field were spread out on shallow trays and air-dried. Afterair-drying, soil texture, organic carbon content, aggregate stability and aggre-gate-size distribution were determined.

ŽSoil texture was determined by a combination of wet sieving )63 mm. Ž .fraction and laser diffraction -63 mm procedures. Prior to sieving, samples

Žwere soaked in Calgon for 12 h and ultrasonically dispersed for 20 min Mikhail.and Briner, 1978 . For silt and clay determination, samples were pretreated with

6% H O to remove the organic matter, chemically dispersed with 0.4% Calgon2 2

Table 1Characteristic of the soils used in the study

Ž . Ž . Ž .Soil Texture Perfil class Clay % Silt % Sand % OrganicŽ .carbon %

SemiaridAbanilla silty clay loam Torriorthent 27.7 66.9 5.4 0.7Color clay loam Calcigypsid 28.0 30.0 42.0 0.8Cemen sandy loam Calciorthid 5.1 36.8 58.1 2.5TemperateDebathe sandy loam Dystric eutochrept 11.0 24.1 64.9 2.9Rowden silty clay loam Dystric gleysol 33.3 51.0 15.7 3.7


Žand mechanically dispersed in an ultrasonic bath for 5 min British Standards.Institution, 1975 . The textural characteristics of the -63 mm fraction was

determined using a Malvern Master Sizer X ‘Laser particle sizer’.Ž .Organic carbon content OC was measured using a carbon analyser. Samples

Žwere pretreated with HCl 1:10 to eliminate carbonates Colombo and Baccanti,.1989 followed by high-temperature catalytic oxidation using a Shimadzu TOC

5000.Aggregate stability was measured using a laboratory rainfall simulator inside

Ž .an environmental chamber Ternan et al., 1996 . Twenty-five air-dry aggregatesof 4.5 to 5 mm diameter were subjected to rainfall simulation at 45 mm hy1

intensity with a mean drop size of 580 mm as determined by the filter paperŽ .technique of Mason and Andrews 1960 . The percentage of water stable

aggregates surviving at 0.5-min intervals was determined and a mean rainfallŽ .simulation survival index RSSI was calculated based on the number of

aggregates surviving at 5, 10, 15 and 20 min during the test.ŽSix hundred grams of each soil was dry sieved on a nest of sieves 16, 8, 5.6,

. Ž .4, 2, 1, 0.5, 0.25 mm for 30 s Calvo, 1991 , for D computation. Aggregatesf

on each sieve were collected and weighed. The density of each aggregate-sizeŽ .class was determined by the bulk density method described by Chepil 1950 .

Aggregate density was determined for all size classes except for those greaterthan 16 mm and smaller than 0.25 mm.

Aggregate-size distribution was determined, based on the mass of the aggre-gates in each class with respect to the total soil sample weight. Average weightof the four subsamples for each plot was used for fragmentation fractal analysis.

Ž .A quantity proportional to the number of aggregates of each size class, N di

Ž y3.Fig. 1. Apparent density mg m as function of aggregate size.


was calculated based on the following relationship given by Rieu and SpositoŽ .1991 ,

N d sM d rd3s Is0,1, . . .Ž . Ž .i i i i

Ž .where M d , d and s are the mass, mean diameter and density of aggregatesi i i

in the ith size class, respectively. Class 0 contains the largest aggregates.Aggregate densities for each size classes are given in Fig. 1.

Ž .The quantity N d isk

N d sÝ N d I s0,1, . . . ,kŽ . Ž .k i i

where d is the mean diameter of size class I sk, was used to estimate D ,k i fŽ . Ž .which is the negative slope of regression line of log N d vs. log d rdik ik g

Ž .Perfect and Kay, 1991 for each soil. In this analysis d is the diameter of theg

largest aggregates, while the regression line intercept indicates the quantity ofthe largest aggregates.

3. Results and discussion

The greatest differences in apparent density values, for the soils studied, wereŽ .observed in the largest aggregates 8–16 mm and smaller than 2 mm aggregates

Ž .Fig. 1 . The density of these aggregates had a bigger influence on D valuesf

obtained than the rest of the sizes considered.High correlation coefficients were obtained between aggregate bulk density

Ž . ŽABD and aggregate-size for all the soils studied rsy0.94, rsy0.97,rsy0.98, rsy0.97 and rsy0.72 for Debathe, Rowden, Abanilla, Color

.and Cemen, respectively .The Debathe and Abanilla soil samples showed theŽhighest increase in apparent density as the aggregate diameter decreased Fig.

. y31 . Aggregate density increased from 0.96 to 1.56 mg m and 1.12 to 1.76 mgmy3 for Debathe and Abanilla soils, respectively, as aggregate diameter de-creased from 12 mm to 0.37 mm. The soil from the Cemen showed the lowestincrease in aggregate density values. The order of increasing density observedamong the five soil types was maintained, Rowden-Cemen-Debathe-Abanilla-Color for each aggregate size group except for aggregates larger than8 mm where Debathe had a lower density than Cemen.

Ž .Soils with a similar texture e.g., Abanilla and Rowden showed dissimilarapparent densities which can be explained by the difference in the organiccarbon content: the Rowden soil contained approximately 5 times more organic

Ž .carbon than the Abanilla soil Table 1 . The correlation between organic carbonand the average of the apparent density for the different sizes of aggregates was

Ž .very high rsy0.82; p-0.01 .Table 2 shows the aggregates size distribution for the different soils. A

Ž .significant difference p-0.01 , between semiarid and temperate soils, was

()

M.M

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Table 2Ž .Aggregate-size distribution percentage, dagrkg of the different soils

Ž . Ž . Ž . Ž . Ž . Ž . Ž .8–16 mm 12 5.6–8 mm 6.8 4–5.6 mm 4.8 2–4 mm 2 1–2 mm 1 0.5–1 mm 0.75 0.25–0.5 mm 0.37a a a a a a aAbanilla 15.70 9.23 7.78 15.27 13.71 12.48 12.64a a a a a b aColor 6.75 5.45 6.60 15.36 14.92 17.13 14.44a b a a,b a,b c aCemen 15.70 12.42 8.40 11.86 9.58 7.82 11.31b b a a b d bDebathe 42.31 15.70 8.78 14.37 8.99 4.91 3.73c b a b b e bRowden 57.33 12.54 7.57 9.46 4.97 2.52 2.74

Values in the same column followed by different letters are significantly different at the 1% probability level.


Ž . Ž .found in the largest 8–16 mm and the smallest aggregates 0.25–0.50 mm . AŽ .significant difference p-0.01 was found for all soils for aggregates between

0.5–1.0 mm. However, no significant differences was found between any of thesamples for aggregates between 5.6–8.0 mm and 4.0–5.6 mm.

Ž .The mean values of D ranged from 2.15 to 3.25 Table 3 . Values of Df f

increased in the following order, Rowden-Debathe-Cemen-Abanilla-Color. Lower D values were associated with soil dominated by larger aggre-f

Žgates. For example, the soil with the lowest D value, Rowden D s2.15"f f. Ž .0.07, Table 3 , had 8 times more aggregates between 8 to 5.6 mm Table 2 than

Ž . Ž .Color D s3.25"0.08 , while Color had 5 times more 0.5–0.25 mm aggre-f

gates than Rowden. Higher D values were obtained for soils dominated byf

smaller aggregates.Ž .A D value higher than 3 was determined for Color Table 3 , in contradic-f

Ž .tion to some authors Crawford et al., 1993 who considered the use of amass-based equation to estimate D for particle-size distribution would constrainf

values of D between 0 and 3, unlike the number-based equations. Values offŽD )3 observed in other studies Perfect and Kay, 1991; Rasiah et al., 1992;f

.Tyler and Wheatcraft, 1992 were attributed to scale-invariant density beingassumed. In our study a density variant-scale was assumed to calculate D , andf

still values over 3 were observed for one of the semiarid soils. Similar resultsŽ .were obtained by Eghball et al. 1993 who assumed variation of density with

the aggregate size and obtained a range in D values from 2.81 to 3.30. ValuesfŽ .of D )3 have also been explained by Perfect et al. 1993 , with a multifractalf

model of soil fragmentation. In other cases, values of D )3 have beenf

explained as an artefact of measurement error, estimation model and theirŽ .underlying assumptions Anderson et al., 1998 .

The RSSI values obtained from the rainfall simulation test were significantlyŽ .correlated rsy0.80, p-0.01 with the soil loss values obtained from the

Ž .field experiments Martinez-Mena, 1995 in the semiarid and temperate areasŽ .Fig. 2 . Soils from temperate areas with 100% of aggregates survived therainfall simulation showed negligible soil loss, while, soils from the semiaridareas which displayed a range of RSSI values from 56% to 75%, showed soil

Table 3Ž .Fragmentation fractal dimension D syslope and intercept of regression line log of aggregatef

number vs. log of aggregate diameterrdiameter of the largest aggregates for the different soils2Ž .D Intercept – R S.E.f

Ž .Abanilla 2.92 "0.06 2.18 99.60 0.103Ž .Color 3.25 "0.08 2.55 99.55 0.130Ž .Cemen 2.84 "0.08 2.12 99.93 0.045Ž .Debathe 2.24 "0.07 1.67 99.31 0.110Ž .Rowden 2.15 "0.07 1.60 98.86 0.127


Fig. 2. Fractal dimension, D , RSSI and soil loss for the different soils studied.f

losses from 0.002 to 0.3 kg my2 yeary1. The order of magnitude of soil lossŽ .among sites was the same Color)Abanilla)Cemen)DebathesRowden as

that obtained from the simulation test.The relationship between percentage of 8–16 mm aggregates and aggregates

Ž .-1 mm, with D , was in accord with the results of the stability test Table 4 .f

High correlations between percentage of aggregates in each class and RSSI wereŽ . Ž .found for 8–16 mm rs0.98, p-0.01 , 0.5–1.0 mm rs0.94, p-0.01 and

Ž .0.25–0.5 mm rsy0.98, p-0.01 aggregates. Stable soils were characterisedŽ .by a high percentage of large aggregates 8–16 mm and the erodible soils by

high percentage of aggregates -1 mm. This result agrees with observations of


Table 4Correlation between percentage of aggregates, in each size class, and RSSI and fragmentationfractal dimension, Df

Ž .Size class mm RSSI Df

UU UU8.0–16 0.98 y0.985.6–8.0 0.82 y0.79

UU U4.0–5.6 0.94 y0.922.0–4.0 y0.60 0.61

U1.0–2.0 y0.88 0.89UU UU0.5–1.0 y0.94 0.95UU UU0.25–0.5 y0.98 0.98

UUSignificant at p-0.01.

USignificant at p-0.05.

Ž .other authors Morgan, 1979; Poesen, 1981 in relation to the sizes of aggregatesthat play an important role in the different mechanisms and processes involvedin soil erosion, such as detachment, rainsplash and overland flow.

Values of D significantly correlated with RSSI and D decreased withf fŽ .increasing RSSI rsy0.99, p-0.01 . Higher values of D indicated reducedf

stability of the aggregates and soils with a very small percentage of largeŽ .aggregates. The two most erodible soils low RSSI values and high soil loss ,

with D s3.28 and D s2.92 contained less than 12% and 25% of largef fŽaggregates, respectively. Soils from the temperate areas, which were stable high

.RSSI values and negligible soil loss , recorded the lowest D values and afŽpredominant percentage of large aggregates between 58% to 70% of aggregates

.larger than 5.6 mm . This result suggests that D calculated from aggregate sizef

distribution could be used as an index of soil erodibility.Soil organic carbon accounted for 81% of the variability in D or RSSIf

Ž .Table 5 . The negative correlation between organic carbon and D , and thef

positive correlation between organic carbon and RSSI, indicated that the value

Table 5Summary of the result of the regression analysis for fragmentation fractal dimension, D and RSSIf

as a function of organic carbon, OC, clay and clay=OC2Variable Slope Intercept Probability level R

Dependent Independent

D OC y0.330 3.39 0.037 0.81f

D Clay y0.010 2.95 0.520 0.15f

D Clay=OC y0.007 2.98 0.140 0.42f

RSSI OC 0.061 y2.82 0.037 0.81RSSI Clay 0.498 71.0 0.600 0.10RSSI Clay=OC 0.280 69.0 0.140 0.33


of the D decreased and the stability increased as organic carbon contentf

increased. Thus, as organic carbon increased, the proportion of larger aggregatesin the distribution increased and this lead to smaller values of D and higherf

values of aggregate stability. The relationship between organic carbon andŽaggregate stability has been confirmed in numerous studies Tisdall and Oades,

.1982; Bartoli et al., 1988; Rasiah et al., 1993 , and indicates the role of thisparameter in determining the soil aggregation and thus the distribution of thedifferent sizes of aggregates in the soil.

The poor relationship between D and soil texture corresponded with the lackf

of a significant correlation between RSSI and soil texture. Within soil texturalŽ . Ž .classes e.g., silty clay loam , a wide range of RSSI 70.25–100% and Df

Ž .from 2.94 to 2.15 values were observed.

4. Conclusions

Higher values of D indicated reduced aggregate stability and soils with af

very low percentage of large aggregates. More than 90% of the variability in Df

was associated with aggregates )8 mm and those -1 mm. A high D valuefŽ .Ds3.25 was reached by soils with -10% of 8–16 mm aggregates, and)30% of aggregates smaller than 1 mm. On the other hand, soils with morethan 40% of aggregates in the largest class and less than 10% in the smaller

Ž .class 1 mm had D values less than 2.24. In the range of aggregate sizesfŽ .included in this study, large aggregates )5.6 mm and those smaller than 1.0

mm were more important in determining erodibility than those in the intermedi-ate size. Considering that aggregates smaller than 1 mm are more likely to be

Ž .transported by overland flow Morgan, 1979 than larger aggregates, the per-centage of the aggregates in these classes could be used as an indicator of thesusceptibility of soil to water erosion.

D increased and RSSI decreased as OC content increased. Relations betweenf

D , RSSI and aggregates size distribution may suggest that as organic carbonf

increases, the proportion of larger aggregates in the distribution increases. TheŽ .biggest difference in the D values was between the semiarid erodible and thef

Ž .temperate soil stable .The relationships found between RSSI and soil loss with D values indicatedf

that fragmentation fractal dimension is an useful index to characterise soilerodibility. Furthermore, fragmentation fractal parameters can be more helpfulthan stability parameters, in describing soil erodibility, because they offer thepotential of being use to describe additional soil characteristics such as poretortuosity and surface roughness.

As this data set is restricted to only a few soil types and because of thedifferent values in D with different models and assumptions invoked inf

Ž .formulating the model Rasiah et al., 1993 , additional experiments are still


needed to compare D values to a wider range of soils and to aggregate stabilityf

using other methodologies.

Acknowledgements

This research was supported by a grant from the Ministerio de Educacion y´Ž .Ciencia Spain , Perfeccionamiento para Doctores y Tecnologos en el Extranjero´

Program. We also wish to thank Richard Hartley and Ann Kelly for thelaboratory technical assistance.

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an evaluation of a fragmentation fractal dimension technique to determine soil erodibility

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