Modeling aggregate size distributionof eroded sediments by rain-splashand raindrop impacted flow processes

Selen Deviren Saygın* Gunay ErpulDepartment of Soil Science and Plant Nutrition, Faculty of Agriculture, Ankara University , 06110 Diskapi-Ankara, Turkey(e-mail: sdeviren@agri.ankara.edu.tr, erpul@ankara.edu.tr)*Presenting authour

Soil Erosion Modelling WorkshopJRC Ispra

20-21-22 March 2017

Research highligths Previous studies have clearly indicated that sediment characteristics and

especially its size distrubution are dynamicly changes under water-inducederosion conditions (Hairsine et al., 1999; Hogarth et al., 2004, Asadi et al., 2007; Baigorria and Romero, 2007; Rose et al., 2007, Asadi et al., 2011).

The size distribution of eroded sediments can provide basic informationregarding erosion processes (Loch and Donnollan, 1982; Miller andBaharuddin, 1987; Mitchell et al., 1983; Proffitt and Rose, 1991; Meyer et al., 1992).

A better understanding of the dynamics of the sediment size distribution willimprove understanding of erosion and sedimentation processes, andconsequently improve erosion modeling.

For next genaration process-based modelling technology it is essential tomodel mass-fragmentation to accurately estimate transport capacity, soilloss rates and erodibility etc. Nearing et al. (1990) indicate that majordeficiency in WEPP model to represent detachment process is in terms of sediment size distrubutions.

Thus, it has been proposed the developing separate predictive equations forsediment sizes from rill and interrill areas and incorporating these equationsinto process-based erosion prediction technologies.

Research highligths At this point, we can say that modelling of the sediment size distribution

with an proper mathematical model would be useful in modeling and monitoring the changing erosional conditions.

From the past to the present, many statistical methods have been proposed to describe the particle-size distribution of sediments (Cooke et al., 1993; Zobeck et al., 2003).

Some of them are the conventional Gaussian or normal, log-normal (Shiraziand Boersma, 1984; Buchan, 1989), modified lognormal (Wagner and Ding, 1994), log-hyperbolic (Hartmann and Christiansen, 1988), bi- or multimodal (Pinnick et al., 1985), Rosin-Rammler (Kittleman, 1964),Weibull (Wohletz et al., 1989), and others (Zobeck et al., 2003).

Although these studies are cruial for mass-fragmentation model developments in terms of process-based approach, performedmeasurements on eroded sediments and modelling of them with a propermethodology are quite limited opposite to wind erosion measurements.

Thus, we tried to find best modelling approach to model eroded sedimentsize variations under water-induced erosion conditions.

In this context, we compared to the three different mathematical aggregate size distribution model (Log-normal, Fractal and Weibull) performance, mostly used for dust modeling in wind erosion process, for eroded sediments derived from rainfall simulations to simulate fragile ecosytem dynamics in semi-arid catchment scale.

Rainfall simulations

Log-normal cumulative distribution function (CDF)

Fractal cumulative distribution function (CDF)

23)(

D

LT

L

Xx

MXxM

−

=

<Fractal

where M(x < xL)s the cumulative mass smaller than diameter x, xLis the diameter of the largestparticle, and MT is the total sample mass

derived from Mandelbrot, 1982;Turcotte 1986; Tyler and Wheatcraft

1989; Tyler and Wheatcraft 1992

MSE: 0,0063 R2: 0,953

D50: 1,828

Sample graph: Dry Aggregate size distrubution modelling for cultivated agricultural land before rainfall simulations

Sample graph: Dry Aggregate size distrubution modelling for cultuvated agricultural land before rainfall simulations

−−=

< c

T bx

MXxM )(exp1)(

Weibull

derived from Wohletz et. al. 1989; Perfect and Kay, 1995; Zobeck et al. 1999

MSE: 0,0015 R2: 0,989

D50: 1,49

where M(x < X ) is the cumulative mass x smaller than diameter X, MTis the total sample mass, the b parameter is a scale factor and the c parameter is a shape factor.

Weibull cumulative distribution function (CDF)

Mea

sure

d an

d pr

edic

ted

D50

valu

es a

long

with

MSE

an

d R

2va

lues

for t

he s

plas

hed

sedi

men

tsLand Use

Slope Intensity Measured

D50

Log-

normal MSE R2 Fractal MSE R2 Weibull MSE R2

Culti

vated

Lan

d

9% 80 mm h-1 0.43 0.37 0.012 0.951 0.56 0.012 0.900 0.43 0.001 0.990

120 mm h-1 0.50 0.42 0.014 0.942 0.63 0.008 0.939 0.51 0.001 0.990

15% 80 mm h-1 0.52 0.43 0.019 0.920 0.66 0.009 0.932 0.54 0.001 0.992

120 mm h-1 0.53 0.46 0.016 0.934 0.67 0.007 0.940 0.56 0.001 0.992

20% 80 mm h-1 0.47 0.40 0.012 0.951 0.60 0.010 0.928 0.47 0.000 0.997

120 mm h-1 0.54 0.46 0.016 0.935 0.66 0.007 0.946 0.56 0.001 0.994

Gras

sland

9% 80 mm h-1 0.41 0.38 0.008 0.966 0.55 0.012 0.908 0.43 0.001 0.989

120 mm h-1 0.49 0.43 0.014 0.944 0.63 0.009 0.932 0.52 0.001 0.995

15% 80 mm h-1 0.42 0.39 0.008 0.967 0.57 0.011 0.915 0.44 0.001 0.990

120 mm h-1 0.52 0.45 0.016 0.934 0.66 0.008 0.938 0.55 0.001 0.992

20% 80 mm h-1 0.43 0.39 0.008 0.965 0.58 0.001 0.920 0.46 0.001 0.991

120 mm h-1 0.52 0.45 0.015 0.938 0.66 0.007 0.941 0.55 0.001 0.993

Fore

st

9% 80 mm h-1 1.14 0.97 0.065 0.732 1.05 0.015 0.748 1.12 0.000 0.996

120 mm h-1 1.08 0.98 0.073 0.789 1.56 0.005 0.950 1.41 0.002 0.980

15% 80 mm h-1 1.17 1.01 0.063 0.738 1.05 0.017 0.720 1.17 0.000 0.997

120 mm h-1 0.91 0.75 0.037 0.845 0.90 0.009 0.887 0.91 0.001 0.994

20% 80 mm h-1 1.10 0.78 0.041 0.883 1.20 0.007 0.932 1.08 0.001 0.949

120 mm h-1 0.73 0.60 0.030 0.875 0.81 0.005 0.946 0.76 0.001 0.998

Cul

tivat

ed

Land

Gra

ssla

ndFo

rest

Land Use Slope Intensity

Measured

D50

Log-

normal MSE R2 Fractal MSE R2 Weibull MSE R2

Culti

vated

Lan

d

9% 80 mm h-1 0.41 0.45 0.009 0.963 0.55 0.013 0.895 0.44 0.003 0.974

120 mm h-1 0.49 0.45 0.014 0.942 0.62 0.011 0.895 0.54 0.005 0.954

15% 80 mm h-1 0.45 0.37 0.005 0.979 0.53 0.011 0.914 0.41 0.002 0.987

120 mm h-1 0.43 0.4 0.004 0.982 0.56 0.01 0.919 0.46 0.002 0.983

20% 80 mm h-1 0.48 0.46 0.009 0.965 0.61 0.01 0.915 0.37 0.004 0.971

120 mm h-1 0.47 0.41 0.008 0.969 0.58 0.009 0.928 0.48 0.001 0.99

Gras

sland

9% 80 mm h-1 0.48 0.47 0.01 0.96 0.62 0.011 0.899 0.55 0.004 0.959

120 mm h-1 0.44 0.42 0.007 0.971 0.58 0.008 0.929 0.49 0.002 0.982

15% 80 mm h-1 0.32 0.34 0.007 0.969 0.47 0.017 0.87 0.36 0.004 0.967

120 mm h-1 0.47 0.42 0.007 0.97 0.59 0.009 0.924 0.49 0.002 0.986

20% 80 mm h-1 0.33 0.35 0.007 0.97 0.49 0.017 0.87 0.37 0.004 0.971

120 mm h-1 0.41 0.38 0.006 0.976 0.55 0.011 0.914 0.43 0.002 0.987

Fore

st

9% 80 mm h-1 No data*

120 mm h-1 0.78 0.65 0.023 0.909 0.79 0.007 0.922 0.77 0.001 0.987

15% 80 mm h-1 1.17 0.93 0.067 0.729 1.05 0.016 0.719 1.16 0.001 0.982

120 mm h-1 0.83 0.77 0.023 0.906 0.79 0.02 0.705 0.89 0.004 0.936

20% 80 mm h-1 1.25 1.17 0.061 0.754 1.46 0.004 0.912 1.25 0.002 0.959

120 mm h-1 0.63 0.61 0.011 0.955 0.71 0.011 0.87 0.7 0.002 0.976

Mea

sure

d an

d pr

edic

ted

D50

valu

es a

long

with

MSE

an

d R

2va

lues

for t

he ru

noff

sedi

men

ts Cul

tivat

ed

Land

Gra

ssla

ndFo

rest

Res

ults

… Results clearly indicated that cultivated land and grassland soils have produced similar size aggregate distributions and D50 values after rainfall simulations for detachment and transport processes opposite to the soils of the forest plantation area under the saturated soil conditions.

And, the all studied models had higher potential to estimate the eroded sediment distributions obtained from various rainfall simulations.

Especially, the Weibull model has shown the best fit with the lowest MSE values (0.0048 ≤ MSE ≤ 0.0002) and the highest determination coefficient (0.998 ≤ R2 ≤0.936) for modeling eroded sediments by RST and RIFT processes.

The Log-normal approach generally resulted in a lower estimated value than the actual value opposite to the Fractal approach which showed a tendency to higher model estimates.

In summary, this study of laboratory rainfall simulations demonstrated that the Weibullcumulative distribution function can be used effectively to model the aggregate size distribution of raindrop and shallow flow-induced sediment transport processes

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