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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: [email protected], [email protected])*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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