IDENTIFICATION OF SEDIMENT SOURCE AREAS WITHIN A
WATERSHED
L. Kalin and M.M. Hantush
U.S. EPA, National Risk Management
Research Lab., Cincinnati, OH, 45268, USA.
e-mail: Kalin.Latif@epamail.epa.gov and
Hantush. Mohamed@epamail. epa. gov
R.S. Govindaraju
School of Civil Engineering, Purdue
University, West Lafayette, IN 47907, USA.
e-mail: govind@ecn.purdue.edu
ABSTRACT
Two methods, one using a travel time approach and the other based on optimization techniques,
were developed to identify sediment generating areas within a watershed. Both methods rely on
hydrograph and sedimentograph data collected at the mouth of the watershed. Data from several
events were examined over two small watersheds, and a statistical procedure was utilized to
assess the erosion vulnerability of different regions within the watersheds. Results from these
two independent methods showed good agreement with USLE-based observations. These
methods seem viable for practical use if the number of sediment generating regions is small, and
good data from several events is available to achieve statistically meaningful results.
INTRODUCTION
Sediment yield from a watershed has important implications for water quality and water
resources, especially from agricultural areas. There are two important time scales associated with
sediment movement and consequently with source assessment. Depending on geomorphologic
properties, nature of the sediment source and size of the storm, the sediment may move from the
source-region to the watershed outlet in a single event. In such instances, the time scale is fairly
short and limited to the duration of surface runoff over the watershed. At this time scale, the
problem of identifying the source areas of sediments based on information available at the outlet
has many practical applications. However, this problem has received very little attention, as most
modeling strategies have focused on the forward problem of predicting sediment concentrations
given the source locations and strengths. The longer time-scale problem arises when sediment
travels more slowly over the watershed. The focus of this study is on the former time scale where
sediment moves to the watershed outlet in a single event.
A limited number of source assessment methods are available in the literature to estimate
potential loadings from hillslopes and banks to receiving waters, for evaluating stream-storage
and transport of sediments, and to estimate sediment yield from basins. The approach proposed
in this study combines the strengths of using a detailed model for the flow field and incorporates
the fate and transport of sediment in a way that is ideally suited for source assessment based on
information gathered at the watershed outlet from the stream hydrograph and sedimentographs.
The overall goal of this study is to identify sediment-generating regions within a watershed using
geomorphologic information over the watershed, available rainfall data, and data on hydrographs
and sedimentographs collected at the outlet of the watershed. The surface flow and sediment
transport model, KINEROS (Woolhiser et al., 1990) has been utilized in this study.

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STUDY WATERSHEDS
Two experimental, field scale watersheds (namely W-2 and W-3) located near Treynor, Iowa,
with areas of approximately 83 and 107 acres (33 and 42 ha), respectively, were adopted for this
study. Measurements of runoff, baseflow, and sediment load using weirs located at the base of
each of these watersheds are available. Watersheds W-2 and W-3 are similar in characteristics
with a rolling topography defined by gently sloping ridges, steep side slopes, and alluvial valleys
with incised channels that normally end at an active gully head, typical of the deep loess soil in
MLRA 107 (Kramer et al., 1990). Slopes usually change from 2 to 4 percent on the ridges and
valleys and 12 to 16 percent on the side slopes. An average slope of about 8.4 percent is
estimated for both watersheds, using first-order soil survey maps. The major soil types are well
drained Typic Hapludolls, Typic Udorthents, and Cumulic Hapludolls (Marshall-Monona-Ida
and Napier series), classified as fine-silty, mixed, mesics. The surface soils consist of silt loam
and silty loam textures that are very prone to erosion, requiring suitable conservation practices to
prevent soil loss (Chung et al., 1999). Corn has been grown continuously on W-2 since 1964, and
on W-3 since 1972. The W-3 watershed was predominantly bromegrass, with small amounts of
orchard grass and alfalfa from 1964 through 1971.
Fig. 1. Watersheds W-2 and W-3 partitioned into 8 elements used for identifying sediment
sources within the watersheds. Elements 2 to 4 are channels, and element 1 is the outlet..
The regional geology is characterized by a thick layer of loess overlying glacial till that together
overlay bedrock. The loess thickness ranges from 3 m in the valleys to 27 m on the ridges. These
watersheds have been the subject of watershed-studies by many researchers for almost 30 years.
THE TRAVEL TIME APPRAOCH
Many studies have utilized the unit sedimentograph method for analyzing sediment output from
watersheds (Singh et al., 1982; Kumar and Rastogi, 1987; Banasik and Walling, 1996). Since the
goal of this paper is development of a methodology for source identification, a modified
approach is described here. The watershed under consideration is partitioned into NE number of
elements (k=l,2,3,.. ,,NE). For a rainfall event (p) under consideration characterized by pulses of

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excess rainfall depths denoted by Pi, P2, Pm each having duration of At, the sediment flux
response of element k from that event at the basin outlet at time t = nAt is
M
Y k (nAt) = y k„ =£Pmli[(n-m + l)At-sk]	(l)
m=i
where hk(t-Sk) is the unit pulse response at the watershed outlet from the kth element and Sk is the
time when sediment from element k is first observed at the basin outlet from element k under
unit amount of rainfall starting at t=0. When the response of all the elements are taken into
account then the sediment discharge expected at the watershed outlet at time t = nAt can be
estimated by
NE M
y(n) = ZZPmhk,„-m+l	(2)
k=l m=l
where hk,n-m+i = h[(n-m+l)At-Sk]. The unit pulse response function hk is called Unit
Sedimentograph (USG) of element k. The Normalized Unit Sedimentograph (NUSG) for an
element k is defined as
NUSGk>t=^ii^	(3)
J"hk,tdt
0
If A,k is used to represent the total sediment load generated from element k due to a unit amount
of rainfall, then the unit pulse response function of an element k can be written
as hk t = Xk ¦ NUSGk t. Equation (2) becomes
NE M
y(n) = 2]^lZp».NUSGl,-«».	<4)
k=l m=l
The problem reduces to finding those values of A,k that minimize differences between observed
sediment discharge and predictions from (4). A common method of achieving this is by
minimization of the error expression
E2=I
-IXIXnusg,™,
k=l
(5)
where yn are the observed values with N being total number of data points. Naturally, large
elements will likely be associated with large X. If erodibility index of an element k is defined as
Ck=Ak/A|x where Ak is the area of the element k, then source strength of different elements can be
evaluated by comparing Ck values, and finally a map of the watershed showing the high and low

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erosion potential areas can be generated. Here Ck is defined as a measure of the erosion potential
of element k.
The NUSGs were generated for each element of the two watersheds and were found to be well-
represented by log-normal distributions. Further, the NUSGs could be characterized completely
in terms of the average travel times of sediments from the element to the outlet of the watershed.
Using the model of equation (4), sample results for some events are shown in Figs. 2a and 2b.
30
180
300
kg/s
O 05/30/82
kg/s
06/18/80
kg/s
06/30/82
200
20
120
10
60
100
0
25
0
40
80
120
25
50
min
min
min
Figure 2a. Observed (hollow circles) and predicted (solid line) sediment discharges for three
sample events from W-2 using travel time approach.
24
45
06/04/80
kg/s
05/19/78
kg/s
30
_©I
30
0
40
80
120
min
min
21
kg/s
08/12/86
14
7
0
0
40
80
120
min
Figure 2b. Observed (hollow circles) and predicted (solid line) sediment discharges for three
sample events from W-3 using travel time approach.
Data from different rainfall events yielded different Ck values. Tukey's procedure was utilized to
evaluate if the erodibilities of different elements were statistically different. Table 1 summarizes
the results of the statistical test for different relative Ck values for W-2.
OPTIMIZATION APPROACH
Details of the governing flow and erosion equations can be found in Woolhiser et al. (1990) and
are not repeated here. The Bagnold/Kilinc (Kilinc and Richardson, 1973) formula is used for the
estimation of the equilibrium concentration Cmx, which states

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where t = ywhs with yw being specific weight of water, h as flow depth and s as the slope, tc is
Shields critical tractive force, u is velocity of water and C0 is a scaling parameter and a measure
of soil erodibility. Then, for a large rainfall event p, the following relationship applies from the
linearity of sediment transport equation
NE
Q")(t) = Xc<.t.)'f',)0)	(7)
1=1
Table 1. Grouping of elements for W-2 according to Tukey's procedure with varying a levels
using travel times approach.
Element
mean
a = 0.10
a = 0.20
a = 0.30
12
0.00
A
A
A
11
0.18
A
A
A
6
1.13
A
A
A
8
4.19
A B
A
A B
7
9.02
ABC
A B
ABC
5
23.89
ABC
ABC
BCD
9
28.26
B C
B C
C D
10
33.33
C
C
D
In (7), Q(p)(t) represents the sedimentograph resulting from rainfall event p. C(p' is the value of
the Co parameter for element i during rainfall event p and f/p)(t) is the unit sedimentograph
resulting from rainfall event p under the condition
Co,k = $i,k	(8)
where 5i k=l for i=k and zero otherwise. Note that f/p,(t), i=l,..,m can be computed from
KINEROS for any rainfall event. The goal now is to estimate the values of C(p) in an
optimization framework. If the error between observed (Q(p)(tn)) and computed sediment
o
discharge (Q(tn)) at nth observation time tn is defined as
NE
4"=Q:(i,)-ic"f"(i,)	(9)
then the objective function to be minimized is

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n=l
(10)
where N is total number of data points in the observed sedimentograph. Since erodibilities
cannot be negative, the constraint C(p' > 0 has to be imposed during optimization. Model results
from equation (7) are shown in Figs. 3a and 3b for the two watersheds, and statistical analysis
results in Table 2.
30
180
240
06/30/82
05/30/82
kg/s o
kg/s
06/18/80
kg/s
20
120
160
80
0
0
40
80
120
75
0
20
min
min
min
Figure 3a. Observed (hollow circles) and predicted (solid line) sediment discharges for three
sample events from W-2 using an optimization approach.
24
45
05/19/78
06/04/80
kg/s
kg/s
16
30
8
0
0
40
80
120
30
60
min
min
18
08/12/86
kg/s
12
6
0
0
40
80
120
min
Figure 3b. Observed (hollow circles) and predicted (solid line) sediment discharges for three
sample events from W-3 using an optimization approach.
Figure 4 shows spatial maps of erosion potential areas for W-2 and W-3 using the two methods.
For comparison with physical properties of the watershed, erosion vulnerability was also studied
using parameters of the USLE, and the results are shown in Fig. 4e and 4f.

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Table 2. Grouping of elements for W-2 according to Tukey's procedure with varying a levels
using the optimization procedure.
nent
mean
a = 0.10
a = 0.20
a = 0.30
11
0.00
A
A
A
8
0.55
A
A
A
9
7.28
A B
A
A
12
9.38
A B
A B
A B
7
9.46
A B
A B
A B
6
10.52
A B
A B
A B
10
30.76
B
B
B C
5
32.06
B
B
C
/
\

[Ck]
~	0-5
~	5-10
I	1 10-15
| 15-20
| |20 - 25
I I 25 - 30
30 - 35
(a) W-2. Travel time approach
[CO]
! H 0-5
I I 5-10
| | 10 - 15
I | 15 - 20
20 - 25
25 - 30
[Ck]
I I 0-5
I I 5 - 10
~ 10-15
J 15-20
I I 20 - 25
(b) W-3. Travel time approach
[CO]
I I 0-5
I 15-10
^2 10 - 15
~	15-20
~	20 - 25
>25-30
¦ 30 - 35
(c). W-2. Optimization approach
(d). W-3. Optimization approach

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[KLS]
I | 3.0- 3.5
| | 3.5-4.0
^2 4.0 - 4.5
I | 4.5-5.0
~	5.0 - 5.5
~	5.5 - 6.0
B 6.0-6.5
[KLS]
	3.0 - 3.5
~	3.5 - 4.0
^ 4.0 - 4.5
4.5 - 5.0
| 5 .0- 5.5
^ 5.5 - 6.0
| 6.0 - 6.5
~	6.5 - 7.0
~	7.0 - 7.5
~	7.5 - 8.0
¦ 8.0 - 8.5
(e) W-2. USLE parameters
(f) W-3. USLE parameters
Fig. 4. Maps showing erosion vulnerability for the two watersheds by different methods. [KLS]
represents erodibility with USLE parameters.
SUMMARY AND CONCLUSIONS
A modified unit sedimentograph method in terms of a travel time approach, along with an
optimization method was implemented to rank sediment generating areas of W-2 and W-3
watersheds based on their erodibilities. The ensemble average of normalized erodibility indices
over several events were compared statistically by employing Tukey's approach at different
levels of statistical significance. The estimated relative erodibilities were more consistent in W-3
than the relative erodibilities in W-2 with major differences in elements having low erodibilities.
Both methods estimated the same areas as the high erosion potential areas. Outcomes from the
two methodologies were also compared to erosion potentials maps generated using the USLE
equation. In general, results from all three methods were comparable. The only inconsistency
was with the element 10 of the W-2 watershed.
ACKNOWLEDGEMENT
This research was funded by EPA, Award No. R-82833901-0. It has not been subjected to
Agency review and therefore does not necessarily reflect the views of the Agency, and no
official endorsement should be inferred. The authors gratefully acknowledge this support.
Special thanks to Larry Kramer, USDA-ARS-NSTL-DLRS, Council Bluffs, IA, for supplying all
the data sets.
REFERENCES
Banasik, K. & D.E. Walling (1996). Predicting sedimentographs for a small catchment, Nordic
Hydrology, 27(4), 275-294.

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Chung, S.W., P.W. Gassman, L.A. Kramer, J.R. Williams & R. Gu (1999). Validation of EPIC
for two watersheds in southwest Iowa, Journal of Environmental Quality, 28(3), 971-979.
Kilinc, M. & E.V. Richardson (1973). Mechanics of soil erosion from overland flow by
simulated rainfall, Hydrology Paper 63, 54 pp, Colorado State University, Fort Collins.
Kramer, L.A., E.E. Alberts, A.T. Hjelmfelt & M.R. Gebhardt (1990). Effect of soil conservation
systems on groundwater nitrate levels from three corn-cropped watersheds in southwest Iowa, in
Proc. of the 1990 Cluster of Conferences, Kansas City, MO.
Kumar, S. & R.A. Rastogi (1987). A conceptual model for estimating suspended sediment flow,
Journal of Hydrology, 95, 155-163.
Singh, V.P., A. Baniukiwicz, V. J. Chen (1982). An instantaneous unit sediment graph study for
small upland watersheds, In: Applied Modeling in Catchment Hydrology, Ed. Singh, V.P., Water
Resources Publications, Littleton, CO.
Woolhiser, D.A., R.E. Smith & D.C. Goodrich (1990). KINEROS-A kinematic runoff and
erosion model: Documentation and user manual, U.S. Dept. of Agriculture, Agricultural
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