Stoch Environ Res Risk Assess (2012) 26:581–597
DOI 10.1007/s00477-011-0515-3
ORIGINAL PAPER
DEM-based numerical modelling of runoff and soil erosion
processes in the hilly–gully loess regions
Tao Yang • Chong-yu Xu • Qiang Zhang •
Zhongbo Yu • Alexander Baron • Xiaoyan Wang
Vijay P. Singh
•
Published online: 10 August 2011
Ó Springer-Verlag 2011
Abstract For sake of improving our current understanding on soil erosion processes in the hilly–gully loess
regions of the middle Yellow River basin in China, a
digital elevation model (DEM)-based runoff and sediment
processes simulating model was developed. Infiltration
excess runoff theory was used to describe the runoff generation process while a kinematic wave equation was
solved using the finite-difference technique to simulate
concentration processes on hillslopes. The soil erosion
processes were modelled using the particular characteristics of loess slope, gully slope, and groove to characterize
the unique features of steep hillslopes and a large variety of
T. Yang (&)
State Key Laboratory of Desert and Oasis Ecology,
Xinjiang Institute of Ecology and Geography, Chinese Academy
of Sciences, CAS, 818, Road BeijingNan, Urumqi,
Xinjiang 830011, The People’s Republic of China
e-mail: enigama2000@hhu.edu.cn
T. Yang A. Baron X. Wang
State Key Laboratory of Hydrology-Water Resources
and Hydraulic Engineering, Hohai University,
Nanjing 210098, China
C. Xu
Department of Geosciences, University of Oslo, Blindern,
P.O. Box 1047, Oslo 0316, Norway
Q. Zhang
Department of Water Resources and Environment, Sun Yat-sen
University, Guangzhou 510275, China
Z. Yu
Department of Geoscience, University of Nevada Las Vegas,
Las Vegas, NV 89154-4010, USA
V. P. Singh
Department of Biological and Agricultural Engineering, Texas A
& M University, College Station, TX 77843-2117, USA
gullies based on a number of experiments. The constructed
model was calibrated and verified in the Chabagou catchment, located in the middle Yellow River of China and
dominated by an extreme soil-erosion rate. Moreover,
spatio-temporal characterization of the soil erosion processes in small catchments and in-depth analysis between
discharge and sediment concentration for the hyper-concentrated flows were addressed in detail. Thereafter, the
calibrated model was applied to the Xingzihe catchment,
which is dominated by similar soil erosion processes in the
Yellow River basin. Results indicate that the model is
capable of simulating runoff and soil erosion processes in
such hilly–gully loess regions. The developed model are
expected to contribute to further understanding of runoff
generation and soil erosion processes in small catchments
characterized by steep hillslopes, a large variety of gullies,
and hyper-concentrated flow, and will be beneficial to
water and soil conservation planning and management for
catchments dealing with serious water and soil loss in the
Loess Plateau.
Keywords Hilly–gully loess region The Yellow River High sediment concentration Runoff Soil erosion
processes DEM-based model Parameter sensitivity
analysis
1 Introduction
The Loess Plateau, located in the middle Yellow River
basin of China, has been commonly reported for the most
serious soil erosion and water losses all over the world
(World Wildlife Fund (WWF) 2004). About 73% of the
eroded soil enters the Yellow River, causing enormous
amounts of sedimentation and a high risk of flooding
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582
downstream. Over 60% of the Loess Plateau suffers from
soil erosion as a result of irrational land use and poor
vegetation coverage, which have negatively impacted
regional eco-environments (BREST-CAS 1992; Fu 1989;
Fu and Gulinck 1994; Shi and Shao 2000; Yang et al. 2008,
2009a, 2009b). Agriculture accounts for a high percentage
of the local economic development; however, centuries of
deforestation and over-grazing, exacerbated by China’s
population increase, have resulted in degenerated ecosystems, desertification, and poor local economies (Chen et al.
2001). The soil loss in the basin can reach four billion tons
per year due to deforestation and agricultural cultivation on
hillsides (WWF 2004).
With the recognition of the negative impacts of soil
erosion on the environment, a number of water and soil
conservation measures have been implemented in the
catchments of the Loess Plateau to control soil erosion,
maintain a healthy eco-environment and regional sustainable development since the 1950s. In 1999, the government
initiated a nationwide project to set aside cropland for
afforestation and soil conservation, known as the Grainfor-Green Program, which has been recognized as one of
the world’s largest conservation projects (WWF 2004).
The Loess Plateau is one of the major target areas in the
Grain-for-Green Program. The program requested that
arable land with a slope higher than 25.8° should be converted into woodland and pasture. Due to a vast cover area
(640,000 km2) and very rich coal resource, the Loess
Plateau is very important to regional eco-environmental
security and the sustainable development of western China
(Yang et al. 2009a). For this purpose, modelling of runoff
and sediment processes are of paramount importance to
understanding the soil erosion processes and formulating
effective countermeasures for soil erosion control for the
region.
Physically-based models such as ANSWERS (Beasley
et al. 1980), WEPP (Nearing et al. 1989), EUROSEM
(Morgan et al. 1998), GUEST (Misra and Rose 1989), and
LISEM (De Roo et al. 1996) are now widely accepted
mathematical models for simulating soil erosion processes.
Murakami et al. (2001) coupled the SWM model with
sediment discharge from overland flow to predict the outflow of soil from an agricultural watershed. Parlange et al.
(1999) and Hairsine and Rose (1991) developed a soil
erosion model to elucidate the rainstorm-induced sediment
transport process. Wongsa et al. (2002) developed a onedimensional hydrodynamic model for simulation of
mountain river systems by combining a kinematic runoff
model, hillslope erosion model, and sediment transport
model of a river channel. Chen et al. (2006) developed a
physiographic soil erosion–deposition model (PSD) by
coupling GIS with a physiographic typhoon-induced storm
event-based rainfall-runoff model for a tropical catchment
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Stoch Environ Res Risk Assess (2012) 26:581–597
in Taiwan. Masoudi et al. (2006) developed a new model
for assessing the risk of water erosion, taking into consideration nine indicators of water erosion the model
identifies areas with ‘Potential Risk’ (risky zones) and
areas of ‘Actual Risk’ as well as projects the probability of
the worse degradation in future. These models provide
significant insights into the dynamic processes of soil
erosion and sediment yield in watersheds.
However, the aforementioned models do not reflect the
unique characteristics of runoff and soil erosion processes
in loess regions with steep hillslopes, a number of gullies of
various sizes, and a high concentration of highly coarse
sediment. Therefore, they cannot be applied directly to
simulate runoff and sediment yield processes on the hilly
and gully-covered Loess Plateau of China. To overcome
these limitations, Tang and Chen (1990, 1997) developed
the Hohai University Model (HUM) with the aim of simulating runoff and sediment processes in small- and medium-size river basins based on differential kinematic wave
theories, and used it to simulate those processes in hilly
Loess Plateau regions. Xie et al. (1990) developed a sediment yield model for medium- and large-size river basins.
Cai and Lu (1998, 1996) took into account the complex
topographical factors and spatial variability of sediment
yield in the loess region of northwestern China in modeling
runoff and sediment yield processes. It should be noted that
there are still several critical limitations to the models
mentioned above when they are used in a loess region: (1)
It is essential to build an appropriate GRID-based runoff
and sediment processes model for small catchments which
is capable of simulating spatial and temporal runoffinduced soil erosion processes in this hilly–gully loess
region. However, reports addressing models that feature
these unique runoff and sediment processes are insufficient
so far. (2) A stream network that is not extracted using GIS
does not properly demonstrate the influence of the topography of the river basin on runoff and sediment yield. (3)
Spatio-temporal characterization of the soil erosion processes in small catchments and in-depth analysis between
discharge and sediment concentration in the hilly–gully
loess regions are still very limited. Therefore, this work
aimed: (1) to construct a Digital Elevation Model (DEM)based runoff and sediment model for sake of more precise
simulating based on improvement of the HUM model
developed by Tang and Chen (1990, 1997) and Yang et al.
(2005, 2007) for small catchments in the hilly and gully
region in order to understand the complex sediment
processes; (2) to assess the spatio-temporal soil erosion
processes based on topographical and geophysical characteristics of loess slopes, gully slopes, and grooves of two
typical catchments in the middle Yellow River basin, the
Chabagou and Xingzihe catchments; and (3) to conduct
sensitivity analysis of the major model parameters using
Stoch Environ Res Risk Assess (2012) 26:581–597
Monte Carlo simulations to quantify different effects of
parameter sets for sake of parameter optimization in further
studies.
2 Study domain and data
2.1 Study domain
A DEM-based runoff and sediment processes numerical
model at the rainstorm event scale requires: (1) that the
study domain have adequate land cover data at a high
resolution (e.g., DEM, soil type distribution, vegetation
cover, and land use patterns, Bek and Ježek 2011), and
high-density runoff and sediment observations; and (2) that
the drainage area of the catchment not be too large (i.e.
\2000 km2) to investigate the physical runoff and sediment processes at this catchment scale, nor too small (i.e.
583
[100 km2) for application in actual practices of water and
soil loss planning and management in the catchments
(normally, 100–2000 km2 scale) of the Loess region.
For these reasons, the Chabagou River (Fig. 1a), a
second-order tributary of the Yellow River, was selected as
the study area to calibrate and verify the DEM-based runoff
and sediment processes model using intensive hydrological
observations. The Chabagou River has a drainage area of
205 km2 with the CP hydrological station as its outlet
(Table 1). The rainfall in July, August, and September
accounts for 60–70% of the annual total precipitation, most
of which is produced by rainstorms resulting in large yields
of highly coarse sediment. Therefore, sediment yield
mostly occurs in these periods. The catchment is covered
by Quaternary loess and is one of the main sources of
sediment yield in the middle Yellow River basin. Furthermore, poor vegetation cover and excessive agricultural
development further intensifies soil erosion in the region.
Fig. 1 Location of Chabagou and Xingzihe catchments on the Loess Plateau
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Stoch Environ Res Risk Assess (2012) 26:581–597
Table 1 List of hydrological and sediment stations for two typical catchments on the hilly–gully Loess Plateau
No.
Stations
Location
1.
CP-Caoping
110.25°E
2.
XH-Xinghe
110.52°E
Catchment
Drainage area (km2)
37.14°N
Cabagou Catchment
205
37.42°N
Xingzihe Catchment
1,486
Source of data: Hydrology Bureau, Yellow River Conservancy Commission
Table 2 List of selected storm events used for model calibration and
validation in Cabagou Catchment
No.
Selected
storm
events
Total
rainfall
(mm)
Runoff
peak
(m3/s)
Sediment
peak
(kg/m3)
19700701
10.2
70
875
Calibration
2
19700702
58.4
532
854
Calibration
3
19710701
14.8
131
741
Calibration
4
19720702
24.7
119
875
Calibration
5
19740702
59.7
106
742
Calibration
6
19780802
45.2
180
855
Calibration
7
19790701
18.9
32
858
Calibration
8
19800701
13.4
18.1
765
Calibration
9
19830702
35.8
88.8
911
Calibration
10
19880703
46.2
119
647
Validation
11
19890701
66.6
309
822
Validation
19940804
65.6
313
776
Validation
13
19950902
42.7
313
673
Validation
14
15
19960731
19990720
43.5
24.8
315
133
685
518
Validation
Validation
16
20000704
14.3
141
687
Validation
17
20010818
39.3
183
714
Validation
Source of data: Hydrology Bureau, Yellow River Conservancy
Commission
Another similar hilly–gully loess region of the middle
Yellow River basin, the Xingzihe River catchment
(Fig. 1b; Table 1) is also characterized by high soil loss
rates in China. The main stream of the Xingzihe River is
102.8 km long and has a drainage area of 1,486 km2 at
Xingzihe Station. The calibrated model was applied to the
Xingzihe catchment to assess the model’s ability in simulating runoff and sediment processes in the Loess Plateau
region.
2.2 Data
Observation data from seventeen typical storm events,
including half-hourly rainfall, streamflow, and sediment
load data from the CP gauge of the Chagbagou catchment
in the middle Yellow River basin (1970–2001), were collected and used in this study (Table 2). These observations
123
Cover or treatment
Value recommended
Range
Concrete or asphalt
0.011
0.010–0.013
Purpose
1
12
Table 3 Recommended Manning’s coefficients for overland flow
Bare sand
0.01
0.010–0.016
Graveled surface
0.02
0.012–0.03
Bare clay—loam (eroded)
0.02
0.012–0.033
Fallow—no residue
0.05
0.006–0.16
Chisel plow
0.07
0.006–0.17
Disk/harrow
0.08
0.008–0.41
No till
0.04
0.03–0.07
Moldboard plow (Fall)
0.06
0.02–0.10
Coulter
0.10
0.05–0.13
Range (natural)
Range (Clipped)
0.13
0.10
0.01–0.32
0.02–0.24
Grass (bluegrass sod)
0.45
0.39–0.63
Short grass prairie
0.15
0.10–0.20
Dense grass
0.24
0.17–0.30
Bermuda grass
0.41
0.30–0.46s
Source: Engman 1986
were compiled and provided by the Hydrology Bureau of
the Yellow River Conservancy Commission (YRCC) of
China. Among these observations, nine storm events were
used for model calibration and the other eight were used for
validation. The slope, soil type, vegetation cover, land use,
Manning roughness, and erosion distribution of the catchment are widely recognized as the basic information for a
runoff and sediment processes model (Chen et al. 2001;
Chen et al. 2006). Mean slope, land use, and topographical
features of the Chabagou catchment were extracted from
the catchment DEM and a Landsat ETM remote sensing
image with a grid resolution of 20 m 9 20 m, using the
ArcGIS software package and ERDAS image processing
tools (Yang et al. 2007). Raw soil distribution, vegetation
cover, and erosion distribution data were provided by the
YRCC, and processed using ArcGIS into raster format with
a 20 m 9 20 m resolution. Manning’s roughness parameters were assigned to the study area in terms of the recommended Manning’s coefficients for overland flow linked
with different land use types (Engman 1986; Table 3).
Details can be found in the report by Yang (2007).
Stoch Environ Res Risk Assess (2012) 26:581–597
585
3 Model structure
3.1 Overview of model components
A DEM-based model, utilizing the simplified St. Venant
equations over grid cells with the finite-difference numerical solution, was developed to simulate the runoff and
sediment yield processes. The structure of the model is
shown in Fig. 2. The model parameters were calibrated
using nine observed storm events. The runoff and sediment
yield were routed from cell to cell in order to obtain the
processes at the catchment outlet. The soil-dependent
infiltration for each discretized cell was computed using the
Horton infiltration model. The cell topographical properties, including elevation, land use, and comprehensive
roughness for each discretized cell of the catchment, were
extracted using the GIS. In modeling storm events with
short durations, which are very common in arid areas,
actual evapotranspiration can be ignored. The calculation
procedure and major equations of the runoff and sediment
yield simulation model presented in the following sections
were modified from Tang and Chen (1990, 1997), Tang
(2003), and Yang et al. (2005, 2007). More detailed
information about the calculation procedure and major
equations can be referred to these literatures. For the sake
of better understanding of the modelling results, major
equations of the model are briefly presented in the
Precipitation
RS =
following section. In particular, this paper mainly presents
the spatio-temporal soil erosion processes using the DEMbased sediment model, offers profound discussions of the
scaling and uncertainty issues in soil erosion processes with
aims to construct a series of runoff and soil erosion processes models in the hilly–gully loess region eventually.
3.2 Infiltration excess runoff generation
The infiltration excess runoff generation is calculated as
follows:
0
PE F
RS ¼
ð1Þ
PE F PE [ F
where RS is the excess runoff (mm/min), PE (mm/min) is
the precipitation minus evapotranspiration, and F is the
infiltration (mm/min). In this study, evapotranspiration was
ignored for high-intensity rainfall events with short
durations. Thus, PE = P, and
0
PF
RS ¼
ð2Þ
P F P[F
where P is precipitation (mm/min). The Horton infiltration
model was used in this study because of its clear physical
basis and simplicity. The Horton infiltration model is
ft ¼ fc þ ðf 0 fc Þekd t
{
P≤F
0
P−F P F
ð3Þ
Excess runoff
Infiltration
V, q, h
Outlet discharge
Computation priority
Computation priority
Overland runoff
Loess slope e1
Soil erosion e
Gully slope e2
Outlet sediment
Groove e3
Runoff generation component
Runoff concentration component
Soil erosion component
Fig. 2 Overview of model structure and components
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586
Stoch Environ Res Risk Assess (2012) 26:581–597
where ft is the infiltration rate at time t (mm/min); fc is the
constant or equilibrium infiltration rate after soil has been
saturated, or the minimum infiltration rate (mm/min); f0 is
the initial infiltration rate (mm/min); and kd is a decay
constant specific to the soil conditions (dimensionless).
3.3 Overland runoff computation
The partial differential equation for describing kinematic
wave flow, which is suitable for overland flow computation
for the steeper slopes in the Loess Plateau region, is as
follows:
oq oh
þ
¼ re ðtÞ
ox ot
ð4Þ
Sf ¼ S0
ð5Þ
where q is the overland discharge per unit width (m2/s), h
is the water depth (m), x is the streamwise distance (m),
t is time (s), re(t) is the rainfall excess, or lateral inflow
(mm/min), Sf is the friction-induced head loss per unit
length between the moving fluid and the bed (m/m), and S0
is the slope of the land surface (m/m).
Equation 5 can be replaced with the Darcy–Weisbach
equation (Tang and Chen 1990, 1997):
Sf ¼ S0 ¼ f
q2
8gh2 R
ð6Þ
where f is the Darcy–Weisbach friction loss coefficient (dimensionless), which can be determined from a
Moody diagram; g is the local gravitational acceleration
(g & 9.8 m/s2); and R is the hydraulic radius (here R = h for
overland flow (m)). Equation 5 can also be replaced by
Eq. 7:
1 2 1
v ¼ h3 S2
n
ð7Þ
oq 1 1 1e oq
þ
qe
¼ re ðtÞ
ox Ks1e e
ot
where the boundary
8
qð0; tÞ ¼ 0
for
>
>
<
qðx; 0Þ ¼ 0 for
r ðtÞ ¼ 0
for
>
>
: e
re ðtÞ ¼ QðtÞ for
ð11Þ
conditions are
t[0
0 x l1 þ l2
t[T
0tT
where l1 is the length of the loess slope (m), l2 is the length
of the gully slope (m), T is the full duration of a storm
event (min), and Q(t) is accumulated runoff production
(mm).
A Preissmann implicit scheme is used to solve Eq. 11
for q as follows:
1e 1e 1 h 1e
1e
h
e
nþ1 e
nþ1 e
n
n e
qjþ1
qjþ1
þ qj
þ qj
þ
2
2
nþ1
n
qnþ1
qnj
jþ1 qjþ1 þ qj
¼ reðtÞ
2Dt
ð12Þ
where h is a weighting factor. With the Newton iterative
method, water depth and velocity of overland flow are
computed along the flow path at any time and place. More
details on the technical solution of the kinematic equation
for the Loess Plateau region can be found in previous literature (Tang and Chen 1990, 1997).
3.4 Sediment yield computation
Generally, the Loess Plateau soil erosion forms can be
categorized into three typical types: loess slope, gully
slope, and groove (Tang and Chen 1990, 1997; Yao and
Tang 2001; see Fig. 3). The soil erosion rates for gully
areas of the Loess Plateau can be derived from the energy
balance principle.
and
1
2 1
q ¼ h1þ3 S2
n
ð8Þ
where n is the Manning’s roughness (dimensionless), S is
the slope of the flow surface (m/m), and S & S0 is
gradually varied flow. If r ¼ 23 ; k ¼ 12 ; e ¼ 1 þ
r; and Ks ¼ 1n Sk0 ; then Eqs. 7 and 8 can be written as
v ¼ K s hr
ð9Þ
and
q ¼ K s he
ð10Þ
where Ks is the hydraulic roughness coefficient (dimensionless), and e is a weighting factor in the Preissmann
implicit scheme (dimensionless). Thus, a first-order nonlinear differential equation can be derived as follows:
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3.4.1 Loess slope erosion
The power of soil erosion on a loess slope per unit area
(Tang and Chen 1990, 1997; Yao and Tang 2001), Ws1 ; can
be determined as follows:
c cm
Ws1 ¼ g1 s
e1 g tga1
ð13Þ
cm
where g1 is a distance related coefficient m1 for loess slope
erosion, cs and cm are the bulk densities of dry and wet
sediments (kg/m3), respectively; e1 is the soil erosion rate
of the loess slope (kg/s); and a1 is the degree (or angle) of
the loess slope (°).
The effective power of soil erosion of the loess slope per
unit area (Tang and Chen 1990, 1997; Yao and Tang 2001),
Wf1, can be computed as follows:
Stoch Environ Res Risk Assess (2012) 26:581–597
587
concentration and high coarseness runoff processes in
loess regions. ðs0 sc Þ in Eqs. 14 and 15 can be calculated
as follows:
s0 sc ¼ cm h1 J1 þ ðcs cm Þd sin a1 f ðcs cm Þd cos a1
ð19Þ
where d is the sediment diameter (cm).
3.4.2 Gully slope erosion
Similarly, the gully slope erosion rate e2 (Tang and Chen
1990, 1997; Yao and Tang 2001) can be calculated as
follows:
cm
e 2 ¼ f 2 A1
ðs0 sc ÞV
ð20Þ
cs cm
where f2 is the energy coefficient for gully soil erosion
(dimensionless). If A2 = f2 A1 , then
cm
e 2 ¼ A2
ðs0 sc ÞV
ð21Þ
cs cm
where
s0 sc ¼ cm h2 J2 þ ðcs cm Þd sin a2 f ðcs cm Þd cos a2
ð22Þ
Fig. 3 Typical landscape and illustration of topography in the hilly
Loess Plateau
Wf 1 ¼ Aðso sc ÞV
ð14Þ
where so is the shear stress (N/m2), sc is the critical yield
stress (N/m2), V is the cross-sectional average velocity of
surface flow (m/s), and A is a non-dimensional coefficient.
If Ws1 = Wf1, then
cm
e 1 ¼ A1
ðso sc ÞV
ð15Þ
cs cm
where A1 ¼ gg Atga1 is calibrated using the monitoring data,
1
and cm can be obtained from Eqs. 16, 17 and 18 as follows:
c
cm ¼ c þ 1 SC
ð16Þ
cs
Qc
ð17Þ
SC ¼ 1000c 1 Qh
J10:017 J00:098
Qh ¼ 1:2365Q1:030
c
ð18Þ
3
where c is the bulk density of the clear water (kg/m ); SC is
the sediment concentration (kg/km3); Qh, and Qc are the
discharges of clear water and muddy water (m3/s),
respectively; J1 is the slope of the loess slope (%); and
J0 is the slope of the surface flow (%). Equation 18 is
proposed by Tang and Chen (1990, 1997) through a
number of field experiments for the hyper sediment
where h2 is the flow depth in the gully (m), d is the sediment diameter (cm), J2 is the slope of the gully (%), a2 is
the degree (or angle) of the gully slope (°), and other
variables are defined in the ‘‘Appendix 1’’ section.
3.4.3 Groove erosion
The soil erosion power of the groove per unit area (Tang
and Chen 1990, 1997; Yao and Tang 2001), Ws3, can be
obtained as follows:
c cm
x
Ws3 ¼ g3 s
ð23Þ
e3 g V
cm
where g3 is a distance related coefficient m1 for groove
erosion, e3 is the groove soil erosion rate (kg/s), and x is
the settling velocity (cm/s).
The actual soil erosion power of the groove per unit
area (Tang and Chen 1990, 1997; Yao and Tang 2001),
Wf3, is
CB0 f3 cm h3 J3 U
ð24Þ
j
pffiffiffiffiffiffiffiffiffiffiffi
where U ¼ gh3 J3 is the friction velocity (m/s), h3 is the
groove depth (m), J3 is the groove slope (%), j is the
Karman constant, f3 is the energy coefficient for groove soil
erosion (dimensionless), and C and B0 are dimensionless
coefficients and can be calibrated with the observed data. If
Ws3 ¼ Wf 3 ; then
Wf 3 ¼
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588
e3 ¼
Stoch Environ Res Risk Assess (2012) 26:581–597
Cf3 B0 cm
c h3 J 3 U V
jxg3 g cs cm m
Let A3 ¼
e 3 ¼ A3
Cf3 Bo
jxg3
ð25Þ
; then,
3 3
c2m
pffiffiffi h23 J32 V
ðcs cm Þ g
ð26Þ
where A3 is a coefficient and can be calibrated using the
observed data. The choice of formulas for sediment yields e1
(loess slope), e2 (gully), and e3 (groove) was made using the
spatial map of soil erosion, including loess slopes, gullies,
and grooves. This method has been reported in the literature
(Tang and Chen 1990, 1997; Yao and Tang 2001; Yang et al.
2007). Yang et al. (2007) constructed a spatial map of soil
erosion for the Chabagou catchment covering loess slopes,
gullies, and grooves at a scale of 20 m 9 20 m, providing a
key reference for choosing the soil erosion formula.
Previous investigations (Bureau of Resource, Environmental Science and Technology, Chinese Academy of
Sciences (BREST-CAS) 1992; Cai and Lu 1998; Tang and
Chen 1990, 1997; Tang 2003) demonstrated that the sediment transport rate of small catchments in loess regions is
approximately 1.0, which means the sediment yield in the
catchment has been transported almost to the outlet
downstream; hence, the sediment transport calculation has
been simplified in this model.
3.5 Sensitivity analysis of key model parameters
Generally, there are many different groups of grid element
parameters that can produce equally accurate predictions,
the so-called equifinality problem in hydrological modeling
(Beven 1992, 1993). Parameter uncertainty is one of the
main causes of model simulation uncertainty. Quantitative
determination of parameter uncertainty and its effect on
model simulation uncertainty is not the main focus of the
present study. However, in order to learn how serious the
equifinality problem is in the model and provide a basis for
future studies on the quantification of parameter uncertainty, we tested key parameters using the Monte Carlo
simulation approach. To perform the test, the Nash–Sutcliffe efficiency measure (CE) as defined in Eq. 27 was
used:
CE ¼ 1 r2e =r20
ð27Þ
where r2e is the variance of model residuals, and r2o is the
variance of observations.
Prior information about parameters may take a number
of forms, and uniform distribution of parameters was
chosen with a range wide enough to encompass the
expected models of the catchment response in this investigation. This procedure was applied to parameter sets,
rather than to individual parameter values, so that any
interactions between parameters were taken into account
implicitly in the procedure.
4 Results
4.1 Model calibration and validation
Four key model parameters (f0, fc, Kd, and h) were singled
out for evaluating uncertainty in the Monte Carlo simulation. The ranges and mean values of the four parameters
are listed in Table 4. The likely values of the selected four
parameters derived through Monte Carlo simulations of the
Chabagou catchment are shown in Fig. 4. Two of the four
parameters, fc (the equilibrium infiltration rate) and Kd (the
flow generation parameter), were well confined by the
likelihood function, while the other two, fo (maximum
infiltration rate) and h (overland flow routing coefficient),
showed strong equifinality.
Table 5 shows that the CE values for modeling runoff
ranged from 0.60 to 0.89, with a mean CE of 0.76; the
sediment CE ranged from 0.58 to 0.79, with a mean CE of
0.65 in model calibration. Meanwhile, Table 6 shows that
the validation runoff CEs ranged from 0.61 to 0.76, with a
mean CE of 0.69, and the sediment CE ranged from 0.51 to
0.65, with a mean CE of 0.58. Figure 5 indicates that most
of the simulated results compared well with observed
runoff and sediment yield in calibration and validation,
except for those events 19700702 and 19780802. Therefore, the simulation results are reliable and appropriate for
practical use.
Simulated results for event 19700702 had a CE of 0.60
for runoff and a CE of 0.58 for sediment yield, far below
Table 4 Parameter ranges used in Monte Carlo simulation for Chabagou Catchment
Parameter
Physical meaning
Minimum value
Maximum value
Mean value
fo
Maximum (or initial) infiltration rate
8 mm/min
9 mm/min
8.5 mm/min
fc
Minimum (or equilibrium) infiltration rate
1.6 mm/min
1.7 mm/min
1.65 mm/min
Kd
Infiltration constant
0.1
0.5
0.25
h
Overland flow routing coefficient (in formula 12)
0.6
1
0.8
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Stoch Environ Res Risk Assess (2012) 26:581–597
589
0.8
Likelihood measure
Likelihood measure
0.8
0.6
0.4
0.2
0.0
8.0
8.2
8.4
8.6
8.8
0.6
0.4
0.2
0.0
1.60
9.0
1.62
1.64
f0 (mm/min)
1.68
1.70
0.8
Likelihood measure
Likelihood measure
0.8
0.6
0.4
0.2
0.0
0.1
1.66
fc (mm/min)
0.2
0.3
0.4
0.6
0.4
0.2
0.0
0.5
0.6
0.7
0.8
0.9
1.0
Kd
Fig. 4 Scatter plots of likelihood values for selected four parameters from Monte Carlo simulation of Chabagou catchment during storm event
on July, 2nd 1974
Table 5 Runoff and sediment yield results for calibration storms in Chabagou Catchment
No.
Storm event
Rainfall (mm)
Runoff volume (104 9 m3)
Obs.
Sim.
Sediment yield (104 9 t)
CE
Obs.
Sim.
CE
1
19700701
10.2
34.7
29.2
0.68
26.5
19.6
0.61
2
3
19700702
19710701
58.4
14.8
326.8
40.3
541.9
64.3
0.60
0.81
257.6
27.1
441.7
47.7
0.58
0.69
4
19720702
24.7
67.8
58.6
0.79
50.5
37.2
0.62
5
19740702
59.7
188.3
161.9
0.74
103.2
77.9
0.61
6
19780802
45.2
305.5
271.9
0.77
187.2
196.7
0.63
7
19790701
18.9
35.4
34.4
0.79
19.1
17.5
0.66
8
19800701
13.4
13.1
14.0
0.76
6.7
7.6
0.65
9
19830702
35.8
158.2
165.4
0.89
89.4
108.1
0.76
Mean
Mean
the mean level in calibration. One of the reasons might be
that the model parameter sets used for simulation were
averages weighted by small, medium-size and large storm
events; thus, they did not reflect the properties of the runoff
and sediment yield for the largest flood events, such as
19700702. Furthermore, the studied drainage basin is a
complex system characterized by non-linear and dynamic
processes (Yang et al. 2008, 2009a). Temporal and spatial
variability of the meteorological factors, land use, human
0.79
0.65
activities, and other factors may contribute to increasing
uncertainties in the modeling of runoff and sediment processes in the hilly–gully loess region.
The sediment yield process, controlled by a variety of
factors, including regional meteorological characteristics,
geometric features of sediment grain, different loess hillslopes, gullies, and grooves. Meanwhile, soil erosion and
deposition and transport processes, is far more complicated
than the runoff process (Yao and Tang 2001). Therefore,
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Stoch Environ Res Risk Assess (2012) 26:581–597
Table 6 Runoff and sediment yield results for validation storms in Chabagou Catchment
No.
Selected storm events
Rainfall (mm)
Runoff volume (104 9 m3)
Obs.
Sim.
Sediment yield (104 9 t)
CE
Obs.
Sim.
CE
1
19880703
46.2
132.0
178.4
0.71
101.9
82.9
0.58
2
19890701
66.6
103.2
92.5
0.74
106.1
87.9
0.61
3
19940804
65.6
98.4
107.7
0.69
170.0
305.1
0.57
4
19950902
42.4
76.3
91.9
0.66
80.6
145.1
0.57
5
19960731
43.5
94.7
174.7
0.64
105.2
150.3
0.65
6
19990720
24.8
44.4
29.6
0.71
34.6
17.8
0.51
7
20000704
14.3
14.1
18.2
0.61
47.4
49.5
0.53
8
20010818
39.3
18.3
36.2
0.76
84.2
112.3
0.69
Mean
Mean
A
0.59
0.58
B
Fig. 5 Scatter plots and linear fitting curve of simulated and observed volumes of a runoff and b sediment yield for 17 rainstorm events
sediment process is not closely consistent with the runoff
process. For example, similar amounts of rainfall, 35.6
and 33.5 mm, produced much different sediment yields,
170 9 104 and 105 9 104 tons, respectively, during the
19940804 and 19960731 storm events (Table 6). Similar
phenomena can also be found in the rainstorms 19700701
and 20010818. Complex mechanisms with respect to
hydrological and sediment processes, which need to be
investigated in further studies, have the potential to explain
these phenomena in hilly–gully loess regions.
4.2 Simulation of flow concentration processes
Simulated flow concentration in the Chabagou catchment at
four different times in 1994 is shown in Fig. 6. Generally,
runoff generation reached its peak soon after high-intensity
rainfall, and the flow concentration in the river network
123
increased thereafter (Fig. 6a). After two hours, without
further rainfall, streamflow in tributary networks decreased
and streamflow in the main stream network increased due to
increasing flow accumulation (Fig. 6b). After four hours,
the flow accumulation in the main stream increased more
significantly and the flow depth in the tributary network
decreased to nearly zero (Fig. 6c). Finally, the flow accumulation at the catchment outlet decreased until it reached
zero (Fig. 6d). The loess-slope, gully, and groove flow
processes in above-mentioned phases provides basic driving
force for sediment and soil erosion processes, which will be
addressed in the following section in detail.
4.3 Simulation of sediment yield processes
Simulated sediment yields of the Chabagou catchment at
four different times are shown in Fig. 7. The complexity of
Stoch Environ Res Risk Assess (2012) 26:581–597
591
Fig. 6 Simulated temporal and
spatial variation of flow
concentration for Chabagou
Catchment during storm event
on a Aug. 4th 1994 at 19:00,
b Aug. 4th 1994 at 21:00,
c Aug. 4th 1994 at 23:00,
and d Aug 5th 1994 at 02:00
Fig. 7 Simulated temporal
and spatial variation of sediment
yield of Chabagou Catchment
during storm event on a Aug.
4th 1994 at 19:00, b Aug. 4th
1994 at 21:00, c Aug. 4th 1994
at 23:00, and d Aug 5th 1994 at
02:00
influencing factors in the hilly–gully loess region led to
considerable difficulty and uncertainty in the simulation of
sediment yield from a temporal and spatial perspective.
Figure 7a indicates that high-intensity rainstorms triggered
and increased the sediment yield in areas of high elevation
in the northeast portion of the Chabagou catchment. In this
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592
stage (Fig. 7a), raindrop splash-erosion and sheet flowerosion accounted for a major percentage in the total soil
erosion processes. Continuously increasing runoff induced
by high-intensity rainstorms intensified the sediment yield
processes throughout the drainage catchment (Fig. 7b).
Considerable gully soil erosion is dominated in the sediment processes of this stage. Meanwhile, gravitational soil
erosion occurred when highly sediment-concentration flow
passed through a variety of steep gullies. Gravitational
erosion further improved the sediment concentration of the
hyper-concentrated flow. Therefore, mixed soil-erosion
sources from runoff and gravitational erosion was together
responsible for the sediment processes during this phase.
In past years, some hydraulician and hydrologists have
strive to investigate the percentages of runoff and gravitational erosion in the hilly–gully loess regions (e.g. Yao
and Tang 2001; Li et al. 2009). According to their reports,
the percentage for runoff and gravitational erosion in total
is 60–70% and 40–30% approximately. Of course, the
modeling of gravitational erosion in the loess regions is
limited currently and associated results are still very
coarse. Therefore, it is necessary to study the sediment
processes further to improve our model’s capability in the
region. In the third phase in sediment processes (Fig. 7c),
sediments were transported from tributary gullies to main
gullies, from gullies to grooves, from grooves to the main
channel, and from upstream to downstream. Although the
spatial sizes of channels and flow magnitude increased in
this stage, wide cross-sectional shape and smooth slope
collectively limits the increasing soil erosion and sediment
concentration. In this case, sediment concentration reaches
the maximum of the whole soil erosion processes and
tends to be a constant. The runoff-induced erosion constitutes the majority of soil erosion, and gravitational
erosion can be neglected in this phase. At the last stage,
Fig. 7d illustrates decreasing sediment transport processes
along the main stream gradually followed by decreasing
rainstorms.
4.4 Simulated runoff and sediment yield hydrographs
and influence analysis
Simulated and observed runoff and sediment yield hydrographs at the outlet (CP station) of Chabagou catchment
were compared for eight storm events in model validation,
as shown in Fig. 8. It can be observed from this figure that
the calculated hydrographs reasonably matched measured
hydrographs in most cases. Similar phenomena can be
found in the simulated and observed sediment processes at
the catchment outlet. There was an overestimation of
sediment yield for some large events; this may be due to
the average weighted parameters for these small, mediumsized and large storm events. The performance of the
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Stoch Environ Res Risk Assess (2012) 26:581–597
model can be improved when more detailed information is
available and used for parameter estimation.
The sediment and runoff processes have mutual impacts
on each other (Li et al. 2009), and it is important to explore
these influences. Figure 9 enables us to detect the typical
properties of hyper-concentrated flow processes dominated
in such regions. It indicates that the variability of sediment
concentration (S) is very high for low discharge (Q, bluecolor shaded area in Fig. 9), however, S tend to be a
constant when high discharge (Q, red-color shaded area in
Fig. 9) exceeds a certain upper-threshold. This is partly
because low discharges are generally triggered by a few
rainstorms in different homogeneous areas, different sediment-yielding mechanisms will result in a huge S variability of such homogeneous areas. Consequently, high S
variations are observed at the outlet gauge. Nevertheless,
when large-scale rainstorms occur in the whole catchment
and lead to high discharge, different impacts on S will be
mixed up and result in low S variations at the outlet gauge.
Moreover, both the range and the mean values of S tend to
approach a constant as discharge increases.
4.5 Application to the Xingzihe catchment
The calibrated model was then applied to the Xingzihe
catchment to test its validity under similar meteorological,
geographical, geomorphological, and hydrological conditions as those in the Chabagou catchment. Table 7 shows
that the mean runoff CE was 0.62, and the mean sediment
CE was 0.55, suggesting that the calibrated model can be
used to simulate runoff and soil erosion processes in similar hilly–gully loess regions. However, compared with the
Chabagou catchment (drainage area = 205 km2), Xingzihe
is a middle-size catchment (drainage area = 1,486 km2).
Runoff and soil erosion processes in middle- and large-size
catchments are more complex than in small catchment.
Therefore, attempts to simulate these processes in middleand large-size catchments with the model built for small
catchments may lead to imperfect results. This why the
average runoff CE (0.62) and sediment CE (0.55) in validation (Table 7) for Xingzihe catchment is lower than
Chabagou catchment (runoff CE 0.69, sediment CE 0.58,
Table 6).
5 Conclusion and discussion
In this study, a DEM-based numerical model was constructed and applied in simulating the runoff and sediment
processes for typical storm events (from 1970 to 2001) in
two hilly–gully loess regions along the middle reaches of
Yellow River. The Chabagou catchment with dense rainfall
stations was used to calibrate the model and the Xingzihe
Stoch Environ Res Risk Assess (2012) 26:581–597
593
A
B
C
D
E
F
G
H
Fig. 8 Comparison between simulated and observed runoff and sediment yield hydrographs, in validation results of storm events in the
Chabagou Catchment: a, b 19880703, c, d 19890701, e, f 19940804, g, h 19950902, i, j 19960731, k, l 19990720, m, n 20000704, o, p 20010818
catchment was used for model validation. The major findings of this study include the following: (1) A DEM-based
spatial–temporal model of runoff and sediment processes
in the loess region can provide spatial variations of runoff
and sediment processes with a high grid resolution of
20 m 9 20 m. Comparisons between observed and simulated runoff and sediment yield hydrographs indicate that
the model is capable of simulating runoff and soil erosion
processes for individual storm events in a hilly–gully loess
region. (2) Spatial modeling results of runoff and sediment
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Stoch Environ Res Risk Assess (2012) 26:581–597
I
J
K
L
M
N
O
P
Fig. 8 continued
processes have been analyzed in detail to improve our
understanding of on the soil erosion processes in such
regions. (3) Parameter uncertainty analysis shows that
equifinality is one of the problems causing uncertainty in
the model simulation. Quantitative estimation of parameters
and model uncertainty will be further investigated in future
123
studies. This study presents an improvement over earlier
studies on loess regions, and the results will further our
understanding of spatio-temporal runoff and soil erosion
processes in small catchments characterized by serious
water and soil erosion. They are helpful in water and soil
conservation planning and management in catchments
Stoch Environ Res Risk Assess (2012) 26:581–597
595
Fig. 9 Sediment concentration
vs discharge at CP gauge, the
Chabagou catchment on 18th
August 2001
Table 7 Runoff and sediment validation results for Xingzihe
Catchment
No.
Storm
event
Total rainfall
(mm)
Runoff
CE
Sediment
yield CE
1
19820729
76.2
0.63
0.55
2
19820806
86.6
0.53
0.50
3
4
19850511
19850712
55.6
72.4
0.66
0.67
0.62
0.54
0.62
0.55
Mean
dominated by serious water and soil loss, especially on the
Loess Plateau.
It should be noted that runoff and sediment processes are
highly associated with the geographical scales on which
they occur. Of course, 20 m in this research is not the
highest DEM resolution to date, which is possible to
neglect some gullies with a width less than 20 m in stream
network delineation. Hence, the modeling results are
expected to be improved further when high-resolution
spatial maps (e.g. the DEM, soil, vegetation cover, land use
pattern in 1–5 m) are available in the future. Meanwhile,
other sources of soil erosion, for example, the gravityinduced soil erosion, one of key soil erosion processes
which are particularly active at several meters scale
(\10 m) in this region, contributes to the total soil erosion
considerably. This processes also should be considered and
modelled together with the runoff-induced soil erosion at
this scale (\10 m). Therefore, there is a lot of additional
work to do when developing a DEM-based runoff and
sediment processes model working at finer scales (e.g.
1 m–10 m). However, different runoff and sediment process models at various scales are collectively recognized to
be beneficial, in providing profound insights into formulating different measures for water and soil conservation
planning and management for different-sized catchments
dealing with serious water and soil loss in the Chinese
Loess Plateau. The model in such a scale (C20 m) presented in this paper mainly characterizes the runoffinduced soil erosion processes (Yao and Tang 2001; Li
et al. 2009). The modelling approaches and associated
results presented in this study will still provide beneficial
references for researchers, decision makers and stakeholders in water and soil conservation practices. For these
reasons, a series of DEM-based runoff and sediment model
at various scales (e.g. 1, 20, 100, and 1 km), aiming to
model different physical soil erosion processes, are all
essential to be build up toward improving our current
knowledge for the complex soil erosion processes in
Chinese hilly–gully loess regions. Those work will definitely constitute fresh research deliverables in future.
In addition, parameter sensitivity analysis performed in
the study shows that there exist many different sets of
parameters that could yield equally accurate or inaccurate
results. The equifinality problem, frequently discussed in the
past literature (e.g. Beven 1992; 1993), is also a significant
problem for the soil erosion processes model, which put
forwards essential needs to: (1) identify of the underlying
hydraulic or hydrological properties of soil erosion processes through more specific field experiments for further
model improvement, (2) collect and use high-definition data
to refine model parameters, and (3) quantify uncertainties in
modelling those complex processes in future studies.
Acknowledgments The work was jointly supported by grants from
the National Natural Science Foundation of China (40901016,
40830639, 40830640), a grant from the State Key Laboratory of
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Stoch Environ Res Risk Assess (2012) 26:581–597
Hydrology-Water Resources and Hydraulic Engineering (2009586612,
2009585512), the National Basic Research Program of China ‘‘973
Program’’ (2010CB428405, 2010CB951101, 2010CB951003), and
the Fundamental Research Funds for the Central Universities
(2010B00714). Cordial thanks are also extended to the editor, Professor
George Christakos and three referees for their valuable comments
which greatly improved the quality of this paper.
Appendix: List of symbols
RS
PE
F
P
ft
fc
f0
kd
Kc
v
q
h
re(t)
l1
l2
l3
T
x
t
Sf
S0
S
f
g
R
n
r, k
h
e
Ks
123
The infiltration excess runoff (mm/min)
The precipitation minus evaporation
(mm/min)
The infiltration rate (mm/min)
The precipitation (mm/min)
The infiltration rate at time t (mm/min)
The constant or equilibrium infiltration rate
after soil has been saturated or minimum
infiltration rate (mm/min)
The initial infiltration rate (mm/min)
A decay constant specific to the soil
(dimensionless)
The concentration routing coefficient
(dimensionless)
The cross-sectional velocity (m/s)
The overland discharge per unit width (m2/s)
The water depth in meters (m)
The rainfall excess rate, or lateral inflow
rate (mm/min)
The length of loess slope (m)
The length of gully slope (m)
The length of groove (m)
The duration of a storm event (min)
The streamwise distance (m)
Time (min)
The friction-induced head loss per unit
length between the moving fluid and the
bed (m/m)
The slope of the overland surface (m/m)
The slope of the flow surface (m/m)
The Darcy–Weisbach friction loss
coefficient (dimensionless), which can be
determined from the Moody diagram
The local gravitational
acceleration, & 9.8 m/s2
The hydraulic radius (m)
The Manning’s roughness (dimensionless)
Constant
A weighting factor in the Preissmann
implicit scheme (dimensionless)
A weighting factor in the Preissmann
implicit scheme (dimensionless)
The hydraulic roughness coefficient
g1
c
cs
cm
e1
a1
Wf 1
so
sc
V
A
A1 ¼ gg Atga1
1
c
SC
Qh
Qc
J1
J0
e2
f2
h2
J2
a2
A2 ¼ f 2 A 1 ;
Ws3
g3
e3
x
Wf 3
U*
h3
J3
j
f3
C
B0
A3
CE
r2e
r2o
A distance related coefficient m1
The bulk density of clear water (kg/m3)
The bulk density of dry sediment (kg/m3)
The bulk density of wet sediment (kg/m3)
The soil erosion rate of a loess slope (kg/s)
The degree (or angle) of a loess slope (°)
The effective power of soil erosion of the
loess slope per unit area (W)
The shear stress (N/m2)
The critical yield stress (N/m2)
The average cross-sectional velocity of
surface flow (m/s)
A non-dimensional coefficient
A sediment erosion model coefficient for
loess slope erosion (s2)
The bulk density of the flow
The sediment concentration (kg/km3)
The discharge of the clear-water flow (m3/s)
The discharge of the muddy flow (m3/s)
The loess slope (%)
The slope of the surface flow (%)
The gully slope erosion rate (kg/s)
The energy coefficient for gully soil erosion
(dimensionless)
The flow depth of the gully (m)
The slope of the gully (%)
The degree (or angle) of the gully slope (°)
A sediment erosion model coefficient for
gully slope erosion
The power of soil erosion of the groove per
unit area (W)
A distance related coefficient m1 for groove
erosion
The groove soil erosion rate (kg/s)
The settling velocity (cm/s)
The actual power of soil erosion of the
groove per unit area (W)
The friction velocity (m/s)
The groove depth (m)
The groove slope (%)
The Karman constant
The energy coefficient for groove soil
erosion (dimensionless)
A dimensionless coefficient
A dimensionless coefficient
A sediment erosion model coefficient for
groove erosion
The model efficiency measure
(dimensionless)
Variance of model residuals
(dimensionless)
Variance of observations (dimensionless)
Stoch Environ Res Risk Assess (2012) 26:581–597
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