Soil erosion is one of the most significant environmental problems in China.
From 2010 to 2012, the fourth national census for soil erosion sampled
32 364 PSUs (Primary Sampling Units, small watersheds) with the areas of
0.2–3 km2. Land use and soil erosion controlling factors including rainfall
erosivity, soil erodibility, slope length, slope steepness, biological
practice, engineering practice, and tillage practice for the PSUs were
surveyed, and the soil loss rate for each land use in the PSUs was estimated
using an empirical model, the Chinese Soil Loss Equation (CSLE). Though the
information collected from the sample units can be aggregated to estimate
soil erosion conditions on a large scale; the problem of estimating soil
erosion condition on a regional scale has not been addressed well. The aim of
this study is to introduce a new model-based regional soil erosion assessment
method combining a sample survey and geostatistics. We compared seven spatial
interpolation models based on the bivariate penalized spline over triangulation (BPST)
method to generate a regional soil erosion assessment from the PSUs.
Shaanxi Province (3116 PSUs) in China was selected for the comparison and
assessment as it is one of the areas with the most serious erosion problem.
Ten-fold cross-validation based on the PSU data showed the model assisted by
the land use, rainfall erosivity factor (R), soil erodibility factor (K),
slope steepness factor (S), and slope length factor (L) derived from a 1 : 10 000
topography map is the best one, with the model efficiency coefficient (ME)
being 0.75 and the MSE being 55.8 % of that for the model assisted by the
land use alone. Among four erosion factors as the covariates, the S factor
contributed the most information, followed by K and L factors, and R factor
made almost no contribution to the spatial estimation of soil loss. The LS factor
derived from 30 or 90 m Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) data worsened the estimation when used as the covariates for the interpolation of soil loss. Due to the
unavailability of a 1 : 10 000 topography map for the entire area in this study,
the model assisted by the land use, R, and K factors, with a resolution of
250 m,
was used to generate the regional assessment of the soil erosion for Shaanxi
Province. It demonstrated that 54.3 % of total land in Shaanxi Province
had annual soil loss equal to or greater than 5 t ha-1 yr-1. High
(20–40 t ha-1 yr-1), severe (40–80 t ha-1 yr-1), and
extreme (> 80 t ha-1 yr-1) erosion occupied 14.0 %
of the total land. The dry land and irrigated land, forest, shrubland, and
grassland in Shaanxi Province had mean soil loss rates of 21.77, 3.51, 10.00,
and 7.27 t ha-1 yr-1, respectively. Annual soil loss was about
207.3 Mt in Shaanxi Province, with 68.9 % of soil loss originating from the
farmlands and grasslands in Yan'an and Yulin districts in the northern Loess
Plateau region and Ankang and Hanzhong districts in the southern Qingba
mountainous region. This methodology provides a more accurate regional soil
erosion assessment and can help policymakers to take effective measures to
mediate soil erosion risks.
Introduction
With a growing population and a more vulnerable climate system, land
degradation is becoming one of the biggest threats to food security and
sustainable agriculture in the world. Two of the primary sources of land
degradation are water and wind erosion (Blanco and Lal, 2010). To improve
the management of soil erosion and aid policymakers in taking suitable
remediation measures and mitigation strategies, the first step is to monitor
and assess the related system to obtain timely and reliable information
about soil erosion conditions under present climate and land use.
Assessments of the risks of soil erosion under different scenarios of
climate change and land use are also very important (Kirkby et al., 2008).
Scale is a critical issue in soil erosion modeling and management (Renschler
and Harbor, 2002). When the spatial scale is small, experimental runoff
plots, soil erosion markers (e.g., Caesium 137), or river sediment
concentration measurement devices (e.g., optical turbidity sensors) are
useful tools. However, when the regional scale is considered, it is
impractical to measure soil loss across the entire region. A number of
approaches have been used to assess the regional soil erosion in different
countries and regions over the world, such as expert-based factorial
scoring and plot-based, field-based, and model-based assessments.
Factorial scoring was used to assess soil erosion risk when erosion rates
were not required, and one only needs a spatial distribution of erosion (Guo
and Li, 2009; Le Bissonnais et al., 2001). The classification or scoring of
erosion factors (e.g., land use, rainfall erosivity, soil erodibility, and
slope) into discrete classes and the criteria used to combine the classes
are based on expert experience. The resulting map depicts classes ranging
from very low to very high erosion or erosion risk. However, the factorial
scoring approach has limitations on subjectivity and qualitative
characteristics (Morgan, 1995; Grimm et al., 2002). A plot-based approach
extrapolated the measurements from runoff plots to the region (Cerdan et
al., 2002; Guo et al., 2015a). However, Cerdan et al. (2002) discussed that
the direct extrapolation may lead to poor estimation of regional erosion
rates if the scale issue is not carefully taken into consideration. Evans et
al. (2015) recommended a field-based approach, combining visual
interpretations of aerial and terrestrial photos and a direct field survey of
farmers' fields in Britain. However, its efficiency, transparency, and
accuracy were questioned (Panagos et al., 2016a).
The model-based approach can not only assess soil loss up to the present
time, but it also has the advantage of assessing future soil erosion risk under
different scenarios of climate change, land use, and conservation practices
(Kirkby et al., 2008; Panagos et al., 2015b). USLE (Wischmeier and Smith,
1965, 1978) is an empirical model based on the
regression analyses of more than 10,000 plot years of soil loss data in the
USA and is designed to estimate long-term annual erosion rates of
agricultural fields. (R)USLE (Wischmeier and Smith, 1978; Renard et al.,
1997; Foster, 2004) and other adapted versions (for example, the Chinese Soil
Loss Equation, CSLE; Liu et al., 2002) are the most widely used models in
regional-scale soil erosion assessment due to their relative simplicity and
robustness (Singh et al., 1992; Van der Knijff et al., 2000; Lu et al.,
2001; Grimm et al., 2003; Liu et al., 2013; Bosco et al., 2015; Panagos et al., 2015b).
The applications of USLE and its related models in the assessment of
regional soil erosion can be generally grouped into three categories. The
first category is the area sample survey approach. One representative is the
National Resources Inventory (NRI) survey on US nonfederal lands (Nusser
and Goebel, 1997; Goebel, 1998; Breidt and Fuller, 1999). USDA (2015)
summarized the results from the 2012 NRI, which also included a description
of the NRI methodology and use. A summary of NRI results on rangeland is
presented in Herrick et al. (2010). See for example Brejda et al. (2001) and
Hernandez et al. (2013) for some applications using NRI data. Since a
rigorous probability-based area sampling approach is used to select the
sampling sites, the design-based approach is robust and reliable when it is
used to estimate the soil erosion at the national and state level. However,
due to sample size limitations, estimates at the sub-state level are more uncertain.
The second category is based on the multiplication of erosion factor raster
layers. Each factor in the (R)USLE model is a raster layer and soil loss was
obtained by the multiplication of numerous factors, which was usually
conducted under a GIS environment (Lu et al., 2001; Bosco et al., 2015; Panagos
et al., 2015b; Ganasri and Ramesh, 2015; Rao et al., 2015; Bahrawi et al.,
2016). A European water erosion assessment which introduced high-resolution
(100 m) input layers reported the result that the mean soil loss rate in the
European Union's erosion-prone lands was 2.46 t ha-1 yr-1 (Panagos
et al., 2015b). This work is scientifically controversial, mainly due to
questions on three aspects. (1) Should the assessment be based on the model
simulation or the field survey? (2) Are the basic principles of the (R)USLE
disregarded? (3) Are the estimated soil loss rates realistic (Evans and
Boardman, 2016; Fiener and Auerswald, 2016; Panagos et al., 2016a, b)?
Panagos et al. (2016a, b) argued that the field survey method proposed
by Evans et al. (2015) was not suitable for the application at the European
scale, mainly due to work force and time requirements. They emphasized that their
work focused on the differences and similarities between regions and
countries across the Europe and that the (R)USLE model with its simple transparent
structure was able to meet the requirements if harmonized datasets were inputted.
The third category is based on a sample survey and geostatistics. One
example is the fourth census on soil erosion in China during 2010–2012,
which was based on a stratified unequal probability systematic sampling
method (Liu et al., 2013). In total, 32 364 Primary Sampling Units (PSUs)
were identified nationwide to collect factors for water erosion prediction
(Liu et al., 2013). The CSLE was used to estimate the soil loss for the PSUs. A spatial
interpolation model was used to estimate the soil loss for the non-sampled sites.
The remote sensing technique has unparalleled advantages and potential in the
work of regional-scale soil erosion assessment (Vrieling, 2006; Le Roux et
al., 2007; Guo and Li, 2009; Mutekanga et al., 2010; El Haj El Tahir et al.,
2010). The aforementioned assessment method based on the multiplication of
erosion factors under a GIS interface was largely dependent on the remote
sensing dataset (Panagos et al., 2015b; Ganasri and Ramesh, 2015; Bahrawi et
al., 2016), which also provided important information for the field survey
work. For example, NRI relied exclusively on the high-resolution remote
sensing images taken from fixed-wing airplanes to collect land cover
information. However, many characteristics of soil erosion cannot be derived
from remote sensing images. Other limitations include the accuracy of remote
sensing data, the resolution of remote sensing images, financial constraints,
and so on, which result in some important factors influencing soil erosion not
being available for the entire domain. It is important to note that the
validation is necessary and required to evaluate the performance of a
specific regional soil erosion assessment method, although the validation
process is difficult to implement in the regional-scale assessment and is
not addressed well in the existing literature (Gobin et al., 2004; Vrieling,
2006; Le Roux et al., 2007; Kirkby et al., 2008).
An important issue in regional soil erosion assessment based on survey
samples is how to infer the soil erosion conditions including the extent,
spatial distribution, and intensity for the entire domain from the
information of PSUs. NRI primarily used a design-based approach to estimate
domain-level statistics. While robust and reliable for large domains which
contain enough sample sites, such a method has large uncertainties when it is
used for small domains. The method to obtain domain-level statistics used
in the fourth census of soil erosion in China was different from that used
by NRI. A simple spatial model was used to smooth the proportion of soil
erosion directly in China, which is an attempt to interpolate sample survey
units information using geostatistics. The land use is one of the critical
pieces of information in soil erosion assessment (Ganasri and Ramesh,
2015), which is available for the entire domain. The erosion factors
rainfall erosivity (R) and soil erodibility (K) are also available for the
entire domain. The slope length (L) and slope degree (S) factors can be
derived from 30 and 90 m digital elevation model (DEM) data from the Shuttle
Radar Topography Mission (SRTM). The other factors including the
biological (B), engineering (E), and tillage (T) practice factors are either
impossible or very difficult to obtain for the entire region at this stage.
We sampled small watersheds (PSUs) to collect detailed topography
information (1 : 10 000 topography map with 5 m contour intervals) and
conducted a field survey to collect soil and water conservation practice
information. The purpose of this study is to introduce a new regional soil
erosion assessment method which combines data from the sample survey with
factor information over the entire domain using geostatistics. We compare
seven semi-parametric spatial interpolation models assisted by land use and
single or multiple erosion factors based on the bivariate penalized spline over
triangulation (BPST) method to generate regional soil loss (A) assessment
from the PSUs. A sensitivity analysis of the topography factor derived from
different resolutions of DEM data was also conducted. There are 3116 PSUs in
the Shaanxi Province and its surrounding areas which were used as an example
to conduct the comparison and demonstrate assessment procedures (Fig. 1).
For many regions in the world, data used to derive erosion factors such as
the conservation practice factor are often not available for all area, or the
resolution is not adequate for the assessment. Therefore, the assessment
method combining a sample survey and geostatistics proposed in this study is valuable.
Location of Shaanxi Province. Luohe and Jinghe watersheds were referred
in the Table 5 and discussion part.
Data and methodsSample and field survey
The design of the fourth census on soil erosion in China is based on a map
with a Gauss–Krüger projection, where the whole of China was divided into
22 zones, with each zone occupying a width of 3∘ longitude (from
the central meridian, 1.5∘ towards west and 1.5∘ towards east). Within each zone,
beginning from the central meridian and the equator, we generated grids with
a size of 40 km × 40 km (Fig. 2), which are the units at the first
level (county level). The second level is township level, with a size of
10 km × 10 km. The third level is the control area, with a size of
5 km × 5 km. The fourth level is the 1 km × 1 km grid
located in the middle of the control area. The 1 km × 1 km grid is
the PSU in the plains area, whereas in the mountainous area, a small
watershed with an area between 0.2 and 3 km2, which also intersects with the
fourth-level 1 km × 1 km grid, was randomly picked as the PSU. The
area for the mountainous PSU is restricted to be between 0.2–3 km2,
which is large enough for the enumerator and not too large to be feasible to
conduct field work. There is a PSU within every 25 km2, which suggests
the designed sample density is about 4 %. In practice, due to the
limitation of financial resources, the surveyed sample density is 1 % for
most mountainous areas. The density for the plains area is reduced to 0.25 %
due to the lower soil erosion risk (Li et al., 2012).
The field survey work for each PSU mainly included (1) recording the
latitude and longitude information for the PSU using a GPS; (2) drawing
boundaries of plots in a base map of the PSU; (3) collecting the information
of land use and soil conservation measures for each plot; and (4) taking
photos of the overview of PSUs, plots, and soil and water conservation
measures for future validation. A plot was defined as the continuous area
with the same land use, the same soil and water conservation measures, and
the same canopy density and vegetation fraction in the PSU
(difference <= 10 %, Fig. 3). For each plot, land use type, land use area,
biological measures, engineering measures, and tillage measures were
surveyed. In addition, the vegetation fraction was surveyed if the land use was a
forest, shrubland, or grassland. Canopy density was also surveyed if the land
use was a forest.
Schematic of sampling strategy for the fourth census on soil erosion in China.
An example of a Primary Sample Unit (PSU) with five plots and three
categories of land use (farmland, forest, and residential area).
Distribution of PSUs used in this study.
Database of PSUs in Shaanxi and its surrounding areas
A convex hull of the boundary of Shaanxi Province was generated, with a
buffer area of 30 km outside of the convex hull (Fig. 4). The raster of
the R factor, the K factor, and the 1 : 100 000 land use map with a resolution of
250 m × 250 m pixels for the entire area were collected. PSUs located
inside the entire area were used, which included 1775 PSUs in the Shaanxi Province and 1341 PSUs from the provinces surrounding the Shaanxi Province,
including Gansu (430), Henan (112), Shaanxi (345), Inner Mongolia (41), Hubei (151),
Chongqing (55), Sichuan (156), and Ningxia (51). There were 3116 PSUs
in total. We had the information of longitude and latitude, land use type,
land use area, and factor values of R, K, L, S, B, E, and T for each plot of
the PSU. The classification system of the land use for the entire area and
that for the survey units were not synonymous with each other. Rather, they
were grouped into 11 land use types, including (1) paddy, (2) dry land and
irrigated land, (3) orchard and garden, (4) forest, (5) shrubland, (6) grassland,
(7) waterbody, (8) construction land, (9) transportation land,
(10) bare land, and (11) unused land such as sandy land, Gebi, and uncovered
rock, so that they correspond to each other.
Soil loss estimation for the plot, land use, and PSU
Soil loss for a plot can be estimated using the CSLE as follows:
Auk=Ruk⋅Kuk⋅Luk⋅Suk⋅Buk⋅Euk⋅Tuk,
where Auk is the soil loss for the kth plot with the land use u
(t ha-1 yr-1), Ruk is the rainfall erosivity (MJ mm ha-1 h-1 yr-1),
Kuk is the soil erodibility (t ha h MJ-1 ha-1 mm-1), Luk is the slope length factor, Suk is the
slope steepness factor, Buk is the biological practice factor, Euk is
the engineering practice factor, and Tukis the tillage practice
factor. The definitions of A, R, and K are similar to that of USLE.
biological (B), engineering (E), and tillage (T) factors are defined as the
ratios of soil loss from the actual plot with biological, engineering, or
tillage practices to the unit plot. Biological practices are the measures to
increase the vegetation coverage for reducing runoff and soil loss such as
trees, shrubs, and grass plantation and natural rehabilitation of vegetation.
Engineering practices refer to the changes of topography by engineering
construction on both arable and nonarable land using non-normal farming
equipment (such as an earth mover) for reducing runoff and soil loss, such as
terraces and check dams. Tillage practices are the measures taken on
the arable land during ploughing, harrowing, and cultivation processes using
normal farming operations for reducing runoff and soil loss such as crop
rotation and strip cropping (Liu et al., 2002).
Spatial distributions of land use (a), rainfall erosivity (b),
soil erodibility (c) and topography (d) for Shaanxi Province.
Liu et al. (2013) introduced the data and methods for calculating each
factor. Here we present a brief introduction. The land use map with a scale of
1 : 100 000 is from China's land use/cover datasets (CLUD), which were updated
regularly at a 5-year interval from the late 1980s to the year 2010
with standard procedures based on Landsat TM/ETM images (Liu et al.,
2014). The land use map used in this study was the 2010 version (Fig. 5a).
A total of 2678 weather and hydrologic stations with erosive daily rainfall from 1981
to 2010 were collected and used to generate the R factor raster map
over the whole of China (Xie et al., 2016). And for the K factor, soil maps
with scales of 1 : 500 000 to 1 : 200 000 (for different provinces) from the
Second National Soil Survey in the 1980s generated more than 0.18 million
polygons of soil attributes over mainland China, which was the best
available spatial resolution of soil information we could collect at
present. The physicochemical data of 16 493 soil samples (belonging to
7764 soil series, 3366 soil families, 1597 soil subgroups, and 670 soil groups
according to the Chinese Soil Taxonomy) from the maps and the latest soil
physicochemical data of 1065 samples through field sampling,
data sharing, and consulting literature were collected to generate the
K factor for the entire country (Liang et al., 2013; Liu et al., 2013). We
assumed the result of the soil survey could be used to estimate the K factor
in our soil erosion survey. The R factor raster map for the study area was
extracted from the map of the country as well as the K factor raster map
(Fig. 5b and c). Topography contour maps with a scale of 1 : 10 000 for PSUs were
collected to derive the slope lengths and slope degrees and to calculate the
slope length factors and slope steepness factors (Fu et al., 2013).
Topography contour maps with a scale of 1 : 10 000 for the entire region were
not available at present. Figure 5d was based on the SRTM 90 m DEM dataset and it
was used to demonstrate the variation in the topography. The land use map
was used to determine the boundaries of forest, shrubland, and grassland. For
these three land use types, MODIS NDVI and HJ-1 NDVI were combined to derive
vegetation coverage. For the shrubland and grassland, an assignment table was
used to assign a value of the half-month B factor based on their vegetation
coverage; for the forestland, the vegetation coverage derived from the
aforementioned remote sensing data was used as the canopy density, which was
combined with the vegetation fraction under the trees collected during the
field survey to estimate the half-month B factor. The B factor for the whole
year was weight-averaged by the weight of the rainfall erosivity ratio for this
half-month. Both the C factor in Panagos et al. (2015a) and the B factor in this
study for forest, shrubland, and grassland were estimated based on the
vegetation density derived from satellite images. The difference is that
the C factor in Panagos et al. (2015a) for arable land and nonarable land was
estimated separately based on different methodologies, whereas in this
study, the B factor was used to reflect biological practices on the forest,
shrubland, or grassland for reducing runoff and soil loss and the T factor was
used to reflect tillage practices on the farmland for reducing runoff and
soil loss. For farmland, the biological factor equals 1 and for the other
land uses, the tillage factor equals 1. The engineering practice factor and
tillage practice factor were values assigned based on the field survey and
assignment tables for different engineering and tillage measures, which were
obtained from published sources (Guo et al., 2015a).
In a PSU, there may be several plots within the same land use. Soil loss for
the same land use was weight-averaged by the area of the plots with the same
land use:
Aui=∑k=1qAuikSuik∑k=1qSuik,
where Aui is the average soil loss for the land use u in the sample unit i
(t ha-1 yr-1); Auik is the soil loss for the plot k with the
land use u (t ha-1 yr-1); Suik is the area for the plot k with
the land use u (ha). q is the number of plots with the land use u in the unit i.
Seven spatial models based on the BPST methodSeven spatial models
Model I estimates A with the land use as the auxiliary information. For
the waterbody, transportation land and unused area, the estimation of soil
loss for the uth land use and jth pixel A^uj was set to
be zero. For the rest of the land use types, Aui for each land use was
interpolated separately first and soil loss values for the entire
domain A^uj are the combination of estimation for all land uses.
Model II estimates A with R and land use as the auxiliary information. For
each sampling unit i in land use u, we define
Qui=AuiRui,
where Rui is the rainfall erosivity value. For land use u, we
smooth Qui over the entire domain using the longitude and latitude
information and obtain the estimator Q^uj of Quj for every
pixel j. Then, for the jth pixel in land use u, we estimate the soil loss Auj by
A^uj=Q^uj⋅Ruj.
Model III estimates A with K and land use as the auxiliary information.
This model is similar to Model II, except that we use Kui instead of Rui
in Eq. (3) and Kuj instead of Ruj in Eq. (4).
Model IV estimates A with L and land use as the auxiliary information.
This model is similar to Model II, except that we use Lui instead
of Rui in Eq. (3) and Luj instead of Ruj in Eq. (4).
Model V estimates A with S and land use as the auxiliary information. This
model is similar to Model II, except that we use Sui instead of Rui
in Eq. (3) and Suj instead of Ruj in Eq. (4).
Model VI estimates A with R, K, and land use as the auxiliary information.
This model is similar to Model II, except that we use RuiKui
instead of Rui in Eq. (3) and RujKuj instead of Ruj in Eq. (4).
Model VII estimates A with R, K, L, S, and land use as the auxiliary
information. This model is similar to Model II, except that we use RuiKuiLuiSui
instead of Rui in Eq. (3) and RujKujLujSuj instead of Ruj in Eq. (4).
Bivariate penalized spline over triangulation method
In spatial data analysis, there are mainly two approaches to make the
prediction of a target variable. One approach (e.g., kriging) treats the
value of a target variable at each location as a random variable and uses
the covariance function between these random variables or a variogram to
represent the correlation; another approach (e.g., spline or wavelet
smoothing) uses a deterministic smooth surface function to describe the
variations and connections among values at different locations. In this
study, the bivariate penalized spline over triangulation (BPST) method, which belongs
to the second approach, was used to explore the relationship between
location information in a two-dimensional (2-D) domain and the response
variable. The BPST method we consider in this work has several advantages.
First, it provides good approximations of smooth functions over complicated
domains. Second, the computational costs for spline evaluation and parameter
estimation are manageable. Third, the BPST does not require the data to be
evenly distributed or on a regular-spaced grid.
To be more specific, let (xi, yi) ∈Ω be the latitude
and longitude of unit i for i= 1, 2, …, n. Suppose we observe
zi at locations (xi, yi) and {(xi, yi, zi)}i=1n
satisfies
zi=fxi,yi+εi,i=1,2,…,n,
where εi is a random variable
with mean zero, and f(xi, yi) is some
smooth but unknown bivariate function. To estimate f, we adopt the bivariate
penalized splines over triangulations to handle irregular domains. In the
following we discuss how to construct basis functions using bivariate
splines on a triangulation of the domain Ω. Details of
various facts about bivariate splines stated in this section can be found in
Lai and Schumaker (2007). See also Guillas and Lai (2010) and Lai and Wang (2013)
for statistical applications of bivariate splines on triangulations.
A triangulation of Ω is a collection of triangles
Δ=τ1τ2, …, τN whose
union covers Ω. In addition, if a pair of triangles in
Δ intersects, then their intersection is either a common vertex or a
common edge. For a given triangulation Δ, we can construct
Bernstein basis polynomials of degree p separately on each triangle, and the
collection of all such polynomials form a basis. In the following, let
Srp(Δ) be a spline space
of degree p and smoothness r over triangulation Δ. Bivariate
B splines on the triangulation are piecewise polynomials of degree p
(polynomials on each triangle) that are smoothly connected across common
edges, in which the connection of polynomials on two adjacent triangles is
considered smooth if directional derivatives up to the rth degree are
continuous across the common edge.
To estimate f, we minimize the following penalized least-squares problem:
f∈srp(Δ)min=zi-fxi,yi2+λPEN(f),
where λ is the roughness penalty parameter, and PEN(f)
is the penalty given below:
PEN(f)=∫τ∈Δ∂2f(x,y)∂x22+∂2f(x,y)∂x∂y27+∂2f(x,y)∂y22dxdy.
For Models I–VII defined in Sect. 2.4.1, we consider the above minimization
to fit the model, and we obtain the smoothed surface using the Q data and their
corresponding location information.
Assessment methods
The mean squared prediction error (MSE) and the Nash–Sutcliffe model efficiency
coefficient (ME) are used to assess the performance of models. We estimate
the out-of-sample prediction errors of each method using the ten-fold cross-validation. We randomly split all the observations over the entire domain
(with the buffer zone) into 10 roughly equal-sized parts. For each t= 1,
2, …, 10, we leave out part t, fit the model using the
other nine parts (combined) inside the boundary with the buffer zone, and
then obtain predictions for the left-out tth part inside the boundary
of Shaanxi Province. The overall mean squared prediction error (MSEoverall)
is calculated by the average of the sum of the product of
individual MSEu and the corresponding sample size. We first calculated
the MSE of land each use u, u= 1, 2, …, 11:
MSEu=∑t=110SSEt10,
where SSEt is the sum of squared prediction errors for the tth part.
Then, the overall MSE can be calculated using
MSEoverall=∑u=111MSEu⋅Cu∑u=111Cu,
where Cu is the sample size for the land use u.
Model efficiency coefficient MEu for the land use u is calculated as
follows (Nash and Sutcliffe, 1970):
MEu=1-∑iCuApre,u(i)-Aobs,u(i)2∑iCuAobs,u(i)-Aobs,u‾(i)2.Apre,u(i) and Aobs,u(i) are the predicted and observed soil
loss for the plot i for land use u. MEoverall stands for the overall
model efficiency by pooling all samples for different land uses together.
The ME compares the simulated and observed values relative to the line of
perfect fit. The maximum possible value of ME is 1, and the higher the value,
the better the model fit. An efficiency of ME < 0 indicates that the
mean of the observed soil loss is a better predictor of the data than the
model. The soil loss rate is divided into six soil erosion intensity levels,
which were mild (less than 5 t ha-1 yr-1), slight (5–10 t ha-1 yr-1),
moderate (10–20 t ha-1 yr-1), high (20–40 t ha-1 yr-1),
severe (40–80 t ha-1 yr-1), and extreme (no less
than 80 t ha-1 yr-1). Each pixel in the entire domain
was classified into an intensity level according to Auj. The
proportion of intensity levels, soil loss rates for different land uses, and
the spatial distribution of soil erosion intensity levels were computed
based on the soil erosion conditions of pixels located inside of the Shaanxi boundary.
Sensitivity analysis of topography factors derived from different resolutions of DEM on the regional soil loss estimation
Previous research has suggested topography factors should be derived from
high-resolution topography information (such as 1 : 10 000 or topography
contour maps with finer resolutions; Thomas et al., 2015). Topography
factors based on topography maps with coarser resolutions (such as 1 : 50 000
or 30 m DEM) in the mountainous and hilly areas have large uncertainties
(S. Y. Wang et al., 2016). Topography contour maps with a scale of 1 : 10 000 for the
entire region were not available at present. To detect whether coarser resolution
topography data available for the entire region, such as SRTM 30 and 90 m DEM, can be used as the covariate in the interpolation process,
L and S factors were derived from 30 and 90 m DEM data, respectively (Fu
et al., 2013). The L and S factors derived from the 1 : 10 000 topography map for
PSUs were used for the cross-validation analysis of Model IV, V, and VII to
determine the relative contribution of erosion factors as the covariates to
the spatial estimation of soil loss. The L and S factors generated from
30 and 90 m DEM data, together with those generated from the 1 : 10 000 topography
map, were used for the sensitivity analysis based on Model VII. MSEu
and MSEall based on Eqs. (8) and (9) were used to assess the effect of
DEM resolution, from which topography factors were derived, on the
interpolation accuracy of soil loss.
Scatterplot of estimated and observed soil loss based on Model VII for
(a) dry and irrigated land, (b) forest, (c) shrubland, and (d) grassland.
ResultsComparison of MSEs and MEs for seven models and sensitivity of DEM resolution on the MSEs
Table 1 summarizes the MSEs of the soil loss estimation based on different
methods. Model VII assisted by R, K, L, S, and land use generated the least
overall MSE values and the best result, when L and S were derived based on
the 1 : 10 000 topography map. MSE for Model VII was 55.8 % of that for Model I.
The comparison of four models with the single erosion factor as the covariate
(Model II–V) showed the S factor is the best covariate, with
MSEoverall for Model V being 80.1 % of that for Model I, whereas
R is the worst, with the MSEoverall for Model II being 99.3 % of that for
Model I. For dry land and irrigated land and shrubland, Model II with
the R factor and land use as the auxiliary information performed even worse than
Model I assisted by the land use. K and L contributed the similar amount of
information for the spatial model, decreasing the MSE about 10 %
comparing with Model I. Model VI with R, K, and land use as the auxiliary
information is superior to any model with land use and the single erosion factor
as the covariates (Models I–V). When L and S factor were derived from
30 or 90 m DEM, the MSEs are much greater than Model I, which suggested the
topography factors help the interpolation only if the resolution of DEM used
to generate them is high enough, such as the 1 : 10 000 topography map. The use of
factors derived from DEM with a resolution equal to or lower than 30 m seriously worsens the estimation.
Table 2 summarized the MEs for different land uses and overall data based on
different models. All MEs were greater than 0, except four cases for the
paddy land, which may be due to the limited sample size. Shrubland and
grassland were the best estimated land use for Model I–VI. All seven models
had an overall ME of no less than 0.55, with Model VII having the highest (0.75).
The improvements of Model VII compared with the other six models
were obvious for most land uses. Figure 6 showed the comparison of predicted
and observed soil loss based on Model VII for four main land uses including
dry land and irrigated land, forest, shrubland, and grassland, occupying 30.2,
15.9, 7.2, and 37.7 % of the total area for Shaanxi Province, respectively. It also showed the predictions of soil erosion in
the shrubland and grassland were superior to those in the dry land and
irrigated land and forest, the latter for which there was a degree of
underestimation for larger soil loss values (Fig. 6).
Mean squared error of soil loss (A) using bivariate penalized spline
over triangulation (BPST) for each type of land use1.
Model2Land use and sample size OverallPaddyDry land andOrchardForestShrub-GrasslandConstructionBareirrigatedand gardenlandlandlandland823104834363128835743684332333234467I0.1513.5181.525.646.619.81.44623.1187.8II0.0518.5181.425.546.719.51.44283.3186.5III0.1461.7175.824.338.717.21.43854.5167.8IV0.0458.7164.324.540.215.61.34381.3169.8V0.1424.3148.224.541.115.21.13033.0150.5VI0.1464.0175.924.137.816.61.43495.1165.5VII (1 : 10 000 map)0.0331.7140.824.128.510.30.9143.1104.8VII (30 m DEM)0.21155.8309.194.2510.3331.61.312 319.3533.2VII (90 m DEM)0.11309.4239.581.0317.1227.01.515 341.0539.4
1 Since Fig. 6 showed no obvious systematic bias for four main
land uses, we did not list the bias separately in this table. 2 Model I
estimates A with the land use as the auxiliary information; Model II estimates with land
use and the R factor as auxiliary information; Model III estimates with land use and the K factor
as auxiliary information; Model IV estimates with land use and the L factor as auxiliary
information; Model V estimates with land use and the S factor as auxiliary information; Model VI
estimates with land use and R and K factors as auxiliary information; Model VII (1 : 10 000
map) estimates with land use and R, K, L, and S factors as auxiliary information and derives the
L factor and S factor from 1 : 10 000 topography maps for
the PSUs; Model VII (30 m DEM) estimates with land use and R, K, L, and S factors as
auxiliary information and derives the L factor and S factor from 30 m
SRTM DEM data for the PSUs; Model VII (90 m DEM) estimates with land use and R, K, L, and
S factors as auxiliary information and derives the L and S factor from 90 m SRTM DEM data for the PSUs. 3 Sample size for each land use.
Proportion of soil erosion intensity levels for four models including Model I–VI.
Soil erosion intensity levels and soil loss rates for different land uses
Models IV, V, and VII require the high resolution of topography maps to
derive L and S factors, which we cannot afford in this study; therefore, four
soil loss maps based on Models I, II, III, and VI were generated. The
proportion pattern of soil erosion intensity levels for all land uses (Fig. 7)
and that for different land use (Fig. 8) were very similar among the four models.
Proportion of soil erosion intensity levels for different land use for
four models including Model I–VI.
Model efficiency coefficient (ME) for seven models using bivariate
penalized spline over triangulation (BPST) per land use.
ModelLand use and sample size OverallPaddyDry land andOrchardForestShrub-GrasslandConstructionBareirrigatedand gardenlandlandlandland8210484361288574684323324467I-0.680.340.230.200.600.520.060.180.55II0.050.340.230.200.600.530.080.240.55III-1.980.410.260.240.670.590.080.320.60IV0.150.410.310.230.650.620.160.220.59V-0.080.460.370.230.650.630.260.460.64VI-0.650.410.260.240.680.600.100.380.60VII (1 : 10 000 map)0.820.580.400.250.760.750.430.970.75
Error bar plot of soil loss rates for four models for different land
uses: (a) dry land and irrigated land, (b) forest,
(c) shrubland, and (d) grassland. The star symbols stand for the
mean values and the error bars stand for standard deviations.
Distribution of soil erosion intensity levels for four models:
(a) Model I, (b) Model II, (c) Model III, and (d) Model VI.
The result of Model VI with the BPST method showed that the highest percentage
is mild erosion (45.7 %), followed by the slight (20.7 %),
moderate (19.7 %), and high erosion (8.0 %). The severe and extreme
erosion were 5.5 and 0.4 %, respectively (Fig. 7). When it came to
the land use (Fig. 8), the largest percentage for the dry land and
irrigated land was high erosion, which occupied 23.2 % of the total
dry land and irrigated land. The severe and extreme erosion for the dry
land and irrigated land were 18.3 and 1.3 %, respectively. The
largest percentage for the forestland and grassland was the mild erosion,
being 75.1 and 41.7 %, respectively. The percentage of the mild,
slight, and moderate erosion for the shrubland occupied about 30 %.
Figure 9 shows soil loss rates for the four main land uses generated from
four models. Similar to the estimation of soil erosion intensity levels,
there were slight differences among the four models. The soil loss rates for
four main land uses (dry land and irrigated land, forest, shrubland, and
grassland) by Model VI were reported in Table 3.
Spatial distribution of soil erosion intensity
All four models predicted generally similar spatial patterns of soil erosion
intensity, with mild, moderate, and high erosion mainly occurring in the
farmlands and grassland in the northern Loess Plateau region and severe and
extreme soil erosion mainly occurring in the farmlands in the southern
Qingba mountainous area (Fig. 10a–d). The estimation from Model VI
showed that annual soil loss from Shaanxi Province was about 207.3 Mt,
49.2 % of which came from dry and irrigated lands and 35.2 % from
grasslands (Table 4). The soil loss rate in Yan'an and Yulin in the northern
part was 16.4 and 13.4 t ha-1 yr-1 and ranked the highest among
10 prefecture cities. More than half of the soil loss for the entire
province was from these two districts (Table 4). Ankang and Hanzhong in the
southern part also showed a severe soil loss rate and contributed nearly one-quarter of soil loss for the entire province. The soil loss rate in
Tongchuan in the middle part was 10.2 t ha-1 yr-1, ranking the
fourth most severe, whereas the total soil loss amount was 3.9 Mt, ranking
last, due to its area being the smallest.
Soil loss rates (t ha-1yr-1) for farmland, forest, shrubland, and grassland by Model VI in this study and in the northwest region of China
from Guo et al. (2015).
Land useMeanStandarddeviationThis studyDry land and irrigated land21.7720.06Forest3.512.77Shrubland10.007.51Grassland7.275.20Guo et al. (2015)Farmland (conventional)49.3857.61Farmland (ridge tillage)19.2713.35Farmland (terracing)0.120.28Forest0.100.12Shrubland8.067.47Grassland11.5712.72
Annual soil loss amount, mean rate, and main sources by Model VI for
10 prefecture cities in Shaanxi Province.
PrefectureAreaAmountMean rateSource (%) city(104 ha)(106 t yr-1)(t ha-1 yr-1)Dry land andForestShrubGrassirrigated landlandlandXi'an100.96.56.455.011.27.819.6Ankang234.127.411.746.79.42.538.5Baoji180.114.88.236.410.87.339.6Hanzhong268.120.97.845.511.43.236.5Shangluo194.85.83.038.319.48.427.4Tongchuan38.83.910.240.17.223.228.2Weinan129.87.55.759.63.28.824.6Xianyang102.85.65.546.33.13.514.2Yan'an369.160.516.445.74.812.037.0Yulin422.756.513.456.32.23.636.4Overall2041.4207.310.249.26.77.135.2
Soil erosion rate for the forest and sediment discharge for two watersheds.
AreaRunoffSedimentSoil lossPercentSoil loss rate(104 ha)(109 m3 yr-1)dischargerate3of forestfor forest(106 t yr-1)(t ha-1 yr-1)(%)(t ha-1 yr-1)Jinghe1454.21.837246.754.36.519.0Luohe2284.30.90682.629.138.41.3–2.1
1 Based on the observation at Zhangjiashan hydrological station
from 1950 through 1989. 2 Based on the observation at Zhuanghe hydrological
station from 1959 through 1989. 3 The sediment delivery ratio, the ratio of
sediment discharge from the watershed outlet to the total soil loss, was assumed
to be 1. Soil loss rate was defined as the soil loss per unit area.
DiscussionThe uncertainty of the assessment
The uncertainty of the regional soil loss assessment method combining the
survey sample and geostatistics mainly came from the estimation of erosion
factors in the PSU, the density of survey sampling, and interpolation
methods. Previous studies have shown that the resolution of topography data
source largely affected the calculated slope steepness, length, and soil
loss. Thomas et al. (2015) showed that the range of LS factor values derived
from four sources of DEM (20 m DEM generated from 1 : 50 000 topographic maps,
30 m DEM from Advanced Spaceborne Thermal Emission and Reflection Radiometer – ASTER,
90 m DEM from SRTM, and 250 m DEM from global multi-resolution
terrain elevation data – GMTED) were considerably different, which suggested
the grid resolutions of factor layers are critical and determined by the
data resolution used to derive the factor. S. Y. Wang et al. (2016) compared data
sources including topographic maps at 1 : 2000, 1 : 10 000, and 1 : 50 000 scales
and 30 m DEM from the ASTER V1 dataset and reported that slope steepness generated
from the 30 m ASTER dataset was 64 % lower than the reference value
generated from the 1 : 2000 topography map (2 m grid) for a mountainous
watershed. The slope length was increased by 265 % and soil loss
decreased by 47 % compared with the reference values. A study conducted
by our research group indicated L and S factor and the soil loss prediction
based on the DEM grid size less than or equal to 10 m were close to those of
2 m DEM (Fu et al., 2015); therefore, topography maps with a scale of
1 : 10 000 were collected in this study to derive the LS factor for the PSU. Note
that R and K factors for PSUs were extracted from the map of the entire
country, which may include some errors compared with those from at-site
rainfall observations and soil field sampling for each PSU, which requires
further research.
The density of sample units in our survey depends on the level of
uncertainty and the budget of the survey. We tested sample density of 4 %
in four experimental counties in different regions over China and found a
density of 1 % was acceptable given the current financial condition.
Since our data are a little sparse in some areas, we employed the roughness
penalties to regularize the spline fit; see the energy functional defined in
Eq. (7). When the sampling is sparse in a certain area, the direct BPST
method may not be effective since the results may have high variability due
to the small sample size. The BPST is more suitable for this type
of data because the penalty regularizes the fit (Lai and Wang, 2013).
Cross-validation in Sect. 3.1 evaluated the uncertainty in the
interpolation. The results consolidated the conclusion on the importance of
topography factors and the DEM resolution used to calculate topography
factors from previous research. It clarified that the S factor is the most important
auxiliary factor in terms of the covariate in the interpolation of soil loss
and K and L factors ranked the second most important, when topography
factors were generated from a 1 : 10 000 map. Inclusion of topography factors
from 30 m or coarser resolution of DEM data worsened the estimation.
Comparison with the other assessments
The Ministry of Water Resources of the People's Republic of China (MWR) has
organized four nationwide soil erosion investigations. The first three
(in the mid-1980s, 1999, and 2000) were mainly based on field surveys, visual
interpretation by experts, and a factorial scoring method (X. Wang et al., 2016).
The third investigation used 30 m resolution of Landsat TM images and
1 : 50 000 topography map. Six soil erosion intensities were classified, mainly
based on the slope for the arable land and a combination of slope and
vegetation coverage for the nonarable land. The limitations for the first
three investigations include the limited resolution of satellite images and
topography maps, limited soil erosion factors considered (rainfall erosivity
factor, soil erodibility factor, and practice factor were not considered),
incapability of generating the soil erosion rate, and incapability of
assessing the benefit from the soil and water conservation practices. The
spatial pattern of soil erosion in Shaanxi Province in this study is similar
to the result of the third national investigation. Since the expert
factorial scoring method did not generate the erosion rate for each land
use, we compared the percentage of soil erosion area for 10 prefecture
cities in Shaanxi Province with the third and the fourth investigations.
Both investigations indicated that Yan'an and Yulin in the northern part, Tongchuan
in the middle part, and Ankang in the southern part showed the most serious soil
erosion. The difference is that Hanzhong was underestimated and Shangluo was
overestimated in the third investigation, compared with the fourth investigation.
Guo et al. (2015a) analyzed 2823 plot-year runoff and soil loss data from
runoff plots across five water erosion regions in China and compared the
results with previous research around the world. The results convey that
there were no significant differences for the soil loss rates of forest,
shrubland, and grassland worldwide, whereas the soil loss rates of farmland
with conventional tillage in northwest and southwest China were much higher
than those in most other countries. Shaanxi Province is located in the
northwest (NW) region. Soil loss rates for the farmland, forest, shrubland,
and grassland based on the plot data for the NW region in Guo et al. (2015a)
are extracted and presented in Table 3 for comparison. The soil loss rate for
the farmland based on the plot data varied greatly with the management and
conservation practices and the result in this study was within the range
(Table 3). The soil loss rate for the shrubland is similar to that
reported in Guo et al. (2015b). The soil loss rate for the forest in this
study was 3.51 t ha-1 yr-1 with a standard deviation of 2.77 t ha-1 yr-1,
which is much higher than 0.10 t ha-1 yr-1 reported in Guo et al. (2015a, Table 3). Our analysis proves that it
came from the estimation of PSUs and was not introduced by the spatial
interpolation process. Possible reasons include (1) the different
definitions of forest and grassland, (2) concentrated storms with intense
rainfall, (3) the unique topography in the Loess Plateau, and (4) the sparse
vegetation cover due to intensive human activities (Zheng and Wang, 2014).
The minimum canopy density (crown cover) threshold for the forest across the
world varies from 10 to 30 % (Lambrechts et al., 2009) and a threshold of
10 % was used in this study, which suggests on average a lower vegetation coverage and a higher B factor. Annual average precipitation varies between
328 and 1280 mm in Shaanxi, with 64 % concentrated in June through
September. Most rainfall comes from heavy storms of short duration, which
suggests the erosivity density (rainfall erosivity per unit rainfall amount)
is high. The field survey result on the PSUs in this study discovered that
the slope degree is steeper and slope length is longer for the forest than
the forest plots in Guo et al. (2015a). The forest plots in Guo et al. (2015a)
were with an averaged slope degree of 25.9∘ and slope length of
21.1 m, whereas 74.0 % of forestland was with a slope degree greater
than 25∘ and 97.2 % of them with a slope length longer than 20 m.
The runoff and sediment discharge observation information for two
watersheds (Fig. 1, Table 5) depicted that the soil loss rate for the forest
in the study area has large variability ranging from 1.3 to 19.0 t ha-1 yr-1
(Wang and Fan, 2002). Our estimation is within the range. The soil
loss rate for the grassland in this study was 7.27 t ha-1 yr-1,
which was smaller than 11.57 t ha-1 yr-1 reported in Guo et al. (2015a).
This may be due to the lower slope degree for the grassland in
Shaanxi Province. The mean value of the slope degree for grassland plots was
30.7∘ in Guo et al. (2015a), whereas 68.6 % of the grasslands
were with a slope degree smaller than 30∘ from the survey in this study.
Raster multiplication is a popular model-based approach due to its lower
cost, simpler procedures, and easier explanation of resulting map. If the
resolution of input data for the entire region is high enough to derive all the
erosion factors, raster multiplication approach is the best choice. However,
there are several concerns about raster multiplication approach for two
reasons: (1) the information for the support practices factor (P) in the
USLE was not easy to collect given the common image resolution and was not
included in some assessments (Lu et al., 2001; Rao et al., 2015), in which
the resulting maps do not reflect the condition of soil loss but the risk of
soil loss. Without the information of the P factor, it is impossible to assess
the benefit of the soil and water conservation practices (Liu et al.,
2013). (2) The accuracy of the soil erosion estimation for each cell is of
concern if the resolution of database used to derive the erosion factors is
limited. For example, the LS factor in the new assessment of soil loss by
water erosion in Europe (Panagos et al., 2015b) was calculated using the
25 m DEM, which may result in some errors for the mountainous and hilly
areas due to the limited resolution of DEM data for each cell (S. Y. Wang et al.,
2016). In this study, the information we can get at this stage for the
entire region is land use, rainfall erosivity (R), and soil erodibility (K).
The other factors were not available or did not have high enough resolution. It is not
difficult to conduct raster layer multiplication technically; however, we
think the multiplication of R and K factors (assuming L= 1, S= 1, B= 1,
E= 1, T= 1) reflects the potential of soil erosion, which is different
from the soil loss estimated in this study. Therefore, we did not compare
our method with the raster layer multiplication method. Our recommended approach
uses all the factor information that is available in the entire region
(land use, rainfall, soils) and uses spatial interpolation to impute other
factor information which is only available at the sampled PSU (slope
degree, slope length, practice and management, aggregated as Q) to the
entire region. The rationale behind this approach is to exploit the spatial
dependence among these factors to come up with better regional estimates.
Since the reality in many countries is that we cannot have all factors
measured in all areas in the foreseeable future, or the resolution of data
for deriving the factors is limited, we believe our approach provides a
viable alternative which is of practical importance.
Practical implications
Remarkable spatial heterogeneity of soil erosion intensity was observed in
the Shaanxi Province. The Loess Plateau region is one of the most severe
soil erosion regions in the world due to seasonally concentrated and high intensity rainfall, high erodibility of loess soil, highly dissected
landscape, and long-term intensive human activities (Zheng and Wang, 2014).
Most of the sediment load in the Yellow River is originated and transported
from the Loess Plateau. Recently, the sediment load of the Yellow River
declined to about 0.3 billion tons per year from 1.6 billion tons per year
in the 1970s, thanks to the soil and water conservation practices implemented in
the Loess Plateau region (He, 2016). However, more efforts to control
human accelerated soil erosion in the farmlands and grasslands are still
needed. Soil erosion in the southern Qingba mountainous region is also very
serious, which may be due to the intensive rainfall, farming in the steep
slopes, and deforestation (Xi et al., 1997). According to the survey in
Shaanxi Province, 11.1 % of the farmlands with a slope degree ranging
15–25∘ and 6.3 % of them with a slope degree greater than 25∘ did not have any conservation practices in place. Mountainous areas with a slope steeper
than 25∘ need to be sealed off for afforestation (grass) without
disturbance of humans and livestock. For those farmlands with a slope
degree lower than 25∘, terracing and tillage practices are
suggested, which can greatly reduce the soil loss rate (Guo et al., 2015a,
Table 3). The survey result determined that 26.5 % of
grasslands with a slope degree of 15–25∘ and 57.6 % with a slope degree
steeper than 25∘ did not have any conservation practices in place. Enclosure and
grazing prohibition are suggested on the grasslands with a steep slope and low
vegetation coverage.
Note that the CSLE as well as other USLE-based models only simulate sheet and
rill erosion, and erosion from gullies is not taken into consideration in
this study. Erosion from gullies is also very serious in the Loess Plateau
area, and there were more than 140 000 gullies longer than 500 m
in Shaanxi Province (Liu, 2013).
Conclusions
This regional soil erosion assessment focused on the extent, intensity, and
distribution of soil erosion on a regional scale and it provides valuable
information for stakeholders to take proper conservation measures in erosion
areas. Shaanxi Province is one of the most severe soil erosion regions in
China. A field survey in 3116 PSUs in the Shaanxi Province and its
surrounding areas was conducted, and the soil loss rates for each land use
in the PSU were estimated from an empirical soil loss model (CSLE). Seven
spatial interpolation models based on the BPST method were compared, which
generated regional soil erosion assessment from the PSUs. The following is a summary of our
conclusions.
The slope steepness (S) factor derived from a 1 : 10 000 topography map is the
best single covariate. The MSE of the soil loss estimator using the model
with the land use and S factor is 20 % less than those using the model
assisted by the land use alone. Soil erodibility (K) and slope length (L)
information each reduce about 10 % of the MSE. Contribution of
rainfall erosivity (R) to the decrease of MSE is less than 1 %.
Model VII with the land use and R, K, L, S as the auxiliary information
has a model efficiency of 0.75 and is superior to any model with land use
and single or two erosion factors as the covariates (Model I–VI), which has
a model efficiency varying from 0.55 to 0.64.
The LS factor derived from 30 or 90 m DEM was not useful when it
was used as the covariate together with the land use, R, and K, with the
MSEs increased by about 2 times compared with those for the model assisted by
the land use alone.
Four models assisted by the land use (Model I), the land use and
the R factor (Model II), the land use and the K factor (Model III), and the land use,
the R factor, and the K factor (Model VI) provided similar estimates for proportions in each
soil erosion intensity level, soil loss rates for different land uses, and
spatial distribution of soil erosion intensity.
There is 54.3 % of total land in Shaanxi Province with annual soil
loss rate no less than 5 t ha-1 yr-1, and total annual soil loss
amount is about 207.3 Mt. Most soil loss originated from the farmlands and
grasslands in Yan'an and Yulin districts in the northern Loess Plateau
region and Ankang and Hanzhong districts in the southern Qingba mountainous
region. Special attention should be given to the 0.11 million km2 of
lands with soil loss rate equal to or greater than 5 t ha-1 yr-1,
especially 0.03 million km2 of farmlands with severe and extreme
erosion (greater than 20 t ha-1 yr-1).
A new model-based regional soil erosion assessment method was proposed,
which is valuable when input data used to derive soil erosion factors are not
available for the entire region or the resolution is not adequate. When the
resolution of input datasets is not adequate to derive reliable erosion
factor layers and the budget is limited, our suggestion is sampling a
certain number of small watersheds as primary sampling units and putting the
limited money into these sampling units to ensure the accuracy of soil
erosion estimation in these units. Limited money could be used to collect
high-resolution data such as satellite images and topography maps and
conduct field research to collect information such as conservation practices
for these small watersheds. Then we can use the best available raster layers
for land use, R, and K factors for the entire region, construct spatial
models to exploit the spatial dependence among the other factors, and
combine them to generate better regional estimates. The information
collected in the survey and the generated soil erosion degree map (such as
Fig. 10d) can help policymakers to take suitable erosion control measures
in the severely affected areas. Moreover, climate and management scenarios
could be developed based on the database collected in the survey process to
help policymakers in decision-making for managing soil erosion risks.
Data availability
Data will be available on a dedicated database website after
a contract is accepted on behalf of all institutions. Until then, the corresponding author can be
contacted for any requests regarding data.
Competing interests
The authors declare that they have no conflict of interest.
Acknowledgements
This work was supported by the National Natural Science Foundation of China
(no. 41301281) and the China Scholarship Council.
Edited by: Axel Bronstert
Reviewed by: three anonymous referees
ReferencesBahrawi, J. A., Elhag, M., Aldhebiani, A. Y., Galal, H. K., Hegazy, A. K.,
and Alghailani, E.: Soil erosion estimation using remote sensing techniques in
Wadi Yalamlam Basin, Saudi Arabia, Adv. Mater. Sci. Eng., 2016, 9585962, 10.1155/2016/9585962, 2016.
Blanco, H. and Lal, R.: Principles of Soil Conservation and Management, Springer,
New York, 2010.Bosco, C., de Rigo, D., Dewitte, O., Poesen, J., and Panagos, P.: Modelling soil
erosion at European scale: towards harmonization and reproducibility, Nat.
Hazards Earth Syst. Sci., 15, 225–245, 10.5194/nhess-15-225-2015, 2015.
Breidt, F. J. and Fuller, W. A.: Design of supplemented panel surveys with
application to the National Resources Inventory, J. Agr. Biol. Environ. St., 4, 391–403, 1999.
Brejda, J. J., Mausbach, M. J., Goebel, J. J., Allan, D. L., Dao, T. H., Karlen,
D. L., Moorman, T. B., and Smith J. L.: Estimating surface soil organic carbon
content at a regional scale using the National Resource Inventory, Soil. Sci.
Soc. Am. J., 65, 842–849, 2001.
Cerdan, O., Govers, G., Le Bissonais, Y., Van Oost, K., Poesen, J., Saby, N.,
Gobin, A., Vacca, A., Quinton, J., Auerswald, K., Klik, A., Kwaad, F. J. P. M.,
Raclot, D., Ionita, I., Rejman, J., Rousseva, S., Muxart, T., Roxo, M. J., and
Dostal, T.: Rates and spatial variations of soil erosion in Europe: a study
based on erosion plot data, Geomorphology, 122, 167–177, 2002.El Haj El Tahir, M., Kääb, A., and Xu, C.-Y.: Identification and mapping
of soil erosion areas in the Blue Nile, Eastern Sudan using multispectral ASTER
and MODIS satellite data and the SRTM elevation model Hydrol. Earth Syst. Sci.,
14, 1167–1178, 10.5194/hess-14-1167-2010, 2010.
Evans, R. and Boardman, J.: The new assessment of soil loss by water erosion in
Europe, Panagos, P. et al., 2015 Environ. Sci. Policy, 54, 438–447 – A response,
Environ. Sci. Policy, 58, 11–15, 2016.
Evans, R., Collins, A. L., Foster, I. D. L., Rickson, R. J., Anthony, S. G.,
Brewer, T., Deeks, L., Newell-Price, J. P., Truckell, I. G., and Zhang, Y.:
Extent, frequency and rate of water erosion of arable land in Britain – benefits
and challenges for modelling, Soil Use Manage., 32, 149–161, 2015.
Fiener, P. and Auerswald, K.: Comment on “The new assessment of soil loss
by water erosion in Europe” by Panagos et al. (Environmental Science & Policy
54 (2015) 438–447), Environ. Sci. Policy, 57, 140–142, 2016.
Foster, G. R.: User's Reference Guide: Revised Universal Soil Loss Equation (RUSLE2),
US Department of Agriculture, Agricultural Research Service, Washington, D.C., 2004.
Fu, S. H., Cao, L. X., Liu, B. Y., Wu, Z. P., and Savabi, M. R.: Effects of
DEM grid size on predicting soil loss from small watersheds in China, Environ.
Earth Sci., 73, 2141–2151, 2015.
Fu, S. H., Wu, Z. P., Liu, B. Y., and Cao, L. X.: Comparison of the effects of
the different methods for computing the slope length factor at a watershed scale,
Int. Soil Water Conserv. Res., 1, 64–71, 2013.
Ganasri, B. P. and Ramesh, H.: Assessment of soil erosion by RUSLE model using
remote sensing and GIS – A case study of Nethravathi Basin, Geosci. Front.,
7, 953–961, 2015.
Gobin, A., Jones, R., Kirkby, M. J., Campling, P., Govers, G., Kosmas, C., and
Gentile, A. R.: Indicators for pan-European assessment and monitoring of soil
erosion by water, Environ. Sci. Policy, 7, 25–38, 2004.
Goebel, J. J.: The National Resources Inventory and its role in U.S. agriculture,
Agricultural Statistics 2000, International Statistical Institute, Voorburg, 1998.
Grimm, M., Jones, R., and Montanarella, L.: Soil erosion risk in Europe,
European Commission, EUR 19939 EN, Joint Research Centre, Ispra, 2002.
Grimm, M., Jones, R., Rusco, E. and Montanarella, L.: Soil Erosion Risk in Italy:
a revised USLE approach, EUR 20677 EN, European Commission, Luxembourg, 2003.
Guillas, S. and Lai, M. J.: Bivariate splines for spatial functional regression
models, J. Nonparametr. Statist., 22, 477–497, 2010.
Guo, Q. K., Hao, Y. F., and Liu, B. Y.: Rates of soil erosion in China: A study
based on runoff plot data, Catena, 24, 68–76, 2015a.
Guo, Q. K., Liu, B. Y., Xie, Y., Liu, Y. N., and Yin, S. Q.: Estimation of USLE
crop and management factor values for crop rotation systems in China, J. Integr.
Agr., 14, 1877–1888, 2015b.
Guo, S. Y. and Li, Z. G.: Development and achievements of soil and water
conservation monitoring in China, Sci. Soil Water Conserv., 7, 19–24, 2009.He, C. S.: Quantifying drivers of the sediment load reduction in the Yellow
River Basin, National Sci. Rev., 3, 155–156, 10.1093/nsr/nww014, 2016.
Hernandez, M., Nearing, M. A., Stone, J. J., Pierson, E. B., Wei, H., Spaeth,
K. E., Heilman, P., Weltz, M. A., and Goodrich, D. C.: Application of a rangeland
soil erosion model using National Resources Inventory data in southeastern Arizona,
J. Soil Water Conserv., 68, 512–525, 2013.
Herrick, J. E., Lessard, V. C., Spaeth, K. E., Shaver, P. L., Dayton, R. S.,
Pyke, D. A., Jolley, L., and Goebel, J. J.: National ecosystem assessments
supported by scientific and local knowledge, Front. Ecol. Environ., 8, 403–408, 2010.
Kirkby, M. J., Irvine, B. J., Jones, R. J. A., Govers, G., Boer, M., Cerdan,
O., Daroussin, J., Gobin, A., Grimm, M., Le Bissonnais, Y., Kosmas, C., Mantel,
S., Puigdefabregas, J., and van Lynden, G.: The PESERA coarse scale erosion model
for Europe. I. – Model rationale and implementation, Eur. J. Soil Sci., 59, 1293–1306, 2008.
Lai, M. J. and Schumaker, L. L.: Spline functions on triangulations, Cambridge
University Press, Cambridge, 2007.
Lai, M. J. and Wang, L.: Bivariate penalized splines for regression, Statist.
Sin., 23, 1399–1417, 2013.
Lambrechts, C., Wilkie, M. L., Rucevska, I., and Sen, M. (Eds.): Vital Forest
Graphics, United Nations Environment Programme (UNEP), United Nations Food and
Agriculture Organisation (FAO), United Nations Forum on Forests (UNFF),
UNEP/GRID-Arendal, Arendal, Norway, 2009.
Le Bissonnais, Y., Montier, C., Jamagne, M., Daroussin, J., and King, D.:
Mapping erosion risk for cultivated soil in France, Catena, 46, 207–220, 2001.
Le Roux, J. J., Newby, T. S., and Sumner, P. D.: Monitoring soil erosion in
South Africa at a regional scale: review and recommendations, S. Afr. J. Sci.,
207, 329–335, 2007.
Li, Z. G., Fu, S. H., and Liu, B. Y.: Sampling program of water erosion inventory
in the first national water resource survey, Sci. Soil Water Conserv., 10, 77–81, 2012.
Liang, Y., Liu, X. C., Cao, L. X., Zheng, F. L., Zhang, P. C., Shi, M. C., Cao,
Q. Y., and Yuan, J. Q.: K value calculation of soil erodibility of China water
erosion areas and its Macro-distribution, Soil Water Cons. China, 10, 35–40, 2013.
Liu, B. Y., Zhang, K. L., and Xie, Y.: An empirical soil loss equation, in
Proceedings – Process of soil erosion and its environment effect (Vol. II),
12th international soil conservation organization conference, Tsinghua University
Press, Beijing, 21–25, 2002.
Liu, B. Y., Guo, S. Y., Li, Z. G., Xie, Y., Zhang, K. L., and Liu, X. C.: Sample
survey on water erosion in China, Soil Water Conserv. China, 10, 26–34, 2013.
Liu, J. Y., Kuang, W. H., Zhang, Z. X., Xu, X. L., Qin, Y. W., Ning, J., Zhou,
W. C., Zhang, S. W., Li, R. D., Yan, C. Z., Wu, S. X., Shi, X. Z., Jiang, N.,
Yu, D. S., Pan, X. Z., and Chi, W. F.: Spatiotemporal characteristics, patterns
and causes of land use changes in China since the late 1980s, Acta Geogr. Sin.,
69, 3–14, 2014.
Liu, Z.: The national census for soil erosion and dynamic analysis in China,
Int. Soil Water Conserv. Res., 1, 12–18, 2013.
Lu, H., Gallant, J., Prosser, I. P., Moran, C., and Priestley, G.: Prediction
of sheet and rill erosion over the Australian continent, incorporating monthly
soil loss distribution, CSIRO Land and Water Technical Report, CSIRO, Canberra, 2001.
Morgan, R. P. C.: Soil Erosion and Conservation, 2nd Edn., Longman, Essex, 1995.
Mutekanga, F. P., Visser, S. M., Stroosnijder, L.: A tool for rapid assessment
of erosion risk to support decision-making and policy development at the Ngenge
watershed in Uganda, Geoderma, 160, 165–174, 2010.
Nash, J. E. and Sutcliffe, J. V.: River flow forecasting through conceptual models,
Part 1 – a discussion of principles, J. Hydrol., 10, 282–290, 1970.
Nusser, S. M. and Goebel, J. J.: The National Resources Inventory: A long-term
multi-resource monitoring programme, Environ. Ecol. Stat., 4, 181–204, 1997.
Panagos, P., Borrelli, P., Meusburger, K., Alewell, C., Lugato, E., and Montanarella,
L.: Estimating the soil erosion cover-management factor at the European scale,
Land Use Policy, 48, 38–50, 2015a.
Panagos, P., Borrelli, P., Poesen, J., Ballabio, C., Lugato, E., Meusburger, K.,
Montanarella, L., and Alewell, C.: The new assessment of soil loss by water
erosion in Europe, Environ. Sci. Policy, 54, 438–447, 2015b.
Panagos, P., Borrelli, P., Poesen, J., Meusburger, K., Ballabio, C., Lugato,
E., Montanarella, L., and Alewell, C.: Reply to “The new assessment of soil
loss by water erosion in Europe. Panagos P. et al., 2015 Environ. Sci. Policy
54, 438–447 – A response” by Evans and Boardman [Environ. Sci. Policy 58,
11–15], Environ. Sci. Policy, 59, 53–57, 2016a.
Panagos, P., Borrelli, P., Poesen, J., Meusburger, K., Ballabio, C., Lugato,
E., Montanarella, L., and Alewell, C.: Reply to the comment on “The new
assessment of soil loss by water erosion in Europe” by Fiener & Auerswald,
Environ. Sci. Policy, 57, 143–150, 2016b.Rao, E. M., Xiao, Y., Ouyang, Z. Y., and Yu, X. X.: National assessment of soil
erosion and its spatial patterns in China, Ecosyst. Health Sustain., 1, 1–10,
10.1890/EHS14-0011.1, 2015.
Renard, K. G., Foster, G. R.,Weesies, G. A., McCool, D. K., and Yoder, D. C.:
Predicting soil erosion by water, in: Agriculture Handbook 703, US Department
of Agriculture, Agricultural Research Service, Washington, D.C., 1997.
Renschler, C. S. and Harbor, J.: Soil erosion assessment tools from point to
regional scales – the role of geomorphologists in land management research and
implementation, Geomorphology, 47, 189–209, 2002.
Singh, G., Babu, R., Narain, P., Bhushan, L. S., and Abrol, I. P.: Soil erosion
rates in India, J. Soil Water Conserv., 47, 97–99, 1992.Thomas, J., Prasannakumar, V., and Vineetha, P.: Suitability of spaceborne
digital elevation models of different scales in topographic analysis: an
example from Kerala, India, Environ. Earth Sci., 73, 1245–1263, 2015.
USDA: Summary report: 2012 National Resources Inventory, National Resources
Conservation Service, Washington, D.C., and Center for Survey Statistics and
Methodology, Iowa State University, Ames, Iowa, 2015.
Van der Knijff, J. M., Jones, R. J. A., and Montanarella, L.: Soil erosion
risk assessment in Europe, EUR 19044 EN, European Commission, Luxembourg, 2000.
Vrieling, A.: Satellite remote sensing for water erosion assessment: A review,
Catena, 65, 2–18, 2006.
Wang, G. and Fan, Z.: Study of Changes in Runoff and Sediment Load in the Yellow
River (II), Yellow River Water Conservancy Press, Zhengzhou, China, 2002.Wang, S. Y., Zhu, X. L., Zhang, W. B., Yu, B., Fu, S. H., and Liu, L.: Effect
of different topographic data sources on soil loss estimation for a mountainous
watershed in Northern China, Environ. Earth Sci., 75, 1382, 10.1007/s12665-016-6130-3, 2016.
Wang, X., Zhao, X. L., Zhang, Z. X., Li, L., Zuo, L. J., Wen, Q. K., Liu, F.,
Xu, J. Y., Hu, S. G., and Liu, B.: Assessment of soil erosion change and its
relationships with land use/cover change in China from the end of the 1980s
to 2010, Catena, 137, 256–268, 2016.
Wischmeier, W. H. and Smith, D. D.: Predicting rainfall-erosion losses from
cropland east of the Rocky Mountains, in: Agriculture Handbook 282, US Department
of Agriculture, Agricultural Research Service, Washington, D.C., 1965.
Wischmeier, W. H. and Smith, D. D.: Predicting Rainfall Erosion Losses: A Guide
to Conservation Planning, in: Agriculture Handbook 537, US Department of
Agriculture, Agricultural Research Service, Washington, D.C., 1978.
Xi, Z. D., Sun, H., and Li, X. L.: Characteristics of soil erosion and its
space-time distributive pattern in southern mountains of Shaanxi province,
Bull. Soil Water Conserv., 17, 1–6, 1997.
Xie, Y., Yin, S. Q., Liu, B. Y., Nearing, M., and Zhao, Y.: Models for estimating
daily rainfall erosivity in China, J. Hydrol., 535, 547–558, 2016.Zheng, F. L. and Wang, B.: Soil Erosion in the Loess Plateau Region of China,
in: Restoration and Development of the Degraded Loess Plateau, China, Ecological
Research Monographs, edited by: Tsunekawa, A., Liu, G., Yamanaka, N., and Du,
S., Springer, Japan, 10.1007/978-4-431-54481-4_6, 2014.