Introduction

Sediment yield is defined as the amount of eroded soil that is transported by water to a certain point in a landscape or a river system (Lu et al. 2005). Sediment yield at a point along the main channel of a drainage basin is an integrated result of upland, gully, channel erosion, transportation, and deposition processes (Şen 2014). The sediment delivery ratio (SDR), an important parameter reflecting the sediment yield from an area divided by the gross erosion of the same area (Dong et al. 2013), shows a very strong spatiotemporal variability due to the changes of climate, hydrology, topography, soil, land use, and management practices in different regions (Golosov et al. 2017). The main factors influencing SDR can be summarized as three aspects: (i) the landscape and environmental factors, such as drainage area, watershed shapes and channel characteristics (Tang et al. 2001); (ii) the underlying surfaces, such as the size of soil particles, soil texture, vegetation, and land-use types (Cai and Fan 2004); and (iii) the hydrometeorological factors, such as rainfall amount, rainfall duration, runoff depth, runoff coefficient, peak runoff, channel density, gully density, and sediment concentration (Kiniry et al. 2000; Liu et al. 2007).

In general, the SDR algorithms can be classified into four categories (Wu et al. 2018a): (i) the definition of SDR (Zhang et al. 2014); (ii) the single-factor linear, logarithmic, power or polynomial equations based on the watershed area, slope length, river channel slope ratio, runoff, and the valley shape (Zhu et al. 2007; Wu et al. 2020); (iii) the double-factor linear, logarithmic, exponential, or polynomial equations based on the different combination of watershed shape parameters (length, height, width), drainage density, drainage area, runoff, slope, soil infiltration rate, soil erosivity factor, soil particle composition, runoff depth, and rainfall intensity (Wang et al. 2008a); (iv) the multi-factor linear, power or polynomial equations based on the watershed area, elevation, slope, rainfall, curve number (CN), the ratio of height to width, runoff coefficient, rainfall intensity, rainfall duration, antecedent precipitation, the fractal dimension of sediment transport, suspended sediment, gully density, rainfall amount, flood-peak discharge, soil erodibility factor, actual evapotranspiration, potential evapotranspiration, vegetation interception rate, and field water capacity (Wang et al. 2013).

Most of the above SDR algorithms are available and generated by the statistical regression of a large number of experimental or field monitoring data (Xie and Li 2012; Zhang et al. 2014), each with particular strengths and limitations. However, these estimates are largely focused on the long-term average or event-based level of SDR, and the parameters used by the SDR empirical equations are difficult to be obtained in some specific regions, which further limit their practical application scopes (Li et al. 2009a; Gao 2012).

What’s more, modeling techniques play a crucial role in the quantitative estimation of soil loss in highly erodible regions (Markose and Jayappa 2016), but there are few dynamic multi-scale studies in the application of SDR because of the obvious difference in the hydrometeorological characteristics of the specific catchments (Wang et al. 2013; Wu et al. 2014); it is usually difficult to establish the most appropriate sediment yield model for the loess hill and gully region (Liu et al. 2007), let alone a universal ensemble modeling approach for multiple scales under long time series hydrometeorological data (Wang et al. 2013). Therefore, there is a tremendous demand to develop a dynamic multi-scale SDR algorithm which can provide the desired information, be easy to practice, use readily available long-term input data, and instill user confidence and comfort to meet the demands of accurate sediment yield predictions in different catchments.

The aims of this study are to (i) develop a dynamic multi-scale SDR algorithm using five long time series hydrometeorological data of different hydrological stations in the Yanhe River Watershed; (ii) calibrate and evaluate the nonlinear SDR algorithm in multi-scale catchments of the Yanhe River Watershed; and (iii) apply the dynamic SDR algorithm and the modified USLE/RUSLE (Revised Universal Soil Loss Equation) model to predict the spatiotemporal sediment yields in the upstream catchment of Ansai hydrological station.

Materials and methodology

Study region

Yanhe River, with a length of 286.9 km, is the first-grade tributary of the Yellow River, it is originated from Baiyu Mountain and flows through Zhidan, Ansai, Yan’an, and Yanchang counties (cities), and eventually merges into the Yellow River via the Nanhegou River in Yanchang County (Zhang et al. 2005). The Yanhe River Watershed (108° 38′~110° 29′ E and 36° 21′~37° 19′ N), with a drainage area of 7725 km2, has features of broken and complicated terrain, criss-cross ravines and gullies, and low vegetation coverage. The hilly and gully region accounts for 94.6% of the whole watershed, the gully density is (2.1~4.6) km•km−2, and the average slope ratio of the river channel is 3.26‰ (Wang et al. 2008b).

The annual average precipitation is 495.6 mm, the annual average runoff is 293 million m3, and the average sediment concentration is 244–311 kg•m−3 (Miao et al. 2018). About 75% of annual precipitation, > 99.95% of annual runoff, and > 94% of annual sediment yield are all concentrated in June–September (Ma et al. 2008). Land-use types in this watershed mainly include forestland, farmland, and grassland. The soil types are dominated by the loessial soil, accounting for > 85% of the total drainage area (Zhang et al. 2017). The loessial soil particles are mainly composed of silty sands, which have loose soil structure and poor erosion resistance (Wang and Feng 2017).

There are three important nested hydrological stations in the Yanhe River Watershed, including Ansai, Yan’an, and Ganguyi (Fig. 1). According to geospatial statistics, there are strong geomorphological similarities and small attribute differences in soil, land use, and slope among the three nested catchments, although they differ greatly in the area of catchments. Firstly, the soil types of Calcaric Cambisols and Calcaric Fluvisols (Harmonized World Soil Database, version 1.1) account for > 90% in each catchment, of which the Calcaric Cambisols accounts for > 81%. Specifically, the Calcaric Cambisols and Calcaric Fluvisols account for 81.6% and 12.01% in Ansai catchment, 84.2% and 10.23% in Yan’an catchment, and 81.28% and 9.59% in Ganguyi catchment, respectively. Secondly, the dry land, grassland and forestland are the three main land-use types in each catchment, all accounting for > 95%. Among them, the dry lands respectively account for 35.43%, 38.28%, and 40.70% in Ansai, Yan’an, and Ganguyi catchments; 22.66%, 23.66%, and 16.81% for the middle-coverage grasslands; 32.06%, 28.19%, and 28.59% for the low-coverage grasslands; 6.48%, 4.37%, and 3.12% for the other forestlands; and 0.43%, 0.3%, and 0.44% for the common forestlands. Thirdly, the three catchments all belong to the typical loess hilly and gully regions, and 5–25° slopes account for an absolute advantage of about 85%. Specifically, 0–5° slopes respectively account for 5.49%, 5.07%, and 4.97% in Ansai, Yan’ an, and Ganguyi catchments; 27.2%, 25.21%, and 25.25% for 5–10° slopes; 35.89%, 35.79%, and 36.51% for 10–15° slopes; 22.73%, 24.71%, and 25.07% for 15–20° slopes; 7.58%, 8.2%, and 7.5% for 20–25° slopes; and 1.11%, 1.01%, and 0.69% for > 25° slopes.

Fig. 1
figure 1

Study region. a The relative location of Yanhe River Watershed in China. b Three main catchments in the Yanhe River Watershed: the upstream catchment of Ansai hydrological station (1334 km2), the upstream catchment of Yan’an hydrological station (3208 km2), and the upstream catchment of Ganguyi hydrological station (5891 km2)

Full size image

The Ansai hydrological station, one of the three primary hydrological stations in the Yanhe River Watershed, is located in the second sub-regions of Chinese loess hilly and gully region (Fig. 1). The annual average runoff amount is about 48.7 million m3. The upstream catchment of Ansai hydrological station, with an area of 1334 km2, has a steep slope, deep gully, and easily eroded loessial soil. Grassland and sloping farmland (dry land) are the main land-use types that account for about 89.09% of the total catchment area. To reduce soil erosion, a series of soil and water conservation practices such as warp land dams, terracing, contour tillage, eco-clean small watershed, man-made afforestation and grass planting, and the natural recovery of forestland or grassland by land closure were successively implemented in the Loess Plateau since the 1950s (Wu et al. 2020). More significantly, the historically unprecedented project, “Grain-for-Green,” was officially initiated in western China for soil erosion control and vegetation improvement by converting sloping farmland into forests or grassland in 1999 (Wang et al. 2006).

Data sources and descriptions

The environmental database, which includes the digital elevation model (DEM) (Fig. 2), land-use types (Fig. 3), normalized difference vegetation index (NDVI), soil properties, runoff, sediment, and meteorological data, is given in Table 1.

Fig. 2
figure 2

Digital Elevation Model (DEM) in the upstream catchment of Ansai hydrological station

Full size image
Fig. 3
figure 3

Spatial distribution of 2010 land-use types in the upstream catchment of Ansai hydrological station (21 forest land, 22 shrubland, 23 sparse forest land, 24 other forest land, 31 high coverage grassland, 32 middle-coverage grassland, 33 low-coverage grassland, 43 reservoir or pond, 51 urban, 52 rural residential area, 53 industrial, traffic, and constructional land, 122 dry land in hilly area, 123 dry land in plain area)

Full size image
Table 1 Sources and descriptions of the environmental database in the study region
Full size table

Dynamic sediment yield model

An important consideration in selecting a model is whether an established user base exists for the model (Toy et al. 2002). The USLE/RUSLE was selected as the original version to modify the dynamic sediment yield model (Kinnell 2016). This is because the USLE/RUSLE model is now frequently used for erosion estimates at a catchment scale by combining with GIS spatial analysis techniques (de Vente et al. 2008; Mhangara et al. 2012; Akbarzadeh et al. 2016), although it was originally designed for estimating long-term average sheet and rill erosion from specific field slopes in specified cropping and management systems and from rangeland (Wischmeier and Smith 1978; Renard et al. 1997). In the process of studying the dynamic sediment yield model based on geospatial technology, the following three issues need to be emphatically considered: (i) ephemeral gully, one of the main ways of soil erosion in the middle and lower parts of slopes (Jiang et al. 2005), is a typical kind of erosion channel formed due to the alternative action of runoff scouring and tillage in the Loess Plateau of China (Kang et al. 2016); (ii) the topography and soil types in a watershed are basically unchanged for a relatively short time (Long et al. 2012), so the factors of K, L, and S that reflect topographical features and soil properties can be assumed to be constants in the USLE/RUSLE model; and (iii) the hydrometeorological situations and land management practices changed greatly year by year (Wu et al. 2016a; Molla and Sisheber 2017), so the factors of R, C, P, and λ might change at any time with climatic conditions and human activities (Wu et al. 2016b). Thus, the USLE/RUSLE model can be modified as the dynamic sediment yield model:

$$ {Q}_{s,i}=K\cdotp L\cdotp S\cdotp G\cdotp {R}_i\cdotp {C}_i\cdotp {P}_i\cdotp {\lambda}_i $$
(1)

where Qs is the average annual sediment yield rate, t•km−2•year−1; K is the soil erodibility factor, t•ha•h•ha−1•MJ−1•mm−1; LS is the slope length and slope gradient factor (topographic factor); G is the ephemeral gully erosion factor; R is the rainfall-runoff erosivity factor, MJ•mm•ha−1•h−1•year−1; C is the cover and management factor; P is the support practice factor; λ is the average sediment delivery ratio (SDR) factor; subscript i represents the i-th year and no subscript for the average year.

The variation of Ri in Eq. (1) depends only on the meteorological conditions while Ci and Pi only on the land management activities, but λi depends not only on hydrometerological conditions but also on land management activities. Supposing that the factor expression of Ci · Pi · λi can be approximately defined as the product of C·P and the comprehensive SDR factor (SDRi), Eq. (1) can be rewritten as:

$$ {Q}_{s,i}=K\cdotp L\cdotp S\cdotp G\cdotp {R}_i\cdotp C\cdotp P\cdotp \mathbf{SD}{\mathbf{R}}_i $$
(2)

where SDRi the comprehensive SDR factor that is not only related to hydrometeorological conditions but also to land management activities.

Factor algorithms

R factor

The rainfall erosivity factor (R) was estimated by an approach proposed by Renard and Freimund (1994). This approach is based on an empirical relationship between rainfall erosivity and the Fournier Index (FI), and has been applied in various watersheds (Beskow et al. 2009; Diodato and Bellocchi 2010). The specific equations of R factor are as follows,

$$ F{I}_{i,j}=\frac{p_{i,j}^2}{p_i} $$
(3)
$$ {r}_{i,j}=\frac{125.92\cdot F{I}_{i,j}^{0.603}-111.173\cdot F{I}_{i,j}^{0.691}+68.73F{I}_{i,j}^{0.841}}{3} $$
(4)
$$ {R}_i={\sum}_{j=1}^{12}{r}_{i,j} $$
(5)

where FIi, j is the FI for month j in the i-th year; pi, j is the monthly rainfall (mm) for month j in the i-th year; pi is the annual rainfall (mm) in the i-th year; and ri, j is the monthly rainfall-runoff erosivity for month j in the i-th year (MJ•mm•ha−1•h−1•month−1). Ri is the annual rainfall-runoff erosivity factor in the i-th year (MJ•mm•ha−1•h−1•year−1).

K factor

The soil erodibility factor, K, is a quantitative value experimentally determined in the USLE/RUSLE model (Alewell et al. 2019). It can be calculated by the following empirical equation (Liu et al. 2010; Zhang et al. 2007),

$$ K=\left\{0.2+0.3\exp \left[-0.0256{S}_{\mathrm{a}}\left(1-\frac{S_i}{100}\right)\right]\right\}{\left(\frac{S_i}{C_i+{S}_i}\right)}^{0.3}\times \left[1-\frac{0.25{\mathrm{C}}_0}{{\mathrm{C}}_0+\exp \left(3.72-2.95{C}_0\right)}\right]\times \left[1-\frac{0.7 Sn}{Sn+\exp \left(-5.51+22.9 Sn\right)}\right] $$
(6)

where K is the soil erodibility factor, t•ha•h•ha−1•MJ−1•mm−1; Sais the sand mass fraction (0.05~2 mm), %; Si is the silt mass fraction (0.002~0.05 mm), %; Ci is the clay mass fraction (< 0.002 mm), %; and, C0 is the percentage of organic matter, %.

LS factor

The topographical factor (LS) is an important index to characterize the effect of terrain on soil erosion (Wang et al. 2004). Both the slope length and the slope steepness affect the rate of soil erosion substantially (Yavuz and Tufekcioglu 2019). The two factors have been evaluated and represented in the USLE/RUSLE model by L and S respectively (Wischmeier and Smith 1978).

The L factor values were estimated by the formulas proposed by Wischmeier and Smith (1965) and Foster and Wischmeier (1974). The specific equations based on the location of DEM grid are as follows,

$$ {L}_i=\frac{\lambda_{out}^{m+1}-{\lambda}_{in}^{m+1}}{\left({\lambda}_{out}-{\lambda}_{in}\right){(22.13)}^m}\kern0.50em \ {\lambda}_{out}-{\lambda}_{in}>0 $$
(7)
$$ {L}_i={\left(\frac{\lambda_{out}}{22.13}\right)}^m\kern0.50em \ \ \ \ \ \ \ \ \ {\lambda}_{out}-{\lambda}_{in}<0 $$
(8)
$$ {L}_i={L}_{flow}\kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ \kern0.50em \ {\lambda}_{out}-{\lambda}_{in}=0 $$
(9)
$$ {L}_i=0\kern0.50em \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ {\lambda}_{out}=0 $$
(10)

where Li is the slope length factor in the i-th grid, Lflow is defined as the slope length factor in the grid with the longest flow path, λout and λin are the slope length respectively in the grid outlet and the grid inlet, m is the slope length index.

The slope length index can be determined by the previous research results (Liu et al. 2000),

$$ {\displaystyle \begin{array}{l}m=0.2\kern4.399998em \theta <0.5{}^{\circ}\\ {}m=0.3\kern4.399998em 0.5{}^{\circ}\le \theta <1.5{}^{\circ}\\ {}m=0.4\kern4.299998em 1.5{}^{\circ}\le \theta <3{}^{\circ}\\ {}m=0.5\kern4.399998em 3{}^{\circ}\le \theta \end{array}} $$
(11)

where θ is the slope gradient (°).

The S factor values in the gentle slope (≤ 10°) and steep slope (> 10°) were respectively calculated by the formulas proposed by McCooL et al. (1987) and Liu et al. (2010). The specific piecewise expressions are as follows,

$$ {\displaystyle \begin{array}{l}S=10.8\sin \theta +0.03\kern1.8em \theta <5{}^{\circ}\\ {}S=16.8\sin \theta -0.5\kern1.8em 5{}^{\circ}\le \theta \le 10{}^{\circ}\\ {}S=21.9\sin \theta -0.96\kern1.7em \theta >10{}^{\circ}\kern0.7em \end{array}} $$
(12)

where S is the slope gradient factor, θ is the slope gradient (°).

C factor

The cover and management factor (C) is the ratio of soil loss from an area with specified cover and management to that from an identical area in tilled continuous fallow (Wischmeier and Smith 1978). The C factor can be estimated by the equations proposed by Cai et al. (2000) and Ma et al. (2001). The specific expressions are as follows,

$$ {c}_j=\frac{NDV{I}_j- NDV{I}_{soil,j}}{NDV{I}_{veg,j}- NDV{I}_{soil,j}} $$
(13)
$$ {C}_j=\left\{\begin{array}{l}1\\ {}0.6508-0.3436\lg {c}_j\\ {}0\end{array}\right.{\displaystyle \begin{array}{c}{c}_j=0\\ {}0<{c}_j<78.3\%\\ {}{c}_j\ge 78.3\%\end{array}} $$
(14)
$$ C=\sum \limits_{j=1}^{12}\frac{R_j}{R}{C}_j $$
(15)

where cj is the monthly vegetation coverage (%), NDVIsoil, j is the Normalized Difference Vegetation Index (NDVI) value of nonvegetated areas (or, NDVI of a pure soil pixel), NDVIveg, j is the NDVI value of vegetated areas (or, NDVI of a pure vegetation pixel). Cj is the monthly cover and management factor, C is the annual cover and management factor, Rj is the monthly rainfall-runoff erosivity factor, R is the annual rainfall-runoff erosivity factor.

P factor

The support practice factor (P) in the USLE/RUSLE model is the ratio of soil loss with a specific support practice to the corresponding soil loss with up-and down-slope cultivation (Wischmeier and Smith 1978). The most important cropland supporting practices are contour tillage, strip cropping, and terraces. The P factor values were determined by different support practices under different land-use types (Cheng et al. 2012; Xie 2008).

G factor

The ephemeral gully erosion factor (G) reflects the effects of the shallow gully on the processes of soil erosion (Zheng and Xiao 2010). G factor was primarily affected by precipitation, the convergent intensity of flow, slope steepness, slope length, and soil properties (Jiang et al. 2008). According to the previous studies (Li et al. 2009b; Wu et al. 2016c), the specific equation was determined as follows:

$$ G=1+\sigma =1+\frac{\left(\alpha -{\theta}_c\right)\left(1.003{\left({R}_e\cdot {I}_{30}\right)}^{0.013}-1\right)}{30-{\theta}_c} $$
(16)

where: G is the ephemeral gully erosion factor; σ is the correction coefficient; α is the surface slope (°); θc is the critical slope gradient (°); Re is the event-based rainfall amount (mm); I30 is the 30-min maximum rainfall intensity (mm/min); when there is no ephemeral gully erosion on the slope, σ = 0, and G = 1; when the slope gradient is < 15°, G = 1.

SDR factor

The rainfall, runoff, rainfall erosivity, maximum peak flow, and the sediment transport rate were exactly proven to be the main hydrometeorological factors affecting the sediment yield processes in the loess hilly and gully region (Wu et al. 2018b). Meanwhile, the comprehensive surface roughness factor estimated by the long time series data of soil erosion and sediment yield from 1957 to 1989 was introduced to dynamically identify the potential impacts of the underlying surfaces on sediment transport under different catchment scales. Based on these two prerequisites, the annual SDR values in the upstream catchment of Ansai hydrological station were used to develop and calibrate the dynamic SDR algorithm by the repeated multivariate nonlinear regression, while the statistical sediment transport rate of the large-scale loess hilly catchments was used to fit the equation of the comprehensive surface roughness factor,

$$ SD{R}_i=9.3644{Q}_i^{-0.14045}\kern0.2em R{I}_i^{-0.80984}\kern0.2em {F}_i^{-0.053245}\kern0.2em {S}_i^{1.0861}\kern0.2em {P}_i^{-0.19049}{N}_i $$
(17)
$$ {N}_i=0.5834{e}^{-0.00009\kern0.3em {S}_i}\ \left({R}^2=0.58,n=33,p<0.05\right) $$
(18)

where SDRi is the annual SDR value, Qi is the annual runoff amount (104 m3), RIi is the annual rainfall intensity (MJ•mm•hm−2•h−1•year−1), Fi is the annual maximum peak flow (m3•s−1), Si is the annual average sediment transport rate (kg•s−1), Pi is the annual rainfall amount (mm), Ni is annual comprehensive land roughness factor (Ni = 1, when the watershed area is equal to 1334 km2).

Factor estimation and rasterization

The mean estimated values of R, K, LS, CP, G and SDR in the upstream catchment of Ansai hydrological station are given in Table 2.

Table 2 Mean value of each factor in the modified sediment yield model
Full size table

The R, K, LS, CP factors were respectively calculated by rasterization and shown in Fig. 4.

Fig. 4
figure 4

Spatial distribution of the rainfall-runoff erosivity factor (R) (MJ•mm•ha−1•h−1•year−1), the soil erodibility factor (K) (t•ha•h•ha−1•MJ−1•mm−1), the topographic factor (LS), the cover and management factor (C), and the support practice factor (P) in the upstream catchment of Ansai hydrological station in the Yanhe River Watershed

Full size image

Results

Calibration performance of the SDR algorithm

The measured SDR by its definition from 1981 to 2015 and the calculated SDR by the developed SDR algorithm were compared to test the calibration performance in the upstream catchment of Ansai hydrological station Fig. 5. The specific results are as follows: (i) The SDR values calculated by the dynamic algorithm were close to the SDR values by the definition method (y = 1.0006x − 0.0114, R2 = 0.986, n = 35, p < 0.01), the relative error ranges between − 24.3% and 10.91%, which confirms that the dynamic SDR algorithm had good applicability in the upstream catchment of Ansai hydrological station. (ii) Although the SDR values in individual years were relatively large, the calculated SDR in the upstream catchment of Ansai hydrological station presented an overall decreasing trend, and this trend was well consistent with the effective implementation of the large-scale “Grain for Green” project in Western China since 1997, which also indicates that the dynamic SDR algorithm had strong applicability in the ecological restoration regions. Moreover, the sharp decrease of SDR after 2005 supported again that the reduction benefits of runoff and sediment by soil conservation practices were considerable. (iii) The variation trends of SDR from 1981 to 2015 were highly consistent with the sediment yield rate (y = 0.0001x + 0.036, R2 = 0.834, n = 35, p < 0.01), maximum peak flow (y = 0.0018x + 0.0579, R2 = 0.68, n = 35, p < 0.05), and runoff amount (y = 0.0004x − 1.1095, R2 = 0.658, n = 35, p < 0.05), indicating that the linear correlation between SDR and sediment yield rate was more significant than the other two hydrological factors in the upstream catchment of Ansai hydrological station. The relative importance of maximum peak flow and runoff amount in the erosion processes was similar although the impact of maximum peak flow was slightly higher than runoff amount. (iv) The correlations between SDR and rainfall amount (y = 1.0095e−0.0017x, R2 = 0.0196, n = 35, p > 0.05) or rainfall erosivity (y = − 0.2943lnx + 2.9727, R2 = 0.029, n = 35, p > 0.05) in the upstream catchment of Ansai hydrological station were both very weak, indicating that there was no direct causal relationship between SDR and rainfall indicators in the loess hilly and gully regions. In other words, soil erosion (soil detachment) is not equal to sediment yield, the eroded soil was not always able to be delivered from the eroding portions of a hillslope to the outlet of a watershed (sediment yield) before deposition due to the effective runoff and sediment reduction effects of large-scale soil conservation practices (Wu et al. 2020), although the heavy rainstorms might cause serious soil erosion. (v) There were still high sediment yield rates in 2004 and 2005 although the SDR values in these 2 years decreased significantly due to the effective implementation of soil conservation practices since 1997, indicating that the SDR dynamics might be more sensitive and identifiable to the soil conservation practices than the sediment yield rate.

Fig. 5
figure 5

Calibration results of the dynamic sediment delivery ratio (SDR) algorithm in the upstream catchment of Ansai hydrological station from 1981 to 2015. a Rainfall (mm) and relative error between measured SDR and calculated SDR (%). b Trends of soil erosion rate (t•km−2•year−1), sediment yield rate (t•km−2•year−1), measured SDR, and calculated SDR

Full size image

Spatial variations of sediment yield

The spatial distributions of soil erosion grade and sediment yield rate varied greatly in the upstream catchment of Ansai hydrological station in 2010 (Fig. 6). The soil erosion grade ranged from micro erosion to severe erosion, and the percentages of micro, mild, moderate, intensive, extreme, and severe erosion accounted for 2.35%, 0.31%, 11.51%, 39.73%, 27.12%, and 18.99% respectively, which indicates that the proportion of high erosion rates (> intensive) was particularly evident in the upstream catchment of Ansai hydrological station in 2010 with a total sum of 85.84%. The extreme erosion and severe erosion were mostly located in the northwest mountainous regions, in reverse, the micro erosion and mild erosions were located in the southeast of the catchment, but there were also some scattered extreme erosion zones in the middle and lower reaches of the catchment. The above results are related not only to the spatial distribution of erosive rainstorms in 2010 but also to the implementation background and effect of the large-scale soil conservation practices since 1997.

Fig. 6
figure 6

Spatial distribution of soil erosion grade and sediment yield rate (t•km−2) in the upstream catchment of Ansai hydrological station in 2010. Chinese Soil Erosion Classification and Grading Standards (SL190–2007): water erosion (a) micro (< 200, < 500, < 1000 t•km−2•year−1), (b) mild (200, 500, 1000–2500 t•km−2•year−1), (c) moderate (2500–5000 t•km−2•year−1), (d) intensive (5000–8000 t•km−2•year−1), (e) extremely intensive (8000–15,000 t•km−2•year−1), and (f) severe (> 15,000 t•km−2•year−1)

Full size image

Unlike soil erosion grade, the sediment yield rate in the middle and lower reaches of Ansai hydrological station was still severe particularly in the case of heavy rainstorms and intense human activities in 2010, although the large-scale soil conservation practices had been effectively implemented since 1997. The sediment yield risk map also suggests that the regions with greatest sediment yield potential were primarily concentrated in the extensive sloping farmlands located at the two sides of main river banks from northwest to southeast of the catchment, but the peak sediment yield rate gradually decreased as the distance from the river bank increased.

Temporal variations of sediment yield

The temporal variations of sediment yield rate, rainfall erosivity and runoff amount in the upstream catchment of Ansai hydrological station are presented in Fig. 5b. First, the sediment yield rate showed an overall decreasing trend from 1981 to 2015. The maximum sediment yield rate in the upstream catchment of Ansai hydrological station appeared in 1992 with a value of 30,700 t•km−2, while the minimum occurred in 2015 with a value of 65 t•km−2. Second, the average annual sediment yield rate from 1981 to 1997 was 10,238.35 t•km−2, there was no obvious downward trend for annual sediment yield rate during this period, on the contrary, a sharp increase of the sediment yield rate occurred in 1992. Third, after 1997, the annual sediment yield rate presented a very significant downward trend, and particularly, the annual sediment yield rate decreased dramatically from 11,844.08 t•km−2 in 2005 to 65 t•km−2 in 2015.

The sediment yield rate presented a significantly positive correlation with runoff amount (y = 3.7509x-10,664, R2 = 0.730, n = 35, p < 0.05), although there were several conspicuous mutation points in the trend line of sediment yield rate and runoff amount from 1981 to 2015, e.g., the annual sediment yield rates in 1988, 1992, 1996 and 2002 were 18,300, 30,700, 21,200, and 22,900 t•km−2, respectively, which are significantly higher than the average level. However, the interactions between sediment yield rate and rainfall erosivity were relatively complex in the upstream catchment of Ansai hydrological station, and there was no obvious correlation between sediment yield rate and rainfall erosivity (y = 2628.8e0.0003x, R2 = 0.024, n = 35, p > 0.05).

Discussion

Evaluation of the dynamic multi-scale SDR algorithm

The average observed sediment yield rates in different catchment scales were used to verify the confidence and reliability of the modified sediment yield model (Table 3). The main findings might involve the following: (i) The average relative errors between the simulated and observed sediment yield rates in the upstream catchments of Ganguyi (1952–2013), Yan’an (1958–2007) and Ansai (1981–2015) hydrological stations were − 11.7%, 6.2%, and 10.7% respectively. These acceptable relative errors illustrate that the combination of the dynamic multi-scale SDR algorithm and the modified USLE/RUSLE model was reliable and feasible for the improvement of prediction accuracy of sediment yield, and it could be used as a powerful methodology tool in evaluating the dynamic evolutions of sediment yield in any other ecological restoration regions. (ii) The introduction of G factor in the modified sediment yield model has been proven to be important for improving the estimation accuracy of soil erosion in the loess hilly and gully region. This is because the soil erosion caused by ephemeral gullies contributes greatly to the total soil losses and is one of the major processes of land degradation (Taguas et al. 2012), moreover, the gullies in cultivated fields are not only the main channel of sediment transport (Martinez-Casasnovas et al. 2005) but also the main source of eroded soil particles (Zhu 2012). (iii) Although the SDR values in the dry period were always found to be lower than that in the flood period (Woznicki and Pouyan Nejadhashemi 2013), the dynamic SDR algorithm can be successfully applied in the spatiotemporal sediment yield predictions of the ecological restoration watersheds. More importantly, the structure and function of the sedimentary cascade in a watershed can still provide useful information for the design of cost-effective hydrological surveys and appropriate conservation planning and mitigation strategies (Yu et al. 2011). (iv) This novel approach for modeling sediment input to surface waters has less uncertainty originating from the sporadic model variability (Wang et al. 2013), which can be considered as part of the particulate nutrient loss model for the source-differentiated quantification of dynamic nutrient inputs in large river basins or landscapes (Tetzlaff et al. 2009). (v) The correlation between SDR and sediment yield rate in the upstream catchment of Ansai hydrological station is similar to the findings that the SDR values were positively related to the sediment yield rate in Chabagou River Watershed (Liu et al. 2007). Overall, the above new understanding may provide key insights into the development of a time-space scale transformation methodology framework of regional sediment yield predictions (Ondráčková and Máčka 2019).

Table 3 Comparison of the average simulated and observed sediment yield rates in the three upstream catchments of Ganguyi, Yan’an, and Ansai hydrological stations
Full size table

In general, the model selection criteria are primarily based on either model performance or consensus (Lin et al. 2018). Although the modified model shows promising results in modeling the spatiotemporal sediment yield characteristics in multi-scale catchments, it is still far from achieving performance comparable to that of other physically-based watershed models in the microscopic mechanism of the sediment transport process (Keesstra et al. 2014; Batista et al. 2017). In other words, the model still has some limitations that can be improved in the future, e.g., (i) the scale extension of SDR algorithm is only based on the difference of comprehensive roughness coefficient factor, which is likely to be an abstractive, black-box concept that lacks the in-depth interpretation of spatial scale effect for different catchments (Wu et al. 2017), so the future model improvements will focus on the effective integration in dynamic variation and spatial visualization of sediment delivery based on the hydrometeorological and topographical data (Lee and Kang 2013); (ii) the model structure is of utmost importance since it determines both how the real-world phenomena are simplified and whether the complex input data are required (Watling et al. 2015), but the physical mechanism deficiency of the multi-scale SDR algorithm and the complexity of sediment transport process increase the uncertainty of the empirical-based modified model (Tetzlaff et al. 2013), it is essential to continue examining both the sources of model uncertainty and the effects they have on the key source identification and the mitigation practice application (Swarnkar et al. 2018); (iii) the dynamic multi-scale SDR algorithm based on rainfall, runoff, rainfall erosivity, maximum peak flow, sediment transport rate, and underlying surfaces are more sensitive to soil conservation practices, but the model output is at the grid level rather than the hydrological response unit (HRU) level, affecting the identification accuracy of highly eroded areas, so it is often exceedingly difficult or impractical to select the optimal best management practices (BMPs) for all priority control regions considered in a specific conservation initiative (Sarma et al. 2015); (iv) the modified sediment yield model has primarily relied upon annual hydrometeorological data; however, the widely available data such as event-based or daily precipitation and discharge are disregarded resulting in a reduction in temporal accuracy (Temme et al. 2011); (v) the importance of this modeling tool is practical, but understanding the relationships between patterns at various scales cannot be strictly done with this modeling tool because it has no close connection with physically-based erosion processes and can only prove post-factum effects when the catchments are rather large. Most noteworthy, the existing large data sets might be used in the future process-based erosion models, especially for the multi-scale patterns of sediment production; and, (vi) undeniably, the innovative process-based modeling framework of distributed hydrological model and sediment yield model, by integrating long time series hydrometeorological data, geographical information system (GIS) and remote sensing techniques, and the four modules of raindrops splashing, soil detachment, runoff driven and sediment routing, will become the key direction of soil erosion research at catchment scales (Wu et al. 2019a). It can not only overcome the limitation of the deficiency of physical mechanism of the USLE/RUSLE model but also can estimate the erosion potential and identify critical erosion-prone areas in watersheds effectively, which can eventually provide strategy support for policy-makers and practitioners.

Spatial analysis of soil erosion and sediment yield

The soil erosion grade and sediment yield rate under different land-use types differed greatly in the upstream catchment of Ansai hydrological station in 2010 (Table 4). The land-use types were mainly composed of dry land in hilly area, middle-coverage grassland, and low-coverage grassland, accounting for 35.76%, 22.25%, and 31.08% of the total catchment area respectively. The soil erosion grades of these three land-use types were all between intensive erosion and extreme intensive erosion. The results exactly conform to the dominated grade level of extreme erosion in the second sub-regions of loess hilly and gully region (Wang et al. 2003). The largest sediment yield amount occurred in the hilly dry land area (sloping farmland) with a value of 124.901 × 104 tons. The results are similar to the sediment yield level under different land-use types in purple soil: farmland>orchard>grassland>shrubland>forestland (Zhang and Li 2018). Therefore, it is of great significance to implement effective soil conservation practices in sloping farmland and low-coverage grassland for sustainable agriculture (Wu et al. 2019a). However, the maximum sediment yield rate appeared in the rural residential area, which can be primarily attributed to the relatively large sediment source and small areal size of rural settlements (Ndomba et al. 2009).

Table 4 Geospatial statistics of land-use type, land-use percentage, soil erosion grade, sediment yield, Minimum, Maximum and Mean sediment yield rate in the upstream catchment of Ansai hydrological station in 2010
Full size table

Catchment estimates of sediment yield and its spatial and temporal variations are needed for the evaluation of the effects of various land-use management practices (Sadeghi et al. 2008). The high-risk regions of sediment source in the upstream catchment of Ansai hydrological station were mainly from the hilly dry land, middle-coverage grassland, low-coverage grassland, and other forest lands. This is because soils are generally vulnerable and lands are often degraded with steep slopes and declining vegetation cover (Steegen et al. 2001), and the increase of agricultural activities inevitably causes the increase of sediment yield (Huang and Lo 2015). The results are similar to the findings by Op de Hipt et al. (2019) that the enlarging cropland was an important and growing contribution source to total soil loss in a tropical West African catchment. The results also support the fact that hill slopes are the primary source of erosion by pulsed runoff with channel bank and flood plains as the secondary sources in arid regions (Şen 2014). The middle- and low-coverage grasslands accounted for 22.25% and 31.08% of the total catchment area, but the sediment yield amount in middle-coverage grassland was higher than that in low-coverage grassland in 2010. The results supported the fact that reasonable soil conservation practices could reduce soil erosion in sloping farmland and low-coverage grassland effectively (Lovell and Sullivan 2006) because the land management activities changed slope gradient and reduced flow accumulation (Melakua et al. 2018).

Hydrometeorological and landscape factors influencing sediment yield

Sediment yield in watersheds is heterogeneous in both time and space because it depends on many factors, such as climate, geology, soil type, geomorphology, land use, vegetation, and human activities (Verbist et al. 2010; Gourfi et al. 2018). First, the possible reasons for the irregular relationship between sediment yield and rainfall erosivity can be attributed to the actuality that the influencing factors of sediment yield process were more complex than soil erosion: (i) the upstream catchment of Ansai hydrological station is located in the semiarid and arid region, the precipitation in this region is scarce and concentrated, the rainfall kinetic energy of few transient rainstorms may be easily lessened by vegetation interception, evaporation, and infiltration (Wu et al. 2018c), thus resulting in the reduction of erosive rainfall kinetic energy and sediment yield rate (Ai et al. 2017); (ii) there was a significant spatiotemporal difference for the distribution of erosive rainfall in this region (Wu et al. 2016d), the severe soil erosion may be always caused by a few pulsed heavy rainstorms or the medium intensity rainfalls with long duration, thus producing considerable sediment yield rate (Zheng et al. 2008).

Second, the soil conservation practices can effectively reduce runoff and sediment in the watersheds (Yan et al. 2015). The overall decreasing trends of sediment yield rate in the upstream catchment of Ansai hydrological station from 1981 to 2015 supported the findings that the large-scale “Grain for Green” project implemented in the late 1990s played a positive role in runoff and sediment reduction (Ai et al. 2013). Specifically, the decrease of sloping farmland (dry land) and the increase of forestland/grassland can change land-use structures, which may cause an overall decrease in sediment yield rate from 1981 to 2015. More interestingly, it was not until 2007 that there was a sharp decrease in sediment yield rate and SDR. The delayed phenomenon of sediment reduction can be attributed to the cumulative effects of soil and water conservation practices since 1997 (López-Vicente et al. 2008), in other words, there is a practical lag period for the regulation of sediment delivery processes by the artificial vegetation construction because vegetation communities intercept sediment primarily by intercepting raindrops kinetic energy and reducing runoff erosivity (Zheng et al. 2007; Zhang et al. 2007) but vegetation needs a certain growth cycle before it can play an effective role in soil and water conservation (Qin et al. 2014).

Third, analysis of the relationships between sediment yield and rainfall-runoff characteristics can help to understand the factors and processes determining sediment responses (Nadal-Romero et al. 2008; Fang et al. 2011). In general, the annual variations of runoff and sediment yield are closely related to rainfall (Wei et al. 2015). The sharp increase of sediment yield in some extreme hydrological years can be partly explained by increased rainfall and larger peak flow events in the upstream catchment of Ansai hydrological station (Wu et al. 2019b). e.g., (i) The rainfall of 579.3 mm in 1988 was 1.12 times over the average annual rainfall of 519.5 mm, the runoff amount of 7446.82 × 104 m3 was 1.53 times than the average annual runoff amount of 4870.27 × 104 m3, the maximum peak flow was 1.83 times over the average value of 403 m3•s−1, and the average sediment yield rate was 1.9 times higher than the average value of 305.5 kg•s−1. Actually, the transient rainstorm of only 50 min from 1:10 to 2:00 am in 1st September 1988 reached 17.5 mm, this rainstorm event was statistically characterized by a large covering area, short duration, and heavy intensity, which fully explained the reason for the abnormal increase of sediment yield rate in 1988. (ii) The rainfall of 548.1 mm in 1992 was 1.06 times over the average annual rainfall of 519.5 mm, the runoff amount of 9499 × 104 m3 was 1.95 times over the average annual runoff amount of 4870.27 × 104 m3, the maximum peak flow was 3.05 times over the average value of 403 m3•s−1, and the average sediment yield rate was 4.27 times than the average value of 305.5 kg•s−1. The results indirectly supported the findings by Qin et al. (2010) that annual runoff, sediment yield, and rainfall in large and medium watersheds were difficult to build direct interrelationships because the magnitude and timing of peak flow events were major determinants of the variability of sediment yield level (Ebabu et al. 2018).

Fourth, the annual change of the hydrometeorological parameters especially the increase of maximum peak flow was the main reason for the abrupt increase of sediment yield in the extreme hydrological years. However, the heavy rainstorm not only increased the sediment yield rate in the current year but also reduced the sediment yield rate in the following years, which is similar to the rules of sediment depletion during flood periods in some typical watersheds over the world (Gomez et al. 1997; Hudson 2003). Moreover, topography is also an important parameter affecting water erosion (Lee et al. 2012), as it is significantly related to the processes of sediment transport under different underlying surfaces (Zheng et al. 2007). The study of sediment yield in the loess hilly and gully region has proven to be very complicated because of the numerous hydrometeorological and topographical parameters involved (Ebabu et al. 2018), the inconsistency or interrelation among these parameters (Ahmadi Mirghaed et al. 2018), and the lack of an appropriate method to quantify some of these parameters (Tetzlaff et al. 2013). This new overall understanding can act as an invaluable reference for decision-makers or planners who are interested in reducing soil loss, especially under heavy rainstorms.

Conclusions

Improved knowledge of the watershed-scale spatial and temporal variability of sediment yield is crucial to support the planning of conservation practices to control soil erosion, particularly in most severely eroded regions. (i) The dynamic multi-scale SDR algorithm supported by five long time series hydrometeorological data can be conveniently and legitimately applied in the spatiotemporal sediment yield predictions of the loess hilly and gully region, which provides extremely important clues for use in further developing a multi-scale ecohydrological decision-support system for watershed land-use planning, management, and policy. (ii) The annual dynamics of sediment yield depend on the inter-annual variation of SDR in a catchment. The overall decreasing trend of sediment yield rate especially after 2007 was closely related to the effective implementation and delayed effects of large-scale soil and water conservation practices. The high-risk regions of sediment yield mainly concentrated in the sloping farmlands locating at two sides of the river banks. The magnitude of SDR in the other two larger catchments with similar hydrometeorology, soil, topography, and land-use types varies greatly due to the scale effect of sediment transport process. (iii) Future sediment transport studies can focus on the development of physically-based SDR at different time and space scales, the quantification of SDR algorithm uncertainty, sensitivity analyses, and the integrated identification of microscopic mechanisms and macroscopic management for sediment or even pollutants, such as nutrients and chemicals. This new overall understanding creates opportunities for improving the prediction accuracy of sediment yield and designing the sustainable soil conservation planning in loess hilly and gully regions.