Analysis of scale-specific factors controlling soil erodibility in southeastern China using multivariate empirical mode decomposition

Highlights

• MEMD was used to decompose K and its influencing factors in southeastern China.

• K and other factors varied most at small or moderate spatial scales (IMF1-IMF4).

• Main factors that influencing K were different in different spatial scales.

• Prediction function of K that based on MEMD had good accuracy.

Abstract

Soil erodibility (K) is a key factor in predicting the erosion of soil by water. K is spatially influenced by many environmental factors, but studies of the scales of factors influencing K are rare. The objective of this study was to identify the scale-dependent relationships between K and various environmental factors using multivariate empirical mode decomposition (MEMD). K and nine environmental factors were investigated at 101 locations along a 4200-km sinuous transect in southeastern China and then they were decomposed and analyzed using MEMD. Mean K was 0.043 ± 0.008 t ha h MJ⁻¹ mm⁻¹ ha⁻¹ and had a weakly moderate spatial variability. Six intrinsic mode functions (IMFs) and a residue were obtained for K and the environmental factors after decomposition. The mean scales for IMF1 to IMF6 were 123.4, 192.4, 347.0, 598.9, 1268.3 and 1559.2 km, respectively. IMF1 for each variable explained most of the spatial variability for the variable, and IMF1 and IMF2 or IMF1 and IMF3 explained half of the spatial variability of the variable. K was mainly associated with soil-particle composition and soil organic-matter content at small scales (IMF1-IMF2), with soil-particle composition and pH at moderate scales (IMF3-IMF4) and with elevation, saturated hydraulic conductivity and clay content at large scales (IMF5-IMF6). Modeled prediction functions of K at each scale of decomposition were accurate, but the total prediction accuracy at the sampling scale was slightly lower than for multiple linear regression. The MEMD method was nevertheless valuable and provided detailed information about the factors influencing K at different spatial scales.

Introduction

The erodibility of soil (K) is a key factor in the classical universal soil loss equation (USLE) for predicting the loss of soil and is an inherent property of soil representing the sensitivity to the detachment and loss of particles during erosion (Zhu et al., 2021). Accurate estimates of K can improve the accuracy of predicting soil loss, which is important for preventing and treating the loss of soil and water.

K was widely studied after USLE was proposed (Zhu et al., 2019a). This accurate method of calculation uses data for sediment yield divided by the erosivity of rainwater in standard runoff plots. The standard method, however, requires data from the long-term monitoring of many standard runoff plots. The method is time-consuming and laborious due to the need to establish multiple standard runoff plots at large scales, and the standard plots have limited spatial representativeness (Wang et al., 2013, Zhang et al., 2018). Many studies have thus established locally applicable models of empirical prediction by considering the relationship between K and the environmental factors, e.g. the nomograph model (Wischmeier et al., 1971), the erosion/productivity impact calculator (EPIC) (Sharpley and Williams, 1990), the Torri model (Torri et al., 1997), the Shirazi model (Shirazi et al., 1988), the Mulengera model (Mulengera and Payton, 1999) and the Wang model (Wang et al., 2013). These methods can be directly used to estimate K for a new research area or watershed, and the accuracies can be assessed by comparing outputs with data from runoff plots. Each of these methods, however, has specific applicable conditions, and errors of estimation will occur when the methods are used arbitrarily under local conditions (Zhu et al., 2020). Establishing an equation for estimating K locally in areas lacking long-term data is therefore necessary. Correlation analysis of K and potential influencing factors is the primary condition for establishing equations for the local estimation of K.

K is an inherent property of soil and is influenced by the nature of the soil. Ostovari et al. (2019) reported that K in a 350-km² area on the Iranian Plateau was positively significantly correlated with silt content (Silt), was negatively significantly correlated with soil permeability, the stability of aggregates in water, CaCO₃ content, soil organic-matter content (SOM) and the geometric mean diameter of soil particles and was not significantly correlated with the contents of clay (Clay) and fine sand. Mallick et al. (2016) reported that K in a 370-km² area in Saudi Arabia was significantly negatively correlated with SOM and sand content (Sand) and significantly positively correlated with Silt and Clay. Bonilla and Johnson (2012) studied the relationships between K and soil texture and organic-carbon content, Ahmadi et al. (2011) studied the influence of soil aggregates on K, and Singh et al. (2012) studied the influence of soil chemistry on K. K has also been correlated with terrain, climate, vegetation and type of soil use, because these environmental factors indirectly influence soil properties (Sanchis et al., 2008, Zhao et al., 2018a, Zhu et al., 2019a). Studies have also found that K was spatially variable and scale-dependent, like many other soil properties (Adhikary et al., 2014, Baskan et al., 2010, Buttafuoco et al., 2012, Jamshidi et al., 2014, Parysow et al., 2003). Most studies of K, however, have focused on the relationships between K and the environmental factors at their sampling scales, but studies with scale-specific analyses of the relationships between K and environmental factors are rare. Many studies have reported that prediction functions based on scale-specific analyses improved the accuracy of estimation (She et al., 2017, Yang et al., 2019a, Zhao et al., 2018b, Zhou et al., 2016, Zhu et al., 2019b, Zhu et al., 2016). Scale-specific analyses of factors influencing K would thus theoretically improve the accuracy of models for the local estimation of K.

Multivariate empirical mode decomposition (MEMD) is a multivariate and multiscale method of analysis developed from empirical mode decomposition (EMD) (Huang et al., 1998, Rehman and Mandic, 2010). EMD and MEMD are applicable to nonlinear and nonstatic systems, are adaptive and fully data-driven methods and can decompose data series into intrinsic mode functions (IMFs) that can represent variable scales of oscillation. The decomposed scales are physically meaningful (Rehman and Mandic, 2010), unlike traditional methods, e.g. Pearson correlation, spectral, wavelet and fractal analyses. EMD can only decompose a single variable, but MEMD can be used to concurrently decompose multivariate data sequences. The advantages of MEMD allow it to be used in soil physics for analyzing correlations between soil physical properties and associated influencing factors (Hu et al., 2014, Hu and Si, 2013, Liu et al., 2019, She et al., 2017, Yang et al., 2019a, Zhao et al., 2018b, Zhu et al., 2019b), but no exploration or application has been reported in the study of soil erosion.

Southeastern China contains basins of Taihu Lake and rivers. This area has a subtropical monsoon climate and abundant and concentrated rainfall. The area also has many mountains and hills. The combination of terrain and rainfall leads to substantial soil erosion. Landslides, collapsing gullies and debris flows are widely distributed and frequent in the area (Zhang et al., 2016, Zhang and Zhang, 2016). Studies of the prevention and treatment of the loss of soil and water in this area thus have practical importance, and the investigation and analysis of K can provide necessary information for predicting the loss of soil. The objectives of this study were therefore to: (1) identify multiscale spatial correlations between K and its associated environmental factors and (2) estimate K at the measurement scale based on a multiscale analysis in southeastern China.