Noise-assisted multivariate empirical mode decomposition of saturated hydraulic conductivity along a south-north transect across the Loess Plateau of China

Saturated hydraulic conductivity (K_s) usually varies at multiple scales in space, as affected by different soil and environmental processes operating at diverse scales. Identifying spatial process relationships can be challenging due to overlapping of underlying processes at different scales. The objective of this study was to evaluate noise-assisted multivariate empirical mode decomposition (NA-MEMD) for characterizing K_s variability and depicting its scale-dependent relationships with different soil properties and environmental factors. At an interval of 10 km along an 860-km south-north transect across the Loess Plateau of China, K_s, bulk density, soil organic carbon content, sand and clay contents at three depths of 0 to 10, 10 to 20 and 20 to 40 cm were investigated as well as four environmental factors of elevation, slope gradient, annual precipitation and temperature. Decomposed into different intrinsic mode functions (IMFs) and residues by NA-MEMD, K_s at all depths were found to vary at the smallest scale of 29 km mainly, corresponding to IMF1s, which manifested 33.0 to 48.1% of the total K_s variance. The small-scale variations of K_s reflected not only in IMF1s but also in IMF2s and IMF3s were dominated by soil properties especially bulk density, and the large-scale variations corresponding to IMF4s and IMF5s were controlled by environmental factors in general. For each depth, K_s at the scale of investigation was estimated by adding all the IMFs and residue derived from the factor components at equivalent scales using multiple linear regression (MLR). Such K_s estimations after NA-MEMD evidently outperformed the MLR before NA-MEMD by explaining additional 9.4 to 18.7% of the total K_s variance, but underperformed the artificial neural network and state-space approach also implemented on undecomposed spatial series of K_s and its underlying factors. NA-MEMD serves as a useful tool for K_s characterization and its incorporation with nonlinear functions or spatial interactions with impact factors is suggested for the estimation of K_s and other soil processes.