Multivariate Empirical Mode Decomposition Derived Multi-Scale Spatial Relationships between Saturated Hydraulic Conductivity and Basic Soil Properties

Saturated hydraulic conductivity (K-s) is affected by various factors operating at different scales. This study identified the multi-scale spatial relationships between Ks and selected basic soil properties (soil organic matter [SOM], clay, silt, and sand contents, and bulk density) along two landscape transects (with various soil textures and land use covers) on the Loess Plateau. Multivariate empirical mode decomposition (MEMD) yielded four different intrinsic mode functions (IMFs) for the multivariate data series of each transect according to the scale of occurrence. The dominant scales in terms of explained variance of Ks were IMF1 (scale: 403 m) for transect 1, and IMF1 and IMF2 (scale: 407 and 775 m) for transect 2. The multi- scale correlation between Ks and soil properties was more complex for transect 1 due to a more fragmented landscape. For each IMF or residue, Ks was predicted using the identified factors that significantly affected it at that IMF scale or residue. The summation of the four predicted IMFs and the residue predicted Ks at the measurement scale, and was more accurate than predictions based on simple multiple linear regressions between Ks and the other soil properties. Soil particle size components were the main contributors in explaining Ks variability for both landscape transects, mostly due to their contributions from IMF1; however, SOM was also a major contributor for transect 2, mainly due to contributions from IMF2. Using MEMD has great potential in characterizing scale- dependent spatial relationships between soil properties in complicated landscape ecosystems.