Multi-scale spatial relationships between soil total nitrogen and influencing factors in a basin landscape based on multivariate empirical mode decomposition

The relationships between soil total nitrogen (STN) and influencing factors are scale-dependent. The objective of this study was to identify the multi-scale spatial relationships of STN with selected environmental factors (elevation, slope and topographic wetness index), intrinsic soil factors (soil bulk density, sand content, silt content, and clay content) and combined environmental factors (including the first two principal components (PC1 and PC2) of the Vis-NIR soil spectra) along three sampling transects located at the upstream, midstream and downstream of Taiyuan Basin on the Chinese Loess Plateau. We separated the multivariate data series of STN and influencing factors at each transect into six intrinsic mode functions (IMFs) and one residue by multivariate empirical mode decomposition (MEMD). Meanwhile, we obtained the predicted equations of STN based on MEMD by stepwise multiple linear regression (SMLR). The results indicated that the dominant scales of explained variance in STN were at scale 995 m for transect 1, at scales 956 and 8852 m for transect 2, and at scales 972, 5716 and 12,317 m for transect 3. Multi-scale correlation coefficients between STN and influencing factors were less significant in transect 3 than in transects 1 and 2. The goodness of fit root mean square error (RMSE), normalized root mean square error (NRMSE), and coefficient of determination (R2) indicated that the prediction of STN at the sampling scale by summing all of the predicted IMFs and residue was more accurate than that by SMLR directly. Therefore, the multi-scale method of MEMD has a good potential in characterizing the multi-scale spatial relationships between STN and influencing factors at the basin landscape scale.