Hilbert-Huang Transform: A New Approach of Analyzing Non-Stationary and Nonlinear Soil Spatial Variation.

Soil varies considerably from location to location and its characterization is fundamental in understanding soil-landscape processes. Different aspects of soil spatial variability including spatial similarity, periodicity, scale dependency, and nonstationarity have been characterized using geostatistics, spectral analysis, and wavelet analysis. However, these methods assumed soil processes to be linear. Hilbert Huang Transform (HHT), a combination of Empirical Mode Decomposition (EMD) and Hilbert Spectral Analysis (HSA), can deal with both nonstationarity and nonlinearity. This paper examines the spatial variability of soil water storage using HHT. Field soil water storage (0-140 cm depth) was measured along a 128 point transect established at St Denis National Wildlife Area, Saskatchewan, Canada, using Time Domain Reflectometry and Neutron Moisture Meter. The nonstationarity and the nonlinearity in the soil water storage were identified. EMD separated the variations in soil water storage into 6 different mode functions (intrinsic mode function, IMF) based on their characteristic scales. The first IMF separated very small scale variations that might be caused from measurement errors, localized activities of roots, micro or macro organisms. While, the second and third IMF represented the variations of elevation and organic carbon, the fifth and sixth IMF represented the variations of soil textures. Fourth IMF represented the mixture of variations from different factors. The third IMF explained the majority of the variations of soil water storage at that scale indicating the elevation to be major control. HSA was used to calculate the instantaneous spatial scales (from instantaneous frequency) of soil variation explaining the scale and location dependent variability of soil water storage. This adaptive method is useful in delineating nonstationary and nonlinear controls of different factors of soil water storage.