Traditional statistical analysis of the correlations between spatially distributed variables takes no account of their regionalised nature. Factorial kriging analysis (FKA) was developed and widely used to overcome this problem. In our study, we applied FKA to investigate scale-dependent correlations between selected soil properties and environmental factors across the Loess Plateau of China. Surface soil samples were collected from 382 sampling sites throughout the region, and soil organic carbon (SOC), soil total nitrogen (STN), soil total phosphorus (STP), soil total potassium (STK), soil pH, bulk density (BD), and clay and silt contents were determined. Five environmental factors (elevation, precipitation, temperature, land-use type, and soil type) were also included in the FKA to identify influential processes. A linear model of co-regionalisation, including a nugget effect and two spherical structures (effective ranges of 200 and 400 km), was fitted to the experimental auto- and cross-variograms of the variables. Scale-dependent correlations were calculated for nugget-effect scale (<30–50 km), short-range scale with a range of 200 km, and long-range scale with a range of 400 km. Principal component analysis was conducted to clearly illustrate the correlations at each spatial scale. The scale-dependent correlations were different from the general correlations and varied at different scales. Generally, SOC and STN were strongly correlated at the nugget-effect scale and the long-range scale, but not at the short-range scale. Precipitation and clay content showed close correlations with STP at the nugget-effect scale and long-range scale. The STK was weakly correlated with the other variables at each spatial scale, and closely correlated with soil type at the long-range scale. Soil pH was closely correlated with BD, soil type, and elevation at the nugget-effect, short, and long spatial scales, respectively. Close correlations were found between BD and land-use type at each spatial scale. Land use and soil type were considered to be the important factors controlling spatial variation of soil properties at the short-range scale, while at the long-range scale the likely factors were identified as precipitation, temperature, and elevation. Our study provided an insight into the spatial-dependent correlations between soil properties and environmental factors from a regional perspective.
