Featured Application Spatial variability has always been a hot topic in soil science. Through an example of calculation, we compare and analyse the results of four methods: classical statistics, geostatistics, fractal and multifractal. Given this research scale, different methods have different conclusions. Considering that classical statistics, geostatistics and the fractal method have different disadvantages in application, we think that the multifractal method has broad prospects in the quantitative evaluation of spatial variability. The spatial variability of soil properties has always been a significant research field in geoscience. The types of soil properties cover a wide range, but most studies have focused on the spatial variability of soil physicochemical properties over the past decades. Studies on soil hydraulic characteristics are limited, and most of them are limited to the farmland scale. However, the spatial variability of regional soil properties (soil texture and hydraulic properties) is valuable for the study of sedimentation processes and soil water transport. Therefore, here, the spatial variation of six soil properties (sand, silt, clay content, bulk density, saturated water content and saturated hydraulic conductivity) in the typical alluvial plain area of the lower Yellow River is quantitatively studied, by using classical statistics, geostatistics and single fractal and multifractal methods. This study mainly quantitatively analysed the spatial variability of different soil properties and compared four research methods. Although the coefficient of variation, nugget coefficient, single fractal dimension and multifractal spectral width can reflect spatial variability, diverse conclusions are drawn (on variability) if different methods are used, and the different soil properties show large disparities. These four methods show a different variation order of soil properties, but there are some common conclusions based on analysis and judgment. In general, the silt content in the study area is stable, mainly originating from loess transported by Yellow River erosion, which is also reflected in the Kriging interpolation maps under the geostatistical models. The variation in bulk density and saturated water content is weak, and the spatial variability of sand and clay content is moderate. In addition, the saturated hydraulic conductivity fluctuates violently. This may be related to the differences in local topography, human activity and the content of sand and clay, each of which significantly affects the saturated hydraulic conductivity. Classical statistics has a limitation because it fails to corelate with spatial location. Due to the small sample capacity and calculation error of lag distance, the accuracy of geostatistics and single fractal dimensions needs to be improved. Multifractal spectral analysis does not need to consider the normality of data and can quantitatively represent local characteristics; therefore, its results have high reliability.
