Multifractal detrended fluctuation analysis in examining scaling properties of the spatial patterns of soil water storage

Abstract

Abstract. Knowledge about the scaling properties of soil water storage is crucial in transferring locally measured fluctuations to larger scales and vice-versa. Studies based on remotely sensed data have shown that the variability in surface soil water has clear scaling properties (i.e., statistically self similar) over a wider range of spatial scales. However, the scaling property of soil water storage to a certain depth at a field scale is not well understood. The major challenges in scaling analysis for soil water are the presence of localized trends and nonstationarities in the spatial series. The objective of this study was to characterize scaling properties of soil water storage variability through multifractal detrended fluctuation analysis (MFDFA). A field experiment was conducted in a sub-humid climate at Alvena, Saskatchewan, Canada. A north-south transect of 624-m long was established on a rolling landscape. Soil water storage was monitored weekly between 2002 and 2005 at 104 locations along the transect. The spatial scaling property of the surface 0 to 40 cm depth was characterized using the MFDFA technique for six of the soil water content series (all gravimetrically determined) representing soil water storage after snowmelt, rainfall, and evapotranspiration. For the studied transect, scaling properties of soil water storage are different between drier periods and wet periods. It also appears that local controls such as site topography and texture (that dominantly control the pattern during wet states) results in multiscaling property. The nonlocal controls such as evapotranspiration results in the reduction of the degree of multiscaling and improvement in the simple scaling. Therefore, the scaling property of soil water storage is a function of both soil moisture status and the spatial extent considered.

Multifractal analysis of vertical profiles of soil penetration resistance at the field scale

“…In agricultural soils, the complexity due to natural factors may be modified by man-made factors (e.g. Biswas et al, 2012). Depth-dependent PR profiles vary with soil properties that may show great spatial heterogeneity (Vaz et al, 2011), which, in turn, may be either relatively constant over time (i.e.…”

“…Dexter et al, 2007;Vaz et al, 2011). In turn, soil water content near the soil surface is highly variable (Biswas et al, 2012) because of the influence of external factors such as rainfall and evaporation. Therefore, soil PR may be also indirectly influenced by environmental factors, and soil surface layers are more responsive to these factors than deep soil layers.…”

“…Over the past few decades scaling analysis, such as fractal and multifractal analysis have been applied to characterize soil properties and processes, and many studies have revealed scale-dependent patterns of soil variability from very short distances (e.g. Pachepsky et al, 1996;PazFerreiro et al, 2010) to geomorphologic landscapes units (Biswas et al, 2012), or even continents and the whole planetary scale (Caniego et al, 2006). Both fractal and multifractal scaling assume a hierarchical distribution of mass in space so that the whole results from the union of similar subsets.…”

Multifractal Detrended Fluctuation Analysis of Streamflow in the Yellow River Basin, China

“…The relationships of (a) the generalized Hurst exponent h(q) and q; (b) the mass exponent function τ(q) and q; and (c) the singularity spectrum f(α) and singularity exponent α for the streamflow series at the Toudaoguai, Longmen, Ganguyi and Huangfu stations of the Yellow River. The nonlinear τ(q) means multiple scaling, and the degree of nonlinearity of the τ(q) function can reflect the degree of multifractality [35]. The slopes of τ(q) at the Toudaoguai and Longmen stations are similar, indicating a similar degree of multifractality.…”

Multifractal Dimensional Dependence Assessment Based on Tsallis Mutual Information

“…Methods based on entropy are among the most relevant and successfully applied to describe such systems. Multifractal measures are formally used to explain systems with scaling properties [6][7][8][9][10]. On the other hand, non-extensive statistics are used to characterize systems with long-range interactions, heavy-tail distributions and anomalous diffusion, among other aspects [11][12][13][14].…”