A soil property may be related to another and the relationships may change depending on the scale and location. Understanding these scale‐ and location‐dependent relationships is important for prediction of one soil property based on another. The objective of this study is to use wavelet coherency analysis to examine whether the relationship between hydraulic properties and soil physical properties are scale‐ and location‐dependent. Undisturbed cores were collected along a transect from the sandy loam soil of a farm field in northern Saskatchewan, Canada. Saturated hydraulic conductivity (Ks), sand content, and organic carbon content (OC) were measured on these cores, and their relationships as a function of scale and location were analyzed using wavelets. Results indicated that the wavelet coherency between Ks and sand content is only significantly different from that of red noises at the scales around 48 m. The cross‐wavelet spectrum and wavelet coherency are predominantly in phase, suggesting a positive correlation between Ks and sand. For Ks and OC, significant coherency exists at scales from 30 to 48 and around 80 m. At the scales of 30–48 and around 80 m the relationships are predominantly out of phase, suggesting negative correlation. Therefore relationships between Ks and sand or Ks and OC are not only scale‐dependent but also location‐dependent. Scale and location dependence have an important implication for understanding the scaling relationships between Ks and sand and OC and for the prediction of Ks from sand and OC.

Saturated hydraulic conductivity (Ks) is an important soil hydraulic property that affects water flow and the transport of dissolved solutes. Obtaining sufficient and reliable Ks data for large‐scale process modeling is always a challenge due to the extremely high spatial variability. The objectives of this study were (i) to determine if a monofractal or multifractal approach is needed to describe the variability in Ks and its soil surrogates, and (ii) to identify which soil property best reflects the spatial distribution of Ks across a wider range of scales. Saturated hydraulic conductivity and soil physical property data were collected from a 384‐m transect, located at Smeaton, SK, Canada. Observation scale variability and relationships were examined using statistical and geostatistical methods. Statistical scale‐invariance was evaluated through the Hurst scaling parameter (H). Multiple scale variability and relationships were studied using multifractal and joint multifractal techniques. Results indicate that for all the studied variables 0.80 < H < 0.90, suggesting a certain degree of statistical scale‐invariance and long‐range dependency. At the observation scale, the variability in Ks was significantly related to sand (SA) and silt (SI) distribution (R = 0.40 for SA and −0.39 for SI, P < 0.01; n = 128), whereas, across a wider range of scales, the variability in Ks was related only to clay (CL) and organic C (OC). The result indicates scale dependent relationships between Ks and soil physical properties, which implies that the success of predictive models such as pedotransfer functions (PTFs) and Ks aggregation techniques depends largely on the correspondence between observation and implementation scales.

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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.

Topography controls soil water distribution in semiarid environments where water is the major growth‐limiting factor. Identification of the topographic index that best represents the spatial variability and scaling properties of crop yield is important for precision farming. Our objective was to characterize the scaling properties of four topographic indices [relative elevation (RE), wetness index (WI), upslope length (USL), and curvature (CR)] and their relationships to wheat (Triticum aestivum L.) grain yield and biomass using multifractal and joint multifractal approaches. Wheat grain yield and terrain data were collected at 6‐m intervals along a 576‐m‐long transect on a nonlevel landscape with dominant soil type of Aridic Ustoll, under the semiarid environment of Saskatchewan, Canada. Results indicated that CR and RE had a fractal type of scaling only for a narrow range of moment orders. Wetness index showed a monofractal scaling with fractal dimension of 0.98; whereas yield, biomass, and USL showed a multifractal scaling. Joint multifractal analyses showed a high correlation coefficient between the scaling indices of grain yield and USL (r = 0.93). Wetness index appeared to be effective as a yield covariate only at low slope areas and depressions where it has similar scaling to that of USL. Results from this study suggested that USL was the best indicator of grain yield and biomass at any scale. The implication for precision farming is that USL can be used as a guideline for varying production inputs such as fertilizer as well as for yield prediction.