Multiscale Soil Investigations: Physical Concepts and Mathematical Techniques

A DN on multiscale landscape analysis defined soils as "four dimensional natural bodies... with the key characteristic of varying with place and time " (Sommer, 2006). Such variation affects how tions are interpreted regarding the evolution, diversity, and dynamics of the soil ecosystem (Heuvelink and Webster, 2001). Soil variability has often been considered to be composed of "functional " (explained) variations plus random fluctuations or noise. However, the distinction between these two components is scale dependent because increasing the scale of observation almost always reveals structure in the noise (Burrough, 1983). Soils can be seen as the result of spatial variation operating over several scales, indicating that factors influencing spatial variability differ with scale. This observation points to variability as a key soil attribute that should be studied (Burrough et al., 1994). Geostatistical methods and, more recently, fractal—multifractal and wavelet techniques have been used to characterize scaling of soil properties (Zhang et al., 1997; Kravchenko et al., 1999; Eghball et al., 1999). The book edited by Sposito (1998) includes several chapters that discuss various hydrological applications of scaling. Western et al. (2002) reviewed different techniques for scaling soil moisture, including statistical approaches and process-based indices. Hopmans et al. (2002) presented the historical use of scaling in hydrology and discussed the need to extend measurements beyond the laboratory scale to the field or watershed scale. The book by Pachepsky et al. (2003) covers many aspects of scaling and how to reconstruct landscape and watershed processes from small-scale measurements. McBratney et al. (2003) reviewed soil mapping at different scales and approaches for relating soil