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 processbased 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 properties to processes. The group of papers introduced by Pachepsky et al. (2006) dealt with applications of fractal geometry to scaling in soil and related hierarchical systems. Lin et al. (2006) detailed several hypotheses related to the concept of hydropedology to help bridge across disciplines that focus on different ranges of scale. Vereecken et al. (2007) reviewed techniques to upscale soil hydraulic properties, including several "forward" techniques as well as inverse modeling approaches. An integration of various sources of information and synthesis of diverse approaches is required to study multiscale features that are the product of coexistence, hierarchy, complexity, chaos, and in some cases, self-organization. Understanding the interrelationships between physical, chemical, and biological factors at different scales is essential for research in agriculture, engineering, hydrology, and the environment. The emergence of a more holistic approach to soil science may facilitate a better understanding of both temporal and spatial variability. Concurrent with this recognition, there is a growing interest in the application of multiscale approaches (e.g., Coops and Waring, 2001; Zhang et al., 2002) for studying the critical zone. Such methodologies may help to identify typologies of system behavior that many scientists have anticipated to be highly complex, with chaotic characteristics at a fine scale of examination to more regulated or ordered and stable characteristics at larger scales (Svoraya and Shoshany 2004). The 18th World Congress of Soil Science took place in July 2006 in Philadelphia, PA, with the theme "Frontiers of Soil Science: Technology and the Information Age." The scientific program included topics on remote sensing, geographic information systems, landscape analysis, computer modeling, precision agriculture, and other applications of information science and technology as related to soils. A symposium held at the congress titled "Multiscale Mapping of Soil Properties for Environmental Studies, Agriculture, and Decision-Making" focused on techniques used in multiscale mapping of soil properties and processes. Papers covered theoretical and applied aspects of interpolation and extrapolation schemes, self-similar, hierarchal, and fractal organizations, spatial associations between variables,