Sustainable soils are a requirement for maintaining human civilizations (Carter and Dale 1974; Lal 1989). However, as the “most complicated biomaterial on the planet” (Young and Crawford 2004), soils represent one of the most difficult systems to understand and model with respect to chemical, physical, and biological coupling over time (Fig. 1).

Despite the complexity of these interactions, certain patterns in soil properties and development are universally observed and have been used in soil science as a means for classification. Elemental, mineralogical, or isotopic concentrations in soils plotted versus depth beneath the land surface comprise such patterns. Soil depth profiles are often reported for solid soil materials, and, less frequently, for solutes in soil pore waters. These profiles cross a large range in spatial scales that traditionally have been studied by different disciplines. For example, shallow, biologically active horizons are commonly defined as the soil zone in agronomic studies whereas the mobile layer of the regolith is referred to as soil in geomorphological studies. In contrast, many geochemical studies target chemical weathering to tens or even hundreds of meters in depth, sometimes extending the definition of “soils” to include the entire regolith down to parent bedrock or alluvium.

Soil profiles also exhibit a large range in temporal scales (Amundson 2004; Brantley 2008b). Solid-state profiles document chemical and mineralogical changes integrated over the time scales of evolution of regolith from protolith. This “geologic time” can vary from tens to hundreds of years for weathered material developed on moraines deposited by active glaciers (Anderson et al. 1997), to millions or possibly hundreds of millions of years of regolith evolution as documented in laterites and bauxites on stable cratons (Nahon 1986). In contrast, solute profiles reflect much shorter time scales corresponding to the residence time of the soil water which commonly ranges from days to decades (Stonestrom et al. 1998). Factors impacting soil minerals can therefore be related to geologically old processes while those impacting pore waters are related to contemporary processes.

We first discuss a geochemical frame work for modeling soil profiles, including a simple scheme that depends on the extent of enrichment or depletion. Such profiles are comprised of reaction fronts affected by chemical, hydrologic, geologic and biologic processes that control soil evolution. We then present a hierarchy of models that have been used to interpret both solid state and solute compositions in regolith. The more simple approaches to model depletion in soils, using analytical models, are first described. The most elementary of these is a linear model that calculates rate constants from the slopes of either solid or solute weathering gradients: these rate constants represent lumped parameters that describe weathering in terms of an integrated reaction rate. Two other analytical models are then presented that have been used to fit solid state elemental profiles with exponential and sigmoidal functions. All of these analytical approaches are derived for models of soils as containing a limited number of components, phases, and species.

At a more complex level, numerical models are then presented to elucidate how kinetic and transport parameters as well as chemical, hydrologic, and physical soil data can be incorporated. We consider two forms of these models, first relatively simple spreadsheet calculators and then more sophisticated multi-component, multi-phase reactive-transport numerical codes. Our treatment of reactive transport modeling is relatively cursory, in recognition of the treatment in the chapter by Steefel and Maher (2009, this volume). Because these models incorporate more phases, components, and species than the other approaches and explicitly model the more fundamental reaction mechanisms involved, they generally have a greater need for parameterization. In our conclusion section, we discuss how this hierarchy of approaches can yield generalizations about soils that are often complementary.