Multicompartmental Models

The distinction between simple kinetic models and multicompartmental models is somewhat arbitrary since the sum of exponentials model above described C

mineralization from two pools or compartments. Generally, compartmental models are needed when a single equation is insufficient to describe the multiple transformation processes that occur simultaneously in soils. A multicompartmental model is depicted graphically as a set of boxes, each of which represents a pool or compartment. Most often, the pools are defined conceptually, but they can also be measurable fractions of SOM (see Alternative SOM Models). A series of arrows connecting the various pools represents transformations of organic matter or a nutrient element from one form to the other. The graphical representation of the model can be written as a series of simultaneous reactions. Some simple compartmental models can be solved analytically (e.g., in equation form), such as the sum of exponentials describe above, but as the models become more complex and include more compartments, it becomes necessary to solve them numerically.

The advent of computers permitted the solution of complex systems models that require iterative solving of multiple equations to address multicompartment dynamics. The modeling of soil biological processes began with ecologists working in natural ecosystems in the 1960s and 1970s. Early modeling in agricultural systems focused on crop production in response to physical parameters, rather than biological processes. A new emphasis in the 1970s on the environmental impacts of agriculture led to early models of N dynamics, including nitrate leaching and denitrification. Further emphasis on agroecology and SOM management in the 1980s and 1990s has led to the development of a large number of models of soil organic matter dynamics. Several reviews comparing many of these models are available (e.g., McGill, 1996; Molina and Smith, 1998; Paustian, 1994; Smith et al, 1997). A subset of these comparisons is provided in Table 16.3.

Paustian (1994) classified multicompartmental models of SOM dynamics as either "process-oriented" or "organism-oriented." There are far fewer organism-oriented models (Table 16.3), which are sometimes called "food web models" and describe the flow of organic matter and nutrients through different functional or taxonomic groups of soil organisms. Process-oriented models are those that focus on the processes mediating the transformations of organic matter and nutrients, rather than on the activity of specific organisms or groups of organisms. In process-oriented model types, soil organisms, if present, tend to be represented as a generic biomass or as part of a pool of active SOM. This approach precludes the possibility of modeling changes in organic matter dynamics or nutrient cycling that might occur due to changes in the activity or composition of the soil organism community. Schimel (2001), however, points out that the microbiological underpinnings in process-oriented models are not absent, but are implicit and buried in the equation structure of the model as kinetic constants and response functions.

If most biochemical reactions in soils are mediated by enzymes and follow Michaelis-Menton kinetics, and if soil microbial populations grow and die back regularly, why is it that most process-oriented models use first-order kinetics to describe SOM and nutrient dynamics (Table 16.3)? As demonstrated previously, Monod or Michaelis-Menton kinetics can be simplified to first-order kinetics when substrate concentrations are sufficiently low. Several studies have shown that soil respiration usually occurs at 20 to 65% of its maximum potential rate.

TABLE 16.3 Comparison of Basic Attributes of Several Multicompartmental Models of Soil Organic Matter and Nutrient Dynamics"

Resolution Explicit Nonliving SOM pools Regulation Other - Litter/SOM decomposer - by soil Rate nutrient

Model Spatial" Temporal' distinction pool No. Names texture kinetics elements

CANDY (Franko et al., 1995,1997)

CENTURY (Parton et al., 1987; Parton, 1996; Kelly et al, 1997)

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