Kemanian, Armen R. (Washington State University, Biological Systems Engineering Dept., Smith Hall, Pullman, WA, 99164-6120; Phone: 509-335-3661; Fax: 509-335-2722; Email: armen@wsunix.wsu.edu)

Assessing the Usefulness of Simple Mathematical Models to Describe the Soil Carbon Dynamics

A.R. Kemanian*, V.S. Manoranjan, D.R. Huggins, S.O. Stockle

The rate of C storage in the soil (Cs) depends on the balance between the inputs of C from organic residues (Ci) and the outputs due to microbial oxidation of organic matter. Due to the complexity of the processes affecting the input and output rates, analytical solutions to Cs dynamics are not feasible. Partial information regarding particular processes like residue decomposition and Cs turnover, together with the effect of environmental factors on microbial activity, have been compiled and encapsulated in so-called mechanistic models of soil organic matter dynamics. The use of these models has been promoted under the assumption that complex interactions among several factors are accounted for quantitatively. It must be noted, however, that the structure of these mechanistic models is relatively simple. We hypothesize that simple mathematical models could be equally or more effective at representing soil carbon dynamics.   We present empirical models of soil C dynamics of the general form dCs/dt = h(Cs)Ci + k(Cs)Cs, where h and k are the residue humification and apparent soil C decomposition coefficients. The simplest solution to this equation results from assuming that h and k are constant, which implies that under steady state Cs = hCi/k. This implies that the storage capacity of the soil is linearly dependent on Ci. There is evidence, however, that soils have a finite capacity to store C. In addition, the Cs constituents have different turnover rates i.e. k is a weighted average of the individual k’s of each soil C fraction. We know that as Cs changes k does not remain constant, as each individual C constituent changes at different rates.   We explore the behavior of models in which h and k are functions of Cs. The general behavior of these models in response to changes in Ci and Cs is presented. When possible, some models were parameterized based on observed values of soils at steady state and a small set of assumptions. The analysis indicates that making h a function of Cs provides a simple way of representing a “Cs carrying capacity”. Making k a function of Cs provides a means for accelerating the turnover rate as Cs increases, with the underlying assumption that the higher the Cs content the lower the soil recalcitrant C fraction. As a result, if properly parameterized, a single mathematical function can be used for different soil layers provided that the texture does not change dramatically and that the inputs from roots at different depth are known. The effect of residue composition such as variations in lignin content on h can also be accommodated.   The analysis of these models suggest that the set of rules usually used in mechanistic simulation models to allocate carbon to different C pools (i.e. humification rules) should depend not only on soil texture but on the C level of each pool. These simple models could, therefore, not only be useful to predict Cs dynamics but also provide feedback information to improve existing mechanistic models.