Kemanian, Armen R. (

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.