The Dual Arrhenius and Michaelis-Menten kinetics model for decomposition of soil organic matter at hourly to seasonal time scales

Decomposition of soil carbon stocks is one of the largest potential biotic feedbacks to climate change. Models of decomposition of soil organic matter and of soil respiration rely on empirical functions that relate variation in temperature and soil water content to rates of microbial metabolism using soil-C substrates. Here, we describe a unifying modeling framework to combine the effects of temperature, soil water content, and soluble substrate supply on decomposition of soluble soil-C substrates using simple functions based on process concepts. The model's backbone is the MichaelisMenten equation, which describes the relationship between reaction velocity and soluble organic-C and O2 substrate concentrations at an enzyme's reactive site, which are determined by diffusivity functions based on soil water content. Temperature sensitivity is simulated by allowing the maximum velocity of the reaction (Vmax) to vary according to Arrhenius function. The Dual Arrhenius and MichaelisMenten kinetics (DAMM) model core was able to predict effectively observations from of laboratory enzyme assays of beta-glucosidase and phenol-oxidase across a range of substrate concentrations and incubation temperatures. The model also functioned as well or better than purely empirical models for simulating hourly and seasonal soil respiration data from a trenched plot in a deciduous forest at the Harvard Forest, in northeastern United States. The DAMM model demonstrates that enzymatic processes can be intrinsically temperature sensitive, but environmental constrains of substrate supply under soil moisture extremes can prevent that response to temperature from being observed. We discuss how DAMM could serve as a core module that is informed by other modules regarding microbial dynamics and supply of soluble-C substrates from plant inputs and from desorption of physically stabilized soil-C pools. Most importantly, it presents a way forward from purely empirical representation of temperature and moisture responses and integrates temperature-sensitive enzymatic processes with constraints of substrate supply.