Debut of a flexible model for simulating soil respiration-soil temperature relationship: Gamma model

A number of empirical models are used in literature to simulate the response of soil respiration (Rs) to soil temperature (Ts). The most widely used ones are the exponential Q(10) model and the sigmoid-shaped Lloyd-Taylor and logistic models. None of these models are applicable across a wide range of ecosystems or climates, and none allow Rs to decrease at high Ts values. Here we present a new, more flexible, empirical model, the so-called Gamma model, which can take on the shapes of the three models mentioned above and is mathematically flexible enough to allow for Rs to decrease at high Ts values, as dictated by data. We compared the Gamma model fits to the Q(10), Lloyd-Taylor, and logistic models, using coefficient of determination (R-2), residual sum of squares, and Akaike's Information Criterion. The models were tested across a wide Ts range (-18 to 35 degrees C), in five forest ecosystems, spanning three different climate zones: boreal, temperate, and Mediterranean. Compared to the other three models, the Gamma model performed either better or as good as the other models in simulating the Rs-Ts relationship at all sites. Simulations were carried out using models parameterized by the ordinary least squares and weighted absolute deviation estimation methods. Rs values derived from the two estimation methods were comparable once the proper functional form for the Rs-Ts model was chosen. We also show how the Gamma model can be expanded, using simple mathematics to help researchers analyze the Rs-Ts relationship in the context of other environmental factors, such as soil moisture and nutrients.