An analytical model for relating global terrestrial carbon assimilation with climate and surface conditions using a rate limitation framework

We develop an analytical model for estimating mean annual terrestrial gross primary productivity (GPP) based on a rate limitation framework. Actual GPP (climatological mean from 1982 to 2010) is calculated as a function of the balance between two GPP potentials defined by the climate (i.e., precipitation and solar radiation) and a third parameter that encodes other environmental variables and modifies the GPP-climate relationship. The model was tested using observed GPP from 94 flux sites and modeled GPP (using the model tree ensemble approach) at 48,654 (0.5 degrees) grid cells globally. Results show that the model could account for the spatial GPP patterns, with a root-mean-square error of 0.70 and 0.65 g Cm-2 d(-1) and R-2 of 0.79 and 0.92 for the flux site and grid cell scales, respectively. This analytical GPP model shares a similar form with the Budyko hydroclimatological model, which opens the possibility of a general analytical framework to analyze the linked carbon-water-energy cycles.