An inverse ecosystem model of year-to-year variations with first order approximation to the annual mean fluxes

Ecosystems exhibit nonlinear dynamics that are often difficult to capture in models. Consequently, linearization is commonly applied to remove some of the uncertainties associated with the nonlinear terms. However, since the true model is unknown and the operating point to linearize the model about is uncertain, developing linear ecosystems models is non-trivial. To develop a linear ecosystem model, we assume that the annual mean state of an ecosystem is a minor bias from the long-term mean state. A first order approximation inverse model to govern the year-to-year dynamics of ecosystems whose characteristic time scales are less than 1 year is developed, through theoretically formulation, on the basis of steady state analysis, time scale separation and nondimensionalization. The approach is adept at predicting year-to-year variations and to tracking system response to changes in environmental drivers when compared to data generated with a standard nonlinear NPZD model.