Modelling ocean carbon cycle with a nonlinear convolution model

Abstract

A nonlinear convolution integral is developed to model the response of the ocean carbon sink to changes in the atmospheric concentration of CO₂. This model can accurately represent the atmospheric response of complex ocean carbon cycle models in which the nonlinear behavior stems from the nonlinear dependence of CO₂ solubility in seawater on CO₂ partial pressure, which is often represented by the buffer factor. The kernel of the nonlinear convolution model can be constructed from a response of such a complex model to an arbitrary change in CO₂ emissions, along with the functional dependence of the buffer factor. Once the convolution kernel has been constructed, either analytically or from a model experiment, the convolution representation can be used to estimate responses of the ocean carbon sink to other changes in the atmospheric concentration of CO₂. Thus the method can be used, e.g., to explore alternative emissions scenarios for assessments of climate change. A derivation for the nonlinear convolution integral model is given, and the model is used to reproduce the response of two carbon cycle models: a one-dimensional diffusive ocean model, and a three-dimensional ocean-general-circulation tracer model.