An efficient closure based method for inverse climate modelling

In this study, a new method is developed for attributing changes in climate states by calculating the anomalous forcing functions responsible for these changes. The method relies on an iterative procedure to calculate improved estimates of the forcing function starting from an initial estimate. Running a sequence of climate models can be computationally demanding and therefore computational efficiency is an important ingredient in formulating a tractable inverse modelling scheme. It is therefore crucial to initialise the iterative procedure with a forcing function that is a good estimate of the correct forcing function to reduce the number of iterations required. This is achieved by formulating a statistical closure scheme. A statistical closure scheme enables one to overcome the closure problem in which statistical moments of higher order appear in the prognostic equations for the statistical moments of a given order. For example, the equation for the mean field depends on second-order moments and the second-order moment equations in turn depend on third-order moments. The closure scheme that we employ involves a linearisation of the second-order moment terms, which physically represent the feedback of transient eddies on the mean circulation, in terms of the mean fields. The parameters required in this closure scheme are calculated by employing perturbation experiments. We demonstrate that the closure scheme leads to simulated climate states that are in close agreement to idealised and observed climate states with pattern correlations generally greater than 0.8. These closure based estimates may then be further improved by employing the iterative method.