### Computationally efficient methods for climate model inversion

#### Abstract

The dynamical equations of a model are used to obtain the `forcing function', which is a representation of climate change drivers, from an observed climatic anomaly. This inversion problem is mathematically difficult because of the two-way interaction between the mean field and transient eddies; this is known as the turbulence closure problem. The first method that we explore for overcoming the closure problem involves iteratively nudging a climate simulation towards the observed climate. We demonstrate how this method is used to successfully calculate the climatic forcing function. The second method that we explore involves finding approximations to the turbulence closure problem. In this method, the transient eddy feedback term in the mean field equation is represented as a linear combination of the mean fields and a constant term. We demonstrate that the closure method yields a good approximation to the climatic forcing function. This forcing function is then used as an improved first estimate in the iterative method, thereby yielding a scheme that converges very quickly to the correct solution in only a few iteration steps.

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#### Keywords

climate change attribution; geophysical fluid dynamics; nonlinear dynamics; statistical dynamics; non-equilibrium statistical mechanics; inverse modelling

DOI: http://dx.doi.org/10.21914/anziamj.v54i0.6266

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