Climate sensitivities via a Planck adjoint approach

The traditional method for computing the sensitivity of a particular climate diagnostic to some input parameter, using a climate model, is to carry out integrations of the climate model for control and perturbed values of the parameter. However, when the sensitivity of the diagnostic to many parameters is required, this method becomes very expensive. Motivated by the need to calculate such sensitivities more cheaply, a new approach is developed here. Theoretically, it is based on considering the climate to be described by the probability density function that satisfies the relevant steady Fokker-Planck equation. The climate sensitivity (i.e. the derivative of the diagnostic with respect to the input parameters) can then be expressed in terms of the solution of the adjoint of the steady Fokker-Planck equation. This adjoint solution could be computed in practice via an ensemble of climate model integrations. Currently the theory is valid only for climate models that include stochastic forcing. A practical demonstration is given of two methods based on the new theory, applied to a stochastic version of the famous Lorenz equations. Some further refinements are needed, however, to achieve a method that would be computationally practicable for a full climate model.