Sensitivity Analysis of a Radiative-Convective Model by the Adjoint Method

The adjoint method of sensitivity analysis is demonstrated on a radiative-convective climate model. A single adjoint calculation, which requires about the same computation time as the original model, suffices to calculate sensitivities of surface air temperature to all 312 model parameters. The uses of these sensitivities are discussed and illustrated. The sensitivities accurately predict the effect on surface air temperature of small variations in the model parameters. Relative sensitivities are used to rank the importance of all the parameters. Several of the sensitivities to parameters customarily considered in previous works (e.g., solar constant, surface albedo, relative humidity, CO sub(2) concentration) are reproduced, but the largest sensitivities are to constants used to compute the saturation vapor pressure of water. The uncertainties in the model results are expressed formally in terms of all the sensitivities and parameter covariances. For results that cannot readily be compared with observation (e.g., the results of a CO sub(2) doubling experiment), this method of uncertainty analysis is the only systematic way to estimate the reliability of model results. The radiative-convective model contains complex nonlinear processes of the type found in general circulation models; therefore, the fact that the adjoint method works successfully and efficiently for the radiative-convective model provides valuable information about subsequent application of the method to general circulation models.