Efficient calculation of sensitivity coefficients for complex atmospheric models

Abstract

Sensitivity coefficients describe how the solution to a set of equations depends on the parameters in the problem. We discuss here the direct method of calculating these coefficients for atmospheric models based on nonlinear, partial differential equations. A detailed analysis indicates for which models the method will be efficient and shows that calculating several sensitivity coefficients simultaneously improves the efficiency. A technique is given to derive an algorithm for implementing the direct method from the algorithm for solving the governing equations of the model. As a realistic test of the method, we have computed first-order sensitivity coefficients for a photochemical model describing the transport and chemical reactions of pollutants. In this example the direct method has a limiting speed six times faster than the indirect method.