Adjoint sensitivity theory and its application to LEAP Model 22C

Adjoint sensitivity theory can be used to determine the sensitivity of results of interest to each of the data elements that enter into the calculations. In this paper adjoint sensitivity theory is discussed, and its applicability to a large energy-economics model is demonstrated by applying it to a specific calculation carried out with the Long-Term Energy Analysis Program (LEAP). Numerical results for dR/dx, where R is the result of interest and x is any one of the data elements, are presented for all x for which dR/dx is appreciable and for several definitions of R. In a number of cases the accuracy of the dR/dx obtained by adjoint methods has been verified by direct calculations and these comparisons are also presented. The application of the theory as presented requires extensive development work in that a large amount of analytic differentiation must be carried out and a substantial effort is needed to evaluate these derivatives. In the course of the work, a method was developed that would allow all of the required derivatives to be obtained numerically using LEAP and this method is presented and discussed. This numerical method is applicable only to codes with the very special modular structure ofmore » LEAP.« less