AN AUTOMATIC DIFFERENTIATION TECHNIQUE FOR SENSITIVITY ANALYSIS OF NUMERICAL ADVECTION SCHEMES IN AIR-QUALITY MODELS

Sensitivity analysis, which characterizes the change in model output d ue to variations in model input parameters, is of critical importance in simulation models. Sensitivity coefficients, defined as the partial derivatives of the model output with respect to the input parameters, are useful in assessing the reliability of the output from a complex model with many uncertainty parameters. Most existing sensitivity meth ods, however, have one or more of the following limitations: inaccurac y in the results, high cost in human effort, and difficulty in mathema tical formulation and computer program implementation. To overcome the se limitations, we are exploring ADIFOR, an automatic differentiation technique for systematically studying sensitivities. One can apply ADI FOR without having an intimate knowledge of the algorithms implemented in a model, sb manual preparation of sensitivity code is avoided. In this paper, ADIFOR's accuracy and computational efficiency are demonst rated by calculating the sensitivity of concentration to a global pert urbation of wind velocity in advection models and comparing this with results from the brute-force method of sensitivity analysis. ADIFOR-ge nerated code can produce exact sensitivity information up to the machi ne epsilon, and can reduce computer CPU time requirements by up to 57% compared with the brute-force method for a single sensitivity calcula tion (and the savings increases with the number of parameters). Furthe rmore, we demonstrate the applicability of ADIFOR to models with a lar ge number of uncertainty parameters by calculating the sensitivity of model output to initial conditions in a two-dimensional advection mode l. Copyright (C) 1996 Elsevier Science Ltd