An automatic differentiation technique for sensitivity analysis of numerical advection schemes in air quality models

Sensitivity analysis, which characterizes the change in model output due 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 methods, however, have one or more of the following limitations: inaccuracy in the results, high cost in human effort, and difficulty in mathematical formulation and computer program implementation. To overcome these limitations, we are exploring ADIFOR, an automatic differentiation technique for systematically studying sensitivities. One can apply ADIFOR without having an intimate knowledge of the algorithms implemented in a model, so manual preparation of sensitivity code is avoided. In this paper, ADIFORʹs accuracy and computational efficiency are demonstrated by calculating the sensitivity of concentration to a global perturbation of wind velocity in advection models and comparing this with results from the brute-force method of sensitivity analysis. ADIFOR-generated code can produce exact sensitivity information up to the machine epsilon, and can reduce computer CPU time requirements by up to 57% compared with the brute-force method for a single sensitivity calculation (and the savings increases with the number of parameters). Furthermore, we demonstrate the applicability of ADIFOR to models with a large number of uncertainty parameters by calculating the sensitivity of model output to initial conditions in a two-dimensional advection model.