Sensitivity analysis of the MM5 weather model using automatic differentiation

Abstract

We present a general method for using automatic differentiation to facilitate model sensitivity analysis. Automatic differentiation techniques augment, in a completely mechanical fashion, an existing code such that it also simultaneously and efficiently computes derivatives. Our method allows the sensitivities of the code’s outputs to its parameters and inputs to be determined with minimal human effort by exploiting the relationship between differentiation and formal perturbation theory. Employing this methodology, we performed a sensitivity study of the MM5 code, a mesoscale weather model jointly developed by Penn State University and the National Center for Atmospheric Research, that is composed of roughly 40,000 lines of Fortran 77 code. Our results show that automatic differentiation-computed sensitivities exhibit superior accuracy compared to divided difference approximations computed from finite-amplitude perturbations. We also comment on a numerically induced precursor wave that would almost certainly have been undetectable if one used a divided difference method. © 1996 American Institute of Physics.