Sensitivity Analysis of the Mm5 Weather Model Using Automatic Diierentiation

We present a general method for using automatic diierentiation to facilitate model sensitivity analysis. Automatic diierentiation techniques augment, in a completely mechanical fashion, an existing code such that it also simultaneously and eeciently computes derivatives. Our method allows the sensitivities of the code's outputs to its parameters and inputs to be determined with minimal human eeort by exploiting the relationship between diierentiation and formal perturbation theory. Employing this method, 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, comprising roughly 40,000 lines of Fortran 77 code. Our results show that AD-computed sensitivities exhibit superior accuracy compared with divided diierences approximations computed from nite-amplitude perturbations, while consuming comparable or less CPU time and less human labor. We also comment on a numerically induced precursor wave that would almost certainly have been undetectable if one used a divided diierence method.