Linearization and adjoint of parameterized moist diabatic processes

The problems related to the development and applications of an adjoint model for a nonlinear model that has discontinuities in the governing equations are discussed in this study. We examine the hypothesis that a useful tangent linear model and its associated adjoint model can be developed for such a nonlinear model by using the reference state to determine the regimes associated with the discontinuities. Our nonlinear and linear experiments for the Pennsylvania State University/National Center for Atmospheric Research regional forecast model show that linearization of moist diabatic parameterizations is feasible using this method, but significant errors may be expected in the regions where transitions are frequent and associated with large tendency changes due to the model's moist diabatic parameterizations. We conclude that the tangent linear model and its associated adjoint model would be more accurate for a nonlinear model that has more well-behaved regime transitions. We suggest that nonlinear tests similar to the analysis shown in this study be performed prior to developing these linear models. If these tests show high nonlinearity due to regime transitions as a consequence of model deficiencies, we recommend first improving the nonlinear model before performing the linearization.