Development and applications of the adjoint of the non-hydrostatic GEOS-5 FV3 dynamical core

The adjoint of GEOS-5 is used for a number of important practical and research based applications at NASA. It provides a framework for computing real time observation impacts, assessing forecast sensitivity, calculating singular vectors and estimating surface fluxes of constituents. To match the setup now used in the nonlinear version of GEOS-5 the adjoint of the non-hydrostatic version of the FV3 cubed sphere dynamical core has been developed. We compare the performance of the linearized dynamical core and the fully nonlinear version for a number of realistic perturbation test cases. The degree of linearity for FV3 is found to be sufficient for all practical applications and the linearity of the hydrostatic and non-hydrostatic modes is compared. Some simplifications are necessary in the linearized transport schemes to improve linearity and divergence damping coefficients are slightly increased to limit arbitrary perturbation growth. Stability of the FV3 core is achieved through a sub-cycling, which can result in excessive re-computation during the backwards adjoint integration. We discuss the balancing between re-computation and so-called checkpointing of variables and how this is developed while maintaining a framework for efficient intake of future code changes. Observation impacts computed using the non-hydrostatic FV3 adjoint are shown. Some examples are presented where the adjoint of FV3 is used to understand track and intensity errors for tropical cyclones and used to track the cause of a major sudden stratospheric warming. We also discuss recent efforts to use the FV3 adjoint to infer surface fluxes of CO₂.