Title:Adjustment toward "balance" in the adjoint shallow water system

Author: Michael C. Morgan (University of Wisconsin – Madison)

Analytical and numerical studies of the adjoint of the shallow water system are conducted using an adjoint model to apprehend the emergence of "balanced" adjoint sensitivity fields (i.e., sensitivities to both wind and mass thatare related through a "geostrophic-type" balance). The emergence of "balance" in the adjoint system resembles the emergence of geostrophic balance seen in the classical Rossby adjustment problem. In that problem, an unbalanced distribution of wind and mass evolves to a state of geostrophic balance determined by the initial distribution of potential vorticity (PV). In this presentation, it is shown that, like the geostrophic adjustment problem, the adjoint shallow water system possesses a conserved dynamical variable (the sensitivity to "balanced" height – related to the sensitivity to PV) from which the sensitivities to the long-term height and wind are immediately diagnosed. In addition, expressions for sensitivities to unbalanced fields including the ageostrophic wind and divergent flow are derived and interpreted.

GMAO Head: Steven Pawson Global Modeling and Assimilation Office NASA Goddard Space Flight Center

Curator: Nikki Privé Last Updated: Feb 9 2015