Observation sensitivity calculations using the adjoint of the Gridpoint Statistical Interpolation (GSI) analysis system

The adjoint of a data assimilation system provides an efficient way of estimating sensitivities of analysis or forecast measures with respect to observations. The NASA Global Modeling and Assimilation Office (GMAO) has developed an exact adjoint of the Gridpoint Statistical Interpolation (GSI) analysis scheme developed at the National Centers for Environmental Prediction (NCEP). The development approach is unique in that the adjoint is derived from a line-by-line tangent linear version of the GSI Availability of the tangent linear scheme provides an explicit means of assessing not only the fidelity of the adjoint, but also the effects of nonlinear processes in the GSI itself. In this paper, the development of the tangent linear and adjoint versions of the GSI are discussed and observation sensitivity results for a near-operational version of the system are shown. Results indicate that the GSI adjoint provides accurate assessments of the sensitivities with respect to observations of wind, temperature, satellite radiances, and, to a lesser extent, moisture. Sensitivities with respect to ozone observations are quite linear for the ozone fields themselves, but highly nonlinear for other variables. The sensitivity information provided by the adjoint is used to estimate the contribution, or impact, of various observing systems on locally defined response functions based on the analyzed increments of temperature and zonal wind. It is shown, for example, that satellite radiances have the largest impact of all observing systems on the temperature increments over the eastern North Pacific, while conventional observations from rawinsondes and aircraft dominate the impact oil the zonal wind increments over the continental United States. The observation impact calculations also provide an additional means of validating the observation sensitivities produced by the GSI adjoint.