Development of a Four-Dimensional Variational Analysis System Using the Adjoint Method at GLA. Part 1: Dynamics

Abstract

Recent developments in the field of data assimilation have Pointed to variational analysis (essentially least- squares fitting, of a model solution to observed data) using the adjoint method as a new direction that holds the potential of major improvements over the current optimal interpolation (0I) method. The shortcomings of the existing OI analysis method, such as the questionable basic assumptions underlying some of the statistical formulations and the linearity between the analysis and the observation, do not exist in variational analysis. Moreover, variational analysis, by fitting a model solution to data, has the potential of avoiding the long-standing spinup problem in numerical weather prediction. Finally, when the resulting analysis is used as the initial condition for forecasting, since initialization will be performed internally to the analysis procedure, no separate initialization procedure is required before forecast starts. This paper describes the initial effort in the development of a four-dimensional variational analysis system. Although the development is based on the Goddard Laboratory for Atmospheres General Circulation Model (GLA GCM), the methods and procedures described in this paper can he applied to any model. The adjoint code that computes the gradients needed in the analysis can be written directly from the GCM code. An easy error-detection technique was devised in the construction of the adjoint model. Also, a method of determining the weights and the preconditioning scales for the cases where model-generated data, which are error free, are used as observation is proposed. Two test experiments show that the dynamics part of the system has been successfully completed. A limited comparison of two minimization codes was conducted. The procedures presented in this work are general and can be applied to various variational and sensitivity studies.