Performance of 4D-Var with different strategies for the use of adjoint physics with the FSU global spectral model

A set of four-dimensional variational data assimilation ( 4D-Var) experimen ts were conducted using both a standard method and an incremental method in an identical twin framework. The full physics adjoint model of the Florida State University global spectral model (FSUGSM) was used in the standard 4 D-Var, while the adjoint of only a few selected physical parameterizations was used in the incremental method. The impact of physical processes on 4D- Var was examined in detail by comparing the results of these experiments. T he inclusion of full physics turned out to be significantly beneficial in t erms of assimilation error to the lower troposphere during the entire minim ization process. The beneficial impact was found to be primarily related to boundary layer physics. The precipitation physics in the adjoint model als o tended to have a beneficial impact after an intermediate number (50) of m inimization iterations. Experiment results confirmed that the forecast From assimilation analyses with the full physics adjoint model displays a short er precipitation spinup period. The beneficial impact on precipitation spin up did not result solely from the inclusion of the precipitation physics in the adjoint model, but rather from the combined impact of several physical processes, The inclusion of full physics in the adjoint model exhibited a detrimental impact on the rate of convergence at an early stage of the mini mization process, but did not affect the final convergence. A truncated Newton-like incremental approach was introduced for examining t he possibility of circumventing the detrimental aspects using the full phys ics in the adjoint model in 4D-Var but taking into account its positive asp ects. This algorithm was based on the idea of the truncated Newton minimiza tion method and the sequential cost Function incremental method introduced by Courtier et al., consisting of an inner loop and an outer loop. The inne r loop comprised the incremental method, while the outer loop consisted of the standard 4D-Var method using the full physics adjoint. The limited-memo ry quasi-Newton minimization method (L-BFGS) was used for both inner and ou ter loops, while information on the Hessian of the cost function was jointl y updated at every iteration in both loops, In an experiment with a two-cyc le truncated Newton-like incremental approach, the assimilation analyses tu rned out to be better than those obtained from either the standard 4D-Var o l the incremental 4D-Var in all aspects examined. The CPU time required by this two-cycle approach was larger by 35% compared with that required by th e incremental 4D-Var without almost any physics in the adjoint model, while the CPU time required by the standard 4D-Var with the full physics adjoint model was more than twice that required by the incremental 4D-Var. Finally , several hypotheses concerning the impact of using standard 4D-Var full ph ysics on minimization convergence were advanced and discussed.