Performance of 4D-Var strategies using the FSU Global Spectral Model with its full physics adjoint

Zhijin Li, I.M. Navon

A set of four-dimensional variational assimilation (4D-Var) experiments were conducted using both a standard method and an incremental method. The full physics adjoint model of the FSU Global Spectral model (FSUGSM) was used in the standard 4D-Var, while the adjoint of only selected physical parameterizations was used in the incremental method. We examined in detail the impact of physical processes on 4D-Var by comparing the results of above experiments. As a whole, the inclusion of full physics in the adjoint model was detrimental to the rate of convergence of the minimization process prior to iteration 50, while full convergence was attained only after a large number of iterations. The detrimental impact was found to be primarily related to precipitation physics in the adjoint model, and was limited over precipitation regions. The inclusion of full physics turned out to be significantly beneficial in terms of assimilation error to the lower troposphere during the entire minimization process. The beneficial impact was found to be primarily related to boundary layer physics. The precipitation physics in the adjoint model also tended to have a beneficial impact starting from iteration 50. Experiment results confirmed that assimilation analyses with the full physics adjoint model display a shorter precipitation spin-up 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.

A truncated Newton-like incremental approach was introduced for examining the possibility of circumventing the detrimental aspects using the full physics in the adjoint model in 4D-Var but taking into account its positive aspects. This algorithm is based on the idea of the truncated Newton minimization method and the sequential cost function incremental method introduced by Courtier et al. (1994), consisting of an inner loop and an outer loop. The inner loop comprised the incremental method, while the outer loop consisted of the standard 4D-Var method using the full physics adjoint. The limited-memory quasi-Newton minimization method (L-BFGS) was used for both inner and outer loops, while information on the Hessian of the cost function was jointly updated at every iteration in both loops. In an experiment with a two-cycle truncated Newton-like incremental approach, the quality of the assimilation analyses turned out to be better than that obtained from either the standard 4D-Var or 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 the incremental 4D-Var without 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. Several hypotheses concerning the impact of using standard 4D-Var full physics on minimization convergence were discussed.