The impact of diabatic processes on 4-dimensional variational data assimilation (4DVAR) was studied using the global spectral model (1995 version) with full physics at National Centers for Environmental Prediction (NCEP) and the developed adjoint. With a cost function measuring spectral errors of 6-hour forecasts, the adaibatic and diabatic 4DVAR experiments were carried out based on the same NCEP re-analysis data set by employing the limited memory quasi-Newton algorithm (L-BFGS). Comparisons on results found that the decrease of the diabatic cost function remains stuck after some iterations in minimization due to discontinuities in parameterizations of the model while the adiabatic cost function continuously decreases. In order to seek a sounder performance of the diabatic minimization, the decrease in minimization of the defined cost function in different spectral domains was first investigated. Results found that at the beginning stage (before iteration 10) the minimization process mainly adjusts large-scale flows, in which discontinuous parameterizations in diabatic model have almost no hurt on minimization. As iterations increase, the adjustment gradually moves to relatively small scales through around 20-iteration for transition. During the transition period, discontinuities in parameterizations may start to damage minimization to cause the diabatic cost function to be stuck instead of continuously decreasing as an adiabatic one does. Then a mixed 4DVAR experiment scheme was designed. The scheme first uses the adiabatic model and adjoint to adjust large-scale flows and then the diabatic model and adjoint is invoked to adjust relatively small scales. The switch occurs once the adjustment goes through some critical period (iteration 10 to 20, in this case) where discontinuous parameterizations may have the most impact on minimization. Experiment results showed that the new mixed scheme causes 29% more reduction on the cost function and 35% on the gradient norm for 60 iterations and saves 21% CPU time on the NCAR Cray cluster. The resulted optimal initial conditions from the new scheme improve the short-range forecast skills with 48-hour statistics.

The results suggest that in solving a diabatic 4DVAR problem, ones may choose an economical differentiable optimization algorithm if the addressed is a relatively large-scale problem. And also, The mixed 4DVAR scheme, to some degree, is able to avoid the hurt on minimization due to discontinuities in parameterizations of a diabatic model with a cheaper computation cost and it is therefore a practicable choice in operational applications.