The Development of NCEP 4D-Var System: Experimental Results Compared to those of 3D-Var

Abstract:

We introduce the NCEP (National Centers for Environmental Prediction) global spectral forecast model and its ``full-physics'' tangent linear and adjoint models into the NCEP's SSI (Spectral Statistical Interpolation) analysis system and thus developed a 4D-Var system. The tangent linear and adjoint models used in 4D-Var include all the physical processes except radiation, i.e., the surface processe, vertical diffusion, shallow convection, gravity wave drag parameterization, large-scale precipitation and cumulus convection. Radiation is treated as an external forcing in these models. Numerical experiments were carried out at a resolution of 28 vertical layers and 62 waves triangularly truncated. The 4D-Var analysis is formulated similarly as the 3D-Var analysis and minimizes a cost function consisting of (i) the distance between the desired analysis and background field which is the 6-h forecast from the previous analysis ($J_b$), (ii) the distance between observations and the 6-h forecast from the desired analysis ($J_o$); and (iii) a penalty term constraining the norm of the time tendency of the divergence to eliminating large-amplitude gravity waves ($J_c$). The only difference between the 3D-Var and the current implementation of 4D-Var formulation is in the $J_o$ term in which the times of observations are taken care of more precisely in 4D-Var than in 3D-Var and the NCEP spectral model is used in 4D-Var as a strong constraint describing the time evolution of the analysis increment during the assimilation window. A parallel run of the 3D-Var and 4D-Var experimentations was undertaken to examine the performance of the 4D-Var system and to assess the computational requirement of 4D-Var. Results from a one week testing are encouraging. Compared with the 3D-Var parallel runs, 4D-Var showed good convergences, smaller analysis increments, better fits to data, and improved forecasts verified by the targeted dropwinsondes from the 1998 NORPEX (NORth Pacific EXperiment).