The ECMWF operational implementation of four-dimensional variational assimilation. I: Experimental results with simplified physics

A comprehensive set of physical parametrizations has been linearized for use in the European Centre for Medium-Range Weather Forecasts (ECMWF's) incremental four-dimensional variational (4D-Var) system described in Part I. The following processes are represented: vertical diffusion, subgrid-scale orographic effects, large-scale precipitation, deep moist convection and long-wave radiation. The tangent-linear approximation is examined for finite-size perturbations. Significant improvements are illustrated for surface wind and specific humidity with respect to a simplified vertical diffusion scheme. Singular vectors computed over 6 hours (compatible with the 4D-Var assimilation window) have lower amplification rates when the improved physical package is included, due to a more realistic description of dissipative processes, even though latent-heat release contributes to amplify the potential energy of perturbations in rainy areas. A direct consequence is a larger value of the observation term of the cost-function at the end of the minimization process when improved physics is included in 4D-Var. However, the larger departure of the analysis state from observations in the lower-resolution inner-loop is in better agreement with the behaviour of the full nonlinear model at high resolution. More precisely, the improved physics produces smaller discontinuities in the value of the cost-function when going from low to high resolution. In order to reduce the computational cost of the linear physics, a new configuration of the incremental 4D-Var system using two outer-loops is defined. In a first outer-loop, a minimization is performed at low resolution with simplified physics (50 iterations), while in the second loop a second minimization is performed with improved physics (20 iterations) after an update of the model trajectory at high resolution. In this configuration the extra cost of the physics is only 25%, and results from a 2-week assimilation period show positive impacts in terms of quality of the forecasts in the Tropics (reduced spin-down of precipitation, lower root-mean-square errors in wind scores). This 4D-Var configuration with improved physics and two outer-loops was implemented operationally at ECMWF in November 1997.