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

Abstract

SUMMARYThis paper presents results of a comparison between four-dimensional variational assimilation (4D-Var). using a 6-hour assimilation window and simplified physics during the minimization, and three-dimensional variational assimilation (3D-Var). Results have been obtained at 'operational' resolution T2 13L3 1/T63L3 1. (T defines the spectral triangular truncation and L the number of levels in the vertical, with the first parameters defining the resolution of the model trajectory, and the second the resolution of the inner-loop.) The sensitivity of the 4D-Var performance to different set-ups is investigated. In particular, the performance of 4D-Var in the Tropics revealed some sensitivity to the way the adiabatic nonlinear normal-mode initialization of the increments was performed. Going from four outer-loops to only one (as in 3D-Var), together with a change to the 1997 formulation of the background constraint and an initialization of only the small scales, helped to improve the 4D-Var performance. Tropical scores then became only marginally worse for 4D-Var than for 3D-Var. Twelve weeks of experimentation with the one outer-loop 4D-Var and the 1997 background formulation have been studied. The averaged scores show a small but consistent improvement in both hemispheres at all ranges. In the short range, each two-to three-week period has been found to be slightly positive throughout the troposphere. The better short-range performance of the 4D-Var system is also shown by the fits of the background fields to the data. More results are presented for the Atlantic Ocean area during FASTEX (the Fronts and Atlantic StormTrack Experiment), during which 4D-Var is found to perform better. In individual synoptic cases corresponding to interesting Intensive Observing Periods, 4D-Var has a clear advantage over 3D-Var during rapid cyclogeneses. The very short-range forecasts used as backgrounds are much closer to the data over the Atlantic for 4D-Var than for 3D-Var. The 4D-Var analyses also display more day-to-day variability. Some structure functions are illustrated in the 4D-Var case for a height observation inserted at the beginning, in the middle or at the end of the assimilation window. The dynamical processes seem to be relevant, even with a short 6-hour assimilation period, which explains the better overall performance of the 4D-Var system.

Forecast impact experiment with a constellation of GPS radio occultation receivers

“…The assimilation experiments are performed with ECMWF's 4D-Var system (Rabier et al, 2000) at T511 horizontal resolution and 91 levels in the vertical. The COSMIC measurements are the BUFR product provided by the University Corporation for Atmospheric Research (UCAR) (Kuo et al, 2004).…”

Interpolating sparse scattered data using flow information

“…For example, the 3D-Var [11] and 4D-Var [12] methods have entered into common usage. In general, such methods can be viewed as inverse problems in that they attempt to reconstruct continuous scalar fields based on a discrete (and often sparse) set of measurements.…”

Convergence properties of the primal and dual forms of variational data assimilation

“…Several NWP centres are currently using the fourdimensional variational scheme (4D-Var), such as the European Centre for Medium-range Weather Forecast (ECMWF; Rabier et al, 2000), the UK Met Office (Rawlins et al, 2007), Météo-France (Gauthier and Thépaut, 2001) and Environment Canada (Gauthier et al, 2007). The 4D-Var was made possible and practically affordable by using the adjoint methods introduced by Lewis and Derber (1985), LeDimet and Talagrand (1986) and Talagrand and Courtier (1987).…”