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

This 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 T213L31/T63L31. (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 Storm‐Track 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.

[1]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. Ii: Numerical Results , 2007 .

[2]  P. Courtier,et al.  Variational Assimilation of Meteorological Observations With the Adjoint Vorticity Equation. I: Theory , 2007 .

[3]  J. Mahfouf,et al.  The ecmwf operational implementation of four‐dimensional variational assimilation. III: Experimental results and diagnostics with operational configuration , 2000 .

[4]  Heikki Järvinen,et al.  Variational assimilation of time sequences of surface observations with serially correlated errors , 1999 .

[5]  Ronald M. Errico,et al.  Singular-Vector Perturbation Growth in a Primitive Equation Model with Moist Physics , 1999 .

[6]  Jean-François Mahfouf,et al.  Influence of physical processes on the tangent‐linear approximation , 1999 .

[7]  J. Derber,et al.  A reformulation of the background error covariance in the ECMWF global data assimilation system , 1999 .

[8]  R. Gelaro,et al.  Estimation of key analysis errors using the adjoint technique , 1998 .

[9]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). II: Structure functions , 1998 .

[10]  P. Courtier,et al.  The ECMWF implementation of three‐dimensional variational assimilation (3D‐Var). I: Formulation , 1998 .

[11]  P. Courtier,et al.  Extended assimilation and forecast experiments with a four‐dimensional variational assimilation system , 1998 .

[12]  J. Thepaut,et al.  Multiple‐truncation incremental approach for four‐dimensional variational data assimilation , 1998 .

[13]  Chris Snyder,et al.  The Fronts and Atlantic Storm-Track Experiment (FASTEX) : Scientific objectives and experimental design , 1997 .

[14]  Tadashi Tsuyuki,et al.  Variational Data Assimilation in the Tropics Using Precipitation Data. Part II: 3D Model , 1996 .

[15]  Roberto Buizza,et al.  The Singular-Vector Structure of the Atmospheric Global Circulation , 1995 .

[16]  P. Courtier,et al.  A strategy for operational implementation of 4D‐Var, using an incremental approach , 1994 .

[17]  Ionel M. Navon,et al.  Variational data assimilation with moist threshold processes using the NMC spectral model , 1993 .

[18]  D. Zupanski,et al.  The effects of discontinuities in the Betts’Miller cumulus convection scheme on four-dimensional variational data assimilation , 1993 .

[19]  R. Errico,et al.  Linearization and adjoint of parameterized moist diabatic processes , 1993 .

[20]  J. Bao,et al.  Treatment of on/off switches in the adjoint method: FDDA experiments with a simple model , 1993 .

[21]  Milija Zupanski,et al.  Regional Four-Dimensional Variational Data Assimilation in a Quasi-Operational Forecasting Environment , 1993 .

[22]  Ronald M. Errico,et al.  Sensitivity Analysis Using an Adjoint of the PSU-NCAR Mesoseale Model , 1992 .

[23]  J. Derber,et al.  Variational Data Assimilation with an Adiabatic Version of the NMC Spectral Model , 1992 .

[24]  Philippe Courtier,et al.  Four‐Dimensional Assimilation In the Presence of Baroclinic Instability , 1992 .

[25]  P. Courtier,et al.  Four-dimensional variational data assimilation using the adjoint of a multilevel primitive-equation model , 1991 .

[26]  P. Courtier,et al.  Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations , 1990 .

[27]  Claude Lemaréchal,et al.  Some numerical experiments with variable-storage quasi-Newton algorithms , 1989, Math. Program..

[28]  F. L. Dimet,et al.  Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects , 1986 .

[29]  J. M. Lewis,et al.  The use of adjoint equations to solve a variational adjustment problem with advective constraints , 1985 .

[30]  Philippe Courtier,et al.  The ECMWF implementation of three-dimensional variational assimilation ( 3 D-Var ) . 111 : Experimental results , 2006 .

[31]  Heikki Järvinen,et al.  Variational quality control , 1999 .

[32]  Ronald M. Errico,et al.  An examination of the accuracy of the linearization of a mesoscale model with moist physics , 1999 .

[33]  Jean-Noël Thépaut,et al.  Simplified and Regular Physical Parameterizations for Incremental Four-Dimensional Variational Assimilation , 1999 .

[34]  Philippe Courtier,et al.  Dynamical structure functions in a four‐dimensional variational assimilation: A case study , 1996 .

[35]  Roberto Buizza,et al.  Sensitivity of optimal unstable structures , 1994 .