This documentation on 3D and 4D-Var is meant to serve as a scientific guide to the 3D/4D-Var codes, a part of the IFS. The documentation is divided into eleven chapters. This, the first chapter deals with the scientific formulation, the practical implementation of the incremental method, and it includes some comments on minimization and preconditioning. The code structure and the computational details of the 3D/4D-Var cost-functions and their gradients are explained in Chapter 2 `3D variational assimilation' . There is a separate chapter on subjects specific to 4D-Var (Chapter 3 `4D variational assimilation' ). Thereafter follows a description of the background term (Chapter 4 `Background term' ) and two chapters respectively on observation operators for conventional data (Chapter 5 `Conventional observational constraints' ) and satellite data (Chapter 6 `Satellite observational constraints' ). Chapter 7 `Background, analysis and forecast errors' deals with the computation of background and analysis errors and Chapter 8 `Gravity-wave control' is on initialization. The modules for observation sorting and screening are described in Chapter 9 `Data partitioning (OBSORT)' and Chapter 10 `Observation screening' . Chapter 11 outlines the snow analysis, Chapter 12 describes the land surface analysis, Chapter 13 describes the sea surface temperature and sea-ice analysis and the final chapter Chapter 14 provides details of the reduced Kalman filter.

An extensive scientific description of 3D/4D-Var has been published in QJRMS, in ECMWF workshop proceedings and Technical Memoranda over the years. The incremental formulation was introduced by Courtier et al. (1994). The ECMWF implementation of 3D-Var was published in a three-part paper by Courtier et al. (1998), Rabier et al. (1998) and Andersson et al. (1998). The observation operators for conventional data can be found in Vasiljevic et al. (1992). The methods for assimilation of TOVS radiance data and ERS scatterometer data were developed by Andersson et al. (1994) and Stoffelen and Anderson (1997), respectively. The pre-operational experimentation with 4D-Var has been documented in three papers by Rabier et al. (1998), Mahfouf and Rabier (1998) and Klinker et al. (1999).

3D-Var was implemented in ECMWF operations on 30 January 1996. The three-part paper mentioned above chiefly presented the scheme as it was at that point in time. There have been very significant developments of the system during its time in operations. The first upgrade took place in connection with the move from a CRAY C90 system to a distributed memory Fujitsu VPP700 machine. The observation handling and data screening modules were replaced with new codes, see Chapter 9 `Data partitioning (OBSORT)' and Chapter 10 `Observation screening' , respectively, and the paper by Järvinen and Undén (1997). Variational quality control of observations (Andersson and Järvinen, 1999, and Section 2.6) and a new algorithm for computing estimates of analysis and background errors (Fisher and Courtier 1995, and Chapter 7 `Background, analysis and forecast errors' ) were introduced.

In May 1997 there was a complete revision of the background term, see Derber and Bouttier (1999) and Chapter 4 `Background term' . The old background term, which was described in Courtier et al. (1998), is not covered by this documentation as it is now considered obsolete. Later that year (25 November 1997) 6-hour 4D-Var was introduced operationally, at resolution T213L31, with two iterations of the outer loop: the first with 50 iterations (simplified physics) and the second with 20 iterations (with tangent-linear physics). In April 1998 the resolution was changed to T_L319 and in June 1998 we revised the radiosonde/pilot usage (significant levels, temperature instead of geopotential) and we started using time-sequnces of data (Järvinen et al. 1999), so-called 4D-screening. Finally, the data assimilation scheme was extended higher into the atmosphere on 10 March 1999, when the T_L319L50 model was introduced, which in turn enabled the introduction in May 1999 of ATOVS radiance data (McNally et al. 1999). In October 1999 the vertical resolution of the boundary layer was enhanced taking the number of model levels to a total of 60. In summer 2000 the 4D-Var period was extended from 6 to 12 hours, whereas the ERA configuration was built as an FGAT (first guess at the appropriate time) of 3D-Var with a period of 6 hours. At the time of writing it is planned to increase the horizontal resolution of 4D-Var to T_L511L60, with inner loop resolution enhanced from T63L60 to T_L159L60 using the linearized semi-Lagrangian scheme.

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21.03.2002

DATA ASSIMILATION

IFS documentation Front Page

Table of contents

1.1 Introduction