Four-dimensional variational assimilation and predictability in a quasi-geostrophic model

Four-dimensional variational assimilation (4DVAR) of noisy observations in a multi-layerquasi-geostrophic model is studied, in both the perfect and imperfect model settings. Withinthe perfect model setting, the quality of the assimilated state improves significantly when theassimilation period is extended more than one week into the past. Specifically, when observationsare supplied every 6 h, the squared error in the assimilated state at the end of the assimilationtime period (the present) saturates at a value two orders of magnitude smaller than theimposed observational error for an assimilation period of 10 days. Further, this reduction inerror occurs not only in measures explicitly minimized by 4DVAR, but for all standard measuresof error. For realistic levels of observational error, the extension of forecast lead times is large,exceeding 15 days for global forecasts when the assimilation period is 10 days. This holds evenfor weather regime transitions, which are shown to be predictable at lead times of 10 days. Theuse of long assimilation periods extends forecast lead times approximately 5 days over the casewhen assimilation periods are on the order of one day. The structure of the analysis error whenlong assimilation period 4DVAR is applied is examined. This error is primarily concentratedin the midlatitude storm tracks. The reduction in analysis error is increasingly efficient at smallscales as the assimilation period is increased; consequently, for long assimilation periods theanalysis error projects strongly into the subspace of the leading Lyapunov vectors. The performanceof 4DVAR in an imperfect model setting is also examined, and is found to depend uponthe growth rate of the model errors. For rapidly growing model errors, extension of the assimilationperiod beyond about 1–2 days results in a degradation in the quality of the assimilatedstate as well as in the forecast quality. However, for model error growth rates similar to thegrowth rates of the leading Lyapunov vectors of the system, improvements in the assimilatedstate similar to those found for the perfect model are obtained. As such, it is estimated thatassimilation times of 3–5 days for current levels of model error may improve the quality ofassimilated states and forecasts in an operational setting. DOI: 10.1034/j.1600-0870.1998.t01-4-00001.x

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

[2]  Eugenia Kalnay,et al.  Ensemble Forecasting at NMC: The Generation of Perturbations , 1993 .

[3]  Michael Ghil,et al.  Advanced data assimilation in strongly nonlinear dynamical systems , 1994 .

[4]  Tomislava Vukicevic,et al.  Nonlinear and Linear Evolution of Initial Forecast Errors , 1991 .

[5]  P. Holmes,et al.  Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[6]  I. Held,et al.  Sensitivity of the Eddy Momentum Flux to Meridional Resolution in Atmospheric GCMs , 1993 .

[7]  Jeffrey L. Anderson.  The Climatology of Blocking in a Numerical Forecast Model. , 1993 .

[8]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[9]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[10]  F. Molteni,et al.  The ECMWF Ensemble Prediction System: Methodology and validation , 1996 .

[11]  P. Courtier,et al.  Quasi‐continuous variational data assimilation , 1996 .

[12]  P. L. Houtekamer,et al.  Methods for Ensemble Prediction , 1995 .

[13]  Franco Molteni,et al.  On the operational predictability of blocking , 1990 .

[14]  P. L. Houtekamer.  The Construction of Optimal Perturbations , 1995 .

[15]  C. Nicolis,et al.  Lyapunov Vectors and Error Growth Patterns in a T21L3 Quasigeostrophic Model , 1997 .

[16]  Franco Molteni,et al.  Predictability and finite‐time instability of the northern winter circulation , 1993 .

[17]  Monique Tanguay,et al.  Four‐dimensional data assimilation with a wide range of scales , 1995 .

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

[19]  David J. Stensrud,et al.  Behaviors of Variational and Nudging Assimilation Techniques with a Chaotic Low-Order Model , 1992 .

[20]  T. Palmer.  Extended-range atmospheric prediction and the Lorenz model , 1993 .

[21]  Franco Molteni,et al.  Toward a dynamical understanding of planetary-scale flow regimes. , 1993 .

[22]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

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

[24]  Roberto Buizza,et al.  Singular Vectors: The Effect of Spatial Scale on Linear Growth of Disturbances. , 1995 .

[25]  R. Lindzen.  Instability of plane parallel shear flow (toward a mechanistic picture of how it works) , 1988 .

[26]  Qing Liu,et al.  On the definition and persistence of blocking , 1994 .

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

[28]  Jan Barkmeijer,et al.  Perturbations that optimally trigger weather regimes , 1995 .

[29]  Yong Li.  A note on the uniqueness problem of variational adjustment approach to four-dimensional data assimilation , 1991 .

[30]  Brian F. Farrell,et al.  Small Error Dynamics and the Predictability of Atmospheric Flows. , 1990 .

[31]  M. Ghil,et al.  Data assimilation in meteorology and oceanography , 1991 .

[32]  M. Déqué,et al.  The Skill of Extended-Range Extratropical Winter Dynamical Forecasts , 1992 .

[33]  Pierre Gauthier,et al.  Chaos and quadri-dimensional data assimilation: a study based on the Lorenz model , 1992 .