Adaptive observations and assimilation in the unstable subspace by breeding on the data-assimilation system

Results of targeting and assimilation experiments in a quasi-geostrophic atmospheric model are presented and discussed. The basic idea is to assimilate observations in the unstable subspace (AUS) of the data-assimilation system. The unstable subspace is estimated by breeding on the data assimilation system (BDAS). By the combination of AUS and BDAS the analysis update has the same local structure as the observationally forced bred modes. Use of adaptive observations, taken at locations where bred vectors have maximum amplitude, enhances the efficiency of the procedure and allows the use of a very limited number of observations and modes. The performance of the targeting and assimilation design is tested in an idealized context, under perfect model conditions. It is shown that the process of driving the control solution toward the true trajectory accomplished by the observational forcing reduces the number and growth of unstable modes. By observing and assimilating the unstable structures it is possible to stabilize the assimilation system so that few observations are sufficient to keep the analysis error within very low bounds. Furthermore the number of observations needed to control the system is shown to be related to the number and growth rate of the unstable modes.

[1]  Philippe Courtier,et al.  Unified Notation for Data Assimilation : Operational, Sequential and Variational , 1997 .

[2]  Anna Trevisan,et al.  Detecting unstable structures and controlling error growth by assimilation of standard and adaptive observations in a primitive equation ocean model , 2006 .

[3]  R. Morss,et al.  Adaptive observations : idealized sampling strategies for improving numerical weather prediction , 1998 .

[4]  K. Emanuel,et al.  Optimal Sites for Supplementary Weather Observations: Simulation with a Small Model , 1998 .

[5]  Christopher K. Wikle,et al.  Atmospheric Modeling, Data Assimilation, and Predictability , 2005, Technometrics.

[6]  E. Lorenz.  The local structure of a chaotic attractor in four dimensions , 1984 .

[7]  R. Bleck.  Simulation of coastal upwelling frontogenesis with an isopycnic coordinate model , 1978 .

[8]  Xuguang Wang,et al.  A Comparison of Breeding and Ensemble Transform Kalman Filter Ensemble Forecast Schemes , 2003 .

[9]  Alberto Carrassi,et al.  Developing a dynamically based assimilation method for targeted and standard observations , 2005 .

[10]  Michael Ghil,et al.  Tracking Atmospheric Instabilities with the Kalman Filter. Part II: Two-Layer Results , 1996 .

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

[12]  Michael Ghil,et al.  Tracking Atmospheric Instabilities with the Kalman Filter. Part 1: Methodology and One-Layer Resultst , 1994 .

[13]  Erry,et al.  Idealized Adaptive Observation Strategies for Improving Numerical Weather Prediction , 2022 .

[14]  Florence Rabier,et al.  Impact study of the 2003 North Atlantic THORPEX Regional Campaign , 2006 .

[15]  Istvan Szunyogh,et al.  Propagation of the effect of targeted observations: The 2000 Winter Storm Reconnaissance program , 2002 .

[16]  E. Kalnay,et al.  Ensemble Forecasting at NCEP and the Breeding Method , 1997 .

[17]  Anna Trevisan,et al.  Periodic Orbits, Lyapunov Vectors, and Singular Vectors in the Lorenz System , 1998 .

[18]  Michael Ghil,et al.  Advances in Sequential Estimation for Atmospheric and Oceanic Flows , 1997 .

[19]  T. Hamill,et al.  Using Improved Background-Error Covariances from an Ensemble Kalman Filter for Adaptive Observations , 2002 .

[20]  John Derber,et al.  The National Meteorological Center's spectral-statistical interpolation analysis system , 1992 .

[21]  T. Hamill,et al.  Leading Lyapunov Vectors of a Turbulent Baroclinic Jet in a Quasigeostrophic Model , 2003 .

[22]  V. I. Oseledec.  A multiplicative ergodic theorem: Lyapunov characteristic num-bers for dynamical systems , 1968 .

[23]  G. Benettin,et al.  Lyapunov Characteristic Exponents for smooth dynamical systems and for hamiltonian systems; a method for computing all of them. Part 1: Theory , 1980 .

[24]  T. Hamill,et al.  A Hybrid Ensemble Kalman Filter-3D Variational Analysis Scheme , 2000 .

[25]  Anna Trevisan,et al.  Assimilation of Standard and Targeted Observations within the Unstable Subspace of the Observation–Analysis–Forecast Cycle System , 2004 .

[26]  Istvan Szunyogh,et al.  Use of the breeding technique to estimate the structure of the analysis "errors of the day" , 2003 .

[27]  R. Daley.  Atmospheric Data Analysis , 1991 .

[28]  S. Vannitsem.  Intrinsic Error Growth in a Large-Domain Eta Regional Model , 2003 .

[29]  T. Hamill,et al.  Analysis-Error Statistics of a Quasigeostrophic Model Using Three-Dimensional Variational Assimilation , 2002 .

[30]  Jian-Wen Bao,et al.  A Case Study of Cyclogenesis Using a Model Hierarchy , 1996 .