Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances

By R. Purser, Wan Wu, David F. Parrish, N. Roberts. 2003

360 citations recorded by the source corpus.

Subfields: Atmospheric Science, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/233a65f6bd451a1491dcc56f46f937764aba5676

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atmospheric Science

1. R. Bannister
2. Xuguang Wang
3. Juanzhen Sun
4. C. Snyder
5. Ming Xue
6. J. Whitaker
7. Q. Xiao
8. Thomas M. Hamill

In Environmental Engineering

1. Xuguang Wang
2. R. Bannister
3. Thomas M. Hamill
4. J. Whitaker
5. C. Snyder
6. Juanzhen Sun
7. Q. Xiao
8. Ming Xue

Citations in the corpus

• Multiple-Radar Data Assimilation and Short-Range Quantitative Precipitation Forecasting of a Squall Line Observed during IHOP_2002 (2007, methodology): “ments of model variables, a vertical transformation via an empirical orthogonal function (EOF) decomposition, and a horizontal transformation by recursive filters (Hayden and Purser 1995; Purser et al. 2003), respectively.”
• divand-1.0: n -dimensional variational data analysis for ocean observations (2013, methodology): “Another commonly used technique is based on a recursive filter (Lorenc, 1992; Hayden, 1995; Purser et al., 2003a, b; Martin et al., 2007; Dobricic and Pinardi, 2008).”
• Feasibility of a 100-Year Reanalysis Using Only Surface Pressure Data (2006, background): “One can speculate that an advanced 3DVAR with reformulated, more complex background error covariances that vary spatially (e.g., Wu et al. 2002; Purser et al. 2003) or with the f low (e.”
• A Description of the Advanced Research WRF Model Version 4 (2019, methodology): “Recent advances permit the use of flow-dependent forecast error covariances in 3D/4D-Var through, for example, grid transformations (Desroziers, 1997), anisotropic recursive filters (Wu et al., 2002; Purser et al., 2003), or observation-space formulations of the variational problem (Daley and Barker”
• A Three-Dimensional Variational Data Assimilation System for MM5: Implementation and Initial Results (2004, methodology): “In 4DVAR, flow-dependent structure functions are implicit through the use of the forecast model as part of the analysis solution [although a climatological estimate of background error is still applied in the calculation of J b (Rabier et al. 2000)].”
• B‐preconditioned minimization algorithms for variational data assimilation with the dual formulation (2014, background): “This situation can arise with general covariance models constructed from spectral or grid-point filters (Fisher, 2003; Purser et al., 2003; Weaver and Mirouze, 2013) and with hybrid ensemble-variational B formulations (Buehner, 2005; Wang et al., 2007, 2008).”
• A Three-Dimensional Variational Data Analysis Method with Recursive Filter for Doppler Radars (2004, methodology): “In section 3, the basic capabilities of the recursive filter are tested by placing a single observation in the center of model domain.”
• Air-Sea Enthalpy and Momentum Exchange at Major Hurricane Wind Speeds Observed during CBLAST (2012, neutral): “For the current study, the background error correlations were assumed to be Gaussian and isotropic, and were calculated using an efficient recursive filter operator that replicates the effects of this correlation (Purser et al. 2003).”
• Incorporating Ensemble Covariance in the Gridpoint Statistical Interpolation Variational Minimization: A Mathematical Framework (2010, methodology): “In the original GSI, B1 is approximated by the recursive filter transform (Hayden and Purser 1995; Wu et al. 2002; Purser et al. 2003a,b).”
• Linear Filtering of Sample Covariances for Ensemble-Based Data Assimilation. Part I: Optimality Criteria and Application to Variance Filtering and Covariance Localization (2015, background): “…operators are often climatological, even if some flow dependency can be added through nonlinear balance operators and specific representations of the spatial transforms to allow a certain degree of heterogeneity and anisotropy (Fisher 2003; Purser et al. 2003; Deckmyn and Berre 2005; Michel 2013).”
• On the Theoretical Equivalence of Differently Proposed Ensemble 3DVAR Hybrid Analysis Schemes (2007, methodology): “Techniques are also being developed to include some spatial inhomogeneity and anisotropy in the standard covariance models used in 3DVAR (e.g., Desroziers 1997; Riishøjgaard 1998; Purser et al. 2003; Wu et al. 2002).”
• An extended specification of flow‐dependent background error variances in the Météo‐France global 4D‐Var system (2011, background): “Other ideas are also described in works by Purser et al. (2003), Lindskog et al. (2006) and Miyoshi and Kadowaki (2008), for instance.”
• An oceanographic three-dimensional variational data assimilation scheme (2008, background): “To deal with the variable horizontal resolution it is necessary to calculate coefficients of the recursive filter for each model point on the horizontal grid and it is necessary to rescale the filtered field by a spatially varying normalization factor (Weaver and Courtier, 2001; Purser et al., 2003)”
• A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics (2008, background): “The operator acting upon δf (r) in (51) is an approximation of B−11 and can be written as a Cholesky decomposition (Purser et al., 2003a), which comprises a lower triangular matrix, L, and an upper triangular matrix, U where U = LT, giving B−11 = UTU.”