Correlation modelling on the sphere using a generalized diffusion equation

By A. T. Weaver, P. Courtier. 2001

449 citations recorded by the source corpus.

Subfields: Atmospheric Science, Global and Planetary Change, Oceanography

View Paper: https://www.semanticscholar.org/paper/12658bc6e9a3980004dede841265422561693ec0

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In Atmospheric Science

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Citations in the corpus

Determination of optimal nudging coefficients (2003, methodology): “Roughly (for more explanation see Weaver and Courtier, 2001) following Derber and Bouttier (1999) we can write, for instance: B = KBuKT where K is a balance operator that relates one state variable to the other (here K uses the geostrophic balance to compute the balanced part of u and v from h) and…”
Three- and Four-Dimensional Variational Assimilation with a General Circulation Model of the Tropical Pacific Ocean. Part I: Formulation, Internal Diagnostics, and Consistency Checks (2003, methodology): “The correlation functions are made anisotropic and varied geographically by introducing a ‘‘diffusion’’ tensor in the Laplacian operator (Weaver and Courtier 2001).”
Application of the Multigrid Data Assimilation Scheme to the China Seas’ Temperature Forecast (2008, background): “Many ocean data assimilation schemes have been substantially developed since the mid-1980s (Derber and Rosati 1989; Behringer et al. 1998; Gaspari and Cohn 1999; Weaver and Courtier 2001).”
The Regional Ocean Modeling System (ROMS) 4-dimensional variational data assimilation systems Part I - System overview and formulation (2011, methodology): “Generalizations of the solution of (17) on a sphere are considered by Weaver and Courtier (2001) who show that L2 2jsd still holds to good approximation.”
Dynamically and Kinematically Consistent Global Ocean Circulation and Ice State Estimates (2013, background): “Little is known about the space–time covariances of these errors, information, which if it were known, could improve the solutions (see Weaver and Courtier, 2001, for a useful direction now being used in representing spatial covariances).”
Ensemble‐derived stationary and flow‐dependent background‐error covariances: Evaluation in a quasi‐operational NWP setting (2005, unknown): “Several approaches for efficiently representing the background-error correlations without these assumptions have been proposed in the literature (e.g. Derber and Rosati 1989; Desroziers 1997; Weaver and Courtier 2001; Wu et al. 2002).”
Incorporating State-Dependent Temperature–Salinity Constraints in the Background Error Covariance of Variational Ocean Data Assimilation (2005, unknown): “These univariate correlations are modeled using a diffusion operator (Weaver and Courtier 2001) and are approximately Gaussian.”
Stochastic parametrization and model uncertainty (2009, background): “A variance spectrum has been chosen that yields a spatial autocorrelation corresponding to the equivalent of a Gaussian on the sphere (Weaver and Courtier, 2001).”
A multivariate balance operator for variational ocean data assimilation (2005, unknown): “The univariate 3D smoothing operator for T is defined as the product of a 1D and 2D anisotropic diffusion operator (Weaver and Courtier 2001).”
Data Assimilation for Numerical Weather Prediction: A Review (2009, methodology): “Navon (1981) used it to enforce conservation of total enstrophy, total energy and total mass in one and two-dimensional shallow water equations models on a rotating place.”
Numerical Aspects of the Application of Recursive Filters to Variational Statistical Analysis. Part II: Spatially Inhomogeneous and Anisotropic General Covariances (2003, background): “…considered consistent alternatives to the direct application of diffusion operators proposed by Derber and Rosati (1989) and recently generalized by Weaver and Courtier (2001). a. Inhomogeneities of grids or filter scales One should not be led to believe that our construction of quasi-Gaussian…”
A coupled data assimilation system for climate reanalysis (2016, methodology): “The spatial univariate correlations between values of the same physical field at different grid points are computed by integrating diffusion equations that give the smoothing effect of the backgrounderror covariance matrix, as well as the length-scales for the univariate correlation operators (Weave”
A review of forecast error covariance statistics in atmospheric variational data assimilation. II: Modelling the forecast error covariance statistics (2008, methodology): “The action of a covariance matrix on a state can be shown to be equivalent to the integration of a carefully constructed diffusion equation over a finite time period using the same state as the initial conditions (Weaver and Courtier, 2001).”
Three-Dimensional Variational Analysis with Spatially Inhomogeneous Covariances (2002, methodology): “Other methods have been tested for inhomogeneous and/or anisotropic covariance, for example, Derber and Rosati (1989), Desrozier (1997), Riishojgaard (1998), Weaver and Courtier (2001) .”
An oceanographic three-dimensional variational data assimilation scheme (2008, background): “…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).”
Introducing independent patterns into the Stochastically Perturbed Parametrization Tendencies (SPPT) scheme (2017, background): “Each spectral coefficient is auto-correlated in space in the form of a Gaussian on the sphere (following Weaver and Courtier, 2001); the time correlations arise via a first-order autoregressive process.”