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  • Author or Editor: Roger W. Daley x
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Andrew N. Staniforth
and
Roger W. Daley

Abstract

A baroclinic primitive equations model is formulated using a variable resolution finite-element discretization in all three space dimensions. The horizontal domain over which the model is integrated is a rectangle on a polar stereographic projection which approximately covers the Northern Hemisphere. A wall boundary condition is imposed at this rectangular boundary giving rise to a well-posed initial boundary value problem. The mesh is specified to be of Cartesian product form with arbitrary non-uniform spacing. By choosing the mesh to be uniformly high over an area of interest and degrading smoothly away from this area, it is possible to use the model to produce a high-resolution local forecast for a limited time period. This choice of mesh avoids the noise problems of a so-called nested grid. A semi-implicit time discretization is used for efficiency. Some results for forecast periods of 24 and 48 h are also given to demonstrate its viability in an operational context.

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Andrew N. Staniforth
and
Roger W. Daley

Abstract

A finite-element formulation for the vertical structure of primitive equation models has been developed. The finite-element method is a variant of the Galerkin procedure in which the dependent variables are expanded in a finite, set of basis functions and then the truncation error is orthogonalized to each of the basis functions. In the present case, the basis functions are Châpeau functions in sigma, the vertical coordinate. The procedure has been designed for use with a semi-implicit time discretization algorithm.

Although this vertical representation has been developed for ultimate implementation in a three-dimensional finite-element model, it has been first tested in a spherical harmonic, baroclinic, primitive equations model. Short-range forecasts made with this model are very encouraging.

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David L. Williamson
,
Roger Daley
, and
Thomas W. Schlatter

Abstract

The relative importance of various sources of imbalance in analyses produced by multivariate optimal interpolation is determined. The experimental design uses the shallow-water equations and nonlinear normal mode initialization to define the correct balanced reference atmospheric state and thus restricts this study to horizontal aspects of the problem. The experiments show that the analysis procedure itself introduces systematic imbalances in lows due to the use of the geostrophic relationship to determine the height–wind covariances from the height–height covariances. Random observational errors introduce imbalances but not out of proportion to the observational errors themselves. Data-void areas are responsible for a region of imbalance with width approximately equal to the maximum radius of influence of the analysis on the data-void side of the data-void/data-rich boundary. Model errors in the form of equivalent depth errors do not introduce large imbalances.

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