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A Variable-Resolution Semi-Lagrangian Finite-Element Global Model of the Shallow-Water Equations

Jean CôtéRecherche en prérision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Michel RochRecherche en prérision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Andrew StaniforthRecherche en prérision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Luc FillionRecherche en prérision numérique, Service de l'environnement atmosphérique, Dorval, Quebec, Canada

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Abstract

To meet the needs of short- and medium-range operational forecasting, the authors propose a unified strategy based on the use of a global variable-resolution model, run in two different configurations. These are as follows: (i) a variable-resolution “regional” configuration (with resolution focused over an area of interest) for detailed forecasts to 2 days, and (ii) a uniform-resolution “medium-range” one, for forecasts to 7 days or longer. This otters significant economy in an operational environment, since there is only one model—instead of the usual two—to maintain, develop, and optimize. It also provides an efficient and conceptually simple solution to the nesting problem for regional forecasting: the planetary waves are adequately resolved around a high-resolution subdomain (which resolves mesoscale disturbances), there are no artificial lateral boundaries with their attendant problems, and there is no abrupt change of resolution across an internal boundary since the resolution varies smoothly away from the area of interest.

To demonstrate the potential of this strategy, we have developed a shallow-water prototype using highly efficient numerical techniques, such as a two time-level semi-implicit semi-Lagrangian integration scheme. This model is a generalization of that of Côté and Staniforth (1990) to variable resolution on an arbitrarily rotated latitude-longitude mesh. Sample integrations indicate that it is possible to almost exactly reproduce a 2-day forecast on an 80° × 60° uniform-resolution (0.5°) subdomain (covering North America) of the variable-resolution mesh, for one-seventh the cost (both computational and storage) of running the model with uniform resolution (0.5°) everywhere, and for a cost about two orders of magnitude lower than running a conventional uniform-resolution Eulerian spectral model. For this variable-resolution mesh, fully 70% of the points in each direction are on the uniform-resolution area of interest. Thus, the overhead associated with using a model of global extent for short-range forecasting is indeed small, and is a small price to pay to avoid the lateral boundary condition problems of regional models.

Abstract

To meet the needs of short- and medium-range operational forecasting, the authors propose a unified strategy based on the use of a global variable-resolution model, run in two different configurations. These are as follows: (i) a variable-resolution “regional” configuration (with resolution focused over an area of interest) for detailed forecasts to 2 days, and (ii) a uniform-resolution “medium-range” one, for forecasts to 7 days or longer. This otters significant economy in an operational environment, since there is only one model—instead of the usual two—to maintain, develop, and optimize. It also provides an efficient and conceptually simple solution to the nesting problem for regional forecasting: the planetary waves are adequately resolved around a high-resolution subdomain (which resolves mesoscale disturbances), there are no artificial lateral boundaries with their attendant problems, and there is no abrupt change of resolution across an internal boundary since the resolution varies smoothly away from the area of interest.

To demonstrate the potential of this strategy, we have developed a shallow-water prototype using highly efficient numerical techniques, such as a two time-level semi-implicit semi-Lagrangian integration scheme. This model is a generalization of that of Côté and Staniforth (1990) to variable resolution on an arbitrarily rotated latitude-longitude mesh. Sample integrations indicate that it is possible to almost exactly reproduce a 2-day forecast on an 80° × 60° uniform-resolution (0.5°) subdomain (covering North America) of the variable-resolution mesh, for one-seventh the cost (both computational and storage) of running the model with uniform resolution (0.5°) everywhere, and for a cost about two orders of magnitude lower than running a conventional uniform-resolution Eulerian spectral model. For this variable-resolution mesh, fully 70% of the points in each direction are on the uniform-resolution area of interest. Thus, the overhead associated with using a model of global extent for short-range forecasting is indeed small, and is a small price to pay to avoid the lateral boundary condition problems of regional models.

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