Variable-resolution Model Research Articles

Improvement of the Spectral Representation of the Earth Topography with a Variational Method

Abstract The orography representation in spectral models has always led to problems. These problems become critical in high-resolution models, like the variable-resolution spectral model used at Meteo-France, because they interact with the physical fields. The author describes a variational process to compute a spectral approximation of a gridpoint field. The method is used to improve the representation of the earth topography, and it is compared to a simple spectral filter. The author presents first, in the variable-resolution model, some unsuccessful attempts to show that it is not easy to find the more relevant cost function and then describes the best results obtained. In the variable-resolution case, Gibbs waves are eliminated from the high-resolution area. In the constant-resolution model, Gibbs waves are eliminated from all of the flat areas. In the two cases, the improvement of the orography representation is better with the variational process than with the spectral fitter.

An introduction to variable-resolution modeling

It is commonly necessary in analysis and other activities involving models to work at two or more levels of resolution. Resolution is a relative concept, but at any given level one may think of increasing resolution (e.g., to gain greater insight about phenomenology) or decreasing resolution (e.g., to produce something more comprehensible and more appropriate for policy analysis or operational decision support). Sometimes one can calibrate lower-resolution models with higher-resolution models and, to some extent, vice versa. Ideally, models (or integrated model families) would be built from the outset with variable-resolution capability. Often, however, we find ourselves having to do cross-resolution work by linking existing models that were not designed to be connected. Although there are software techniques for connecting dissimilar models, these techniques do not guarantee that it is substantively meaningful to do so. Similarly, while many workers have found off-line methods for tuning one model of an alleged family to be at least somewhat consistent with another model of the family, the consistency is sometimes more apparent than real. To put it differently, taking existing models with varied resolutions and declaring them to constitute a hierarchical family is sometimes quite misleading because the models are not integrated nor can they be integrated readily. Further, even when means for relating the models sensibly have been developed (either off-line methods or model-connection methods), doing so may involve complex, tedious, error-prone, and expensive calibration efforts. This article describes building models with variable-resolution capability. It also describes generic substantive challenges in connecting models developed independently, and recommends that such model-connection activities be guided by design work to identify how the models would have been developed in the first place if their subsequent integration had been a goal. This approach can make it possible to connect the models usefully and comprehensively with one set of adaptations rather than a series of incremental patches. In other cases it may convince users to commission the building of a new variable-resolution model by demonstrating that the existing models will never work together well. The article also describes a particular design method called integrated hierarchical variable-resolution modeling (IHVR). which is very helpful when it is feasible. It greatly clarifies relationships among levels of resolutions. © 1995 John Wiley & Sons, Inc.

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

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.