Variable Resolution and Robustness

Abstract

Within the context of a semi-Lagrangian shallow-water model, the dependence of forecast accuracy on the distribution of variable resolution and its robustness with respect to rapid variations in resolution is examined. This study also touches on the broader problem of designing a variable-resolution nested grid for regional modeling. It is demonstrated that the widely held belief that variable resolution induces severe noise problems at resolution interfaces?even for simple models?is not of universal applicability. In particular, no evidence of noise is found in the forecasts even when the resolution is changed abruptly by a factor of 3.5 across an internal boundary, thereby demonstrating the robustness of this particular variable-resolution technique. This result is achieved without any numerical smoothing technique other than that implicitly associated with the interpolation of a semi-Lagrangian scheme. The forecast produced on a uniform high-resolution mesh can be accurately reproduced for a limited time period on a subdomain at a fraction of the cost, by using a variable mesh where the resolution is gradually degraded away from this subdomain. The growth of the error variance when using such a mesh is an order of magnitude smaller than for one having the same number of degrees of freedom, except where the resolution changes abruptly at the boundary of the subdomain. It is concluded that variable resolution, using a smoothly varying mesh coupled with a semi-implicit, semi-Lagrangian integration scheme is an attractive approach to regional modeling.