Numerical Methods in Atmospheric Models

The astonishing development of computer technology since the mid-20th century has been accompanied by a corresponding proliferation in the numerical methods that have been developed to improve the simulation of atmospheric flows. This article reviews some of the numerical developments concern the ongoing improvements of weather forecasting and climate simulation models. Early computers were single-processor machines with severely limited memory capacity and computational speed, requiring simplified representations of the atmospheric equations and low resolution. As the hardware evolved and memory and speed increased, it became feasible to accommodate more complete representations of the dynamic and physical atmospheric processes. These more faithful representations of the so-called primitive equations included dynamic modes that are not necessarily of meteorological significance, which in turn led to additional computational challenges. Understanding which problems required attention and how they should be addressed was not a straightforward and unique process, and it resulted in the variety of approaches that are summarized in this article. At about the turn of the century, the most dramatic developments in hardware were the inauguration of the era of massively parallel computers, together with the vast increase in the amount of rapidly accessible memory that the new architectures provided. These advances and opportunities have demanded a thorough reassessment of the numerical methods that are most successfully adapted to this new computational environment. This article combines a survey of the important historical landmarks together with a somewhat speculative review of methods that, at the time of writing, seem to hold out the promise of further advancing the art and science of atmospheric numerical modeling.

A Nonhydrostatic Multiscale Model on the Uniform Jacobian Cubed Sphere

The rapid expansion of contemporary computers is expected to enable operational integrations of global models of the atmosphere at resolutions close to 1 km, using tens of thousands of processors in the foreseeable future. Consequently, the algorithmic approach to global modeling of the atmosphere will need to change in order to better adjust to the new computing environment. One simple and convenient solution is to use low-order finite-differencing models, which generally require only local exchange of messages between processing elements, and thus are more compatible with the new computing environment. These models have already been tested with physics and are well established at high resolutions over regional domains. A global nonhydrostatic model, the Nonhydrostatic Multiscale Model on the B grid (NMMB), developed at the Environmental Modeling Center of the National Centers for Environmental Prediction during the first decade of this century is one such model. A drawback of the original version of global NMMB is that it is discretized on the standard longitude–latitude grid and requires application of Fourier polar filtering, which is relatively inefficient on massively parallel computers. This paper describes a reformulation of the NMMB on the grid geometry of a novel cubed sphere featuring a uniform Jacobian of the horizontal mapping, which provides a uniform resolution close to that of the equiangular gnomonic cubed sphere, but with a smooth transition of coordinates across the edges. The modeling approach and encountered challenges are discussed and several results are shown that demonstrate the viability of the approach.