A Finite-Difference GCM Dynamical Core with a Variable-Resolution Stretched Grid

A finite-difference atmospheric model dynamics, or dynamical core using variable resolution, or stretched grids, is developed and used for regional‐global medium-term and long-term integrations. The goal of the study is to verify whether using a variable-resolution dynamical core allows us to represent adequately the regional scales over the area of interest (and its vicinity). In other words, it is shown that a significant downscaling is taking place over the area of interest, due to better-resolved regional fields and boundary forcings. It is true not only for short-term integrations, but also for medium-term and, most importantly, long-term integrations. Numerical experiments are performed with a stretched grid version of the dynamical core of the Goddard Earth Observing System (GEOS) general circulation model (GCM). The dynamical core includes the discrete (finite-difference) model dynamics and a Newtonian-type rhs zonal forcing, which is symmetric for both hemispheres about the equator. A flexible, portable global stretched grid design allows one to allocate the area of interest with uniform fine-horizontal (latitude by longitude) resolution over any part of the globe, such as the U.S. territory used in these experiments. Outside the region, grid intervals increase, or stretch, with latitude and longitude. The grids with moderate to large total (global) stretching factors or ratios of maximum to minimum grid intervals on the sphere are considered. Dynamical core versions with the total stretching factors ranging from 4 to 32 are used. The model numerical scheme, with all its desirable conservation and other properties, is kept unchanged when using stretched grids. Two model basic horizontal filtering techniques, the polar or high-latitude Fourier filter and the Shapiro filter, are applied to stretched grid fields. Two filtering approaches based on the projection of a stretched grid onto a uniform one are tested. One of them does not provide the necessary computational noise control globally. Another approach provides a workable monotonic global solution. The latter is used within the developed stretched grid version of the GEOS GCM dynamical core that can be run in both the middle-range and long-term modes. This filtering approach allows one to use even large stretching factors. The successful experiments were performed with the dynamical core for several stretched grid versions with moderate to large total stretching factors ranging from 4 to 32. For these versions, the fine resolutions (in degrees) used over the area of interest are 2 3 2.5, 1 3 1.25, 0.5 3 0.625, and 0.25 3 0.3125. Outside the area of interest, grid intervals are stretching to 4 3 5o r 8 310. The medium-range 10-day integrations with summer climate initial conditions show a pronounced similarity of synoptic patterns over the area of interest and its vicinity when using a stretched grid or a control global uniform fine-resolution grid. For a long-term benchmark integration performed with the first aforementioned grid, the annual mean circulation characteristics obtained with the stretched grid dynamical core appeared to be profoundly similar to those of the control run with the global uniform fine-resolution grid over the area of interest, or the United States. The similarity is also evident over the best resolved within the used stretched grid northwestern quadrant, whereas it does not take place over the least-resolved southeastern quadrant. In the better-resolved Northern Hemisphere, the jet and Hadley cell are close to those of the control run, which does not take place for the Southern Hemisphere with coarser variable resolution. The stretched grid dynamical core integrations have shown no negative computational effects accumulating in time. The major result of the study is that a stretched grid approach allows one to take advantage of enhanced resolution over the region of interest. It provides a better representation of regional fields for both mediumterm and long-term integrations.