Michael S. Fox-Rabinovitz

Consistent Vertical and Horizontal Resolution

Abstract Simple physical relations (namely, the Rossby ratio between vertical and horizontal scales in quasi-geostrophic flow and the dispersion relation for internal gravity waves) are used to estimate the vertical resolution consistent with a given horizontal resolution. Using these relations we find that virtually all large scale models and observing systems have inadequate vertical resolutions In models, the excess horizontal resolution can lead to increased model “noise” rather than improved accuracy. In observing systems, the finer horizontal scales can be severely misrepresented.

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.

New approach to calculation of atmospheric model physics: accurate and fast neural network emulation of longwave radiation in a climate model

Abstract A new approach based on a synergetic combination of statistical/machine learning and deterministic modeling within atmospheric models is presented. The approach uses neural networks as a statistical or machine learning technique for an accurate and fast emulation or statistical approximation of model physics parameterizations. It is applied to development of an accurate and fast approximation of an atmospheric longwave radiation parameterization for the NCAR Community Atmospheric Model, which is the most time consuming component of model physics. The developed neural network emulation is two orders of magnitude, 50–80 times, faster than the original parameterization. A comparison of the parallel 10-yr climate simulations performed with the original parameterization and its neural network emulations confirmed that these simulations produce almost identical results. The obtained results show the conceptual and practical possibility of an efficient synergetic combination of deterministic and statist...

Multiscale Diagnosis of the North American Monsoon System Using a Variable-Resolution GCM

Abstract The onset and evolution of the North American monsoon system during the summer of 1993 were examined from regional to large scales using the National Aeronautics and Space Administration (NASA) Goddard Earth Observing System (GEOS) stretched-grid GCM. The models grid spacing for the dynamical core ranges from 0.4° × 0.5° in latitude–longitude over the United States to about 2.5° × 3.5° at the antipode, and the physical package is solved on an intermediate 1° × 1° uniform grid. A diagnostic analysis of the monsoons onset reveals the development of a positive potential temperature (θ) anomaly at the surface that favors a lower-level cyclonic circulation, while a negative potential vorticity (PV) anomaly below the tropopause induces an upper-level anticyclonic circulation. Ignoring diabatic effects, this pattern is consistent with the superimposition of idealized PV and θ anomalies as previously discussed in the literature. The inclusion of the smaller-scale features of the core monsoon in the mod...

A Variable-Resolution Stretched-Grid General Circulation Model: Regional Climate Simulation

Abstract The development of and results obtained with a variable-resolution stretched-grid GCM for the regional climate simulation mode are presented. A global variable-resolution stretched grid used in the study has enhanced horizontal resolution over the United States as the area of interest. The stretched-grid approach is an ideal tool for representing regional- to global-scale interactions. It is an alternative to the widely used nested-grid approach introduced over a decade ago as a pioneering step in regional climate modeling. The major results of the study are presented for the successful stretched-grid GCM simulation of the anomalous climate event of the 1988 U.S. summer drought. The straightforward (with no updates) 2-month simulation is performed with 60-km regional resolution. The major drought fields, patterns, and characteristics, such as the time-averaged 500-hPa heights, precipitation, and the low-level jet over the drought area, appear to be close to the verifying analyses for the stretche...

A Uniform- and Variable-Resolution Stretched-Grid GCM Dynamical Core with Realistic Orography

The impact of introducing a realistic orographic forcing into a uniform- and variable-resolution stretched-grid GCM dynamical core is investigated by performing long-term and medium-range integrations. Comparisons are made between various stretched-grid simulations and a control that consists of a uniform grid integration at high resolution. These comparisons include those where the orography has and has not been filtered to eliminate small-scale noise. Results from the region of interest with highest resolution show that 1) the stretched-grid GCM provides an efficient downscaling over the area of interest, that is, it properly simulates not only largescale but also mesoscale features; and 2) the introduction of orography has a greater impact than the effect of stretching. Results presented here suggest that dynamical core integrations with both uniform and stretched grids should consider orographic forcing as an integral part of the model dynamics.

Computational Dispersion Properties of Horizontal Staggered Grids for Atmospheric and Ocean Models

Abstract The computational dispersion properties of horizontally and time-horizontally staggered grids using corresponding centered-difference schemes for approximation of the Adjustment, or gravity wave equation, are analyzed in terms of their group velocity characteristics. Results are obtained for atmospheric and oceanic models, the latter being characterized by a much smaller Rossby radius of deformation. Three best time-horizontally staggered grids have practically the same advantageous computational dispersion properties as the Arakawa C grid for both atmospheric and oceanic models—namely, the time-staggered D (or Eliassen) and time-staggered C (only with a semi-implicit scheme) grids—and to a certain extent the Lilly grid. Both, the Arakawa B and the time-staggered A grids for atmospheric and oceanic models, along with the Arakawa E and the time-staggered E grids only for atmospheric models (although having worse dispersion properties) also may be used as additional practical options. For all grids...

Computational dispersion properties of 3D staggered grids for a nonhydrostatic anelastic system

Abstract Computational dispersion properties of centered-difference schemes, in terms of frequency and group velocity components, are examined for an anelastic system using a variety of candidates for practically meaningful staggered 3D grids. The numerical analysis is done for dry nonhydrostatic inviscid gravity–inertia wave equations in a Boussinesq system, linearized about a statically stable resting base state with and without Coriolis force. The most advantageous 3D grids are obtained by combining the best horizontal grids, such as the Eliassen and Arakawa C grids, with the best vertical grids, such as the Lorenz and Charney–Phillips grids, and their time-staggemd versions. These best staggered 3D grids provide twice the effective spatial resolution of the regular (unstaggered) 3D grid. The obtained results provide practical guidance for the optimal choice of a grid for anelasfic mesoscale atmospheric models.

Computational Dispersion Properties of Vertically Staggered Grids for Atmospheric Models

Abstract The computational dispersion properties of vertically and time-vertically staggered grids, using corresponding centered-difference schemes for approximation of a linear baroclinic primitive equation system, are analyzed in terms of frequency and group velocity characteristics. The vertical scale ranges with group velocities of the wrong sign are pointed out. It is shown that among all possible vertical grids applicable to primitive equation atmospheric models the best vertical grids have computational dispersion properties corresponding to a regular (equidistant, unstaggered) grid with twice the vertical resolution. These best vertical grids are 1) two well-known vertically staggered grids, namely, the widely used Lorenz grid and the Charney-Phillips grid; 2) two other vertically staggered grids carrying both horizontal and vertical velocity components at the same levels; and 3) the new time-staggered versions of all the aforementioned grids, and the time-staggered regular vertical grid, if used ...

Decadal Climate Simulations Using Accurate and Fast Neural Network Emulation of Full, Longwave and Shortwave, Radiation*

An approach to calculating model physics using neural network emulations, previously proposed and developed by the authors, has been implemented in this study for both longwave and shortwave radiation parameterizations, or to the full model radiation, the most time-consuming component of model physics. The developed highly accurate neural network emulations of the NCAR Community Atmospheric Model (CAM) longwave and shortwave radiation parameterizations are 150 and 20 times as fast as the original/ control longwave and shortwave radiation parameterizations, respectively. The full neural network model radiation was used for a decadal climate model simulation with the NCAR CAM. A detailed comparison of parallel decadal climate simulations performed with the original NCAR model radiation parameterizations and with their neural network emulations is presented. Almost identical results have been obtained for the parallel decadal simulations. This opens the opportunity of using efficient neural network emulations for the full model radiation for decadal and longer climate simulations as well as for weather prediction.