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Timothy F. Hogan and Thomas E. Rosmond

Abstract

We present a description of the development of the spectral forecast components of the Navy Operational Global Atmospheric Prediction System (NOGAPS). The original system, called 3.0, was introduced in January 1988. New versions were introduced in March 1989 (3.1) and August 1989 (3.2). A brief description of each version of the forecast model is given. Each physical parameterization is also described. We discuss the large changes in 3.1 and the motivation behind the changes. Statistical results from forecast comparison tests are discussed. Figures showing the total monthly forecast performance in the Northern Hemisphere and the Southern Hemisphere are also given. A brief discussion is presented of computational details, running times, and memory requirements of the forecast model.

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Francis X. Giraldo and Thomas E. Rosmond

Abstract

A new dynamical core for numerical weather prediction (NWP) based on the spectral element method is presented. This paper represents a departure from previously published work on solving the atmospheric primitive equations in that the horizontal operators are all written, discretized, and solved in 3D Cartesian space. The advantages of using Cartesian space are that the pole singularity that plagues the equations in spherical coordinates disappears; any grid can be used, including latitude–longitude, icosahedral, hexahedral, and adaptive unstructured grids; and the conversion to a semi-Lagrangian formulation is easily achieved. The main advantage of using the spectral element method is that the horizontal operators can be approximated by local high-order elements while scaling efficiently on distributed-memory computers. In order to validate the 3D global atmospheric spectral element model, results are presented for seven test cases: three barotropic tests that confirm the exponential accuracy of the horizontal operators and four baroclinic test cases that validate the full 3D primitive hydrostatic equations. These four baroclinic test cases are the Rossby–Haurwitz wavenumber 4, the Held–Suarez test, and the Jablonowski–Williamson balanced initial state and baroclinic instability tests. Comparisons with four operational NWP and climate models demonstrate that the spectral element model is at least as accurate as spectral transform models while scaling linearly on distributed-memory computers.

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Thomas E. Rosmond and Frank D. Faulkner

Abstract

Poisson's and Helmholtz's equations are perhaps the most frequently occurring and important types of partial differential equations encountered in the atmospheric sciences. This paper presents a very fast, accurate technique for finding the numerical solution known as cyclic reduction and factoralization. This method has not heretofore been brought to the attention of the meteorological community at large.

This direct method essentially reduces the solution of a separable two-dimensional elliptic equation on an N×M grid to N log2 N tri-diagonal systems of order M which are solved by Gaussian elimination. In its simplest form, as described here, the cyclic reduction procedure can be applied if N is 2n−1, 2n2n=1, depending on boundary conditions. However, extensions of the method have been developed which have removed this restrictive limitation. The method is also easily generalized to higher dimensional problems.

The mathematical development of the cyclic reduction method is presented here in complete detail, along with the modifications necessary to make it computationally stable. The results of two numerical experiments comparing optimized SOR versus the direct method for the solution of Poisson=s equation are presented. For Dirichlet boundary conditions the direct method is up to 50 times faster than successive over-relaxation (SOR) for N=M=128. For Neumann boundary conditions, the direct method has even a greater advantage over SOR. The margin of superiority increases as the size of the array increases.

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Ronald M. Errico, Thomas E. Rosmond, and James S. Goerss

Abstract

We have compared analysis increments produced by the optimal interpolation scheme and initialization increments produced by the nonlinear normal-mode initialization scheme in the U.S. Navy Operational Global Atmospheric Prediction System. Results indicate that analysis increments of height in the tropics are partially removed by the subsequent initialization. Similar results are obtained for the field of horizontal velocity divergence within the extratropics as well as tropics. Consequently, for some fields in some areas, the initialized analyses are primarily defined by the model-produced background field, irrespective of the availability of observations or model error estimates.

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David D. Kuhl, Thomas E. Rosmond, Craig H. Bishop, Justin McLay, and Nancy L. Baker

Abstract

The effect on weather forecast performance of incorporating ensemble covariances into the initial covariance model of the four-dimensional variational data assimilation (4D-Var) Naval Research Laboratory Atmospheric Variational Data Assimilation System-Accelerated Representer (NAVDAS-AR) is investigated. This NAVDAS-AR-hybrid scheme linearly combines the static NAVDAS-AR initial background error covariance with a covariance derived from an 80-member flow-dependent ensemble. The ensemble members are generated using the ensemble transform technique with a (three-dimensional variational data assimilation) 3D-Var-based estimate of analysis error variance. The ensemble covariances are localized using an efficient algorithm enabled via a separable formulation of the localization matrix. The authors describe the development and testing of this scheme, which allows for assimilation experiments using differing linear combinations of the static and flow-dependent background error covariances. The tests are performed for two months of summer and two months of winter using operational model resolution and the operational observational dataset, which is dominated by satellite observations. Results show that the hybrid mode data assimilation scheme significantly reduces the forecast error across a wide range of variables and regions. The improvements were particularly pronounced for tropical winds. The verification against radiosondes showed a greater than 0.5% reduction in vector wind RMS differences in areas of statistical significance. The verification against self-analysis showed a greater than 1% reduction from verifying against analyses between 2- and 5-day lead time at all eight vertical levels examined in areas of statistical significance. Using the Navy's summary of verification results, the Navy Operational Global Atmospheric Prediction System (NOGAPS) scorecard, the improvements resulted in a score (+1) that justifies a major system upgrade.

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