High resolution models of the planetary boundary layer
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...-P5 T + M2 D = AT, (2.5.2.3) at ape + N 1 .D = O,and (2.5.2.4) $ = Mi * T. (2.5.2.5) where the right hand sides change slowly over the time scale of the Rossby-waves. Matrices M 1 , M2, and vector N1 are independent of x, y, and t. Notice the similarity to the nonhydrostatic splitting method (equations 2.5.1-2.5.4). However, rather then integrating the "fast" terms on a small time-step directly, the method described below only computes correction terms to the equations, making this process extremely efficient. To illustrate this, we follow Madala (1981). From the governing equations he derives equations for the mass divergence D and the generalized geopotential A....
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...A Description of the Fifth-Generation Penn State/NCAR Mesoscale Model (MM5) Georg A. Grell1 Jimy Dudhia2 David R. Stauffer3 MESOSCALE AND MICROSCALE METEOROLOGY DIVISION 2NATIONAL CENTER FOR ATMOSPHERIC RESEARCH BOULDER, COLORADO 1FORECAST SYSTEMS LABORATORY, NATIONAL OCEANIC AND ATMOSPHERIC ADMINISTRATION BOULDER, COLORADO 3DEPARTMENT OF METEOROLOGY, THE PENNSYLVANIA STATE UNIVERSITY UNIVERSITY PARK, PENNSYLVANIA...
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...This technical report describes the fifth generation Penn State/NCAR Mesoscale Model, or MM5. It is intended to provide scientific and technical documentation of the model for users. Source code documentation is available as a separate Technical Note (NCAR/TN-392) by Haagenson et al. (1994). Comments and suggestions for improvements or corrections, are welcome and should be sent to the authors....
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...A complaint about traditional polynomial-fitting methods used for interpolating scalar fields defined on a discrete mesh is that they often lead to spurious numerical oscillations in regions of steep gradients of the interpolated variables. In order to suppress computational noise, which is characteristic of quadratic and higher-order interpolation schemes, one often implements a smoothing procedure or increased diffusion. These, however, introduce excessive numerical diffusion that smears out sharp features of interpolated fields. A more advanced approach invokes the so-called shape-preserving interpolation, which incorporates appropriate constraints on the derivative estimates used in the interpolation schemes (see Rasch and Williamson (1990) for a review). In MM5 we consider as an alternate approach a class of schemes derived from monotone advection algorithms (Smolarkiewicz and Grell, 1992). Smolarkiewicz and Grell (1992) show that the interpolation problem becomes identical to the advection problem, when the distance vector is replaced by the velocity vector (see also the end of this section). Here we will describe the implementation of the advection algorithm used in MM5. The interested reader is referred to Smolarkiewicz and Grell (1992) for a detailed derivation of the "advection-interpolation" equivalence....
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...Additionally, the divergence damping technique of Skamarock and Klemp (1992) is used to control horizontally propagating sound waves....
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Cites methods from "High resolution models of the plane..."
...This simpler approach employs the ‘‘slab model’’ developed by Blackadar (1976, 1979) and further tested by Zhang and Anthes (1982)....
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