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An Improved Method for Computing Horizontal Diffusion in a Sigma-Coordinate Model and Its Application to Simulations over Mountainous Topography

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  • 1 Meteorologisches Institut der Universität München, Munich, Germany
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Abstract

A set of modifications is presented to reduce the unphysical impact of horizontal diffusion in numerical models with a terrain-following sigma-coordinate system. At model levels sufficiently far away from the ground, vertical interpolation is used to compute diffusion truly horizontally when the coordinate surfaces are sloping. Close to the ground, where truly horizontal computation of diffusion is not everywhere possible without intersecting the topography, a combination of one-sided truly horizontal diffusion and orography-adjusted diffusion along the sigma surfaces is used for most of the variables. The latter means that the diffusion coefficient is reduced strongly when the grid points involved in the computation of horizontal diffusion are located at greatly different heights. For temperature, one-sided horizontal diffusion is not used because it damps the slope wind circulation in an unphysical way. However, a temperature gradient correction is applied to the terrain-following part of the temperature diffusion. Its purpose is to make diffusion neutral with respect to the current vertical temperature gradient. The modifications have been implemented into the Fifth-Generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Idealized simulations of the valley wind circulation in the Inn Valley of the Alps are performed to test the modifications. In its original state, the model turns out to be unable to reproduce this valley wind system because of errors related to diffusion along the coordinate surfaces. However, the model captures all essential features of the observed valley wind with the modified diffusion scheme. Both the temporal evolution and the vertical structure of the valley wind are consistent with observations. This result suggests that the model's ability to simulate flow over mountainous topography is greatly improved by use of the modified scheme.

Corresponding author address: Günther Zängl, Abteilung für Theoretische Meteorologie, Theresienstraße 37, München D-80333, Germany. Email: guenther@meteo.physik.uni-muenchen.de

Abstract

A set of modifications is presented to reduce the unphysical impact of horizontal diffusion in numerical models with a terrain-following sigma-coordinate system. At model levels sufficiently far away from the ground, vertical interpolation is used to compute diffusion truly horizontally when the coordinate surfaces are sloping. Close to the ground, where truly horizontal computation of diffusion is not everywhere possible without intersecting the topography, a combination of one-sided truly horizontal diffusion and orography-adjusted diffusion along the sigma surfaces is used for most of the variables. The latter means that the diffusion coefficient is reduced strongly when the grid points involved in the computation of horizontal diffusion are located at greatly different heights. For temperature, one-sided horizontal diffusion is not used because it damps the slope wind circulation in an unphysical way. However, a temperature gradient correction is applied to the terrain-following part of the temperature diffusion. Its purpose is to make diffusion neutral with respect to the current vertical temperature gradient. The modifications have been implemented into the Fifth-Generation Pennsylvania State University–National Center for Atmospheric Research Mesoscale Model (MM5). Idealized simulations of the valley wind circulation in the Inn Valley of the Alps are performed to test the modifications. In its original state, the model turns out to be unable to reproduce this valley wind system because of errors related to diffusion along the coordinate surfaces. However, the model captures all essential features of the observed valley wind with the modified diffusion scheme. Both the temporal evolution and the vertical structure of the valley wind are consistent with observations. This result suggests that the model's ability to simulate flow over mountainous topography is greatly improved by use of the modified scheme.

Corresponding author address: Günther Zängl, Abteilung für Theoretische Meteorologie, Theresienstraße 37, München D-80333, Germany. Email: guenther@meteo.physik.uni-muenchen.de

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