Application of Two-Dimensional Terrain Height Spectra to Mesoscale Modeling

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  • 1 Department of Geography, The University of British Columbia, Vancouver, B.C., Canada V6T 1W5
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Abstract

A caution is offered with regard to the use of one-dimensional terrain spectra to indicate the grid resolution needed to resolve terrain forcing in mesoscale numerical modeling exercises. To illustrate this, two-dimensional terrain height spectra are presented for two contrasting terrains: a relatively direction free topography (a portion of southcentral British Columbia, Canada) and a highly ordered topography (a portion of the ridge and valley terrain in Pennsylvania). Isoamplitude plots of the two spectra show clearly the morphological differences between the two regions and indicate the degree of directionality of the ordered terrain.

An investigation of the wavenumber dependence of the terrain height spectra shows the spectral roll-off for the first case to be essentially independent of direction and to decay roughly as wavenumber to the -5/2 power over a wavenumber range of 0.04 to 8.33 km−1. By contrast, the spectral roll-off in the second case is strongly dependent on direction with an exponent that may be either greater than or less than the convergence limit (−2.0 for the amplitude spectrum) indicated by Young and Pielke.

Abstract

A caution is offered with regard to the use of one-dimensional terrain spectra to indicate the grid resolution needed to resolve terrain forcing in mesoscale numerical modeling exercises. To illustrate this, two-dimensional terrain height spectra are presented for two contrasting terrains: a relatively direction free topography (a portion of southcentral British Columbia, Canada) and a highly ordered topography (a portion of the ridge and valley terrain in Pennsylvania). Isoamplitude plots of the two spectra show clearly the morphological differences between the two regions and indicate the degree of directionality of the ordered terrain.

An investigation of the wavenumber dependence of the terrain height spectra shows the spectral roll-off for the first case to be essentially independent of direction and to decay roughly as wavenumber to the -5/2 power over a wavenumber range of 0.04 to 8.33 km−1. By contrast, the spectral roll-off in the second case is strongly dependent on direction with an exponent that may be either greater than or less than the convergence limit (−2.0 for the amplitude spectrum) indicated by Young and Pielke.

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