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A Gravity Wave Drag Matrix for Complex Terrain

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  • 1 Yale University, New Haven, Connecticut
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Abstract

We propose a simplified scheme to predict mountain wave drag over complex terrain using only the regional-average low-level wind components U and V. The scheme is tuned and tested on data from the South Island of New Zealand, a rough and highly anisotropic terrain. The effect of terrain anisotropy is captured with a hydrostatically computed, 2 × 2 positive-definite wave drag matrix. The wave drag vector is the product of the wind vector and the drag matrix. The nonlinearity in wave generation is captured using a Gaussian terrain smoothing inversely proportional to wind speed. Wind speeds of |U| = 10, 20, and 30 m s−1 give smoothing scales of L = 54, 27, and 18 km, respectively. This smoothing treatment of nonlinearity is consistent with recent aircraft data and high-resolution numerical modeling of waves over New Zealand, indicating that the momentum flux spectra shift to shorter waves during high-drag conditions. The drag matrix model is tested against a 3-month time series of realistic full-physics wave-resolving flow calculations. Correlation coefficients approach 0.9 for both zonal and meridional drag components.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ronald B. Smith, ronald.smith@yale.edu

Abstract

We propose a simplified scheme to predict mountain wave drag over complex terrain using only the regional-average low-level wind components U and V. The scheme is tuned and tested on data from the South Island of New Zealand, a rough and highly anisotropic terrain. The effect of terrain anisotropy is captured with a hydrostatically computed, 2 × 2 positive-definite wave drag matrix. The wave drag vector is the product of the wind vector and the drag matrix. The nonlinearity in wave generation is captured using a Gaussian terrain smoothing inversely proportional to wind speed. Wind speeds of |U| = 10, 20, and 30 m s−1 give smoothing scales of L = 54, 27, and 18 km, respectively. This smoothing treatment of nonlinearity is consistent with recent aircraft data and high-resolution numerical modeling of waves over New Zealand, indicating that the momentum flux spectra shift to shorter waves during high-drag conditions. The drag matrix model is tested against a 3-month time series of realistic full-physics wave-resolving flow calculations. Correlation coefficients approach 0.9 for both zonal and meridional drag components.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Ronald B. Smith, ronald.smith@yale.edu
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