A gravity wave drag matrix for complex terrain

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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.

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Smith, R. B., & Kruse, C. G. (2018). A gravity wave drag matrix for complex terrain. Journal of the Atmospheric Sciences, 75(8), 2599–2613. https://doi.org/10.1175/JAS-D-17-0380.1

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