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The Effects of Subgrid Model Mixing and Numerical Filtering in Simulations of Mesoscale Cloud Systems

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  • 1 National Center for Atmospheric Research, Boulder, Colorado
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Abstract

Using the newly developed Weather Research and Forecasting (WRF) model, this study investigates the effects of subgrid mixing and numerical filtering in mesoscale cloud simulations by examining the sensitivities to the parameters in turbulence-closure schemes as well as the parameters in the numerical filters. Three-dimensional simulations of squall lines in both no-shear and strong-shear environments have been performed. Using the Smagorinsky or 1.5-order turbulent kinetic energy (TKE) subgrid model with standard values for the model constants and no explicit numerical filter, the solution in the no-shear environment is characterized by many poorly resolved grid-scale cells. In the past, such grid-scale noise was avoided by adding a numerical filter which, however, produces excessive damping of the physical small-scale eddies. Without using such a filter, it was found that by increasing the proportionality constant in the eddy viscosity coefficient in the subgrid turbulence models, the cells become well resolved, but that further increases in the constant overly smooth the cells. Such solution sensitivity is also found in the strong-shear cases. The simulations using the subgrid models with viscosity coefficients 1.5 to 2 times larger than those widely used in other cloud models retain more power in short scales, but without an unwanted buildup of energy; with these optimum values, no numerical filters are required to avoid computational noise. These optimum constants do not depend significantly on grid spacings of O(1 km). Therefore, it is concluded that by using the eddy viscosity formulation appropriate for mesoscale cloud simulations, the use of artificial numerical filters is avoided, and the mixing processes are represented by more physically based turbulence-closure models.

Additional affiliation: Department of Global Architecture, Osaka University, Osaka, Japan

Corresponding author address: Dr. Tetsuya Takemi, Department of Global Architecture, Osaka University, Graduate School of Engineering, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. Email: takemi@ga.eng.osaka-u.ac.jp

Abstract

Using the newly developed Weather Research and Forecasting (WRF) model, this study investigates the effects of subgrid mixing and numerical filtering in mesoscale cloud simulations by examining the sensitivities to the parameters in turbulence-closure schemes as well as the parameters in the numerical filters. Three-dimensional simulations of squall lines in both no-shear and strong-shear environments have been performed. Using the Smagorinsky or 1.5-order turbulent kinetic energy (TKE) subgrid model with standard values for the model constants and no explicit numerical filter, the solution in the no-shear environment is characterized by many poorly resolved grid-scale cells. In the past, such grid-scale noise was avoided by adding a numerical filter which, however, produces excessive damping of the physical small-scale eddies. Without using such a filter, it was found that by increasing the proportionality constant in the eddy viscosity coefficient in the subgrid turbulence models, the cells become well resolved, but that further increases in the constant overly smooth the cells. Such solution sensitivity is also found in the strong-shear cases. The simulations using the subgrid models with viscosity coefficients 1.5 to 2 times larger than those widely used in other cloud models retain more power in short scales, but without an unwanted buildup of energy; with these optimum values, no numerical filters are required to avoid computational noise. These optimum constants do not depend significantly on grid spacings of O(1 km). Therefore, it is concluded that by using the eddy viscosity formulation appropriate for mesoscale cloud simulations, the use of artificial numerical filters is avoided, and the mixing processes are represented by more physically based turbulence-closure models.

Additional affiliation: Department of Global Architecture, Osaka University, Osaka, Japan

Corresponding author address: Dr. Tetsuya Takemi, Department of Global Architecture, Osaka University, Graduate School of Engineering, 2-1 Yamadaoka, Suita, Osaka 565-0871, Japan. Email: takemi@ga.eng.osaka-u.ac.jp

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