A priori test of scale-similarity parameterizations for subgrid-scale fluxes in convective storms

This study evaluates a parameterization scheme for subgrid-scale (SGS) fluxes based on the scale-similarity assumption and employing a large-eddy simulation of an idealized backbuilding convective system. In this parameterization, the SGS fluxes are decomposed into the “Leonard term” which depends only on the resolved scale components, the “Reynolds term” which depends only on the SGS components, and the “cross term” which corresponds to the interaction between the resolved scale and SGS components. Assuming a linear relationship between the Leonard term and the Reynolds and cross terms, SGS fluxes are expressed as the product of an empirical coefficient and the Leonard term. The Leonard term reasonably represents the SGS flux derived by a smooth filter operation, including the counter-gradient vertical SGS transport of potential temperature, which cannot be represented by a traditional eddy-diffusivity model. The dependence of the empirical coefficient on filter width is also evaluated. This dependence is related mainly to the Reynolds term, the magnitude of which varies widely with filter width. The estimation based on the spectral decomposition of the Reynolds term explains the obtained dependence of the empirical coefficient for the vertical flux on filter width. In contrast, the variation of the empirical coefficient with filter width is not required to obtain the horizontal flux. For the parameterization of SGS fluxes in kilometer-scale models that use finite difference or volume methods, the Leonard term is expressed by the horizontal gradient of variables on a discrete grid. The Leonard term on a discrete grid also accurately represents the amplitude and spatial pattern of the SGS flux.