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J. C. Wyngaard
,
L. J. Peltier
, and
S. Khanna

Abstract

The surface fluxes in the fine-mesh numerical codes used in small-scale meteorology are typically diagnosed from resolvable-scale variables through surface-exchange coefficients. This is appropriate if the aspect ratio (length/height) of the grid volume adjacent to the surface is very large, as in mesoscale models. The aspect ratio can approach unity in large-eddy simulation (LES) codes for the planetary boundary layer, however. In that limit the surface-exchange coefficients are random variables, and it is shown through analysis of surface-layer measurements and LES results that their fluctuation levels can be large.

As an alternative to surface-exchange coefficients, the authors derive conservation equations for the surface scalar and momentum fluxes in LES. Scaling relations for resolvable-scale variables in the surface layer are developed and used to simplify these equations. It is shown that, as the grid aspect ratio decreases toward unity, local time change, horizontal advection, production due to horizontal velocity convergence, and random noise terms cause the local surface-exchange coefficients to fluctuate. A simple closure of the equations is adopted, which has little effect on surface-layer structure calculated through LES with a Smagorinsky-based subgrid-scale (SGS) model. Through analysis of very high-resolution LES fields, the authors find the SGS model to be a poor representation of surface-layer physics and conclude that the surface-flux conservation equations need to be coupled with a greatly improved SGS model in the surface layer.

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L. J. Peltier
,
J. C. Wyngaard
,
S. Khanna
, and
J. O. Brasseur

Abstract

A simple approach to modeling spectra in unstable atmospheric surface layers is presented. The authors use a single form for the two-dimensional spectrum of horizontal velocity, vertical velocity, and a scalar in the horizontal plane; it has two free constants, a length scale, and an intensity scale. Continuity is used to relate the vertical and horizontal velocity spectra. The two free constants are determined by matching the variance and the inertial-subrange spectral level with observations. The scales are chosen so that the spectra follow law of the wall and mixed-layer scaling in the neutral and free-convection limits, respectively. The authors model the stability dependence of the spectra by combining these two limiting forms. The one-dimensional spectra, obtained by integration over one wavenumber component, and their variances agree well with observations. Near the surface the vertical velocity variance follows Monin-Obukhov (M–O) similarity and shows a realistic local free-convection asymptote; at greater heights it shows departures from M–O similarity that also agree well with observations. Finally, the two-dimensional spectra are used to calculate the valances of the resolvable and subgrid-scale components of large eddy simulations and their dependence on grid mesh size, distance from the surface, boundary layer depth, and stability.

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