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(www.interscience.wiley.com) DOI: 10.1002/qj.105 Variance scaling in shallow-cumulus-topped mixed layers
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@MISC{Neggers_(www.interscience.wiley.com)doi:,
author = {R. A. J. Neggers and B. Stevens and J. D. Neelin},
title = {(www.interscience.wiley.com) DOI: 10.1002/qj.105 Variance scaling in shallow-cumulus-topped mixed layers},
year = {}
}
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Abstract
ABSTRACT: Scaling of thermodynamic variance in shallow-cumulus-topped mixed layers is studied using large-eddy simulation (LES). First, the performance of the top-down scaling (the turbulent flux at mixed-layer top divided by w∗) is evaluated for transient shallow-cumulus convection over land. The results indicate that this scaling fails to capture all the variance in the top half of the mixed layer when shallow cumulus clouds are present. A variance-budget analysis is then performed, to derive a new scaling for the variance at mixed-layer top, which differs from the standard top-down scaling by a factor of one Richardson number. The essential new features of the proposed scaling are that the local vertical gradient is retained and that a balance is assumed between gradient production of variance and removal by transport and dissipation, using an adjustment time-scale given by w∗/h. Evaluation against LES for a range of different cases, including a dry convective boundary layer as well as steady-state marine and transient continental shallow cumulus, reveals a data-collapse of the newly-scaled variance, for all hours and all cases in the top half of the mixed layer. The corresponding vertical structure is shown to resemble a power-law function. The results suggest that the structure of variance in the dry convective boundary layer is similar to that in the sub-cloud mixed layer. In transient situations, the scaling reproduces the time-development of variance at sub-cloud mixed-layer top. The new cloud-base variance scale is then further interpreted in the context of statistical cloud schemes, which depend on the variance as the second moment of the associated probability density function. The results suggest that the area fraction of the moist convective thermals uniquely depends on the ratio of cloud-base transition-layer depth to sub-cloud mixed-layer depth. This puts ‘valve’- or ventilation-type closures for the cloud-base mass flux in the context of the variance budget for the sub-cloud layer. Copyright 2007 Royal Meteorological
Keyphrases
shallow-cumulus-topped mixed layer variance scaling mixed-layer top dry convective boundary layer mixed layer top half ventilation-type closure thermodynamic variance top-down scaling steady-state marine turbulent flux transient continental shallow cumulus sub-cloud mixed-layer top variance-budget analysis moist convective thermal corresponding vertical structure standard top-down scaling power-law function shallow cumulus cloud sub-cloud layer transient shallow-cumulus convection second moment local vertical gradient new scaling statistical cloud scheme richardson number large-eddy simulation variance budget different case cloud-base mass flux area fraction new cloud-base variance scale cloud-base transition-layer depth royal meteorological gradient production essential new feature sub-cloud mixed-layer depth transient situation associated probability density function sub-cloud mixed layer newly-scaled variance
