Roel Neggers, Bjorn Stevens, and J. David Neelin
Quart. J. Roy. Meteorol. Soc., 305-322. doi:10.100c/qj.105.
Paper (PDF 1.7 MB)
© Copyright 2007 by the Royal Meteorological Society.
Abstract. Scaling of thermodynamic variance in shallow cumulus topped mixed layers is studied using large- eddy simulation (LES). First the performance of top-down scaling, consisting of the turbulent flux at mixed layer top divided by w*, is evaluated for transient shallow cumulus convection over land The results indicate that this top-down scale fails to capture all 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 di ers from the standard top-down scale by one Richardson number. The essential new features of the proposed scaling are that i) the local vertical gradient is retained, and ii) a balance is assumed between gradient production of variance on the one hand, and removal by transport and dissipation on the other, using an adjustment time scale given by w*/h. Evaluation against LES for a range of different shallow cumulus cases, including both steady-state marine and transient continental situations, reveals a data-collapse of the newly scaled variance of all hours and all cases in the top half of the sub-cloud mixed layer. The corresponding vertical structure is shown to resemble a power-law function. 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 rely on the variance as the second moment of the associated probability density function. The result suggests 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.
Citation. Neggers, R., B. Stevens, and J. D. Neelin, 2006: Variance scaling in shallow-cumulus-topped mixed layers. Q. J. R. Meteorol. Soc., 305-322. doi:10.100c/qj.105.