Fluctuations in an Equilibrium Convective Ensemble. Part II: Numerical Experiments

Brenda G. Cohen Department of Meteorology, University of Reading, Reading, United Kingdom

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George C. Craig DLR Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany

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Abstract

The theoretical predictions derived in Part I of this study for the equilibrium fluctuations of an idealized ensemble of noninteracting, pointlike cumulus clouds are tested against three-dimensional cloud resolving model (CRM) simulations of radiative–convective equilibrium. Simulations with different radiative cooling rates are used to give a range of cloud densities, while imposed vertical wind shear of different strengths is used to produce different degrees of convective organization. The distribution of mass flux of individual clouds is found to be exponential in all simulations, in agreement with the theory. The distribution of total mass flux over a finite region also agrees well (to within around 10%) with the theoretical prediction for all simulations, but only after a correction to the modeled variance to take account of the finite size of clouds has been made. In the absence of imposed vertical wind shear, some spatial clustering of convective cells is observed at lower forcings (−2 and −4 K day−1) on a scale of 10–20 km, while at higher forcings (−8, −12, and −16 K day−1), there is a tendency toward spatial regularity on the same scale. These localized cloud interactions, however, appear to have little effect on the magnitude of the mass flux variability. Surprisingly, the convective organization obtained in the simulations with vertical wind shear has only a small effect on the mass flux statistics, even though it shows clearly in the location of the clouds.

Corresponding author address: George C. Craig, DLR Oberpfaffenhofen, Institut für Physik der Atmosphäre, Münchner Strasse 20, D-82234 Wessling, Germany. Email: george.craig@dlr.de

Abstract

The theoretical predictions derived in Part I of this study for the equilibrium fluctuations of an idealized ensemble of noninteracting, pointlike cumulus clouds are tested against three-dimensional cloud resolving model (CRM) simulations of radiative–convective equilibrium. Simulations with different radiative cooling rates are used to give a range of cloud densities, while imposed vertical wind shear of different strengths is used to produce different degrees of convective organization. The distribution of mass flux of individual clouds is found to be exponential in all simulations, in agreement with the theory. The distribution of total mass flux over a finite region also agrees well (to within around 10%) with the theoretical prediction for all simulations, but only after a correction to the modeled variance to take account of the finite size of clouds has been made. In the absence of imposed vertical wind shear, some spatial clustering of convective cells is observed at lower forcings (−2 and −4 K day−1) on a scale of 10–20 km, while at higher forcings (−8, −12, and −16 K day−1), there is a tendency toward spatial regularity on the same scale. These localized cloud interactions, however, appear to have little effect on the magnitude of the mass flux variability. Surprisingly, the convective organization obtained in the simulations with vertical wind shear has only a small effect on the mass flux statistics, even though it shows clearly in the location of the clouds.

Corresponding author address: George C. Craig, DLR Oberpfaffenhofen, Institut für Physik der Atmosphäre, Münchner Strasse 20, D-82234 Wessling, Germany. Email: george.craig@dlr.de

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