Simple Multicloud Models for the Diurnal Cycle of Tropical Precipitation. Part I: Formulation and the Case of the Tropical Oceans

Yevgeniy Frenkel Courant Institute of Mathematical Sciences, New York University, New York, New York

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Boualem Khouider Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, Canada

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Andrew J. Majda Department of Mathematics, and Center for Atmosphere Ocean Science, Courant Institute of Mathematical Sciences, New York University, New York, New York

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Abstract

The variation of tropical precipitation due to the diurnal cycle of solar heating is examined here in the context of two simple models for tropical convection. The models utilize three cloud types—congestus, deep, and stratiform—that are believed to characterize organized tropical convection and are based on the two first baroclinic modes of vertical structure plus a boundary layer mode. The two models differ mainly in the way they treat the boundary layer dynamics. The first one is purely thermodynamical and is reduced to a single equation for the equivalent potential temperature θe connecting the boundary layer to the upper troposphere through downdrafts and to the surface through evaporation while the second uses full bulk boundary layer (FBBL) dynamics with a careful separation between sensible and latent heat fluxes and parameterization of nonprecipitating shallow cumulus. It turns out that in the case of the precipitation over the ocean where the Bowen ratio is small, both models yield a qualitatively similar solution, characterized by an overnight initiation and early morning peak in precipitation consistent with observations. The modeled diurnal cycle of precipitation over the ocean is divided into four cyclic phases: 1) a CAPE (re)generation phase characterized by the enhancement of the boundary layer θe and moisture fluxes during midday and early afternoon that is followed by 2) a (re)moistening phase dominated by congestus heating during the late afternoon and moistening from downdrafts (due to detrainment of shallow cumulus, specifically in the FBBL model) and radiative cooling that lasts until midnight. 3) Deep convection is initiated around midnight when the midtroposphere is sufficiently moist and cool and (re)establishes the precipitation level near its radiative convective equilibrium (1 K day−1) and then 4) peaks with sunrise at 0600 LST to yield a precipitation maximum of roughly 2 K day−1 at around 0900 LST that dries the troposphere and consumes CAPE and closes the cycle.

Corresponding author address: Boualem Khouider, Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, Victoria BC V8W 3P4, Canada. E-mail: khouider@uvic.ca

Abstract

The variation of tropical precipitation due to the diurnal cycle of solar heating is examined here in the context of two simple models for tropical convection. The models utilize three cloud types—congestus, deep, and stratiform—that are believed to characterize organized tropical convection and are based on the two first baroclinic modes of vertical structure plus a boundary layer mode. The two models differ mainly in the way they treat the boundary layer dynamics. The first one is purely thermodynamical and is reduced to a single equation for the equivalent potential temperature θe connecting the boundary layer to the upper troposphere through downdrafts and to the surface through evaporation while the second uses full bulk boundary layer (FBBL) dynamics with a careful separation between sensible and latent heat fluxes and parameterization of nonprecipitating shallow cumulus. It turns out that in the case of the precipitation over the ocean where the Bowen ratio is small, both models yield a qualitatively similar solution, characterized by an overnight initiation and early morning peak in precipitation consistent with observations. The modeled diurnal cycle of precipitation over the ocean is divided into four cyclic phases: 1) a CAPE (re)generation phase characterized by the enhancement of the boundary layer θe and moisture fluxes during midday and early afternoon that is followed by 2) a (re)moistening phase dominated by congestus heating during the late afternoon and moistening from downdrafts (due to detrainment of shallow cumulus, specifically in the FBBL model) and radiative cooling that lasts until midnight. 3) Deep convection is initiated around midnight when the midtroposphere is sufficiently moist and cool and (re)establishes the precipitation level near its radiative convective equilibrium (1 K day−1) and then 4) peaks with sunrise at 0600 LST to yield a precipitation maximum of roughly 2 K day−1 at around 0900 LST that dries the troposphere and consumes CAPE and closes the cycle.

Corresponding author address: Boualem Khouider, Department of Mathematics and Statistics, University of Victoria, 3800 Finnerty Road, Victoria BC V8W 3P4, Canada. E-mail: khouider@uvic.ca
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