A Model for Convectively Coupled Tropical Waves: Nonlinearity, Rotation, and Comparison with Observations

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

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Boualem Khouider Courant Institute of Mathematical Sciences, New York University, New York, New York

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George N. Kiladis NOAA/Aeronomy Laboratory, Boulder, Colorado

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Katherine H. Straub NOAA/Aeronomy Laboratory, Boulder, Colorado

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Michael G. Shefter Courant Institute of Mathematical Sciences, New York University, New York, New York

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Abstract

Recent observational analysis of both individual realizations and statistical ensembles identifies moist convectively coupled Kelvin waves in the Tropics with supercluster envelopes of convection. This observational analysis elucidates several key features of these waves including their propagation speed of roughly 15 m s−1 and many aspects of their dynamical structure. This structure includes anomalously cold temperatures in the lower troposphere and warm temperatures in the upper troposphere (below 250 hPa) within and sometimes leading the heating region and strong updrafts in the wave, and an upward and westward tilting structure with height below roughly 250 hPa. Other key features in the wave are that anomalous increases in convective available potential energy (CAPE) and surface precipitation lead the wave while the trailing part of the supercluster is dominated by stratiform precipitation. The main result in this paper is the development of a simple model convective parameterization with nonlinear convectively coupled moist gravity waves, which reproduce many of the features of the observational record listed above in a qualitative fashion. One key feature of the model convective parameterization is the systematic use of two vertical modes with one representing deep convective heating and the other stratiform heating. The other key feature in the model is the explicit parameterization of the separate deep convective and stratiform contribution to the downdrafts, which change equivalent potential temperature in the boundary layer. The effects of rotation on convectively coupled equatorial waves are also included through a suitable linear stability theory for the model convective parameterization about radiative convective equilibrium.

Corresponding author address: Dr. Andrew J. Majda, Courant Institute of Mathematical Sciences, Center for Atmosphere Ocean Science, New York University, New York, NY 10012.Email: jonjon@cims.nyu.edu

*Current affiliation: University of Victoria, Victoria, British Columbia, Canada

Abstract

Recent observational analysis of both individual realizations and statistical ensembles identifies moist convectively coupled Kelvin waves in the Tropics with supercluster envelopes of convection. This observational analysis elucidates several key features of these waves including their propagation speed of roughly 15 m s−1 and many aspects of their dynamical structure. This structure includes anomalously cold temperatures in the lower troposphere and warm temperatures in the upper troposphere (below 250 hPa) within and sometimes leading the heating region and strong updrafts in the wave, and an upward and westward tilting structure with height below roughly 250 hPa. Other key features in the wave are that anomalous increases in convective available potential energy (CAPE) and surface precipitation lead the wave while the trailing part of the supercluster is dominated by stratiform precipitation. The main result in this paper is the development of a simple model convective parameterization with nonlinear convectively coupled moist gravity waves, which reproduce many of the features of the observational record listed above in a qualitative fashion. One key feature of the model convective parameterization is the systematic use of two vertical modes with one representing deep convective heating and the other stratiform heating. The other key feature in the model is the explicit parameterization of the separate deep convective and stratiform contribution to the downdrafts, which change equivalent potential temperature in the boundary layer. The effects of rotation on convectively coupled equatorial waves are also included through a suitable linear stability theory for the model convective parameterization about radiative convective equilibrium.

Corresponding author address: Dr. Andrew J. Majda, Courant Institute of Mathematical Sciences, Center for Atmosphere Ocean Science, New York University, New York, NY 10012.Email: jonjon@cims.nyu.edu

*Current affiliation: University of Victoria, Victoria, British Columbia, Canada

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