Mean Cold Pool Size of Quasi-Equilibrium Convection. Part II: The Survival Competition Hypothesis

Hao Fu Department of Earth System Science, Stanford University, Stanford, California
Department of the Geophysical Sciences, The University of Chicago, Chicago, Illinois

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Morgan E O’Neill Department of Earth System Science, Stanford University, Stanford, California
Department of Physics, University of Toronto, Toronto, Ontario, Canada

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Abstract

The cold pool is a crucial component of tropical convection. However, what controls the mean cold pool size remains unclear. This two-paper series presents a theory of the mean cold pool radius in idealized quasi-equilibrium convection (Req). Part I derives an energy balance constraint between Req and the maximum potential radius of a cold pool (Rmax), showing that Req cannot reach Rmax. Cold pools must be densely packed and collide frequently. This Part II derives another constraint between Req and Rmax based on a cold pool survival competition hypothesis. A convective life cycle model with various candidate cold pool sizes is built. The type of cold pool producing the most intense next-generation cold pool is hypothesized to survive and set the spacing between convective towers. The size of the dominant cold pool type is determined by the trade-off between the mechanical lifting effect that favors a smaller cold pool, the thermodynamic forcing effect that favors a bigger cold pool, and the cloud radius feedback that also favors a bigger cold pool. Combining the energy balance and survival competition constraints, we obtain a solution for Req, which has an analytically tractable upper bound. The upper bound is set by the cold pool’s fractional entrainment rate and the free-tropospheric relative humidity: a lower fractional entrainment rate or a drier free troposphere raises the upper bound of Req. The Req predicted by the theory agrees with a set of large-eddy simulations with different rainwater evaporation rates.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hao Fu, haofu736@gmail.com

Abstract

The cold pool is a crucial component of tropical convection. However, what controls the mean cold pool size remains unclear. This two-paper series presents a theory of the mean cold pool radius in idealized quasi-equilibrium convection (Req). Part I derives an energy balance constraint between Req and the maximum potential radius of a cold pool (Rmax), showing that Req cannot reach Rmax. Cold pools must be densely packed and collide frequently. This Part II derives another constraint between Req and Rmax based on a cold pool survival competition hypothesis. A convective life cycle model with various candidate cold pool sizes is built. The type of cold pool producing the most intense next-generation cold pool is hypothesized to survive and set the spacing between convective towers. The size of the dominant cold pool type is determined by the trade-off between the mechanical lifting effect that favors a smaller cold pool, the thermodynamic forcing effect that favors a bigger cold pool, and the cloud radius feedback that also favors a bigger cold pool. Combining the energy balance and survival competition constraints, we obtain a solution for Req, which has an analytically tractable upper bound. The upper bound is set by the cold pool’s fractional entrainment rate and the free-tropospheric relative humidity: a lower fractional entrainment rate or a drier free troposphere raises the upper bound of Req. The Req predicted by the theory agrees with a set of large-eddy simulations with different rainwater evaporation rates.

© 2025 American Meteorological Society. This published article is licensed under the terms of the default AMS reuse license. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Hao Fu, haofu736@gmail.com

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