Squires’ Penetrative Downdraft Model

Gerhard W. Reuter Division of Meteorology, Department of Geography, University of Alberta, Edmonton, Alberta, Canada

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Abstract

The parcel model of penetrative downdrafts formulated by Squires is further analyzed. The parcel's velocity is governed by an equation for an oscillator with exponential damping due to mixing and with forcing depending on the evaporation and the cloud updraft. The initial conditions are improved to avoid a discontinuous vertical velocity at the cloud top, resulting in a more realistic penetration depth. The time required to develop the maximum downdraft speed is found to be one-half the Brunt-Väisälä period of the cloudy air. The depth at which this peak downdraft speed occurs is proportional to the cloud-water mixing ratio and does not depend on the cloud updraft. The downdraft speed and penetration depth are primarily regulated by the cloud water content and the cloud temperature lapse rate. Deep penetration is only likely for clouds with high water contents and lapse rates exceeding about 5°C km−1. The presence of ice crystals increases the downdraft speed slightly compared to a liquid water cloud. The use of the parcel model is discussed against its inherent limitations.

Abstract

The parcel model of penetrative downdrafts formulated by Squires is further analyzed. The parcel's velocity is governed by an equation for an oscillator with exponential damping due to mixing and with forcing depending on the evaporation and the cloud updraft. The initial conditions are improved to avoid a discontinuous vertical velocity at the cloud top, resulting in a more realistic penetration depth. The time required to develop the maximum downdraft speed is found to be one-half the Brunt-Väisälä period of the cloudy air. The depth at which this peak downdraft speed occurs is proportional to the cloud-water mixing ratio and does not depend on the cloud updraft. The downdraft speed and penetration depth are primarily regulated by the cloud water content and the cloud temperature lapse rate. Deep penetration is only likely for clouds with high water contents and lapse rates exceeding about 5°C km−1. The presence of ice crystals increases the downdraft speed slightly compared to a liquid water cloud. The use of the parcel model is discussed against its inherent limitations.

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