Theory of In-Cloud Activation of Aerosols and Microphysical Quasi-Equilibrium in a Deep Updraft

Abstract

Abstract The microphysical quasi-equilibrium in an ascending adiabatic parcel is elucidated by an analytical theory in 0D with drastic simplifications. The theory predicts how in-cloud activation is most likely to be triggered by the onset of precipitation during sufficient ascent, with the ascent only needing to approach almost twice the cloud-base updraft speed aloft. The precipitation and cloud condensate mass fields are coupled in a closed system in a simplified version of the model. The initial state of no precipitation is unstable with respect to a perturbation. In the 2D phase space of both mass fields, there is a neutral line. Unstable growth of precipitation mass drives the system to cross the line into a regime of stability. An attractor is then approached consisting of precipitation mass balanced by accretion of cloud mass and fallout. The cloud-particle number concentration also approaches a stable equilibrium governed by the balance between in-cloud activation aloft from the inexorably increasing supersaturation during vertical acceleration and accretion of cloud droplets by precipitation. Dimensionless numbers characterizing the microphysical equilibria and their stability are derived mathematically, including a condensation–precipitation efficiency and an in-cloud activation efficiency. The theory explains common observations of the orders of magnitude of liquid water content in convective and stratiform clouds. Finally, sensitivity tests of the numerically integrated theoretical equations are documented with respect to variations in cloud condensation nucleus (CCN) aerosols and updraft speed. It is shown that this theory of in-cloud activation, with an increasing supersaturation during ascent, applies to both ice-only and liquid-only cloud. Significance Statement The purpose of the study is to create a theory for how equilibria among cloud-microphysical properties are attained during ascent. Continual initiation of fresh cloud droplets far above cloud base in the free troposphere is explained. The theory proposes a balance between creation and depletion of such droplets, in relation to a balance between creation and fallout of precipitation. The transition from positive feedbacks of instability toward negative feedbacks of stability when the equilibria are approached is elucidated. The theory explains why the mass content of cloud liquid in regions of ascent is typically about an order of magnitude lower in layer clouds with weak ascent than in convective clouds with faster ascent. Any future work could extend the theory to treat dilute parcels or coexistence of supercooled liquid and ice.