In-Cloud Activation of Aerosols and Microphysical Quasi-Equilibrium with Precipitation in Deep Cloudy Ascent: a New Theory
Authors: Phillips Vaughan 
Published: February 2023

There are two types of activation of aerosols to become cloud-droplets.&#160;&#160; First, clouds with liquid have a base at the level of water saturation where the first cloud-droplets form during ascent.&#160; In the first 10 m or so above the base, the supersaturation rises to a peak value and aerosols activate to become cloud-droplets (&#8220;cloud base activation&#8221;).&#160; The supersaturation then relaxes to an equilibrium.&#160; Second, if the supersaturation becomes high enough during ascent into the interior of the cloud aloft, then there can be &#8220;in-cloud activation&#8221; as an extra source of cloud droplets.&#160; A possible cause of in-cloud activation is entrainment of aerosols from the environment that are large enough to activate.&#160; Another cause can be an increase with height of the supersaturation, causing it to exceed the peak value at cloud-base.In-cloud activation is often overlooked in cloud-microphysics schemes of atmospheric models and is challenging to represent.&#160; In deep convective updrafts, simulations of storms have shown it can generate most of the droplets at subzero levels aloft.&#160; In-cloud activation of aerosols to become droplets can even generate most of the ice crystals in the anvil cirriform anvils by their homogeneous freezing near -36 degC.&#160;This presentation provides a theoretical analysis of microphysical feedbacks controlling sustained in-cloud activation and precipitation production.&#160; A parcel model with 3 evolution equations for cloud mass, precipitation mass and cloud-particle number is created, during ascent for a cloud of a single phase, liquid or ice.&#160; &#160;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. &#160;The initial state of no precipitation is unstable with respect to a perturbation. In the 2D phase space of cloud mass and precipitation mass, a neutral line is elucidated. Unstable growth of precipitation mass occurs by a positive feedback, driving the microphysical system to cross the line into a regime of stability.&#160; A stable equilibrium, namely an attractor, is approached where precipitation mass is balanced by accretion of cloud mass (source) and its fallout (sink).The cloud-particle number concentration attains a stable equilibrium involving in-cloud activation.&#160; A source of droplets from the inexorably increasing supersaturation, caused by the vertical acceleration, is balanced against losses from accretion of cloud droplets by precipitation. Formulae for novel dimensionless numbers, characterizing the microphysical equilibria and their stability, are derived analytically.&#160; These include a &#8216;condensation&#8211;precipitation efficiency&#8217; and an &#8216;in-cloud activation efficiency&#8217;. &#160;The theory explains the orders of magnitude of liquid water content commonly seen in convective and stratiform clouds. &#160;Sensitivity tests are performed by altering the loading of cloud condensation nucleus (CCN) aerosols and the updraft speed.&#160; Microphysical equilibria are sensitive to the assumed ascent but are insensitive to CCN aerosol concentrations.&#160; Nevertheless, higher aerosol concentrations cause more extreme oscillations of the mass fields during the approach to equilibrium.&#160; &#160;This theory of in-cloud activation applies to both ice-only and liquid-only cloud. &#160;&#160;More details are available in a recent published paper.