A New Theory of Microphysical Quasi-Equilibrium in Precipitating Deep Ascent and In-Cloud Aerosol Activation

Any cloud is a visible wave of ascent and cloud-particle initiation. Ascent in clouds is fundamental for their properties and lifetime. In-cloud ascent defines the time period of exposure of cloud condensate to accretion onto any precipitation, thus determining the equilibrium cloud condensate mass. Ascent also can tend to increase with height, especially in convective clouds, due to the buoyancy force. This can affect activation of aerosols to become cloud-particles.

Generally, there are two types of activation of aerosols in-cloud. First, for clouds consisting of liquid, cloud-droplets can be initiated near cloud-base, which is defined by exact water saturation, in the updraft. As the updraft parcel ascends just above cloud-base, the supersaturation rises and successively smaller aerosols activate. This continues until the rising concentration of growing cloud-droplets causes the supersaturation to reach a maximum, perhaps about 10 metres above cloud-base. The supersaturation then relaxes to an equilibrium defined by the ascent and droplet concentration. Second, there can be aerosol activation far above cloud-base in deep clouds ("in-cloud activation" of aerosols), yielding an extra source of cloud-particles aloft. This can happen either when the supersaturation aloft exceeds the peak value near cloud-base, either due to vertical acceleration of ascent or entrainment of fresh aerosols from the environment.

This presentation shows a recently published theory of microphysical quasi-equilibrium in an ascending adiabatic parcel in a deep precipitating cloud with in-cloud activation. Three dimensionless analytical evolution equations in 0D with drastic simplifications comprise the theory. It predicts how the onset of precipitation triggers the depletion of cloud-particles by accretion during sufficient ascent. Then the ascent only needs to have accelerated to about twice the cloud-base updraft speed somewhere aloft for in-cloud activation to occur.

In the simplified theoretical model, the precipitation and cloud condensate mass fields are coupled in a closed system. Dimensionless numbers characterizing the microphysical equilibria and their stability are derived mathematically, including a condensation–precipitation efficiency and an in-cloud activation efficiency. Expressions for the equilibria of precipitation and cloud mass concentrations and the cloud-particle number concentration are elucidated. The initial state of no precipitation is unstable with respect to any perturbation, with growth of precipitation occurring by a positive feedback. Linear perturbation analysis of feedbacks in the 2D phase space of both mass fields reveals that there is a neutral line. It yields the magnitude of the time-scale of unstable growth of precipitation or of relaxation of both mass fields to equilibrium. Unstable growth of precipitation mass sends the system across the line into the regime of stability. A stable attractor is approached where precipitation mass is balanced by accretion of cloud mass and fallout. Moreover, the cloud-particle number concentration also approaches a stable equilibrium created by the balance between in-cloud activation aloft from the steadily increasing supersaturation during vertical acceleration of ascent, and accretion of cloud particles by precipitation.

Finally, the theory accounts for 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. This theory of in-cloud activation, with an increasing supersaturation during ascent, applies to both ice-only and liquid-only cloud.