Kinetics of Cloud Drop Formation and Its Parameterization for Cloud and Climate Models

Abstract

To study the kinetics of drop nucleation in clouds, the integro?differential equation for integral water supersaturation in cloud is derived and analyzed. Solving the supersaturation equation with an algebraic form of the cloud condensation nuclei (CCN) activity spectrum, analytical expressions are obtained for the time tm of CCN activation process, the maximum supersaturation sm, and droplet concentration Ndr(sm), limited by the total aerosol concentration at high supersaturations. All three quantities are expressed as functions of vertical velocity and characteristics of the CCN size spectra: mean geometric radius, dispersion, and parameters of solubility. A generalized power law for the drop activation, Ndr(sm) = C(sm)sk(sm)m, is formulated that is similar in form to the Twomey power law, but both the coefficient C(sm) and index k(sm) are functions of supersaturation expressed analytically in terms of vertical velocities and CCN microphysical parameters. A simple and economical numerical solution was developed that describes all of these characteristics without conducting numerous simulations using parcel models. An extended series of numerical experiments was performed, in which the dependencies of tm, sm, Ndr(sm), C(sm), k(sm), and several other important characteristics of activation process were studied as functions of vertical velocity and physicochemical properties of the aerosol. In particular, it is shown that a decrease in the condensation coefficient αc leads to slower CCN activation and higher maximum supersaturation and droplet concentration. Uncertainties in αc may prevent correct estimates of the direct and indirect aerosol effects on climate. The solutions and expressions for the parameters presented here can be used for parameterization of the drop activation process in cloud and climate models.