Stochastic stability of aerosols-stimulated rainfall model

Abstract

With increasingly erratic nature of monsoon, especially in Indian Ocean region clamors for artificial rain have gathering pace recently. For artificial rain, aerosols are used which act as cloud condensation nuclei (CCN) in the formation of cloud droplets from water vapors. In this paper, a nonlinear mathematical model is proposed and analyzed to increase the intensity of rain in the rain deficient regions using aerosols. To stimulate rainfall two kinds of aerosols are used. We have considered three different stages of water involved in the process of precipitation namely, (i) the density of water vapors, (ii) the density of cloud droplets, and (iii) the density of raindrops. Previously proposed models consist of a set of ordinary differential equations (ODE), whereas the use of stochastic differential equations (SDE) depicts more realistic situation as they include environmental disturbances. First, we propose a deterministic model and then convert it into a stochastic model by introducing white noise terms. We have found that the deterministic model is globally asymptotically stable without any condition, while the stability of stochastic model solely depends on the intensity of white noise.