Stochastic Dynamics of Water Vapor in the Climate System

Water vapor plays an important role in the climate system. Although there has been much progress in our understanding of how the distribution of moisture arises, there is not well understood because of the complicated effects of condensation and moisture convection. A conceptual stochastic advection-diffusion-condensation model is used to study the fundamental dynamics of water vapor in atmosphere. Moisture source is taken as a noise which is modeled as the generalized time derivative of Brownian motion, and the intensity for noise depends on humidity, i.e., multiplicative noise. By numerically solving the Fokker-Planck equation, we investigate the temporal evolution of probability density function (PDF) of the humidity. The solution resembles some dynamical features of the atmospheric water vapor derived from ERA40. In addition, we analyze multiple equilibrium states of humidity and discuss the dynamical transitions between different basins of equilibrium states. Based on large deviation theory and by applying a new technique on estimating exit probability from a cylindrical domain, we obtain transition probabilities between basins of equilibrium states. These results help understand moisture evolution when multiple equilibria are present, and quantify the likelihood for moist air parcels to move between moist (the deep tropics) and dry regions (subtropics or higher latitudes).