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The time-dependent Ginzburg-Landau equation and the Swift-Hohenberg equation,both added with a stochastic term, are proposed to describe cloud patternformation and cloud regime phase transitions of shallow convective cloudsorganized in mesoscale systems. The starting point is the Hottovy-Stechmannlinear spatio-temporal stochastic model for tropical precipitation, used todescribe the dynamics of water vapor and tropical convection. By taking intoaccount that shallow stratiform clouds are close to a self-organizedcriticallity and that water vapor content is the order parameter, it isobserved that sources must have non-linear terms in the equation to include thedynamical feedback due to precipitation and evaporation. The inclusion of thisnon-linearity leads to a kind of time-dependent Ginzburg-Landau stochasticequation, originally used to describe superconductivity phases. By performingnumerical simulations, pattern formation is observed, specially for cellularconvective phases. These patterns are much better compared with real satelliteobservations than the pure linear model. This is done by comparing the spatialFourier transform of real and numerical cloud fields. Finally, by consideringfluctuation terms for the turbulent eddy diffusion we arrive to aHohenberg-Swift equation. The obtained patterns are much more organized thatthe patterns obtained from the Ginzburg-Landau equation in the case of closedcellular and roll convection.

physical review. e

Description of mesoscale pattern formation in shallow convective cloud  fields by using time-dependent Ginzburg-Landau and Swift-Hohenberg stochastic  equations