The advection-condensation model and water vapour PDFs

TL;DR

This paper develops an analytical model for water vapor distribution considering advection and condensation, providing exact solutions for humidity PDFs that match simulations and real-world data.

Contribution

It introduces a novel advection-condensation model with an exact Fokker-Planck solution for humidity PDFs, linking theory with simulation and observational data.

Findings

Humidity PDFs are broad and non-Gaussian.

The model predicts bimodal relative humidity distributions.

Simulation results agree with the analytical solutions.

Abstract

The statistically steady humidity distribution resulting from an interaction of advection, modeled as an uncorrelated random walk of moist parcels on an isentropic surface, and a vapour sink, modeled as immediate condensation whenever the specific humidity exceeds a specified saturation humidity, is explored with theory and simulation. A source supplies moisture at the deep-tropical southern boundary of the domain, and the saturation humidity is specified as a monotonically decreasing function of distance from the boundary. The boundary source balances the interior condensation sink, so that a stationary spatially inhomogeneous humidity distribution emerges. An exact solution of the Fokker-Planck equation delivers a simple expression for the resulting probability density function (PDF) of the water vapour field and also of the relative humidity. This solution agrees completely with a numerical simulation of the process, and the humidity PDF exhibits several features of interest, such as bimodality close to the source and unimodality further from the source. The PDFs of specific and relative humidity are broad and non-Gaussian. The domain averaged relative humidity PDF is bimodal with distinct moist and dry peaks, a feature which we show agrees with middleworld isentropic PDFs derived from the ERA interim dataset.