Advection–condensation in a channel flow mimicking water vapor transport by baroclinic eddies along moist isentropic surfaces in mid-latitudes. White dashed-lines are streamlines of the velocity. The saturaion humidity profile decreases roughly exponentially with y. A moisture source is located along the bottom boundary. Color scale indicates relative humidity.

(a) Stochastic Lagrangian model: Monte Carlo simulation of the governing stochastic differential equations.

(b) Relative humidity field 'observed' from (a): the domain is divided into small bins, the 'observed' value is obtained by averaging over all parcels inside a bin.

(c) Eulerian model: numerical solution of the governing partial differential equation. Notice the large areas of complete saturation.

(d) Eulerian model with condensation parameterization. The relative humidity field more or less resembles that in (b).