  In this paper we describe the construction of an efficient probabilistic
parameterization that could be used in a coarse-resolution numerical model in
which the variation of moisture is not properly resolved. An Eulerian model
using a coarse-grained field on a grid cannot properly resolve regions of
saturation---in which condensation occurs---that are smaller than the grid
boxes. Thus, in the absence of a parameterization scheme, either the grid box
must become saturated or condensation will be underestimated. On the other
hand, in a stochastic Lagrangian model of moisture transport, trajectories of
parcels tagged with humidity variables are tracked and small-scale moisture
variability can be retained; however, explicitly implementing such a scheme in
a global model would be computationally prohibitive. One way to introduce
subgrid-scale saturation into an Eulerian model is to assume the humidity
within a grid box has a probability distribution. To close the problem, this
distribution is conventionally determined by relating the required
subgrid-scale properties of the flow to the grid-scale properties using a
turbulence closure. Here, instead, we determine an assumed probability
distribution by using the statistical moments from a stochastic Lagrangian
version of the system. The stochastic system is governed by a Fokker--Planck
equation and we use that, rather than explicitly following the moisture
parcels, to determine the parameters of the assumed distribution. We are thus
able to parameterize subgrid-scale condensation in an Eulerian model in a
computationally efficient and theoretically well-founded way. In two idealized
advection--condensation problems we show that a coarse Eulerian model with the
subgrid parameterization is well able to mimic its Lagrangian counterpart.
