  The issue of the parameterization of small scale (``subgrid'') turbulence is
addressed in the context of passive scalar transport. We focus on the Kraichnan
advection model which lends itself to the analytical investigation of the
closure problem. We derive systematically the dynamical equations which rule
the evolution of the coarse-grained scalar field. At the lowest-order
approximation in $l/r$, $l$ being the characteristic scale of the filter
defining the coarse-grained scalar field and $r$ the inertial range separation,
we recover the classical eddy-diffusivity parameterization of small scales. At
the next-leading order a dynamical closure is obtained. The latter outperforms
the classical model and is therefore a natural candidate for subgrid modelling
of scalar transport in generic turbulent flows.
