  Observations of tropical convection from precipitation radar and the
concurring large-scale atmospheric state at two locations (Darwin and
Kwajalein) are used to establish effective stochastic models to parameterise
subgrid-scale tropical convective activity. Two approaches are presented which
rely on the assumption that tropical convection induces a stationary
equilibrium distribution. In the first approach we parameterise convection
variables such as convective area fraction as an instantaneous random
realisation conditioned on the large-scale vertical velocities according to a
probability density function estimated from the observations. In the second
approach convection variables are generated in a Markov process conditioned on
the large-scale vertical velocity, allowing for non-trivial temporal
correlations. Despite the different prevalent atmospheric and oceanic regimes
at the two locations, with Kwajalein being exposed to a purely oceanic weather
regime and Darwin exhibiting land-sea interaction, we establish that the
empirical measure for the convective variables conditioned on large-scale
mid-level vertical velocities for the two locations are close. This allows us
to train the stochastic models at one location and then generate time series of
convective activity at the other location. The proposed stochastic
subgrid-scale models adequately reproduce the statistics of the observed
convective variables and we discuss how they may be used in future
scale-independent mass-flux convection parameterisations.
