  Downscaling aims to link the behaviour of the atmosphere at fine scales to
properties measurable at coarser scales, and has the potential to provide high
resolution information at a lower computational and storage cost than numerical
simulation alone. This is especially appealing for targeting convective scales,
which are at the edge of what is possible to simulate operationally. Since
convective scale weather has a high degree of independence from larger scales,
a generative approach is essential. We here propose a statistical method for
downscaling moist variables to convective scales using conditional Gaussian
random fields, with an application to wet bulb potential temperature (WBPT)
data over the UK. Our model uses an adaptive covariance estimation to capture
the variable spatial properties at convective scales. We further propose a
method for the validation, which has historically been a challenge for
generative models.
