  The weather layers of the gas giant planets, Jupiter and Saturn, comprise the
shallow atmospheric layers that are influenced energetically by a combination
of incoming solar radiation and localised latent heating of condensates, as
well as by upwelling heat from their planetary interiors. They are also the
most accessible regions of those planets to direct observations. Recent
analyses in Oxford of cloud-tracked winds on Jupiter have demonstrated that
kinetic energy is injected into the weather layer at scales comparable to the
Rossby radius of deformation and cascades both upscale, mostly into the
extra-tropical zonal jets, and downscale to the smallest resolvable scales in
Cassini images. The large-scale flow on both Jupiter and Saturn appears to
equilibrate towards a state which is close to marginal instability according to
Arnol'd's 2nd stability theorem. This scenario is largely reproduced in a
hierarchy of numerical models of giant planet weather layers, including
relatively realistic models which seek to predict thermal and dynamical
structures using a full set of parameterisations of radiative transfer,
interior heat sources and even moist convection. Such models include the Jason
GCM, developed in Oxford, which also represents the formation of (energetically
passive) clouds of NH3, NH4SH and H2O condensates and the transport of
condensable tracers. Recent results show some promise in comparison with
observations from the Cassini and Juno missions, but some observed features
(such as Jupiter's Great Red Spot and other compact ovals) are not yet captured
spontaneously by any weather layer model. We review recent work in this vein
and discuss a number of open questions for future study.
