Jetstreams in an axially symmetric, differentially heated, Shallow Water Model on the rotating Earth

The main features of upper tropospheric jetstreams are captured by an axial symmetric, Shallow Water Model (SWM), on the rotating spherical Earth in which the solar differential heating is parameterized. The differential is parameterized by relaxing the height of the troposphere to a prescribed latitude dependent height. Standard numerical integration of the resulting set of nonlinear partial differential equations shows that while the seasonal variability of the jetstearms' latitudes is accurately and robustly reproduced by the parameterized model, their amplitudes (i.e. maximal wind speed) have to be finely tailored by selecting the values of the model parameters. By deriving integral constraints on the free SWM we are able to show that no jets can form when the model is initiated from simple, physically acceptable, initial conditions unless differential solar heating is added. For steady forcing the model generates two westerly, off equatorial, jets and a much weaker easterly equatorial one. Asymmetric (with respect to the equator) differential heating results in asymmetry of the off-equatorial jets and a slight shift in the latitude of the equatorial one. When the annual cycle is included in the differential solar heating forcing the resulting monthly averaged jets are in very good agreement with the observed monthly averaged jets in the NCEP data base at the 250 hPa level.