The effect of the Helmholtz term on a two-layer model baroclinic atmosphere

The effects of the inclusion of a Helmholtz term in a quasi-geostrophic model, formulated as part of a lower boundary condition, are investigated using a two-layer model. The Helmholtz term has two main effects, both of which appear desirable in a quasi-geostrophic model. As well as reducing the phase speed of all waves, and thereby controlling the otherwise large retrograde motion of ultra-long Rossby waves, it reduces growth rates of unstable waves. The Helmholtz term reduces the westward slope with height of unstable waves, more so for shorter wave lengths.

The Helmholtz term is shown to be important for all quasi-geostrophic models. However, its use with an enhanced factor of about 10, although desirable for “best” forecasts, has little physical basis and merely serves to offset shortcomings of the model.