The Matsuno-Gill model and equatorial superrotation

Equatorial superrotation can be generated in global general circulation models (GCMs) when forced with longitudinally varying heating, similar to that postulated in the Matsuno-Gill model. However, the implications of the classical Matsuno-Gill theory for equatorial superrotation have not, to date, been addressed. Here, we show that the classic, shallow-water Matsuno-Gill solutions do not exhibit equatorial superrotation: although the flow converges westerly momentum from high latitudes to the equatorpromoting superrotationthey also contain an artificial source of easterly momentum at the equator that cancels the latitudinal momentum convergence and prevents superrotation from emerging. This artificial momentum source results from a physically inconsistent representation of vertical momentum transport in the model. We show that if the Matsuno-Gill model is modified to properly account for momentum exchange with an underlying quiescent layer, the solutions naturally exhibit equatorial superrotation, at any forcing amplitude.