Sea level, bottom pressure, gyres and overturning: lessons from classical models.

Even in models with vertical sidewalls, bottom pressure torques balance the wind stress curl in a zonal integral, with local modification from nonlinear terms. This can be seen explicitly in Stommel's classic 1948 solution in which, unusually, the sea level was calculated as well as the barotropic streamfunction. Here, I explore what this and other idealised solutions tell us about how coastal sea level relates to gyre circulations, western boundary currents, and simple overturning circulations. I show that the coastal sea level signal related to the gyre (or, particularly, to changes in the gyre) need not be stronger at the western boundary. I also show that, although details of where dissipation occurs can be very important for coastal sea level when sloping sidewalls are accounted for, they are much less important for the boundary bottom pressure torque (in the vertical sidewall case, sea level and torque are closely related, so the influence of dissipation on sea level is diminished). Although the real ocean will inevitably be more complex than these ideal cases, consideration of them does alter common assumptions about how coastal sea level is likely to respond to changing circulation patterns, in response to changing climatic forcing.