A Numerical Model of the Sea-Breeze Phenomenon over a Lake or Gulf

Abstract

A two-dimensional primitive equation model is constructed and used to investigate the circulations induced by differential heating in the vicinity of a land-locked semi-infinite body of water. The semi-empirical boundary-layer formulation of Clarke is used with an expanding σ grid of 15 vertical levels. Surface temperature is computed by means of a heat-flux balance equation and a radiation condition is used at the lateral boundaries. For purposes of comparison, one run was also made with reflective boundary conditions and it was found that the two solutions differ significantly only when the sea-breeze front is in the vicinity of a lateral boundary. The model reproduces the vast sea breezes of Australia, some of which have been observed to penetrate distances of 200–300 km inland. This feature of the model is attributed to the detailed boundary-layer formulation, in which the momentum and heat exchange coefficients are expressed as functions of stability and wind shear at all levels, and also to the determination of surface temperature through a balance of heat fluxes. The latter aspect of the model allows horizontal gradients of surface temperature to exist ahead of and behind the front and thus to produce a greater discrepancy between the sensible heat fluxes on either side of the front, which in turn produces a stranger thermal gradient across the front. A secondary “cutoff” circulation is seen to develop in the late afternoon when the sea-breeze front is well inland. This low-level phenomenon lasts only a couple of hours and is basically due to the modification of air of marine origin as it flows inland. A land breeze develops gradually from the ground surface upward under an opposing overriding flow in much the same manner as has been described in observations studies. However, the model land breeze begins at the center of the body of water and an explanation is given in terms of the limited size of the water area. A run is made in which the water width is slightly more than doubled and it is found that a stronger breeze results. This lake breeze also moves inland at a faster rate. Stronger vertical velocities are obtained, but downward motion over the water is found to be more intense for the smaller lake. All these effects can he traced to the fact that heat produced over the water by advection in the return flow and by subsidence in the very stable lower layers has a lesser area in which to distribute itself in the cast of the smaller lake. The model is integrated for gradient winds of 5 m s−1 front the east, northeast and north. Comparison with limited observations reveals good agreement. It is also seen that the interaction of circulations from opposite shorelines produces effects which could not be predicted by modeling the lake or gulf breeze at one shoreline alone.