A typical speed of a sea breeze, compared to the ambient wind, is 25 knots, or 12 m/s. A typical temperature difference, for a strong sea breeze, is 10 C, or 18 F. Figure out how deep this sea breeze should be.
Most sea breezes are between 0.3 and 1.0 km in depth.
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At the surface, the passage of a sea breeze front (the onset of the sea breeze) is marked by a sudden windshift, a drop in temperature, and a very slight rise in pressure. Depending on the time of day, the maximum temperature may take place just before the sea breeze front comes through, or it may take place later. The timing of the sea breeze front is critical to forecasting the maximum temperature.
When the air mass over land is moist and unstable, the vertical motion at the sea breeze front often triggers convection. If thunderstorms are going to develop on a given day, they can usually be expected to form first along the sea breeze front, and then ahead of it. Often the outflow from the thunderstorms enhances the sea breeze front and the whole thing turns into a squall line. Soon after a sea breeze front comes through, with its cooler air at the surface, the chance for precip. is usually over for the day. The sea breeze continues through the rest of the day, keeping the temperatures lower.
The strength (or existence) of a sea breeze depends on the large-scale wind pattern. If the winds are onshore anyway, the speeds will pick up a little bit during the afternoon, but that's about it. If the winds are calm or light offshore (blowing from land to sea), the sea breeze will be noticeable and a sea breeze front is likely to form. If the winds are strongly offshore, sea breeze formation may be prevented completely. Depending on how warm a day it's going to be, an offshore wind of greater than 10 knots is usually sufficient to prevent sea breeze formation.
Land breezes affect the weather offshore, so they aren't generally a weather producer of concern for the Weather Challenge. They do matter a lot to sailors, though, who tend to be quite concerned (and rightfully so) with shifting winds as they approach harbors. They also matter for metropolitan area air quality, as they keep the pollutants low to the ground and carry them toward coastal areas.