A note on estimating the height of the convective internal boundary layer near shore

When cool air flows from the sea over a warm coast, the air is thermally modified. It is shown that h = cX ^1/2, where h is the height (in meters) of this thermal or convective internal boundary layer (CIBL) over the coast, X is the distance downwind (in meters) from the shoreline (i.e., the fetch), and c is a coefficient that relates to the shear velocity and wind speed inside the CIBL, potential temperature difference and entrainment coefficient across the CIBL, and the lapse rate outside the CIBL. This equation is a simplification of a theoretical equation and is supported by three similar formulations based on thermodynamic and dimensional analyses. Pertinent field experiments conducted near shorelines in France, Sweden, and Japan indicate that c is approximately 1.91, with a standard deviation of 0.38. All observations are within 95% confidence limits.