An Analytical Solution for Three-Dimensional Sea–Land Breeze

Based on the hydrostatic, incompressible Boussinesq equations in the planetary boundary layer (PBL), the three-dimensional sea-land breeze (SLB) circulation has been elegantly expressed as functions of the surface temperature distribution. The horizontal distribution of the horizontal or vertical motion is determined by the first or second derivative of the surface temperature distribution. For symmetric land-sea and temperature distribution, the full strength of the sea breeze occurs inland but not at the coastline, and the maximum updraft associates with the heating center. Setting the temperature difference between land and sea (TDLS), which varies with the island size, there would exist an optimal island size corresponding to the strongest SLB circulation that weakens with both a larger and smaller island size. Each velocity component approaches a peak at a certain vertical level. Both the peak value and the corresponding vertical level link with the vertical scale of the surface temperature: the more significant the influence of the surface temperature vertically, the stronger the SLB circulation at a higher vertical level it induces. The Weather Research and Forecasting (WRF) Model's ideal simulation for the two-dimensional sea breeze is applied to verify the theory. Two cases, land breeze and sea breeze, further support the theory's results despite a certain slight discrepancy due to the highly simplified theoretical equations.