An Analytical Solution for Three-Dimensional Sea–Land Breeze

Abstract

2015: An analytical solution for three-dimensional sea-land breeze. J. Atmos. Sci. Abstract 17 Based on the hydrostatic, incompressible Boussinesq equations in the planetary 18 boundary layer (PBL), the three-dimensional sea-land breeze (SLB) circulation has 19 been elegantly expressed as functions of the surface temperature distribution. The 20 horizontal distribution of the horizontal or vertical motion is determined by the first or 21 second derivative of the surface temperature distribution. For symmetric land-sea and 22 temperature distribution, the full strength of the sea breeze occurs at the inland but not 23 at the coastline and the maximum updraft associates with the heating center. Setting 24 the temperature difference between land and sea (TDLS) varies with the island size, 25 there would exist an optimal island size corresponding to the strongest SLB 26 circulation which weakens with both larger and smaller island size. Each velocity 27 component approaches to a peak at a certain vertical level. Both the peak value and 28 the corresponding vertical level link with the vertical scale of the surface temperature. 29 The more significant the surface temperature influences vertically, the stronger SLB 30 circulation at a higher vertical level it could induce. We apply the Weather Research 31 and Forecasting (WRF) model ideal simulation for two-dimensional sea breeze to 32 verify the theory. Two cases denoting land breeze and sea breeze respectively further 33 support the theory results despite there is certain slight discrepancy due to the highly 34 simplified theoretical equations. 35 Keywords 36 sea-land breeze, surface temperature distribution, Boussinesq equations, planetary 37 boundary layer 38 3 65 157

Theoretical Urban Heat Island Circulation in the Temperature Inversion Profile

“…At this point, we can finally explicitly express the UHI circulation as a function of the temperature distribution. The expressions are similar in form to the derivation presented by [15,16]. The solutions suggest that the induced circulation can be determined once the surface heating distribution is given.…”

“…Following [15,16], we set U = u + iv and substitute Equation (3) into Equations (1) and (2) to eliminate the pressure p. Then, Equations (1) and (2) can be written as…”

“…Our previous works [15,16] assumed an NTI profile, which portrays a temperature profile that exponentially declines with increasing altitude. According to this assumption, they obtained an elegant analytic solution of Equation (10).…”

“…By specifying different parameter values, this approach can reproduce both the NTI case and the STI case. For example, by setting n = 0, we can easily reduce Equation (12) to the NTI case used by [15,16].…”

“…The notations γ and δ are introduced in this study to shorten the expression in Equation (16) and are written as…”