A linear model is applied to study these gravity waves. Analytical analysis is performed for various heating depths, mountain widths, friction, Coriolis effect, background mean wind, and stability. We assess how these affect the amplitude, dissipation, initiation phase, and propagation speed of the diurnal disturbance. Idealized WRF simulations exhibit the propagation of precipitation initially triggered by sea breeze, and distinguished from a mountain-plain circulation. Convection from mountain heating starts earlier; propagates slower; and damps faster than that of the sea breeze; the nonlinear combination of which depends on proximity to mountains. Over the open ocean, the dominant signal propagates as that of the sea breeze but with stronger convection. For mountains near the coast, there is slower propagation and stronger convection for several dynamical reasons to be discussed.