A stochastic linear theory of mesoscale circulation induced by the thermal heterogeneity of the land surface

https://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%281996%29053%3C3349%3AASLTOM%3E2.0.CO%3B2This paper presents a three-dimensional stochastic linear model of the mesoscale circulation induced by the variability of turbulent sensible heat flux over land surface. The primitive equations relating wind field, geopotential, and potential temperature are formulated as a system of stochastic partial differential equations and solved analytically. The solution is based on spectral representations of homogeneous random fields. The flow intensity is found to be proportional to the standard deviation of the turbulent sensible heat flux into the atmosphere. Large (small) scales of spatial variability in the surface heating preferably impact circulations at high (low) altitudes. The mesoscale fluxes associated with the atmospheric flow are related to explicit functions of atmospheric stability, variance of turbulent heat flux, and synoptic wind. The authors find that the vertical momentum flux is significant in the presence of synoptic wind and that the flow perpendicular to the direction of the synoptic wind is responsible for this momentum flux. The proposed linear theory identifies the synoptic conditions under which the land-surface heterogeneity may play a role in atmospheric circulations at the mesoscale.