Temperature stratification and refraction errors in geodetic leveling

Abstract

Refraction errors in geodetic leveling due to temperature stratification of the lower atmosphere are presented within the framework of Monin‐Obukhov similarity theory. Universal expressions for the nondimensional mean temperature gradient, accounting for both buoyant convection and mechanically induced mixing, were incorporated into the integration of ray path height with imposed refractive curvature to obtain estimates of the net error in elevation difference on sloping terrain. Exact solutions were found for the refraction error, but approximate versions had the advantage that a normalized refraction error was independent of shot length and terrain slope. Calculations demonstrated that refraction errors increase monotonically with increasing surface heat flux but that maximum errors are found at a finite value of the wind speed such that the ratio of the telescope height to the Obukhov length is independent of heat flux.A free convection approximation provided a close match to the maximum refraction error found from the more general solution for the same surface heat flux, indicating that a free convection approximation yields an upper bound to the refraction error. Calculations of refraction error based on environmental measurements taken during a 1981 survey between Saugus and Palmdale, California, showed that a free convection approximation overestimated the refraction error by a factor ranging from 1.09 to 1.53 depending on the magnitude of the surface roughness length.