On the Subject of Geometric Spacing of Meteorological Sensors

Abstract : In an earlier study (Rachele et al., 1991), we concluded that to estimate turbulence characteristics such as the friction velocity, temperature scaling length, and the Obukhov (1946) length from discretely measured data, it is desirable and efficient, but not necessary, to have the sensors spaced geometrically with height. In that study we presented the mathematics necessary to show that geometric spacing is not necessary. The mathematical argument for geometric spacing was not developed or presented. Furthermore, we could not find a reference for it. Even so, we considered the traditional geometric spacing equations and compared results from them with our more general formulations based on the mean value theorem for a few examples and found that for practical applications the differences were not significant. For most turbulence studies in the boundary layer, one desires single values of the turbulence characteristics through a layer of perhaps 20, 30, or 100 m; that is, one typically assumes that the characteristic lengths are constant with height. A procedure for determining the total layer values is to compute the values in the geometrically spaced sublayers and then average the sublayer values. In this study we consider the case where the sensors are geometrically spaced. We then present our mathematical development requiring geometric spacing for a single sublayer based on the mean value theorem and assume that the values for the total layer (summation of sublayers) can be determined by averaging the sublayer values.