Exact Averaging of Atmospheric State and Flow Variables

Abstract

A new set of averaging rules is put forward that exactly determines the means of air temperature, mixing ratio, and velocity by incorporating weighting factors in accordance with physical conservation laws. For the temperature and velocity, respectively, the means calculated according to these rules are shown to be in accordance with the gas law and the most fundamental definition from classical mechanics. By contrast, those reckoned according to traditional arithmetic averaging rules are found to be incorrect. For studies of eddy transport, and micrometeorology in particular, such imprecisely determined averages of state and flow variables bias the perturbation variables over the entire averaging domain and thereby skew estimates of mass, heat, and momentum exchange unless appropriate adjustments (such as density corrections) are applied. The exact calculation of gas-phase averages amends this problem and is equally applicable to planetary-, synoptic-, and mesoscale averaging, as well as to climatology.