Exact averaging procedures for atmospheric state and flow variables

A new set of rules exactly determines the averages of the temperature, mixing ratio, and velocity in accordance with the laws of physical conservation. These rules yield both mean temperatures that obey the gas law, and also average velocities that accord with the definition from classical mechanics. The same is not true for the results of traditional arithmetic averaging, which therefore are shown to contain errors. These errors in traditionally calculated mean temperatures and velocities bias the perturbation ("eddy") components of such variables over the whole averaging domain, and thereby skew estimates of turbulent fluxes unless they are adjusted as via "density corrections". The new rules for exactly calculated averages are valid at scales extending beyond the atmospheric boundary layer.