Estimating Variances of Horizontal Wind Fluctuations in Stable Conditions

Information concerning the average wind speed and the variances of lateral and longitudinal wind velocity fluctuations is required by dispersion models to characterise turbulence in the atmospheric boundary layer. When the winds are weak, the scalar average wind speed and the vector average wind speed need to be clearly distinguished and both lateral and longitudinal wind velocity fluctuations assume equal importance in dispersion calculations. We examine commonly-used methods of estimating these variances from wind-speed and wind-direction statistics measured separately, for example, by a cup anemometer and a wind vane, and evaluate the implied relationship between the scalar and vector wind speeds, using measurements taken under low-wind stable conditions. We highlight several inconsistencies inherent in the existing formulations and show that the widely-used assumption that the lateral velocity variance is equal to the longitudinal velocity variance is not necessarily true. We derive improved relations for the two variances, and although data under stable stratification are considered for comparison, our analysis is applicable more generally.