Empirical Observations of Scaling and Symmetry in the Atmospheric Boundary Layer

Using multiple measurement techniques from five locations, including Ecole des Ponts, we study the scaling and symmetries of measured atmospheric quantities in space and time in the atmospheric boundary-layer. Combining LIDAR, SODAR, RADAR, and sonic anemometer data, provides a means to analyse time-scales from 0.02 seconds to 15 years! and heights from 10m to 8km! Understanding and modelling the properties of the atmosphere over these immense ranges of space and time scales with a unique model is only possible through the scales. Moreover, the complex relationships between space and time-scales in the boundary- layer means symmetries differ greatly from classical turbulence theory. Small-temporal scale analysis (<15 minutes) of the velocity fluctuations shows (now) classical models for turbulence are respected over all measurement locations; classical in the sense that a Kolmogorov turbulence model with a significant intermittency correction is respected. Above these time-scales the stability of the atmosphere plays a key role. As such the time-scaling of the velocity is much more complex and classical space-time symmetries aren't respected. Using empirically estimated spectral energies and simple scaling and symmetry arguments we propose a model for the atmospheric boundary-layer that predicts only two possible profiles for the vertical transfer of energy. We discuss the space-time scaling properties of this model and the consequences thereof for the velocity fluctuations.