An analysis of intermittency, scaling, and surface renewal in atmospheric surface layer turbulence

Turbulent velocity and scalar concentration time series were collected in the atmosphere above an ice sheet, a mesic grassland, and a temperate pine forest, thereby encompassing a wide range of roughness conditions encountered in nature. Intermittency and scaling properties of such series were then analyzed using Tsallis's non-extensive thermostatistics. While theoretical links between the Tsallis's non-extensive thermostatistics and Navier-Stokes turbulence remain questionable, the Tsallis distribution (a special interpretation of Student's t-distribution) provides a unifying framework to investigate two inter-connected problems: similarity between scalars and velocity statistics within the inertial subrange and "contamination" of internal intermittency by "external" factors. In particular, we show that "internal" intermittency models, including the She-Leveque, Lognormal, and Log-stable, reproduce the observed Tsallis parameters well for velocities within the inertial subrange, despite the differences in surface roughness conditions, but fail to describe the fluctuations for the scalars (e.g., air temperature CO₂ and water vapor). Such scalars appear more intermittent than velocity when the underlying surface is a large source or sink. The dissimilarity in statistics between velocity and scalars within the inertial subrange is shown to be strongly dependent on "external" intermittency. The genesis of "external" intermittency for scalars is linked to the classical Higbie surface renewal process and scalar source strength. Surface renewal leads to a ramp-like pattern in the scalar concentration (or temperature) time series with a gradual increase (rise-phase) associated with sweeping motion from the atmosphere onto the surface or into the canopy and a sharp drop associated with an ejection phase from the surface (or the canopy) back into the atmosphere. The duration of the rise-phase is on the order of the integral time scale, while the duration of the ejection phase is much shorter and is shown to impact the distributional tails at the small scales. Implications for "scalar turbulence" models are also discussed in the context of biosphere-atmosphere CO₂ exchange.