Extracting Integral-Scale Spatial-Temporal Relationships of Near-Surface Atmospheric Turbulence from Field Experimental Data

Knowing the integral time and length scales is critical for parameterizing the energy-containing turbulent motions. For field experimental data, direct estimates of integral length scales are highly limited owing to insufficient horizontal resolution of sensor deployments. With an objective to improve indirect estimates of integral length scales, a new approach is proposed to extract the spatial-temporal relationships embedded within field experimental data. The interest in integral scales motivates employing spatial correlations computed using both raw and time-block averaged turbulent fluctuations. For statistically stationary, horizontally homogeneous, fully developed turbulence, the spatial correlations are expected to: i) decrease with increasing separation distance in a certain direction given any averaging time block, and ii) increase with increasing averaging time blocks at any given separation distance. The fastest increase of spatial correlations separation distance on a logarithmic scale of the averaging time block provides a time scale related to the given separation distance and yields a spatial-temporal relationship. The new approach is applied to periods of statistically stationary and horizontally homogeneous flow identified during the Canopy Horizontal Array Turbulence Study (CHATS). During periods which satisfy the expectations for fully developed turbulence, the newly extracted spatial-temporal relationships provide convection velocity values consistent with previous field and laboratory measurements, and yield integral length scales in good agreement with available direct estimates based on the $e$-folding distances. For periods which involve non-turbulent motions, the new approach helps identify the responsible physical mechanisms like buoyancy oscillations (i.e., the vertical displacement associated with internal gravity waves).