Random Errors in the Stable Boundary Layer: Implications for Modern Observational Techniques

The stable atmospheric boundary layer (SBL) has significant societal impacts ranging from pollution dispersion to wind energy production. For decades, SBL turbulence has proven challenging to measure, parameterize, simulate, and interpret for a variety of reasons. For example, turbulence intensity in the SBL is often orders of magnitude smaller than in the convective boundary layer as thermal stratification suppresses vertical motions. As atmospheric stability increases, turbulence can also become intermittent in space and time, resulting in poor convergence of temporally-averaged turbulence statistics. Uncrewed aircraft systems (UAS) are becoming a reliable method to sample the atmospheric boundary layer, offering a new perspective for understanding the SBL. Moreover, continual computational advances have enabled the use of large eddy simulations (LES) to simulate the atmosphere at ever-smaller scales. LES is therefore a powerful tool in establishing a baseline framework to understand the extent to which vertical profiles from UAS can represent larger-scale SBL flows. While UAS technology is beginning to revolutionize our abilities to observe the ABL, to fully close the data gap it is imperative to understand how well individual multicopter profiles can represent the larger scales and overall atmospheric flow. To explore this concept, we estimate the relative random errors for various observable and derivable quantities ranging from wind speed and temperature to momentum and heat fluxes. Random errors are different from measurement errors in that they arise due to insufficient temporal averaging of a timeseries that causes discrepancies when compared to the true ensemble means upon which turbulence theories are based. Because it is impossible to determine an ensemble mean for the real atmosphere, here we employ an LES model, where the largest scales of turbulence, responsible for the majority of transport, are resolved explicitly, while the effects of the small scales are represented through a subgrid scale model. We perform a random error analysis across six simulated cases with global stability ranging from 1.6 < h/L < 10.3, where h is the depth of the SBL and L is the Obukhov length at the lowest model gridpoint. For each experiment, we estimate profiles of relative random errors using the relaxed filtering method, which estimates the error variance based on a power law extrapolated from a local filtering decomposition. With this method we can estimate relative random errors for first- and second-order turbulence moments as a function of averaging time, stability, and height above the surface. We then emulate virtual UAS profiles extracted from the LES experiments to show how well the quasi-instantaneous profiles compare with the approximate ensemble mean. Finally, we conclude this section with a discussion on optimal UAS ascent rates and averaging times to minimize the effects of random errors.