Choosing an optimal β factor for relaxed eddy accumulation applications across vegetated and non-vegetated surfaces
Authors: Vogl Teresa , Hrdina Amy , Thomas Christoph K. 
Published: September 2021

Abstract. Accurately measuring the turbulent transport of reactive and conservative greenhouse gases, heat, and organic compounds between the surface and the atmosphere is critical for understanding trace gas exchange and its response to changes in climate and anthropogenic activities. The relaxed eddy accumulation (REA) method enables measuring the land surface exchange when fast-response sensors are not available, broadening the suite of trace gases that can be investigated. The β factor scales the concentration differences to the flux, and its choice is central to successfully using REA. Deadbands are used to select only certain turbulent motions to compute the flux. This study evaluates a variety of different REA approaches with the goal of formulating recommendations applicable over a wide range of surfaces and meteorological conditions for an optimal choice of the β factor in combination with a suitable deadband.
Observations were collected across three contrasting ecosystems offering stark differences in scalar transport and dynamics: a mid-latitude grassland ecosystem in Europe, a loose gravel surface of the Dry Valleys of Antarctica, and a spruce forest site in the European mid-range mountains.
We tested a total of four different REA models for the β factor: the first two methods, referred to as model 1 and model 2, derive βp based on a proxy p for which high-frequency observations are available (sensible heat Ts). In the first case, a linear deadband is applied, while in the second case, we are using a hyperbolic deadband. The third method, model 3, employs the approach first published by Baker et al. (1992), which computes βw solely based upon the vertical wind statistics. The fourth method, model 4, uses a constant βp, const derived from long-term averaging of the proxy-based βp factor. Each β model was optimized with respect to deadband size before intercomparison.
To our best knowledge, this is the first study intercomparing these different approaches over a range of different sites. With respect to overall REA performance, we found that the βw and constant βp, const performed more robustly than the dynamic proxy-dependent approaches. The latter models still performed well when scalar similarity between the proxy (here Ts) and the scalar of interest (here water vapor) showed strong statistical correlation, i.e., during periods when the distribution and temporal behavior of sources and sinks were similar.
Concerning the sensitivity of the different β factors to atmospheric stability, we observed that βT slightly increased with increasing stability parameter z/L when no deadband is applied, but this trend vanished with increasing deadband size. βw was unrelated to dynamic stability and displayed a generally low variability across all sites, suggesting that βw can be considered a site-independent constant. To explain why the βw approach seems to be insensitive towards changes in atmospheric stability, we separated the contribution of w′ kurtosis to the flux uncertainty. For REA applications without deeper site-specific knowledge of the turbulent transport and degree of scalar similarity, we recommend using either the βp, const or βw models when the uncertainty of the REA flux quantification is not limited by the detection limit of the instrument. For conditions when REA sampling differences are close to the instrument's detection limit, the βp models using a hyperbolic deadband are the recommended choice.