Choosing an Optimal β Factor for Relaxed Eddy Accumulation
Applications Across Vegetated and non-Vegetated Surfaces

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. This study evaluates a variety of different REA approaches with the goal of formulating universally applicable recommendations for an optimal choice of the β factor in combination with a suitable deadband. 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. 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 three different REA models for the β factor: The first method derives β0 based on a proxy for which high-frequency observations are available (sensible heat). The second method employs the approach of Baker et al. (1992), which computes βw solely based upon the vertical wind statistics. The third method uses a constant β derived from long-term averaging of the proxy-based β0 factor. Each β model was optimized with respect to deadband type and size before intercomparison. Concerning deadband form and size, we found an optimum in RMSE for linear deadbands with sizes of 0.5 and 0. 9σw. These deadband widths make this method approximately equal to the use of a constant β factor. With respect to overall REA performance, we found that the βw and constant β from long-term measurements performed more robustly than the proxy-dependent approach β0. The latter model still performed well when scalar similarity between the proxy (here sensible heat) and the scalar of interest (here latent heat) show strong statistical correlation, i.e. during periods when the distribution and temporal behavior of sources and sinks were similar. With respect to sensitivity of β to atmospheric stability, we observed that β0 slightly increased with increasing stability parameter z / L when no deadband is applied, but this trend vanished with increasing deadband size. βw was independent of z / L. To explain these surprising differences, we separated the contribution of w' kurtosis to the flux uncertainty, which can be expressed by the median ratio of the REA flux compared to that from classical eddy covariance FREAFEC. Results showed a strong sensitivity to site conditions: While the kurtosis of w' seems to have no effect on the flux estimate at the grassland site, decreasing trends with increasing kurtosis can be observed for the loose gravel and forests sites and could explain the variability of FREAFEC within 10 %. For REA applications without deeper site-specific knowledge of the turbulent transport and degree of scalar similarity, we recommend using either the constant β or βw models when REA scalar fluxes are not expected to be limited by the detection limit of the instrument. For conditions close to the instrument detection limit, the β0 models using a hyperbolic deadband are the optimum choice.