Comparing ensemble- and time-averaged Reynolds flux composites at different scales to capture ecosystem sensitivity to light change.

Abstract:

Flux network data (Baldocchi et al. 2001) are used to generate continuous estimates of fluxes at half- to hourly intervals. However, studying whole-ecosystem sensitivity to particular environmental influences (e.g., to step illumination changes), accurate flux estimates are needed more frequently (KF 2019). To avoid the conundrum that short time-averaged eddy-covariance fluxes have greater uncertainty (convergence of averages criterion; Wyngaard 2010) we use ensembles of the multiple ‘realizations’ of particular events (KF 2018, 2019). We compare 10-s ensemble and short-interval time-averaged fluxes found using three independent timescales: (i) mean-removal scale for time-fluctuation calculation \[X^{T'}\] and \[w^{T'}\]; (ii) offset-removal scale \[[a,b]\] for ensemble-flux estimation \[<w'X'>\]; and (iii) 2D rotation-of-velocity scale (Kaimal and Finnigan 1994) for time averaging. Applying these scales, we found that ensemble fluxes guarantee conservation given offset removal: \[\overline{<w'X'>}=\overline{<w^{T^{[a,b]'}}X^{T^{[a,b]'}}>}=<\overline{w^{T'}X^{T'}}>-\overline{<w^{T'}><X^{T'}>}\] with \[\overline{<w^{T'}><X^{T'}>}\] term representing the role of non-ergodicity. Low-frequency losses in the short-interval fluxes (Lenschow et al. 1993; Sakai et al. 2001) are addressed by applying the long mean- and offset-removal scales.

The resulting heat, net ecosystem exchange, and evapotranspiration ensemble fluxes for different scales (Figs. 1a-c) show consistent behavior for up to the 500-s mark following a shadow-to-light transition, when the number of events sampled becomes < 50 (dashed black line). The offset-removal–scale size is unimportant given at least 100 events total. However, some larger scatter and the respective flux underestimates are obtained for scales ≤ 30 min (Figs. 1d-f).

The long mean removal allows 1-min time-averaged fluxes (Figs. 1g-i) to have the same magnitude as do their respective ensemble values (gray lines). The 1-min flux describes the key features of the exponential ensemble-flux changes in non-steady-state conditions as well as captures the ongoing fluctuations. It fails only when the sharp changes in ensemble flux occur at a transition requiring shorter fluxes with the comparable scales to be used. The best timescales for the 1-min fluxes to match ensemble fluxes are 30-50 minutes.