On the relationship between the eddy covariance, the turbulent flux, and surface exchange for a trace gas such as CO₂

Abstract

In the context of CO₂ surface exchange estimation, an analysis combining the basic principles of diffusion and scalar conservation shows that the mixing ratio is the appropriate variable both for defining the (eddy covariance) turbulent flux and also for expressing the relationship between the turbulent flux and surface exchange in boundary-layer budget equations. Other scalar intensity variables sometimes chosen, both the CO₂ density and molar fraction, are susceptible to the influence of surface exchange of heat and water vapour. The application of a hypsometric analysis to the boundary-layer “control volume” below the tower measurement height reveals flaws in previously applied approaches: (a) incompressibility cannot be assumed to simplify mass conservation (the budget in terms of CO₂ density); (b) compressibility alone makes the analysis of mass conservation vulnerable to uncertainties associated with resultant non-zero vertical velocities too small to measure or model over real terrain; and (c) the WPL (Webb et al. (1980) Quart J Roy Meteorol Soc 106:85–100) “zero dry air flux” assumption is invalidated except at the surface boundary. Nevertheless, the definition and removal of the WPL terms do not hinge upon this last assumption, and so the turbulent CO₂ flux can be accurately determined by eddy covariance using gas analysers of either open- or closed-path design. An appendix discusses the necessary assumptions and appropriate interpretations for deriving the WPL terms.