Extending the flux-variance method for carbon dioxide flux estimation

The flux-variance method is originally proposed by Tillman (1972) to estimate the momentum and sensible heat fluxes under unstable conditions. Since its inception, numerous efforts have been made to extend its applicability for the latent heat flux estimation, based on the scalar similarity between temperature (è) and water vapor (q). The major advantage of this method is its ability to estimate fluxes solely with the variances of relevant scalars, but without the turbulence measurements of wind. Motivated by the potential similarity between carbon dioxide (c) and other scalars, our study further extends its applicability for carbon dioxide flux estimation by proposing feasible strategies. The targeted micrometeorological situation is unstable conditions (positive sensible heat flux, H), evaporation (positive latent heat flux, LE), and carbon uptake (negative carbon dioxide flux, Fc) over a heterogeneous farmland. Recognizing that the density effects (WPL) correction is crucial to Fc estimation, we first make reliable H and LE estimations through a comprehensive intercomparison among various methodologies in the literature. Overall, the formulation of ‘free convection approximation' makes satisfactory H estimations with the calibrated flux-variance similarity relation of è. By choosing è as the ‘reference' scalar, two strategies are recommended for LE and Fc estimations. The first one relies on the calibrated flux-variance similarity relations of the scalars. The second one is based on the parameterization of relative transport efficiency in terms of scalar correlation coefficient and a nondimensional quantity. Currently, the relationship between the è-to-q transport efficiency (ëèq) and è-q correlation coefficient (Rèq) is recalibrated to describe the ‘intermediate' hydrological conditions and found to differ from that in a recent study. Furthermore, the è-to-c transport efficiency (ëèc) is parameterized as a function of è-c correlation coefficient (Rèc) by introducing the nondimensional ratio, namely á=H/åFc, where å is a constant. Our effort to estimate carbon dioxide flux with the flux-variance method introduces a potentially useful gap-filling strategy to the carbon flux community, when only the turbulent measurements of scalars are available.