Correction of eddy-covariance measurements incorporating both advective effects and density fluxes

Equations are presented to correct eddy-covariance measurements for both fluctuations in density and non-zero mean advection, induced by convergence or divergence of flow, and spatial source/sink inhomogeneity, under steady-state and transient conditions. This correction collapses to the Webb-Pearman-Leuning expression if the mean vertical velocity is zero, and formally adds the Webb-Pearman-Leuning expression to the corrections suggested by Lee for conditions of non-zero vertical velocity and source/sink and mean scalar horizontal homogeneity. The equation requires measurement of the mean vertical gradients of the scalar concentration of interest (air temperature, humidity, CO2) as well as an accurate estimation of the mean vertical velocity, in addition to the vertical eddy covariance of the scalar. Simple methods for the approximation of sensor tilt and complex terrain flow angle are presented, to allow estimation of non-zero mean vertical velocities. The equations are applied to data from a maize crop and a forest to give examples of when the correction is significant. In addition, a term for the thermodynamic expansion energy associated with water vapour flux is derived, which implies that the sonic temperature derived sensible heat flux will accurately include this contribution.