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

Equations are presented to correct eddy-covariance measurements for both fl uctuations in density and non-zero mean advection, induced by convergence o r divergence of flow, and spatial source/sink inhomogeneity, under steady-s tate and transient conditions. This correction collapses to the Webb-Pearma n-Leuning expression if the mean vertical velocity is zero, and formally ad ds the Webb-Pearman-Leuning expression to the corrections suggested by Lee for conditions of non-zero vertical velocity and source/sink and mean scala r horizontal homogeneity. The equation requires measurement of the mean ver tical gradients of the scalar concentration of interest (air temperature, h umidity, CO2) as well as an accurate estimation of the mean vertical veloci ty, in addition to the vertical eddy covariance of the scalar. Simple metho ds for the approximation of sensor tilt and complex terrain flow angle are presented, to allow estimation of non-zero mean vertical velocities. The eq uations 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 thermod ynamic expansion energy associated with water vapour flux is derived, which implies that the sonic temperature derived sensible heat flux will accurat ely include this contribution.