The role of secondary circulations and dispersive fluxes for the energy-balance closure problem

Secondary circulations, either cell-like or roll-like, develop frequently in convective conditions. They often fill the entire boundary layer and do not move with the mean wind, thereby violating the ergodic hypothesis. Nevertheless, they contribute to the overall flux of sensible and latent heat and the associated transport can be quantified through the dispersive flux, which is the spatial covariance of the temporal mean of the vertical velocity and the transported scalar. Since this dispersive flux inherently cannot be measured by single-tower eddy covariance, neglecting this flux leads to a systematic underestimation, which is one major contributor to the energy-balance closure problem. It is not the only reason for this problem, but one of the most important ones that generally exists at all sites around the world and that acts in the same direction as the small-scale turbulent flux. We show findings from dedicated measurement campaigns, such as CHEESEHEAD19, aiming at quantifying dispersive fluxes. The results are compared against systematic large-eddy simulations (LES) under different stability regimes. Since it is not feasible to conduct such expensive simulations for all eddy-covariance measurement to quantify the additional, otherwise neglected dispersive flux, similarity relationships are derived from the LES results and their universal applicability is evaluated for several long-term flux measurement sites. In addition, an outlook is provided on the use of machine learning models informed by LES to integrate the effects of surface thermal heterogeneity for the prediction of dispersive fluxes. This analysis demonstrates that dispersive fluxes, being one of the main reasons for the energy balance closure problem, can be readily quantified with a limited amount of additional data, most of all the boundary-layer height, to correct recent and historical eddy-covariance measurements.