The numerical experiment of the energy and CO2 imbalance problem using LES

Recent studies have shown evidence of energy budget deficit using the eddy covariance method. Since the vertical transport processes of heat and CO₂ are analogous, energy budget deficit is possibly associated with CO₂ imbalance. A recent numerical study implies the existence of this CO₂ imbalance as it reveals a physical mechanism of energy imbalance. However, CO₂ imbalance was not verified since investigation for the accuracy of the eddy covariance flux was limited for heat, which may be compared with the energy budget. The analogy between energy and CO2 imbalance was numerically examined using Large-Eddy Simulation (LES). Two numerical fields were used: heat supply and CO2 sink at the ground occur in a horizontal homogenous domain; and surface heating as one-dimensional sinusoidal variation occurs in a horizontal heterogeneous domain while the CO2 sink in a homogenous one. The heat and CO2 transport analogy was simulated better using the former case. To examine the imbalance in the homogenous case, eddy covariance fluxes at all grids on the horizontal surface 100 m above the ground, as well as the total surface budget, were compared. The result shows similarity between energy and CO2 imbalance and an analogy between the dependencies of the horizontal mean wind on these imbalances. It was found that the ratio of an imbalance to its total flux is equivalent to the vertical flux due to the turbulent organized structure (TOS) that remains after the temporal mean of one hour. The transport efficiency and imbalances of CO2 concentration and temperature are similar and analogous, respectively, since the temporal mean-horizontal distributions of both scalars reflect the behavior of the same TOS. In the heterogeneous surface heating case, the surface scalar budget is decomposed into three vertical fluxes: the eddy covariance term F_eddy, the mesoscale flux term F_meso that is invoked by heterogeneous surface heating, and the “TOS flux” term F_TOS that is caused by the vertical transport in TOS. A TOS includes clusters of thermal plumes, each with a time scale much longer than that of individual plumes, but not steady as mesoscale circulation. The surface budget for each scalar is given by: F_total = F_eddy + F_meso. + F_TOS. From the horizontal mean statistics showing a CO₂ and energy imbalance analogy, an increase in the horizontal heterogeneity results in an increase in the mesoscale flux, but a decrease in the TOS flux because the strong mesoscale circulation weaken the individual TOS. In spite of such similarity between the horizontal statistics of heat and CO₂, surface conditions cause a distinct difference between their local TOS fluxes. The ratio of the CO₂ TOS flux over the downdraft region at the mesoscale circulation is larger than that of heat. This disagreement is reflected in the difference in the vertical transport efficiencies of heat and CO₂ at a TOS.