Table 1.
Parameters characterizing the simulated atmosphere for each simulation.
The case names represent near-neutral (NN), weakly unstable (WU), moderately unstable (MU), strongly unstable (SU), and free convection (FC). Inc denotes the incoming energy (sum of the surface fluxes) and zi, u* and w* are time-averaged values during the data output.
Fig 1.
Standard deviation of streamwise velocity (σu) at 20 m height as a function of stability, and normalized by [44].
Fig 2.
Area-averaged spatial covariances (dashed lines) and temporal covariances (solid lines) for the different stabilities, with data up to 160 m from the fine grid, and normalized by the surface fluxes.
Red curves are for the sensible heat fluxes and blue curves for the latent heat fluxes.
Fig 3.
Horizontal cross sections for the SU case, at 20 m height, for the last hour of time-averaged data.
The imbalance term is derived for the sensible and latent heat fluxes separately. Blue is underclosure (positive I), red is overclosure (negative I).
Fig 4.
Probability density functions showing the horizontal variability of the Reynolds flux scaled by the surface flux at different height levels.
Plotted data are for the SU case, with the left panel the sensible and the right panel the latent heat flux. The heights are at 10 m (red), 20 m (magenta), 40 m (blue) and 80 m (cyan). The dashed lines represent the arithmetic mean and dashed-dotted lines the median.
Fig 5.
Imbalance ratios in the mixed layer (a) and the surface layer (b), as a function of the stability parameter u*/w*.
Please note the different range of the ordinates in the panels, because the imbalance is larger in the mixed layer than in the surface layer. The surface layer imbalance was computed at z = 0.04 zi, while the mixed layer imbalance was calculated from a vertical average between [0.3 zi − 0.5 zi]. Red markers are used for the sensible heat data (normalized potential temperature flux) and blue markers for the latent heat data (normalized humidity flux). It is important to note that the data in panel (a) are normalized with the spatial covariance. In the surface layer, the normalization is with the surface flux. The fits for F1H and F1E are given by the red and blue curves, respectively. We find as the coefficient of determination R2 = 93% for F1H and R2 = 82% for F1E. For the standard error of the regression in natural units we find S = 0.30 for F1H and S = 0.48 for F1E.
Fig 6.
Vertical dependence of the horizontally averaged imbalance ratio for different stabilities divided by the stability fit, with vertical values up to 160 m.
The case-independent fit is shown by the black line. Sensible heat flux in panel (a), latent heat flux in panel (b).
Fig 7.
Two-dimensional joint-probability density plots for six variables with reduced imbalance ratio for sensible heat and latent heat, respectively; i.e. the density plots of < I(x, y, z) >/(F1 (u*⁄w*)F2 (z⁄zi)) in function of 6 variables u*, Ruw, tke, , and ΔT or Δq with the latter being the temperature (moisture) difference between the measurement point and the surface.
The respective variables are listed at the abscissa. The different scales for the density follow from the range of the variables, due to the normalization condition on the probability density. For the density plots half-hourly averaged data from all 10 time intervals were considered.
Fig 8.
Relative importance of factors in the regression model for the latent heat flux (a) and the sensible heat flux (b).