Fig 1.
Temperature distribution at the surface for the three sets of simulations with heterogeneous surfaces.
Table 1.
Fitting parameters for all simulation cases with different surface characteristics.
Fig 2.
Imbalance ratios as a function of the atmospheric stability.
Panel a shows the imbalance ratio I at 0.04 z/zi as a function of the stability parameter u⁎/w⁎. The four simulation sets are represented by different colors. For each simulation set, a separate fit of the scaling function F1 was performed, resulting in Eq 11 with different fitting parameters shown in Table 1. The atmospheric stability is steered by changes in Ug, shown by different marker shapes. The grey line shows the fit obtained by De Roo et al. [58] (Eq 3) for comparison. Panel b shows the vertical profiles of the imbalance normalized with the four fits of F1 (Eq 11), respectively. The blue line shows the fitted scaling function F2,R (Eq 12). Again, the respective scaling function derived by De Roo et al. [58] (Eq 4) is shown in grey for comparison.
Table 2.
Overview over characteristic variables that are relevant for this study, including geostrophic wind speed Ug, boundary layer height zi, the friction velocity u⁎, the Deardorff velocity w⁎, the atmospheric stability parameters u⁎/w⁎ and -zi/L, the heterogeneity parameter , and the energy imbalance I for each simulation.
Fig 3.
Vertical profiles of the imbalance all normalized with the same scaling function F1,HM (Eq 11, Table 2).
Fig 4.
Dependence of the imbalances at 0.04 zi all normalized with the same scaling function F1,HM (Eq 11, Table 1) on the heterogeneity parameter .
The data is separated into two groups: (1) simulations with Ug = 1 m s-1 that show cellular shaped secondary circulations and (2) simulations with Ug ≥ 3 m s-1 simulation that show roll-shaped secondary circulations. Simulations with Ug = 2 m s-1 are discarded because they show no clearly cellular nor roll-shaped structures. The two blue lines show the fits of the third scaling function to the two groups (F3,c and F3,r, Eqs 13–14).
Fig 5.
Exemplary horizontal cross-sections of the half-hourly averaged vertical wind speed w at 0.04 zi for HT200 and HT400 simulations with Ug up to 4 m s-1.
Fig 6.
Vertical profiles of the imbalance all normalized with the same scaling function F1,HM (Eq 11, Table 1) and the respective scaling functions F3,c or F3,r (Eqs 13–14).
The blue line shows the fitted scaling function F2,N (Eq 15). The scaling function derived by De Roo et al. [58] is shown in grey for comparison.
Fig 7.
Comparison of different correction methods.
The distribution of the heat flux H among all simulations is shown in box plots, where the blue line represents the median and the dashed red line represents the mean. At the very left, the distribution of the uncorrected H at 0.04 zi is shown. In second and third place, the H corrected with our approaches A and B are shown. In the fourth place, H corrected with the method by De Roo et al. [58] is shown. At the very right, H is corrected with a combination of F1 and F2 derived by De Roo et al. [58] and F3 derived in approach B in this study.