This study presents a wall-modeled large-eddy simulation (WMLES) framework to simulate high-Reynolds-number daytime unstable sheared convective boundary layers (CBL). The framework is implemented using the open-source computational fluid dynamics code OpenFOAM, which employs finite-volume discretization on both uniform and non-uniform grids, and incorporates Hargreaves–Wright-based wall functions to model surface momentum and heat transfer. The Sigma subgrid-scale model, combined with these wall functions, reproduces the characteristic cellular-type convective structures of the moderately convective CBL and demonstrates better agreement with direct numerical simulation data than the universal law of the wall and the widely used Reichardt’s law. Two-point correlation analysis is used to estimate the number of grid cells required to resolve these coherent turbulent structures. Quadrant analysis is also implemented to characterize the momentum flux at the surface layer height as well as the heat flux in the mixed layer and entrainment zone. Based on these analyses, two grid resolution guidelines are proposed for WMLES of the present CBL configuration. The results also indicate that the conventional upper limit of 500 for the dimensionless wall distance ( z^+ ) can, for the present configuration, be extended to values on the order of 10^5 , enabling substantially coarser near-wall resolution. The proposed framework provides a basis for further WMLES studies of CBLs involving surface roughness, heterogeneity, terrain complexity, and advanced wall-modeling approaches.
High-resolution and long-term Doppler wind LiDAR observations obtained over various land cover types in the city of Hong Kong were analyzed in this study. The Monin-Obukhov Similarity Theory (MOST), and its extended forms accounting for an additional length scale and vertical variation of friction velocity ( u_* ), were examined. The analysis revealed that the roughness length ( z_0 ) derived from MOST flux-profile relations exhibited significant variability with changes in wind direction. This suggests the need to incorporate an anisotropic z_0 in numerical models for the area of interest, where there is considerable variability in wind directions. The comparison of non-dimensional wind profiles between MOST and observations suggested that accounting for the vertical variation of u_* improves the wind profiles under stable conditions. Subsequently, the variation of u_* , wind speed (U), and drag coefficient ( C_d ) against the stability was studied. The vertical profile of C_d was compared with the literature focusing on the urban environment, refitted to the present sites, and extended to non-neutral stabilities through a MOST-based stability correction. Overall, the results show that the extended MOST formulations retain meaningful predictive capability over complex and heterogeneous urban terrain when a direction-dependent roughness length, a height-dependent friction velocity ( u_* ), and a capped mixing length are incorporated: Across the five sites, the ensemble-mean normalized differences were generally below 20 50 m and approximately 200 m , although the differences increased above this range and under extremely stable conditions. These findings establish a range of practical applicability for extended MOST based on observations and identify the height and stability conditions governing its performance. The precise stability dependence of this range remains subject to uncertainty because L was obtained from a WRF configuration without a coupled urban canopy model.
Traditional turbulence regime criteria developed over flat terrain remain widely used but have not been rigorously evaluated in urban stable boundary layers (SBLs). Using multi-level turbulence measurements from the 325-m meteorological tower in Beijing, this study evaluates the applicability of classical turbulence transition frameworks in an urban SBL. Flux footprint analysis shows that the 80 4.1 m s^-1 at 140 m to 7.8 m s^-1 at 280 m. The critical gradient Richardson number increases from 0.48 at 140 m to 1.60 at 280 m, whereas the critical horizontal Froude number decreases from 0.49 to 0.23; neither threshold is robustly identified within the RSL. Spectral analysis shows that the dominant wavelength increases from 330 to 640 m at 140 m and from 410 to 1000 m at 280 m, while horizontal velocity variance remains approximately 3 times larger than vertical variance, indicating that turbulence structures above the RSL are consistent with pancake vortex structures. However, persistent three-dimensional mixing within the RSL obscures this organization. These results provide direct observational evidence that turbulence regime transitions in urban SBLs are height- and direction-dependent, highlighting the need for roughness-aware stability criteria in urban boundary-layer parameterizations.
For many decades within the eddy covariance (EC) community, the Webb, Pearman and Leuning (WPL, Webb et al. 1980) theory has been widely accepted as a “density (effect) correction” for flux measurements. However, this concept is potentially oversimplified because it omits the essential but unmeasurable mean vertical velocity ( w ) that the WPL equations ultimately correct. Therefore, we propose “ w correction” as an alternative but more comprehensive interpretation to show the essence of WPL theory, through detailed re-derivations based on mass conservation. To further support this idea, we conducted comprehensive error analysis for the directly measured w , mean CO2 and H2O density ( c ), and the w calculated by WPL correction ( w_WPL ) using EC data collected at a homogeneous agricultural site. Results showed that the directly measured w is (14 ± 57) mm·s−1 (monthly-mean ± standard deviation) at midday, while w_WPL is (0.84 ± 0.04) mm·s−1 with much smaller magnitudes and errors ( 5 c remain 100 times lower than those in w_WPL . Consistent with these results, WPL correction replaces the directly measured w with w_WPL while keeping the density measurement untouched. In this sense, WPL is not a “density” correction but a w correction, highlighting a future direction for more accurate EC measurement through improved anemometry. The idea of w correction rectifies a popular misunderstanding that closed-path EC systems or mixing ratio measurements do not require WPL correction and demonstrates the unnecessary assumption of zero dry air source/sink for the validity of WPL theory.
Estimating and monitoring the mixing‑layer height remains a crucial but difficult task, as it cannot be measured directly by routine surface observations and is typically inferred from remote-sensing measurements with limited spatial coverage. In this context, the inversion of near-surface turbulence measurements from relatively simple, low‑cost sonic anemometer offers a complementary solution. This paper reassesses the spectral approach proposed by Liu and Ohtaki in 1997 for determining the mixing-layer height, showing that its underlying assumptions are not physically justified, and presents a more consistent, although more complex, derivation. In addition, it presents two alternative methods, based on total and partial spectral integration, which yield comparatively simpler formulations.
