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.
The transition of the atmospheric boundary layer from land to sea remains insufficiently documented by observations, particularly under offshore flow conditions, where land-modified air undergoes rapid thermodynamic and dynamical adjustment over the ocean. This study uses high-resolution airborne observations from a series of research flights conducted over the German Bight in late summer 2024 to investigate the early-morning coastal marine boundary layer. From this dataset, two representative cases from the southern and eastern German Bight are analyzed in detail, capturing contrasting coastal and bathymetric conditions. Combined horizontal transects and vertical profiles reveal a shallow marine boundary layer capped by an inversion typically located between 100 and 250 m. The profiles further indicate the presence of low-level jets (LLJs), suggesting that turbulence during the morning hours was largely sustained by vertical wind shear under near-neutral to weakly stable conditions. Sea surface temperature (SST) exhibits pronounced small-scale variability in shallow nearshore regions, likely driven by tidal modulation and complex bathymetry, particularly over the Wadden Sea. These gradients are associated with variations in air–sea temperature contrasts, boundary-layer stability, turbulence, and wind-speed adjustment with increasing offshore distance. Comparison with the Copernicus North-West Shelf (NWS) ocean model and the Operational SST and Sea Ice Analysis (OSTIA) product reveals predominantly warm biases of approximately 0.2–1.0 K relative to the aircraft observations. Larger deviations occur under nearshore conditions due to unresolved shallow-water processes and strong small-scale SST variability. In addition, both datasets show limited skill in capturing the observed temporal evolution of SST, particularly under nearshore conditions with strong spatiotemporal variability. The observations suggest that offshore flow interacting with thermally heterogeneous coastal waters can produce a shallow, predominantly shear-driven marine boundary layer during the early morning across different coastal environments. These results highlight the importance of resolving nearshore SST variability in both space and time and provide observational constraints for improving the representation of coastal boundary-layer processes in atmospheric models and offshore wind applications.
