Observing Entrainment Processes Using a Small Unmanned Aerial Vehicle: A Feasibility Study

Measurement flights with the meteorological mini aerial vehicle (M $^2$ AV) were performed in spring 2011 to assess the capability of an unmanned aerial vehicle (UAV) to measure the structure of the transition zone between the convective boundary layer and the stably stratified free atmosphere. The campaign took place at the Meteorological Observatory Lindenberg/Richard-Aßmann-Observatory of the German Meteorological Service. Besides the M $^2$ AV flights, observations were made from a 12-m and a 99-m tower, a sodar, two ceilometers, radiosondes, and a tethered balloon with sensor packages at six different levels. M $^2$ AV measurements were intentionally combined with remote sensing systems. The height range of the entrainment zone as well as its diurnal cycle were provided by the remote sensing instruments. The UAV provided the high-resolution in situ data of temperature and wind for the study of turbulent processes. It is shown that the M $^2$ AV is able to maintain constant altitude with very small deviations—a pre-requisite to study processes inside the often quite thin entrainment zone and that M $^2$ AV high-resolution wind and temperature measurements allow for very detailed studies of the fine structure of the atmosphere and thus for the identification of quite local and/or short-duration processes such as overshooting thermals or downward intrusions of warm air. Spatial series measured by the M $^2$ AV during horizontal flights show turbulent exchange of heat in short turbulent bursts at heights close to and within the entrainment zone. Scaled vertical profiles of vertical velocity, potential temperature variance, and sensible heat flux confirm the general shape found by previous measurements and numerical studies.     

The Effect of Surface Heterogeneity on the Structure Parameters of Temperature and Specific Humidity: A Large-Eddy Simulation Case Study for the LITFASS-2003 Experiment

We conduct a high-resolution large-eddy simulation (LES) case study in order to investigate the effects of surface heterogeneity on the (local) structure parameters of potential temperature \(C_T^2\) and specific humidity \(C_q^2\) in the convective boundary layer (CBL). The kilometre-scale heterogeneous land-use distribution as observed during the LITFASS-2003 experiment was prescribed at the surface of the LES model in order to simulate a realistic CBL development from the early morning until early afternoon. The surface patches are irregularly distributed and represent different land-use types that exhibit different roughness conditions as well as near-surface fluxes of sensible and latent heat. In the analysis, particular attention is given to the Monin–Obukhov similarity theory (MOST) relationships and local free convection (LFC) scaling for structure parameters in the surface layer, relating \(C_T^2\) and \(C_q^2\) to the surface fluxes of sensible and latent heat, respectively. Moreover we study possible effects of surface heterogeneity on scintillometer measurements that are usually performed in the surface layer. The LES data show that the local structure parameters reflect the surface heterogeneity pattern up to heights of 100–200 m. The assumption of a blending height, i.e. the height above the surface where the surface heterogeneity pattern is no longer visible in the structure parameters, is studied by means of a two-dimensional correlation analysis. We show that no such blending height is found at typical heights of scintillometer measurements for the studied case. Moreover, \(C_q^2\) does not follow MOST, which is ascribed to the entrainment of dry air at the top of the boundary layer. The application of MOST and LFC scaling to elevated \(C_T^2\) data still gives reliable estimates of the surface sensible heat flux. We show, however, that this flux, derived from scintillometer data, is only representative of the footprint area of the scintillometer, whose size depends strongly on the synoptic conditions.     

Thermal Stratification Effects on Flow Over a Generic Urban Canopy

The influence of local surface heating and cooling on flow over urban-like roughness is investigated using large-eddy simulations. By adjusting the incoming or outgoing heat flux from the ground surface, various degrees of local thermal stratification, represented by a Richardson number \((Ri_\tau )\) , were attained. Drag and heat transfer coefficients, turbulence structure, integral length scales, and the strength of quadrant events that contribute to momentum and heat fluxes were obtained and are compared with locally stable, neutral and unstable flows. With increasing \(Ri_\tau \) , or equivalently as the flow characteristics change from local thermal instability to stability, a gradual decline in the drag and heat transfer coefficients is observed. These values are found to be fairly independent of the type of thermal boundary condition (constant heat flux or constant temperature) and domain size. The maps of anisotropy invariants showed that for the values of \(Ri_\tau \) considered, turbulence structures are almost the same in shape for neutral and unstable cases but differ slightly from those in the stable case. The degree of anisotropy is found to decrease as \(Ri_\tau \) increases from \(-2\) to 2.5. Compared to the neutral case, the integral length scales are shortened in the streamwise and vertical direction by ground cooling, but enhanced in the vertical direction with ground heating. Quadrant analysis showed that an increase in floor heating increases the strength of ejections above the canopy. However, the contributions of updrafts or downdrafts to the heat flux are found not to be significantly influenced by the type of local thermal stratification for the values of \(Ri_\tau \) considered. From the octant analysis, the transport mechanisms of momentum and heat above the canopy are found to be very similar in both locally unstable and stable flows.     

Large-Eddy Simulation of Heat Transfer from a Single Cube Mounted on a Very Rough Wall

The local thermal effects in the wake of a single cube with a strong heated rear face, representing a large building in an urban area, are studied using large-eddy simulations (LES) for various degrees of heating, which are characterized by the local Richardson number, $Ri$ . New wall models are implemented for momentum and temperature and comparison of the flow and thermal fields with the wind-tunnel data of Richards et al. (J Wind Eng Ind Aerodyn 94, 621–636, 2006) shows fair agreement. Buoyancy effects are quite evident at low $Ri$ and a significant increase in the turbulence levels is observed for such flows. Apart from the comparisons with experiments, further analysis included the estimation of the thermal boundary-layer thickness and heat transfer coefficient for all $Ri$ . For sufficiently strong heating, the heat transfer coefficient at the leeward face is found to be higher than the roof surface. This suggests that, beyond a certain $Ri$ value, buoyancy forces from the former surface dominate the strong streamwise convection of the latter. Quadrant analysis along the shear layer behind the cube showed that the strength of sweeps that contribute to momentum flux is considerably enhanced by heating. The contribution of different quadrants to the heat flux is found to be very different to that of the momentum flux for lower $Ri$ .     

Scalar Flux–Gradient Relationships Under Unstable Conditions over Water in Coastal Regions

The scalar flux–gradient relationships of temperature ( $\phi _{T}$ ? T ) and specific humidity ( $\phi _{q}$ ? q ) under unstable conditions are investigated using eddy-covariance measurements of air–sea turbulent fluxes and vertical profiles of temperature and specific humidity collected from a marine meteorological platform. The gradients of temperature and specific humidity are obtained from measurements at five heights above the sea surface using the log-square fitting method and the simpler first-order approximation method. The two methods yield similar results. The proposed flux–gradient relationships $\phi _{T}$ ? T and $\phi _{q}$ ? q covers a wide range of instability: the stability parameter $\zeta $ ζ ranges from $-$ ? 0.1 to $-$ ? 50. The functional form of the proposed flux–gradient relationships is an interpolation between the Businger–Dyer relation and the free convection relation, which includes the “ $-$ ? 1/2” and “ $-$ ? 1/3” scaling laws at two different stability regimes. The widely used COARE 3.0 algorithm, which is an interpolation between the integrals of the Businger–Dyer and the free convection relations, is also evaluated and compared. The analysis and comparisons show that both schemes generate reasonable values of $\phi _{q}$ ? q in the whole unstable regime. The COARE 3.0 algorithm, however, overestimates $\phi _{T}$ ? T values under very unstable conditions. The errors in the flux–gradient relationships induced by the random errors in the turbulence measurements are assessed. When the random errors are taken into account, the observations agree with predictions of various schemes fairly well, implying that the dominant transport mechanism is adequately captured by the Monin–Obukhov similarity theory. The study also shows that $\phi _{q}$ ? q is significantly ${>}\phi _{T}$ > ? T under unstable conditions and that the ratio $\phi _{q}/\phi _{T}$ ? q / ? T increases with $-\zeta $ ? ζ . The ratio of $\phi _{q}$ ? q to $\phi _{T}$ ? T and the ratio of turbulent transport efficiencies of heat and water vapour ( $R_{wT}/R_{wq}$ R wT / R wq ) suggest that heat is transported more efficiently than water vapour under unstable conditions.     

Laboratory Experiments on Convective Entrainment Using a Saline Water Tank

Entrainment fluxes in a shear-free convective boundary layer have been measured with a saline water tank set-up. The experiments were targeted towards measuring the entrainment behaviour for medium to high Richardson numbers and use a two-layer design, i.e. two stacked non-stratified (neutral) layers with different densities. With laser induced fluorescence (LIF), the entrainment flux of a fluorescent dye is measured for bulk Richardson numbers in the range 30–260. It is proposed that a carefully chosen combination of top-down and bottom-up processes improves the accuracy of LIF-based entrainment observations. The observed entrainment fluxes are about an order of magnitude lower than reported for thermal water tanks: the derived buoyancy entrainment ratio, $A$ , is found to be $A \approx 0.02$ , which is to be compared with $A\approx 0.25$ for a thermal convection tank (Deardorff et al., J Fluid Mech 100:41–64, 1980). An extensive discussion is devoted to the influence of the Reynolds and Prandtl numbers in laboratory experiments on entrainment.     

An Optimal Inverse Method Using Doppler Lidar Measurements to Estimate the Surface Sensible Heat Flux

Inverse methods are widely used in various fields of atmospheric science. However, such methods are not commonly used within the boundary-layer community, where robust observations of surface fluxes are a particular concern. We present a new technique for deriving surface sensible heat fluxes from boundary-layer turbulence observations using an inverse method. Doppler lidar observations of vertical velocity variance are combined with two well-known mixed-layer scaling forward models for a convective boundary layer (CBL). The inverse method is validated using large-eddy simulations of a CBL with increasing wind speed. The majority of the estimated heat fluxes agree within error with the proscribed heat flux, across all wind speeds tested. The method is then applied to Doppler lidar data from the Chilbolton Observatory, UK. Heat fluxes are compared with those from a mast-mounted sonic anemometer. Errors in estimated heat fluxes are on average 18 %, an improvement on previous techniques. However, a significant negative bias is observed (on average $-63\,\%$ ) that is more pronounced in the morning. Results are improved for the fully-developed CBL later in the day, which suggests that the bias is largely related to the choice of forward model, which is kept deliberately simple for this study. Overall, the inverse method provided reasonable flux estimates for the simple case of a CBL. Results shown here demonstrate that this method has promise in utilizing ground-based remote sensing to derive surface fluxes. Extension of the method is relatively straight-forward, and could include more complex forward models, or other measurements.     

Vertical Distribution of Radiation and Energy Balance Partitioning Within and Above a Lodgepole Pine Stand Recovering from a Recent Insect Attack

The current outbreak of mountain pine beetle (MPB) that started in the late 1990s in British Columbia, Canada, is the largest ever recorded in the north American native habitat of the beetle. The killing of trees is expected to change the vertical distribution of net radiation ( $Q^*$ Q ? ) and the partitioning of latent ( $Q_\mathrm{E}$ Q E ) and sensible ( $Q_\mathrm{H}$ Q H ) heat fluxes in the different layers of an attacked forest canopy. During an intensive observation period in the summer of 2010, eddy-covariance flux and radiation measurements were made at seven heights from ground level up to 1.34 times the canopy height in an MPB-attacked open-canopy forest stand $(\hbox {leaf area index} = 0.55~\mathrm{{m}}^{2}\ \mathrm{{m}}^{-2})$ ( leaf area index = 0.55 m 2 m - 2 ) in the interior of British Columbia, Canada. The lodgepole pine dominated stand with a rich secondary structure (trees and understorey not killed by the beetle) was first attacked by the MPB in 2003 and received no management. In this study, the vertical distribution of the energy balance components and their sources and sinks were analyzed and energy balance closure (EBC) was determined for various levels within the canopy. The low stand density resulted in approximately 60 % of the shortwave irradiance and 50 % of the daily total $Q^*$ Q ? reaching the ground. Flux divergence calculations indicated relatively strong sources of latent heat at the ground and where the secondary structure was located. Only very weak sources of latent heat were found in the upper part of the canopy, which was mainly occupied by dead lodgepole pine trees. $Q_\mathrm{H}$ Q H was the dominant term throughout the canopy, and the Bowen ratio ( $Q_\mathrm{H}/Q_\mathrm{E}$ Q H / Q E ) increased with height in the canopy. Soil heat flux ( $Q_\mathrm{G}$ Q G ) accounted for approximately 4 % of $Q^*$ Q ? . Sensible heat storage in the air ( $\Delta Q_\mathrm{S,H}$ Δ Q S , H ) was the largest of the energy balance storage components in the upper canopy during daytime, while in the lower canopy sensible heat storage in the boles ( $\Delta Q_\mathrm{S,B}$ Δ Q S , B ) and biochemical energy storage ( $\Delta Q_\mathrm{S,C}$ Δ Q S , C ) were the largest terms. $\Delta Q_\mathrm{S,H}$ Δ Q S , H was almost constant from the bottom to above the canopy. $\Delta Q_\mathrm{S,C}$ Δ Q S , C , $\Delta Q_\mathrm{S,B}$ Δ Q S , B and latent heat storage in the air ( $\Delta Q_\mathrm{S,E}$ Δ Q S , E ) varied more than $\Delta Q_\mathrm{S,H}$ Δ Q S , H throughout the canopy. During daytime, energy balance closure was high in and above the upper canopy, and in the lowest canopy level. However, where the secondary structure was most abundant, ${\textit{EBC}} \le 66\,\%$ EBC ≤ 66 % . During nighttime, the storage terms together with $Q_\mathrm{G}$ Q G made up the largest part of the energy balance, while $Q_\mathrm{H}$ Q H and $Q_\mathrm{E}$ Q E were relatively small. These radiation and energy balance measurements in an insect-attacked forest highlight the role of secondary structure in the recovery of attacked stands.     

Surface Heterogeneity Effects on Regional-Scale Fluxes in the Stable Boundary Layer: Aerodynamic Roughness Length Transitions

The effects of abrupt streamwise transitions of the aerodynamic roughness length ( $z_\mathrm{o}$ z o ) on the stable atmospheric boundary layer are evaluated using a series of large-eddy simulations based on the first Global Energy and Water Cycle Experiment Atmospheric Boundary Layer intercomparison study (GABLS1). Four $z_\mathrm{o}$ z o values spanning three orders of magnitude are used to create all possible binary distributions with each arranged into patches of characteristic length scales equal to roughly one-half, one, and two times the equivalent homogeneous boundary-layer height. The impact of the heterogeneity on mean profiles of wind speed and temperature, on surface fluxes of heat and momentum, and on internal boundary-layer dynamics are considered. It is found that $z_\mathrm{o}$ z o transitions do not significantly alter the functional relationship between the average surface fluxes and the mean profiles of wind speed and potential temperature. Although this suggests that bulk similarity theory is applicable for modelling the stable boundary layer over $z_\mathrm{o}$ z o heterogeneity, effective surface parameters must still be specified. Existing models that solve for effective roughness lengths of momentum and heat are evaluated and compared to values derived from the simulation data. The existing models are unable to accurately reproduce both the values of the effective aerodynamic roughness lengths and their trends as functions of patch length scale and stability. A new model for the effective aerodynamic roughness length is developed to exploit the benefits of the other models tested. It accurately accounts for the effects of the heterogeneity and stratification on the blending height and effective aerodynamic roughness length. The new model provides improved average surface fluxes when used with bulk similarity.     

On the Nature of the Transition Between Roll and Cellular Organization in the Convective Boundary Layer

Both observational and numerical studies of the convective boundary layer (CBL) have demonstrated that when surface heat fluxes are small and mean wind shear is strong, convective updrafts tend to organize into horizontal rolls aligned within 10–20\(^\circ \) of the geostrophic wind direction. However, under large surface heat fluxes and weak to negligible shear, convection tends to organize into open cells, similar to turbulent Rayleigh-Bénard convection. Using a suite of 14 large-eddy simulations (LES) spanning a range of \(-z_i/L\) between zero (neutral) and 1041 (highly convective), where \(z_i\) is the CBL depth and L is the Obukhov length, the transition between roll- and cellular-type convection is investigated systematically for the first time using LES. Mean vertical profiles including velocity variances and turbulent transport efficiencies, as well the “roll factor,” which characterizes the rotational symmetry of the vertical velocity field, indicate the transition occurs gradually over a range of \(-z_i/L\); however, the most significant changes in vertical profiles and CBL organization occur from near-neutral conditions up to about \(-z_i/L \approx \) 15–20. Turbulent transport efficiencies and quadrant analysis are used to characterize the turbulent transport of momentum and heat with increasing \(-z_i/L\). It is found that turbulence transports heat efficiently from weakly to highly convective conditions; however, turbulent momentum transport becomes increasingly inefficient as \(-z_i/L\) increases.     

Derivation of Structure Parameters of Temperature and Humidity in the Convective Boundary Layer from Large-Eddy Simulations and Implications for the Interpretation of Scintillometer Observations

We derive the turbulent structure parameters of temperature $C_{T}^2$ and humidity $C_q^2$ from high-resolution large-eddy simulations (LES) of a homogeneously-heated convective boundary layer. Boundary conditions and model forcing were derived from measurements at Cabauw in The Netherlands. Three different methods to obtain the structure-parameters from LES are investigated. The shape of the vertical structure-parameter profiles from all three methods compare well with former experimental and LES results. Depending on the method, deviations in the magnitude up to a factor of two are found and traced back to the effects of discretization and numerical dissipation of the advection scheme. Furthermore, we validate the LES data with airborne and large-aperture scintillometer (LAS) measurements at Cabauw. Virtual path measurements are used to study the variability of $C_{T}^2$ in the mixed layer and surface layer and its implications for airborne and LAS measurements. A high variability of $C_{T}^2$ along a given horizontal path in the LES data is associated with plumes (high values) and downdrafts (low values). The path average of $C_{T}^2$ varies rapidly in time due to the limited path length. The LES results suggest that measured path averages require sufficient temporal averaging and an adequate ratio of path length to height above the ground for the LAS in order to approach the domain average of $C_{T}^2$ .     

Large-Eddy Simulation of Mesoscale Circulations Forced by Inhomogeneous Urban Heat Island

The large-eddy simulation mode of the Weather Research and Forecasting model is employed to simulate the planetary boundary-layer characteristics and mesoscale circulations forced by an ideal urban heat island (UHI). In our simulations, the horizontal heterogeneity of the UHI intensity distribution in urban areas is considered and idealized as a cosine function. Results indicate that the UHI heating rate and the UHI intensity heterogeneity affect directly the spatial distribution of the wind field; a stronger UHI intensity produces a maximum horizontal wind speed closer to the urban centre. The strong advection of warm air from the urban area to the rural area in the upper part of the planetary boundary-layer causes a more stable atmospheric stratification over both the urban and rural areas. The mesoscale sensible heat flux caused by the UHI circulation increases with UHI intensity but vanishes when the background wind speed is sufficiently high $(>$ 3.0  $\mathrm{{m\,s}}^{-1})$ .     

Very-Large-Scale Motions in the Atmospheric Boundary Layer Educed by Snapshot Proper Orthogonal Decomposition

Large-eddy simulations of the atmospheric boundary layer (ABL) under a wide range of stabilities are conducted to educe very-large-scale motions and then to study their dynamics and how they are influenced by buoyancy. Preliminary flow visualizations suggest that smaller-scale motions that resemble hairpins are embedded in much larger scale streamwise meandering rolls. Using simulations that represent more than 150 h of physical time, many snapshots in the \(xy\) -, \(yz\) - and \(xz\) -planes are then collected to perform snapshot proper orthogonal decomposition and further investigate the large structures. These analyses confirm that large streamwise rolls that share several features with the very-large-scale motions observed in laboratory studies arise as the dominant modes under most stabilities, but the effect of the surface kinematic buoyancy flux on the energy content of these dominant modes is very significant. The first two modes in the \(yz\) -plane in the neutral case contain up to 3 % of the total turbulent kinetic energy; they also have a vertical tilt angle in the \(yz\) -plane of about 0 to 30 \(^\circ \) due to the turning effect associated with the Coriolis force. Unstable cases also feature streamwise rolls, but in the convective ABL they are strengthened by rising plumes in between them, with two to four rolls spanning the whole domain in the first few modes; the Coriolis effect is much weaker in the unstable ABL. These rolls are no longer the dominant modes under stable conditions where the first mode is observed to contain sheet-like motions with high turbulent kinetic energy. Using these proper orthogonal decomposition modes, we are also able to extract the vertical velocity fields corresponding to individual modes and then to correlate them with the horizontal velocity or temperature fields to obtain the momentum and heat flux carried by individual modes. Structurally, the fluxes are explained by the topology of their corresponding modes. However, the fraction of the fluxes produced by the modes is invariably smaller than the fraction of energy they contain, particularly under stable conditions where the first modes are found to perform weak counter-gradient fluxes.     

An Approach to Minimizing Artifacts Caused by Cross-Sensitivity in the Determination of Air–Sea \text{ CO }_{2} Flux Using the Eddy-Covariance Technique

The air–sea $\text{ CO }_{2}$ flux was measured from a research vessel in the North Yellow Sea in October 2007 using an open-path eddy-covariance technique. In 11 out of 64 samples, the normalized spectra of scalars ( $\text{ CO }_{2}$ , water vapour, and temperature) showed similarities. However, in the remaining samples, the normalized $\text{ CO }_{2}$ spectra were observed to be greater than those of water vapour and temperature at low frequencies. In this paper, the noise due to cross-sensitivity was identified through a combination of intercomparisons among the normalized spectra of three scalars and additional analyses. Upon examination, the cross-sensitivity noise appeared to be mainly present at frequencies ${<}0.8\,\text{ Hz }$ . Our analysis also suggested that the high-frequency fluctuations of $\text{ CO }_{2}$ concentration (frequency ${>}0.8\,\text{ Hz }$ ) was probably less affected by the cross-sensitivity. To circumvent the cross-sensitivity issue, the cospectrum in the high-frequency range 0.8–1.5 Hz, instead of the whole range, was used to estimate the $\text{ CO }_{2}$ flux by taking the contribution of the high frequency to the $\text{ CO }_{2}$ flux to be the same as the contribution to the water vapour flux. The estimated air–sea $\text{ CO }_{2}$ flux in the North Yellow Sea was $-0.039\,\pm \,0.048\,\text{ mg } \text{ m }^{-2}\,\text{ s }^{-1},$ a value comparable to the estimates using the inertial dissipation method and Edson’s method (Edson et al., J Geophys Res 116:C00F10, 2011).     

Investigation of the Stable Atmospheric Boundary Layer at Halley Antarctica

Boundary-layer measurements from the Brunt Ice Shelf, Antarctica are analyzed to determine flux–profile relationships. Dimensionless quantities are derived in the standard approach from estimates of wind shear, potential temperature gradient, Richardson number, eddy diffusivities for momentum and heat, Prandtl number, mixing length and turbulent kinetic energy. Nieuwstadt local scaling theory for the stable atmospheric boundary-layer appears to work well departing only slightly from expressions found in mid-latitudes. An $E$ E – $l_{\mathrm{m}}$ l m single-column model of the stable boundary layer is implemented based on local scaling arguments. Simulations based on the first GEWEX Atmospheric Boundary-Layer Study case study are validated against ensemble-averaged profiles for various stability classes. A stability-dependent function of the dimensionless turbulent kinetic energy allows a better fit to the ensemble profiles.     

Observational Support for the Stability Dependence of the Bulk Richardson Number Across the Stable Boundary Layer

The bulk Richardson number ( $Ri_{Bh}$ ; defined over the entire stable boundary layer) is commonly utilized in observational and modelling studies for the estimation of the boundary-layer height. Traditionally, $Ri_{Bh}$ is assumed to be a quasi-universal constant. Recently, based on large-eddy simulation and wind-tunnel data, a stability-dependent relationship has been proposed for $Ri_{Bh}$ . In this study, we analyze extensive observational data from several field campaigns and provide further support for this newly proposed relationship.     

Evaluation of the Weather Research and Forecasting Mesoscale Model for GABLS3: Impact of Boundary-Layer Schemes,Boundary Conditions and Spin-Up

We evaluated the performance of the three-dimensional Weather Research and Forecasting (WRF) mesoscale model, specifically the performance of the planetary boundary-layer (PBL) parametrizations. For this purpose, Cabauw tower observations were used, with the study extending beyond the third GEWEX Atmospheric Boundary-Layer Study (GABLS3) one-dimensional model intercomparison. The WRF model (version 3.4.1) contains 12 different PBL parametrizations, most of which have been only partially evaluated. The GABLS3 case offers a clear opportunity to evaluate model performance, focusing on time series of near-surface weather variables, radiation and surface flux budgets, vertical structure and the nighttime inertial oscillation. The model results revealed substantial differences between the PBL schemes. Generally, non-local schemes tend to produce higher temperatures and higher wind speeds than local schemes, in particular, for nighttime. The WRF model underestimates the 2-m temperature during daytime (about \(2\) K) and substantially underestimates it at night (about \(4\) K), in contrast to the previous studies where modelled 2-m temperature was overestimated. Considering the 10-m wind speed, during the night turbulent kinetic energy based schemes tend to produce lower wind speeds than other schemes. In all simulations the sensible and latent heat fluxes were well reproduced. For the net radiation and the soil heat flux we found good agreement with daytime observations but underestimations at night. Concerning the vertical profiles, the selected non-local PBL schemes underestimate the PBL depth and the low-level jet altitude at night by about 50 m, although with the correct wind speed. The latter contradicts most previous studies and can be attributed to the revised stability function in the Yonsei University PBL scheme. The local, turbulent kinetic energy based PBL schemes estimated the low-level jet altitude and strength more accurately. Compared to the observations, all model simulations show a similar structure for the potential temperature, with a consistent cold bias ( \(\approx \) 2 K) in the upper PBL. In addition to the sensitivity to the PBL schemes, we studied the sensitivity to technical features such as horizontal resolution and domain size. We found a substantial difference in the model performance for a range of 12, 18 and 24 h spin-up times, longer spin-up time decreased the modelled wind speed bias, but it strengthened the negative temperature bias. The sensitivity of the model to the vertical resolution of the input and boundary conditions on the model performance is confirmed, and its influence appeared most significant for the non-local PBL parametrizations.     

Improvements in Sensible Heat-Flux Parametrization in the High-Resolution Regional Model (HRM) Through the Modified Treatment of the Roughness Length for Heat

We discuss the impact of the differential treatment of the roughness lengths for momentum and heat ( $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ ) in the flux parametrization scheme of the high-resolution regional model (HRM) for a heterogeneous terrain centred around Thiruvananthapuram, India (8.5°N, 76.9°E). The magnitudes of sensible heat flux (H) obtained from HRM simulations using the original parametrization scheme differed drastically from the concurrent in situ observations. With a view to improving the performance of this parametrization scheme, two distinct modifications are incorporated: (1) In the first method, a constant value of 100 is assigned to the $z_{0\mathrm{m}}/z_{0\mathrm{h}}$ ratio; (2) and in the second approach, this ratio is treated as a function of time. Both these modifications in the HRM model showed significant improvements in the H simulations for Thiruvananthapuram and its adjoining regions. Results obtained from the present study provide a first-ever comparison of H simulations using the modified parametrization scheme in the HRM model with in situ observations for the Indian coastal region, and suggest a differential treatment of $z_{0\mathrm{m}}$ and $z_{0\mathrm{h}}$ in the flux parametrization scheme.     

Bulk Mixing and Decoupling of the Nocturnal Stable Boundary Layer Characterized Using a Ubiquitous Natural Tracer

Vertical mixing of the nocturnal stable boundary layer (SBL) over a complex land surface is investigated for a range of stabilities, using a decoupling index ( $0 < D_{rb} < 1$ ) based on the 2–50 m bulk gradient of the ubiquitous natural trace gas radon-222. The relationship between $D_{rb}$ and the bulk Richardson number ( $R_{ib}$ ) exhibits three broad regions: (1) a well-mixed region ( $D_{rb} \approx 0.05$ ) in weakly stable conditions ( $R_{ib} < 0.03$ ); (2) a steeply increasing region ( $0.05 < D_{rb} < 0.9$ ) for “transitional” stabilities ( $0.03 < R_{ib} < 1$ ); and (3) a decoupled region ( $D_{rb} \approx 0.9$ –1.0) in very stable conditions ( $R_{ib} > 1$ ). $D_{rb}$ exhibits a large variability within individual $R_{ib}$ bins, however, due to a range of competing processes influencing bulk mixing under different conditions. To explore these processes in $R_{ib}$ – $D_{rb}$ space, we perform a bivariate analysis of the bulk thermodynamic gradients, various indicators of external influences, and key turbulence quantities at 10 and 50 m. Strong and consistent patterns are found, and five distinct regions in $R_{ib}$ – $D_{rb}$ space are identified and associated with archetypal stable boundary-layer regimes. Results demonstrate that the introduction of a scalar decoupling index yields valuable information about turbulent mixing in the SBL that cannot be gained directly from a single bulk thermodynamic stability parameter. A significant part of the high variability observed in turbulence statistics during very stable conditions is attributable to changes in the degree of decoupling of the SBL from the residual layer above. When examined in $R_{ib}$ – $D_{rb}$ space, it is seen that very different turbulence regimes can occur for the same value of $R_{ib}$ , depending on the particular combination of values for the bulk temperature gradient and wind shear, together with external factors. Extremely low turbulent variances and fluxes are found at 50 m height when $R_{ib} > 1$ and $D_{rb} \approx 1$ (fully decoupled). These “quiescent” cases tend to occur when geostrophic forcing is very weak and subsidence is present, but are not associated with the largest bulk temperature gradients. Humidity and net radiation data indicate the presence of low cloud, patchy fog or dew, any of which may aid decoupling in these cases by preventing temperature gradients from increasing sufficiently to favour gravity wave activity. The largest temperature gradients in our dataset are actually associated with smaller values of the decoupling index ( $D_{rb} < 0.7$ ), indicating the presence of mixing. Strong evidence is seen from enhanced turbulence levels, fluxes and submeso activity at 50 m, as well as high temperature variances and heat flux intermittencies at 10 m, suggesting this region of the $R_{ib}$ – $D_{rb}$ distribution can be identified as a top-down mixing regime. This may indicate an important role for gravity waves and other wave-like phenomena in providing the energy required for sporadic mixing at this complex terrain site.