Estimating a Lagrangian Length Scale Using Measurements of CO2 in a Plant Canopy

Analytical Lagrangian equations capable of predicting concentration profiles from known source distributions offer the opportunity to calculate source/sink distributions through inverted forms of these equations. Inverse analytical Lagrangian equations provide a practical means of estimating source profiles using concentration and turbulence measurements. Uncertainty concerning estimates of the essentially immeasurable Lagrangian length scale ( ${\mathcal{L}}$ ), a key input, impedes the operational practicality of this method. The present study evaluates ${\mathcal{L}}$ within a corn canopy by using field measurements to constrain an analytical Lagrangian equation. Measurements of net CO₂ flux, soil-to-atmosphere CO₂ flux, and in-canopy profiles of CO₂ concentration provided the information required to solve for ${\mathcal{L}}$ in a global optimization algorithm for 30-min time intervals. For days when the canopy was a strong CO₂ sink, the optimization frequently located ${\mathcal{L}}$ profiles that follow a convex shape. A constrained optimization then fit the profile shape to a smooth sigmoidal equation. Inputting the optimized ${\mathcal{L}}$ profiles in the forward and inverse Lagrangian equations leads to strong correlations between measured and calculated concentrations and fluxes. Coefficients of the sigmoidal equation were specific to each 30-min period and did not scale with any measured variable. Plausible looking ${\mathcal{L}}$ profiles were associated with negative bulk Richardson number values. Once the canopy senesced, a simple eddy diffusivity profile sufficed to relate concentrations and sources in the analytical Lagrangian equations.     

Impact of Megacity Shanghai on the Urban Heat-Island Effects over the Downstream City Kunshan

The impact of upstream urbanization on the enhanced urban heat-island (UHI) effects between Shanghai and Kunshan is investigated by analyzing seven years of surface observations and results from mesoscale model simulations. The observational analysis indicates that, under easterly and westerly winds, the temperature difference between Shanghai and Kunshan increases with wind speed when the wind speed \(<\) 5 m s \(^{-1}\) . The Weather Research and Forecasting (WRF) numerical model, coupled with a one-layer urban canopy model (UCM), is used to examine the UHI structure and upstream effects by replacing the urban surface of Shanghai and/or Kunshan with cropland. The WRF/UCM modelling system is capable of reproducing the surface temperature and wind field reasonably well. The simulated urban canopy wind speed is a better representation of the near-surface wind speed than is the 10-m wind speed at the centre of Shanghai. Without the urban landscape of Shanghai, the surface air temperature over downstream Kunshan would decrease by 0.2–0.4  \(^{\circ }\) C in the afternoon and 0.4–0.6  \(^{\circ }\) C in the evening. In the simulation with the urban landscape of Shanghai, a shallow cold layer is found above the UHI, with a minimum temperature of about \(-0.2\) to \(-\) 0.5  \(^{\circ }\) C during the afternoon hours. Strong horizontal divergence is found in this cold layer. The easterly breeze over Shanghai is strengthened at the surface by strong UHI effects, but weakened at upper levels. With the appearance of the urban landscape specific humidity decreases by 0.5–1 g kg \(^{-1}\) within the urban area because of the waterproof property of an urban surface. On the other hand, the upper-level specific humidity is increased because of water vapour transferred by the strong upward vertical motions.     

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.     

Intercomparison of Methods for the Simultaneous Estimation of Zero-Plane Displacement and Aerodynamic Roughness Length from Single-Level Eddy-Covariance Data

We applied three approaches to estimate the zero-plane displacement $d$ through the aerodynamic measurement height $z$ (with $z = z_{m}- d$ and $z_{m}$ being the measurement height above the surface), and the aerodynamic roughness length $z_{0}$ , from single-level eddy covariance data. Two approaches (one iterative and one regression-based) were based on the universal function in the logarithmic wind profile and yielded an inherently simultaneous estimation of both $d$ and $z_{0}$ . The third approach was based on flux–variance similarity, where estimation of $d$ and consecutive estimation of $z_{0}$ are independent steps. Each approach was further divided into two methods differing either with respect to the solution technique (profile approaches) or with respect to the variable (variance of vertical wind and temperature, respectively). All methods were applied to measurements above a large, growing wheat field where a uniform canopy height and its frequent monitoring provided plausibility limits for the resulting estimates of time-variant $d$ and $z_{0}$ . After applying, for each approach, a specific data filtering that accounted for the range of conditions (e.g. stability) for which it is valid, five of the six methods were able to describe the temporal changes of roughness parameters associated with crop growth and harvest, and four of them agreed on $d$ to within 0.3 m most of the time. Application of the same methods to measurements with a more heterogeneous footprint consisting of fully-grown sugarbeet and a varying contribution of adjacent harvested fields exhibited a plausible dependence of the roughness parameters on the sugarbeet fraction. It also revealed that the methods producing the largest outliers can differ between site conditions and stability. We therefore conclude that when determining $d$ for canopies with unknown properties from single-level measurements, as is increasingly done, it is important to compare the results of a number of methods rather than rely on a single one. An ensemble average or median of the results, possibly after elimination of methods that produce outliers, can help to yield more robust estimates. The estimates of $z_{0}$ were almost exclusively physically plausible, although $d$ was considered unknown and estimated simultaneously with the methods and results described above.     

Numerical Simulations of Laminar Air–Water Flow of a Non-linear Progressive Wave at Low Wind Speed

A numerical simulation for two-dimensional laminar air–water flow of a non-linear progressive water wave with large steepness is performed when the background wind speed varies from zero to the wave phase speed. It is revealed that in the water the difference between the analytical solution of potential flow and numerical solution of viscous flow is very small, indicating that both solutions of the potential flow and viscous flow describe the water wave very accurately. In the air the solutions of potential and viscous flows are very different due to the effects of viscosity. The velocity distribution in the airflow is strongly influenced by the background wind speed and it is found that three wind speeds, $U=0$ , $U=u_m$ (the maximum orbital velocity of a water wave), and $U=c$ (the wave phase speed), are important in distinguishing different features of the flow patterns.     

Weibull-k Revisited: “Tall” Profiles and Height Variation of Wind Statistics

The Weibull distribution is commonly used to describe climatological wind-speed distributions in the atmospheric boundary layer. While vertical profiles of mean wind speed in the atmospheric boundary layer have received significant attention, the variation of the shape of the wind distribution with height is less understood. Previously we derived a probabilistic model based on similarity theory for calculating the effects of stability and planetary boundary-layer depth upon long-term mean wind profiles. However, some applications (e.g. wind energy estimation) require the Weibull shape parameter (k), as well as mean wind speed. Towards the aim of improving predictions of the Weibull- \(k\) profile, we develop expressions for the profile of long-term variance of wind speed, including a method extending our probabilistic wind-profile theory; together these two profiles lead to a profile of Weibull-shape parameter. Further, an alternate model for the vertical profile of Weibull shape parameter is made, improving upon a basis set forth by Wieringa (Boundary-Layer Meteorol, 1989, Vol. 47, 85–110), and connecting with a newly-corrected corollary of the perturbed geostrophic-drag theory of Troen and Petersen (European Wind Atlas, 1989, Risø National Laboratory, Roskilde). Comparing the models for Weibull-k profiles, a new interpretation and explanation is given for the vertical variation of the shape of wind-speed distributions. Results of the modelling are shown for a number of sites, with a discussion of the models’ efficacy and applicability. The latter includes a comparative evaluation of Wieringa-type empirical models and perturbed-geostrophic forms with regard to surface-layer behaviour, as well as for heights where climatological wind-speed variability is not dominated by surface effects.     

The Effect of Wind-Turbine Wakes on Summertime US Midwest Atmospheric Wind Profiles as Observed with Ground-Based Doppler Lidar

We examine the influence of a modern multi-megawatt wind turbine on wind and turbulence profiles three rotor diameters ( $D$ D ) downwind of the turbine. Light detection and ranging (lidar) wind-profile observations were collected during summer 2011 in an operating wind farm in central Iowa at 20-m vertical intervals from 40 to 220 m above the surface. After a calibration period during which two lidars were operated next to each other, one lidar was located approximately $2D$ 2 D directly south of a wind turbine; the other lidar was moved approximately $3D$ 3 D north of the same wind turbine. Data from the two lidars during southerly flow conditions enabled the simultaneous capture of inflow and wake conditions. The inflow wind and turbulence profiles exhibit strong variability with atmospheric stability: daytime profiles are well-mixed with little shear and strong turbulence, while nighttime profiles exhibit minimal turbulence and considerable shear across the rotor disk region and above. Consistent with the observations available from other studies and with wind-tunnel and large-eddy simulation studies, measurable reductions in wake wind-speeds occur at heights spanning the wind turbine rotor (43–117 m), and turbulent quantities increase in the wake. In generalizing these results as a function of inflow wind speed, we find the wind-speed deficit in the wake is largest at hub height or just above, and the maximum deficit occurs when wind speeds are below the rated speed for the turbine. Similarly, the maximum enhancement of turbulence kinetic energy and turbulence intensity occurs at hub height, although observations at the top of the rotor disk do not allow assessment of turbulence in that region. The wind shear below turbine hub height (quantified here with the power-law coefficient) is found to be a useful parameter to identify whether a downwind lidar observes turbine wake or free-flow conditions. These field observations provide data for validating turbine-wake models and wind-tunnel observations, and for guiding assessments of the impacts of wakes on surface turbulent fluxes or surface temperatures downwind of turbines.     

Improving a Two-Equation Turbulence Model for Canopy Flows Using Large-Eddy Simulation

Large-eddy simulations of the neutrally-stratified flow over an extended homogeneous forest were used to calibrate a canopy model for the Reynolds-averaged Navier–Stokes (RaNS) method with the $k-\varepsilon $ k - ε turbulence model. It was found that, when modelling the forest as a porous medium, the canopy drag dissipates the turbulent kinetic energy (acts as a sink term). The proposed model was then tested in more complex flows: a finite length forest and a forested hill. In the finite length forest, the destruction of the turbulent kinetic energy by the canopy was overestimated near the edge, for a length approximately twice the tree height. In the forested hill, the model was less accurate inside the recirculation zone and overestimated the turbulent kinetic energy, due to an incorrect prediction of the production term. Nevertheless, the canopy model presented here provided consistent results in both a priori and a posteriori tests and improved the accuracy of RaNS simulations with the $k-\varepsilon $ k - ε model.     

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.     

Optimizing the Determination of Roughness Parameters for Model Urban Canopies

We present an objective optimization procedure to determine the roughness parameters for very rough boundary-layer flow over model urban canopies. For neutral stratification the mean velocity profile above a model urban canopy is described by the logarithmic law together with the set of roughness parameters of displacement height d, roughness length \(z_0\), and friction velocity \(u_*\). Traditionally, values of these roughness parameters are obtained by fitting the logarithmic law through (all) the data points comprising the velocity profile. The new procedure generates unique velocity profiles from subsets or combinations of the data points of the original velocity profile, after which all possible profiles are examined. Each of the generated profiles is fitted to the logarithmic law for a sequence of values of d, with the representative value of d obtained from the minima of the summed least-squares errors for all the generated profiles. The representative values of \(z_0\) and \(u_*\) are identified by the peak in the bivariate histogram of \(z_0\) and \(u_*\). The methodology has been verified against laboratory datasets of flow above model urban canopies.     

Equilibrium Atmospheric Boundary-Layer Flow: Computational Fluid Dynamics Simulation with Balanced Forces

Forcing relationships in steady, neutrally stratified atmospheric boundary-layer (ABL) flow are thoroughly analyzed. The ABL flow can be viewed as balanced between a forcing and a drag term. The drag term results from turbulent stress divergence, and above the ABL, both the drag and the forcing terms vanish. In computational wind engineering applications, the ABL flow is simulated not by directly specifying a forcing term in the ABL but by specifying boundary conditions for the simulation domain. Usually, these include the inflow boundary and the top boundary conditions. This ‘boundary-driven’ ABL flow is dynamically different from its real counterpart, and this is the major reason that the simulated boundary-driven ABL flow does not maintain horizontal homogeneity. Here, first a dynamical approach is proposed to develop a neutrally stratified equilibrium ABL flow. Computational fluid dynamics (CFD) software (Fluent 6.3) with the standard \(k\) – \(\varepsilon \) turbulence model is employed, and by applying a driving force profile, steady equilibrium ABL flows are simulated by the model. Profiles of wind speed and turbulent kinetic energy (TKE) derived using this approach are reasonable in comparison with the conventional logarithmic law and with observational data respectively. Secondly, the equilibrium ABL profiles apply as inflow conditions to simulate the boundary-driven ABL flow. Simulated properties between the inlet and the outlet sections across a fetch of 10 km are compared. Although profiles of wind speed, TKE, and its dissipation rate are consistently satisfactory under higher wind conditions, a deviation of TKE and its dissipation rate between the inlet and outlet are apparent (7–8 %) under lower wind-speed conditions (2 m s \(^{-1}\) at 10 m). Furthermore, the simulated surface stress systematically decreases in the downwind direction. A redistribution of the pressure field is also found in the simulation domain, which provides a different driving pattern from the realistic case in the ABL.     

Transfer Coefficients of Momentum, Heat and Water Vapour in the Atmospheric Surface Layer of a Large Freshwater Lake

In studies of lake–atmosphere interactions, the fluxes of momentum, water vapour and sensible heat are often parametrized as being proportional to the differences in wind, humidity and air temperature between the water surface and a reference height above the surface. Here, the proportionality via transfer coefficients in these relationships was investigated with the eddy-covariance method at three sites within an eddy-covariance mesonet across Lake Taihu, China. The results indicate that the transfer coefficients decreased with increasing wind speed for weak winds and approached constant values for strong winds. The presence of submerged macrophytes reduced the momentum transfer (drag) coefficient significantly. At the two sites free of submerged macrophytes, the 10-m drag coefficients under neutral stability were 1.8 $(\pm \,0.4) \times \,10^{-3}$ ( ± 0.4 ) × 10 ? 3 and $1.7\,(\pm \,0.3) \times \,10^{-3 }$ 1.7 ( ± 0.3 ) × 10 ? 3 at the wind speed of $9\,\text{ m } \text{ s }^{-1}$ 9 m s ? 1 , which are 38 and 34 % greater than the prediction by the Garratt model for the marine environment.     

A Semi-Analytical Approach for Parametrization of the Obukhov Stability Parameter in the Unstable Atmospheric Surface Layer

A semi-analytical scheme is proposed to parametrize the Obukhov stability parameter \(\zeta \) (= \(z/L\) ; \(z\) is the height above the ground and \(L\) is the Obukhov length) in terms of the bulk Richardson number ( \(R_{iB}\) ) in unstable conditions within the framework of Monin–Obukhov similarity (MOS) theory. The scheme involves, (i) a solution of a cubic equation in \(\zeta \) whose coefficients depend on the gradient Richardson number ( \(R_{i}\) ), and (ii) a relationship between \(R_{i}\) and \(R_{iB}\) . The proposed scheme is applicable for a wide range (i) \(-5\le R_{iB}\le 0\) , (ii) \(0\le \hbox {ln}(z_{0}/z_{h})\le 29.0\) , and (iii) \(10\le z/z_{0}\le 10^{5}\) and performs relatively better than all other schemes in terms of accuracy in computation of surface-layer transfer coefficients. The absolute errors in computing the transfer coefficients do not exceed 7 %. The analysis presented here is found to be valid for different \(\gamma _{m}\) and \(\gamma _{h}\) appearing in the expressions of the similarity functions \(\varphi _{m}\) and \(\varphi _{h}\) (representing non-dimensional wind and temperature profiles), so long as the ratio of \(\gamma _{m}\) to \(\gamma _{h} \ge 1\) . The improved scheme can be easily employed in atmospheric modelling for a comprehensive range of \(R_{iB}\) and a variety of surfaces.     

Storm Surges in New York During Hurricane Sandy in 2012: A Verification of the Wind-Stress Tide Relation

In October 2012 Hurricane Sandy devastated New York City and its vicinity caused mainly by the storm surge, which is the water height above normal astronomical tide level. The meteorological conditions were as follows: minimum central pressure, 962 hPa, highest sustained wind speed 27.1 m s $^{-1}$ ? 1 and maximum gust 37.8 m s $^{-1}$ ? 1 . The peak storm surge was at 3.9 m and the peak storm tide at 4.4 m (which is referenced above mean lower low water). The wind-stress tide relation shows that $S=K\,V^{2}$ S = K V 2 , where $S$ S is the storm surge, $V$ V is the wind speed and $K$ K is the coefficient. It is found that with $S$ S in units of m, and $V$ V in  m s $^{-1}$ ? 1 , $K = 0.0051$ K = 0.0051 with $R^{2}= 0.91$ R 2 = 0.91 ( $R$ R is the correlation coefficient) indicating that 91 % of the total variation of the storm surge can be explained by variations in the wind stress, which is proportional to $V^{2}$ V 2 . Similar results were obtained during Hurricane Irene in 2011, which also affected the New York area. Therefore, this simple wind stress-tide relation should be useful in coastal engineering, urban planning, and emergency management.     

Verification of a One-Dimensional Model of $$\hbox {CO}_{2}$$ Atmospheric Transport Inside and Above a Forest Canopy Using Observations at the Norunda Research Station

A model of \(\hbox {CO}_{2}\) atmospheric transport in vegetated canopies is tested against measurements of the flow, as well as \(\hbox {CO}_{2}\) concentrations at the Norunda research station located inside a mixed pine–spruce forest. We present the results of simulations of wind-speed profiles and \(\hbox {CO}_{2}\) concentrations inside and above the forest canopy with a one-dimensional model of profiles of the turbulent diffusion coefficient above the canopy accounting for the influence of the roughness sub-layer on turbulent mixing according to Harman and Finnigan (Boundary-Layer Meteorol 129:323–351, 2008; hereafter HF08). Different modelling approaches are used to define the turbulent exchange coefficients for momentum and concentration inside the canopy: (1) the modified HF08 theory—numerical solution of the momentum and concentration equations with a non-constant distribution of leaf area per unit volume; (2) empirical parametrization of the turbulent diffusion coefficient using empirical data concerning the vertical profiles of the Lagrangian time scale and root-mean-square deviation of the vertical velocity component. For neutral, daytime conditions, the second-order turbulence model is also used. The flexibility of the empirical model enables the best fit of the simulated \(\hbox {CO}_{2}\) concentrations inside the canopy to the observations, with the results of simulations for daytime conditions inside the canopy layer only successful provided the respiration fluxes are properly considered. The application of the developed model for radiocarbon atmospheric transport released in the form of \(^{14}\hbox {CO}_{2}\) is presented and discussed.     

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.     

Air–Sea \mathrm{CO}_{2} Gas Transfer Velocity in a Shallow Estuary

The air–sea transfer velocity of $\mathrm{CO}_{2}\, (k_{\mathrm{CO}_{2}})$ was investigated in a shallow estuary in March to July 2012, using eddy-covariance measurements of $\mathrm{CO}_{2}$ fluxes and measured air–sea $\mathrm{CO}_{2}$ partial-pressure differences. A data evaluation method that eliminates data by nine rejection criteria in order to heighten parametrization certainty is proposed. We tested the data evaluation method by comparing two datasets: one derived using quality criteria related solely to the eddy-covariance method, and the other derived using quality criteria based on both eddy-covariance and cospectral peak methods. The best parametrization of transfer velocity normalized to a Schmidt number of 600 $(k_{600})$ was determined to be: $k_{600} = 0.3\,{U_{10}}^{2.5}$ where $U_{10}$ is the wind speed in m $\mathrm{s}^{-1}$ at 10 m; $k_{600}$ is based on $\mathrm{CO}_{2}$ fluxes calculated by the eddy-covariance method and including the cospectral peak method criteria. At low wind speeds, the transfer velocity in the shallow water estuary was lower than in other coastal waters, possibly a symptom of low tidal amplitude leading to low intensity water turbulence. High transfer velocities were recorded above wind speeds of 5 m $\mathrm{s}^{-1}$ , believed to be caused by early-breaking waves and the large fetch (6.5 km) of the estuary. These findings indicate that turbulence in both air and water influences the transfer velocity.     

Streamwise Versus Spanwise Spacing of Obstacle Arrays: Parametrization of the Effects on Drag and Turbulence

A Reynolds-averaged Navier–Stokes model is used to investigate the evolution of the sectional drag coefficient and turbulent length scales with the layouts of aligned arrays of cubes. Results show that the sectional drag coefficient is determined by the non-dimensional streamwise distance (sheltering parameter), and the non-dimensional spanwise distance (channelling parameter) between obstacles. This is different than previous approaches that consider only plan area density $(\lambda _\mathrm{p})$ . On the other hand, turbulent length scales behave similarly to the staggered case (e. g. they are function of $\lambda _\mathrm{p}$ only). Analytical formulae are proposed for the length scales and for the sectional drag coefficient as a function of sheltering and channelling parameters, and implemented in a column model. This approach demonstrates good skill in the prediction of vertical profiles of the spatially-averaged horizontal wind speed.     

Evaluation of Urban Local-Scale Aerodynamic Parameters: Implications for the Vertical Profile of Wind Speed and for Source Areas

Nine methods to determine local-scale aerodynamic roughness length \((z_{0})\) and zero-plane displacement \((z_{d})\) are compared at three sites (within 60 m of each other) in London, UK. Methods include three anemometric (single-level high frequency observations), six morphometric (surface geometry) and one reference-based approach (look-up tables). A footprint model is used with the morphometric methods in an iterative procedure. The results are insensitive to the initial \(z_{d}\) and \(z_{0}\) estimates. Across the three sites, \(z_{d}\) varies between 5 and 45 m depending upon the method used. Morphometric methods that incorporate roughness-element height variability agree better with anemometric methods, indicating \(z_{d}\) is consistently greater than the local mean building height. Depending upon method and wind direction, \(z_{0}\) varies between 0.1 and 5 m with morphometric \(z_{0}\) consistently being 2–3 m larger than the anemometric \(z_{0}\). No morphometric method consistently resembles the anemometric methods. Wind-speed profiles observed with Doppler lidar provide additional data with which to assess the methods. Locally determined roughness parameters are used to extrapolate wind-speed profiles to a height roughly 200 m above the canopy. Wind-speed profiles extrapolated based on morphometric methods that account for roughness-element height variability are most similar to observations. The extent of the modelled source area for measurements varies by up to a factor of three, depending upon the morphometric method used to determine \(z_{d}\) and \(z_{0}\).