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 $C_{T}^2$ .     

Advances in Air–Sea \hbox {CO}_2 Flux Measurement by Eddy Correlation

Eddy-correlation measurements of the oceanic \(\hbox {CO}_2\) flux are useful for the development and validation of air–sea gas exchange models and for analysis of the marine carbon cycle. Results from more than a decade of published work and from two recent field programs illustrate the principal interferences from water vapour and motion, demonstrating experimental approaches for improving measurement precision and accuracy. Water vapour cross-sensitivity is the greatest source of error for \(\hbox {CO}_2\) flux measurements using infrared gas analyzers, often leading to a ten-fold bias in the measured \(\hbox {CO}_2\) flux. Much of this error is not related to optical contamination, as previously supposed. While various correction schemes have been demonstrated, the use of an air dryer and closed-path analyzer is the most effective way to eliminate this interference. This approach also obviates density corrections described by Webb et al. (Q J R Meteorol 106:85–100, 1980). Signal lag and frequency response are a concern with closed-path systems, but periodic gas pulses at the inlet tip provide for precise determination of lag time and frequency attenuation. Flux attenuation corrections are shown to be \(<\) 5 % for a cavity ring-down analyzer (CRDS) and dryer with a 60-m inlet line. The estimated flux detection limit for the CRDS analyzer and dryer is a factor of ten better than for IRGAs sampling moist air. While ship-motion interference is apparent with all analyzers tested in this study, decorrelation or regression methods are effective in removing most of this bias from IRGA measurements and may also be applicable to the CRDS.     

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.     

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  $\mathrm{{m\,s}}^{-1})$ .     

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.     

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.     

Estimating the components of the sensible heat budget of a tall forest canopy in complex terrain

Ultrasonic wind measurements, sonic temperature and air temperature data at two heights in the advection experiment MORE II were used to establish a complete budget of sensible heat including vertical advection, horizontal advection and horizontal turbulent flux divergence. MORE II took place at the long-term Carbo-Europe IP site in Tharandt, Germany. During the growing period of 2003 three additional towers were established to measure all relevant parameters for an estimation of advective fluxes, primarily of CO₂. Additionally, in relation to other advection experiments, a calculation of the horizontal turbulent flux divergence is proposed and the relation of this flux to atmospheric stability and friction velocity is discussed. In order to obtain a complete budget, different scaling heights for horizontal advection and horizontal turbulent flux divergence are tested. It is shown that neglecting advective fluxes may lead to incorrect results. If advective fluxes are taken into account, the sensible heat budget based upon vertical turbulent flux and storage change only, is reduced by approximately 30%. Additional consideration of horizontal turbulent flux divergence would in turn add 5–10% to this sum (i.e., the sum of vertical turbulent flux plus storage change plus horizontal and vertical advection). In comparison with available energy horizontal advection is important at night whilst horizontal turbulent flux divergence is rather insignificant. Obviously, advective fluxes typically improve poor nighttime energy budget closure and might change ecosystem respiration fluxes considerably.     

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.     

A New Sensitivity Analysis and Solution Method for Scintillometer Measurements of Area-Averaged Turbulent Fluxes

Scintillometer measurements of the turbulence inner-scale length $l_\mathrm{o }$ l o and refractive index structure function $C_n^2$ C n 2 allow for the retrieval of large-scale area-averaged turbulent fluxes in the atmospheric surface layer. This retrieval involves the solution of the non-linear set of equations defined by the Monin–Obukhov similarity hypothesis. A new method that uses an analytic solution to the set of equations is presented, which leads to a stable and efficient numerical method of computation that has the potential of eliminating computational error. Mathematical expressions are derived that map out the sensitivity of the turbulent flux measurements to uncertainties in source measurements such as $l_\mathrm{o }$ l o . These sensitivity functions differ from results in the previous literature; the reasons for the differences are explored.     

Influence from Surrounding Land on the Turbulence Measurements Above a Lake

Turbulence measurements taken at a Swedish lake are analyzed. Although the measurements took place over a relatively large lake with several km of undisturbed fetch, the turbulence structure was found to be highly influenced by the surrounding land during daytime. Variance spectra of both horizontal velocity and scalars during both unstable and stable stratification displayed a low frequency peak. The energy at lower frequencies showed a daily variation, increasing in the morning and decreasing in the afternoon. This behaviour is explained by spectral lag, where the low frequency energy due to large eddies that originate from the convective boundary layer above the surrounding land. When the air is advected over the lake the small eddies rapidly equilibrate with the new surface forcing. However, the large eddies remain for an appreciable distance and influence the turbulence in the developing lake boundary layer. The variances of the horizontal velocity and scalars are increased by these large eddies, while the turbulent fluxes are mainly unaffected. The drag coefficient, Stanton number and Dalton number used to parametrize the momentum flux, heat flux and latent heat flux respectively all compare well with current parametrizations developed for open sea conditions. The diurnal cycle of the partial pressure of methane, $p\mathrm{CH}_{4}$ , observed at this site is closely related to the diurnal cycle of the lake-air methane flux. An idealized two-dimensional model simulation of the boundary layer at a lake site indicates that the strong response of $p\mathrm{CH}_{4}$ to the surface methane flux is due to the shallow internal boundary layer that develops above the lake, allowing methane to accumulate in a relatively small volume.     

The scaling of flow in vegetative structures

Sensible heat flux data obtained from the U.S. Environmental Protection Agency's Regional Air Pollution Study in St. Louis, Missouri are presented and discussed. Large spatial variations exist in heat flux on both a land-use scale and the urban scale. Arguments based upon empirical data and sampling theory show that estimates of heat flux representative of an upwind fetch l _x require a minimum observation height proportional to z ^3/4. The influence of advection on the magnitude of the heat flux is also explored for both the urban and sub-urban or land-use scales. The data clearly indicate that advection can strongly modulate and even dominate the vertical heat flux above surfaces in areas which maintain large horizontal temperature gradients. The advection contribution is positive for cold air advection and negative for warm air advection, and may result from either the urban heat island or land-use mesoscale features. The depth of advective influence is directly proportional to the horizontal scale of the phenomenon and inversely proportional to horizontal temperature gradient.     

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.     

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.     

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.     

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.     

A New Aerodynamic Parametrization for Real Urban Surfaces

This study conducted large-eddy simulations (LES) of fully developed turbulent flow within and above explicitly resolved buildings in Tokyo and Nagoya, Japan. The more than 100 LES results, each covering a 1,000 $\times $ 1,000 m $^{2}$ area with 2-m resolution, provide a database of the horizontally-averaged turbulent statistics and surface drag corresponding to various urban morphologies. The vertical profiles of horizontally-averaged wind velocity mostly follow a logarithmic law even for districts with high-rise buildings, allowing estimates of aerodynamic parameters such as displacement height and roughness length using the von Karman constant $=$ 0.4. As an alternative derivation of the aerodynamic parameters, a regression of roughness length and variable Karman constant was also attempted, using a displacement height physically determined as the central height of drag action. Although both the regression methods worked, the former gives larger (smaller) values of displacement height (roughness length) by 20–25 % than the latter. The LES database clearly illustrates the essential difference in bulk flow properties between real urban surfaces and simplified arrays. The vertical profiles of horizontally-averaged momentum flux were influenced by the maximum building height and the standard deviation of building height, as well as conventional geometric parameters such as the average building height, frontal area index, and plane area index. On the basis of these investigations, a new aerodynamic parametrization of roughness length and displacement height in terms of the five geometric parameters described above was empirically proposed. The new parametrizations work well for both real urban morphologies and simplified model geometries.     

Evaluation of Two Energy Balance Closure Parametrizations

A general lack of energy balance closure indicates that tower-based eddy-covariance (EC) measurements underestimate turbulent heat fluxes, which calls for robust correction schemes. Two parametrization approaches that can be found in the literature were tested using data from the Canadian Twin Otter research aircraft and from tower-based measurements of the German Terrestrial Environmental Observatories (TERENO) programme. Our analysis shows that the approach of Huang et al. (Boundary-Layer Meteorol 127:273–292, 2008), based on large-eddy simulation, is not applicable to typical near-surface flux measurements because it was developed for heights above the surface layer and over homogeneous terrain. The biggest shortcoming of this parametrization is that the grid resolution of the model was too coarse so that the surface layer, where EC measurements are usually made, is not properly resolved. The empirical approach of Panin and Bernhofer (Izvestiya Atmos Oceanic Phys 44:701–716, 2008) considers landscape-level roughness heterogeneities that induce secondary circulations and at least gives a qualitative estimate of the energy balance closure. However, it does not consider any feature of landscape-scale heterogeneity other than surface roughness, such as surface temperature, surface moisture or topography. The failures of both approaches might indicate that the influence of mesoscale structures is not a sufficient explanation for the energy balance closure problem. However, our analysis of different wind-direction sectors shows that the upwind landscape-scale heterogeneity indeed influences the energy balance closure determined from tower flux data. We also analyzed the aircraft measurements with respect to the partitioning of the “missing energy” between sensible and latent heat fluxes and we could confirm the assumption of scalar similarity only for Bowen ratios $\approx $ 1.     

Divergence of turbulent fluxes in the surface layer: case of a coastal city

This study quantifies the processes that take place in the layer between the mean building height and the measurement level of an energy balance micrometeorological tower located in the dense old core of a coastal European city. The contributions of storage, vertical advection, horizontal advection and radiative divergence for heat are evaluated with the available measurements and with a three-dimensional, high-resolution meteorological simulation that had been evaluated against observations. The study focused on a summer period characterized by sea-breeze flows that affect the city. In this specific configuration, it appears that the horizontal advection is the dominant term. During the afternoon when the sea breeze is well established, correction of the sensible heat flux with horizontal heat advection increases the measured sensible heat flux up to 100 W m⁻². For latent heat flux, the horizontal moisture advection converted to equivalent latent heat flux suggests a decrease of 50 W m⁻². The simulation reproduces well the temporal evolution and magnitude of these terms.     

A Scale-Adaptive Approach for Spatially-Varying Urban Morphology Characterization in Boundary Layer Parametrization Using Multi-Resolution Analysis

Urban morphology characterization is crucial for the parametrization of boundary-layer development over urban areas. One complexity in such a characterization is the three-dimensional variation of the urban canopies and textures, which are customarily reduced to and represented by one-dimensional varying parametrization such as the aerodynamic roughness length $z_{0}$ and zero-plane displacement $d$ . The scope of the paper is to provide novel means for a scale-adaptive spatially-varying parametrization of the boundary layer by addressing this 3-D variation. Specifically, the 3-D variation of urban geometries often poses questions in the multi-scale modelling of air pollution dispersion and other climate or weather-related modelling applications that have not been addressed yet, such as: (a) how we represent urban attributes (parameters) appropriately for the multi-scale nature and multi-resolution basis of weather numerical models, (b) how we quantify the uniqueness of an urban database in the context of modelling urban effects in large-scale weather numerical models, and (c) how we derive the impact and influence of a particular building in pre-specified sub-domain areas of the urban database. We illustrate how multi-resolution analysis (MRA) addresses and answers the afore-mentioned questions by taking as an example the Central Business District of Oklahoma City. The selection of MRA is motivated by its capacity for multi-scale sampling; in the MRA the “urban” signal depicting a city is decomposed into an approximation, a representation at a higher scale, and a detail, the part removed at lower scales to yield the approximation. Different levels of approximations were deduced for the building height $\bar{{H}}$ and planar packing density $\lambda _\mathrm{p}$ . A spatially-varying characterization with a scale-adaptive capacity is obtained for the boundary-layer parameters (aerodynamic roughness length $z_{0}$ and zero-plane displacement $d$ ) using the MRA-deduced results for the building height and the planar packing density with a morphometric model; an attribute that is shown to be of great advantage to multi-scale and multi-resolution numerical weather prediction models.     

Towards a Validation of Scintillometer Measurements: The LITFASS-2009 Experiment

Scintillometry has been increasingly used over the last decade for the experimental determination of area-averaged turbulent fluxes at a horizontal scale of a few kilometres. Nevertheless, a number of assumptions in the scintillometer data processing and interpretation still call for a thorough evaluation, in particular over heterogeneous terrain. Moreover, a validation of the path-averaged structure parameters derived from scintillometer data (and forming the basis for the flux calculations) by independent measurements is still missing. To achieve this, the LITFASS-2009 field campaign has been performed around the Meteorological Observatory Lindenberg ?C Richard-A?mann-Observatory of the German Meteorological Service (DWD) in July 2009. The experiment combined tower-based in-situ turbulence measurements, field-scale laser scintillometers, long-range optical (large-aperture) and microwave scintillometers, and airborne turbulence measurements using an automatically operating unmanned aircraft. The paper describes the project design and strategy, and discusses first results. Daytime near-surface values of the temperature structure parameter, ${C_{T}^{2}}$ , over different types of farmland differ by more than one order of magnitude in their dependence on the type and status of the vegetation. Considerable spatial variability in ${C_{T}^{2}}$ was also found along the flight legs at heights between 50 and 100?m. However, it appeared difficult to separate the effects of heterogeneity from the temporal variability of the turbulence fields. Aircraft measurements and scintillometer data agreed in magnitude with respect to the temporal variation of the path-averaged ${C_{T}^{2}}$ values during the diurnal cycle. The decrease of ${C_{T}^{2}}$ with height found from the scintillometer measurements close to the surface and at 43?m under daytime convective conditions corresponds to free-convection scaling, whereas the aircraft measurements at 54 and 83?m suggest a different behaviour.