Periodic solutions of the set of equations governing the nonadiabatic convection of dry isolated thermals

The changes with timet of a temperature deviation δT(t,α) and of a vertical velocityW _i(t,α) of an isolated dry thermal have been investigated theoretically. Solutions for the functionW _i(t, α) have been derived for stable and unstable environmental stratifications. Comparing these solutions with the corresponding ones for the rise of an adiabatic thermal yield some interesting conclusions. Firstly, there is the evident relation between the rate of entrainment of environmental air (expressed by the parameter α=(1/M _i) dM _i/dz whereM _i is the mass of the thermal) and the vertical velocity of the thermal: an increase in α decreases the velocity. Two similar thermals in stably stratified surroundings, one of them moving adiabatically (α=0) the other nonadiabatically (α>0), would rise for the same length of timet ₂=π/N, whereN is a typical Brunt-Väisälä frequency, but with different velocities and to different heights: the ascent timet ₂ depends only on environmental parameters. In an unstable stratification, the vertical non-adiabatic velocity of the thermal, instead of increasing without limit, tends towards a finite asymptotic velocity $$W_t (\infty ) = (\sqrt { - \mathcal{N}^2 } )/\alpha $$ the value of which depends upon both the stratification of the surroundings and upon the entrainment rate α. In a real atmosphere, where additional retarding forces exist, the motion will certainly be damped.     

Alkyl nitrate formation from the reaction of a series of branched RO2 radicals with NO as a function of temperature and pressure

Alkyl nitrate yields from the NO _x photooxidations of neopentane, 2-methylbutane and 3-methylpentane have been determined over the temperature and pressure ranges 281–323 K and 54–740 torr, respectively. The formation of the alkyl nitrates is attributed to the reaction pathway (1b) $${\text{RO}}_{\text{2}} + {\text{NO}}^{{\text{ }}\underrightarrow {\text{M}}} {\text{ RONO}}_{\text{2}}$$ and rate constant ratios k _1b/(k _1a+k _1b) are estimated, where (1a) is the reaction pathway (1a) $${\text{RO}}_{\text{2}} + {\text{NO}} \to {\text{RONO}}_{\text{2}} .$$ A method for estimating this rate constant ratio for primary, secondary and tertiary alkyl peroxy radicals is presented.     

Numerical simulation of particle trajectories in inhomogeneous turbulence,III: Comparison of predictions with experimental data for the atmospheric surface layer

It is shown that predictions of a numerical trajectory-simulation method agree closely with the Project Prairie Grass observations of the concentrations 100 m downwind of a continuous point source of sulphur dioxide if the height (z) dependence of the Lagrangian length scale Λ _L is chosen as: whereL is the Monin-Obukhov length. The value of 0.5 for Λ _L /z in neutral conditions is consistent with the findings of Reid (1979) for the Porton experiment, and is also shown to be the best choice for simulation of an experiment in which concentration profiles were measured a short distance (< 40 m) downwind of an elevated point source of glass beads (40 μn diameter). $$\begin{gathered} \Lambda _L = 0.5z\left( {1 - 6\frac{z}{L}} \right)^{{1 \mathord{\left/ {\vphantom {1 4}} \right. \kern-\nulldelimiterspace} 4}} L< 0 \hfill \\ \Lambda _L = 0.5z/\left( {1 + 5\frac{z}{L}} \right)L > 0 \hfill \\ \end{gathered} $$      

Tropospheric degradation products of CH2FCF3 (HFC-134a)

Chlorine atom-initiated photooxidations of CH₂FCF₃ (HFC-134a) in O₂-N₂ diluent were carried out to identify the products formed from the \(CF_3 CHF\dot O\) radical reactions and to determine the product yields as a function of temperature, pressure and O₂ concentration. CF₃C(O)F and HC(O)F were the major ‘first-generation’ products observed, along with smaller yields of C(O)F₂ and, as yet, undetermined yields of CF₃OOOCF₃ and CF₃OOC(O)F. The relative importance of the two major \(CF_3 CHF\dot O\) reaction pathways, is expressed by the rate constant ratio $$k_{O_2 } /k_d = 3.2 \times 10^{ - 25} e^{(3510 \pm 470)/T} cm^3 molecule^{ - 1}$$ The decomposition reaction leading to HC(O)F and ?F₃ radical products is predicted to be the dominant pathway at the Earth's surface while mainly CF₃C(O)F formation will occur at the tropopause.     

Surface influence upon vertical profiles in the nocturnal boundary layer

Near-surface wind profiles in the nocturnal boundary layer, depth h, above relatively flat, tree-covered terrain are described in the context of the analysis of Garratt (1980) for the unstable atmospheric boundary layer. The observations at two sites imply a surface-based transition layer, of depth z _*, within which the observed non-dimensional profiles Φ _M ⁰ are a modified form of the inertial sub-layer relation \(\Phi _M \left( {{z \mathord{\left/ {\vphantom {z L}} \right. \kern-0em} L}} \right) = \left( {{{1 + 5_Z } \mathord{\left/ {\vphantom {{1 + 5_Z } L}} \right. \kern-0em} L}} \right)\) according to $$\Phi _M^{\text{0}} \simeq \left( {{{1 + 5z} \mathord{\left/ {\vphantom {{1 + 5z} L}} \right. \kern-\nulldelimiterspace} L}} \right)\exp \left[ { - 0.7\left( {{{1 - z} \mathord{\left/ {\vphantom {{1 - z} z}} \right. \kern-\nulldelimiterspace} z}_ * } \right)} \right]$$ , where z is height above the zero-plane displacement and L is the Monin-Obukhov length. At both sites the depth z _* is significantly smaller than the appropriate neutral value (z _*N ) found from the previous analysis, as might be expected in the presence of a buoyant sink for turbulent kinetic energy.     

Hourly estimation of soil heat flux density at the soil surface with three models and two field methods

Heat flux density at the soil surface (G ₀) was evaluated hourly on a vegetal cover 0.08 m high, with a leaf area index of 1.07 m² m^?2, during daylight hours, using Choudhury et al. (Agric For Meteorol 39:283–297, 1987) ( $ G_0^{\text{rn}} $ ), Santanello and Friedl (J Appl Meteorol 42:851–862, 2003) ( $ G_0^{\text{s}} $ ), and force-restore ( $ G_0^{\text{fr}} $ ) models and the plate calorimetry methodology ( $ G_0^{\text{pco}} $ ), where the gradient calorimetry methodology (G _0R ) served as a reference for determining G ₀. It was found that the peak of G _0R was at 1 p.m., with values that ranged between 60 and 100 W m^?2 and that the G ₀/Rn relation varied during the day with values close to zero in the early hours of the morning and close to 0.25 in the last hours of daylight. The $ G_0^{\text{s}} $ model presented the best performance, followed by the $ G_0^{\text{rn}} $ and $ G_0^{\text{fr}} $ models. The plate calorimetry methodology showed a similar behavior to that of the gradient calorimetry referential methodology.     

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.     

Parametrization of orographical effects in the planetary boundary layer

Studies of the influence of orography on the dynamics of atmospheric processes usually assume the following relation as a boundary condition at the surface of the Earth, or at the top of the planetary layer: $$w = u\frac{{\delta z_0 }}{{\delta x}} + v\frac{{\delta z_0 }}{{\delta y}}$$ where u, v and w are the components of wind velocity along the x, y and z axes, respectively, and z ₀ = z₀(x, y) is the equation of the Earth's orography. We see that w, and consequently the influence of orography on the dynamics of atmospheric processes, depend on the wind (u, v) and on the slope of the obstacle (δz ₀/δx, δz₀/δy). In the present work, it is shown that the above relation for w is insufficient to describe the influence of orography on the dynamics of the atmosphere. It is also shown that the relation is a particular case of the expression: $$\begin{gathered} w_h = \left| {v_g } \right|\left[ {a_1 (Ro,s)\frac{{\delta z_0 }}{{\delta x}} + a_2 (Ro,s)\frac{{\delta z_0 }}{{\delta y}}} \right] + \hfill \\ + \frac{{\left| {v_g } \right|^2 }}{f}\left[ {b_1 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x^2 }} + b_2 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta y^2 }} + b_3 (Ro,s)\frac{{\delta ^2 z_0 }}{{\delta x\delta y}}} \right] \hfill \\ \end{gathered} $$ where ¦vv _g¦ is the strength of the geostrophic wind, a ₁, a₂, b₁, b₂, b₃ are functions of Rossby number Ro and of the external stability parameter s. The above relation is obtained with the help of similarity theory, with a parametrization of the planetary boundary layer. Finally, the authors show that a close connection exists between the effects described by the above expression and cyclo- and anticyclogenesis.     

On the vorticity and energy budgets of the cold vortex in Northeast China: a case study

This study examines the vorticity budgets, turbulent extended exergy and kinetic energy evolution equations to investigate the major dynamical and energy conversion processes contributing to the initiation and intensification of the cold vortex over Northeast China that occurred during June 19–22, 2009. The results show that the cyclonic vorticity was initiated in the lower troposphere due to the intense convergence of horizontal winds. The growth of cyclonic vorticity in the middle troposphere is mainly due to the vertical transportation of the vorticity, yet the increase of cyclonic vorticity in the upper troposphere primarily results from the horizontal advection of vorticity. Of special interest in this study is the evaluation of the role of thermal advections in the baroclinic development of the cold vortex. The results indicate that the rising of the air over relatively warm areas and the sinking of the air in relatively cold regions are favorable for releasing turbulent extended exergy $ \left( {e_{\text{t}} } \right) $ , which is later converted to turbulent kinetic energy $ \left( {k_{\text{t}} } \right) $ , and this process occurs during the initiation and intensification of the cold vortex. In addition, barotropic energy conversion is another important process that contributes to the growth of k _t, and it strengthens gradually after the initiation of the cold vortex. Other than frictional consumption, the flux of k _t in the vertical direction also depletes some of k _t. The fluxes of e _t, baroclinic energy conversions and diabatic generations are favorable factors for the growth of e _t, whereas it decreases with time as a result of a large amount of e _t that is released. Most of the energy conversion processes, including the baroclinic and the barotropic energy transformations and the energy conversions from e _t to k _t, as well as the fluxes of e _t, are stronger in the lower troposphere than the other areas during the formation of the cold vortex. This accounts for the initiation of the cyclonic vorticity in the lower troposphere. Finally, the fact that the turbulent extended exergy releases primarily in the middle troposphere through the vertical thermal circulation is consistent with our understanding based on the vorticity budget analyses.     

Decadal predictability and forecast skill

The “potential predictability” of the climate system is the upper limit of available forecast skill and can be characterized by the ratio p of the predictable variance to the total variance. While the potential predictability of the actual climate system is unknown its analog q may be obtained for a model of the climate system. The usual correlation skill score r and the mean square skill score M are functions of p in the case of actual forecasts and potential correlation ρ and potential mean square skill score $\mathcal{M}$ are the same functions of q in the idealized model context. In the large ensemble limit the connection between model-based potential predictability and skill scores is particularly straightforward with $q=\rho^{2}=\mathcal{M}.$ Decadal predictions of annual mean temperature produced with the Canadian Centre for Climate Modelling and Analysis coupled climate model are analyzed for information on decadal climate predictability and actual forecast skill. Initialized forecast results are compared with the results of uninitialized climate simulations. Model-based values of potential predictability q and potential correlation skill ρ are obtained and ρ is compared with the actual forecast correlation skill r. The skill of externally forced and internally generated components of the variability are separately estimated. As expected, ρ > r and both decline with forecast range τ, at least for the first five years. The decline of skill is associated mainly with the decline of the skill of the internally generated component. The potential and actual skill of a forecast of time-averaged temperature depends on the averaging period. The skill of uninitialized simulations is low for short averaging times and increases as averaging time increases. By contrast, skill is high at short averaging times for forecasts initialized from observations and declines as averaging times increase to about three years, then increases somewhat at longer averaging times. The skills of the initialized forecasts and uninitialized simulations begin to converge for longer averaging times. The potential correlation skill ρ of the externally forced component of temperature is largest at tropical latitudes and the skill of the internally generated component is largest over the North Atlantic, parts of the Southern Ocean and to some extent the North Pacific. Potential skill over extratropical land is somewhat weaker than over oceans. The distribution of actual correlation skill r is broadly similar to that of potential skill for the externally forced component but less so for the internally generated component. Differences in potential and actual skill suggest where improvements in the forecast system might be found.     

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.     

Turbulent Schmidt Numbers Above a Wheat Crop

Measurements of vertical fluxes and concentration differences above a spring wheat crop (height $h=0.9$ – $0.95$  m, row spacing 0.25 m, displacement height $d=0.5$ – $0.6$  m) were analyzed to determine the Schmidt numbers for water vapour ( $S^\mathrm{v}$ ) and carbon dioxide ( $S^\mathrm{c}$ ) based on concentration differences between intakes 2.55 and 3.54 m above the ground. During nearly-neutral stratification $S^\mathrm{v}(0) = 0.68 \pm 0.1$ while $S^\mathrm{c} = 0.78 \pm 0.2$ , implying that the roughness sublayer extended above $2.5 h$ .     

Variability of the Structure Parameters of Temperature and Humidity Observed in the Atmospheric Surface Layer Under Unstable Conditions

The structure parameters of temperature and humidity are important in scintillometry as they determine the structure parameter of the refractive index of air, the primary atmospheric variable obtained with scintillometers. In this study, we investigate the variability of the logarithm of the Monin-Obukhov-scaled structure parameters (denoted as $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ ) of temperature and humidity. We use observations from eddy-covariance systems operated at three heights (2.5, 50, and 90 m) within the atmospheric surface layer under unstable conditions. The variability of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ depends on instability and on the size of the averaging window over which $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ is calculated. If instability increases, differences in $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ between upward motions (large $C_{s}^2$ ) and downward motions (small $C_{s}^2$ ) increase. The differences are, however, not sufficiently large to result in a bimodal probability density function. If the averaging window size increases, the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ decrease. A linear regression of the variances of $\log ({\widetilde{C_{s}^2}_{\mathrm {}}})$ versus the averaging window size for various stability classes shows an increase of both the offset and slope (in absolute sense) with increasing instability. For temperature, data from the three heights show comparable results. For humidity, in contrast, the offset and slope are larger at 50 and 90 m than at 2.5 m. In the end we discuss how these findings could be used to assess whether observed differences in $C_{s}^2$ along a scintillometer path or aircraft flight leg are just within the range of local variability in $C_{s}^2$ or could be attributed to surface heterogeneity. This is important for the interpretation of data measured above a heterogeneous surface.     

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.     

Investigation of the Flow Structure in Step-Up Street Canyons—Mean Flow and Turbulence Statistics

A step-up street canyon is a characteristic urban element composed of two buildings in which the height of the upwind building ( $H_\mathrm{u}$ ) is less than the height of the downwind building ( $H_\mathrm{d}$ ). Here, the effect of canyon geometry on the flow structure in isolated step-up street canyons is investigated through isothermal wind-tunnel measurements. The measurements were acquired along the vertical symmetry plane of model buildings using two-dimensional particle image velocimetry (PIV) for normal approach flow. The building-height ratios considered were: $H_\mathrm{d}/ H_\mathrm{u} \approx 3$ , and $H_\mathrm{d}/ H_\mathrm{u} \approx 1.67$ . For each building-height ratio, the along-wind lengths (L) of the upwind and downwind buildings, and the street-canyon width (S) were kept constant, with $L \approx S$ . The cross-wind widths (W) of the upwind and downwind buildings were varied uniformly from $W/S \approx 1$ through $W/S \approx 4$ , in increments of $W/S \approx 1$ . The objective of the work was to characterize the changes in the flow structure in step-up canyons as a function of W/S, for fixed L, S, and $H_\mathrm{d}/H_\mathrm{u}$ values. The results indicate that the in-canyon flow structure does not vary significantly for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ for the W/S values considered. Qualitatively, for $H_\mathrm{d}/H_\mathrm{u} \approx 3$ , the upwind building behaves as an obstacle in the upwind cavity of the downwind building. In contrast, the flow patterns observed for the $H_\mathrm{d}/H_\mathrm{u} \approx 1.67$ configurations are unique and counter-intuitive, and depend strongly on building width (W/S). For $W/S \approx 1$ and $W/S \approx 2$ , the effect of lateral flow into the canyon is so prominent that even the mean flow patterns are highly ambiguous. For $W/S \approx 3$ and 4, the flow along the vertical symmetry plane is more shielded from the lateral flow, and hence a stable counter-rotating vortex pair is observed in the canyon. In addition to these qualitative features, a quantitative analysis of the mean flow field and turbulence stress field is presented.     

A Test Pattern Identification Algorithm and Its Application to CINRAD/SA(B) Data简

A variety of faulty radar echoes may cause serious problems with radar data applications,especially radar data assimilation and quantitative precipitation estimates.In this study,＂test pattern＂ caused by test signal or radar hardware failures in CINRAD （China New Generation Weather Radar） SA and SB radar operational observations are investigated.In order to distinguish the test pattern from other types of radar echoes,such as precipitation,clear air and other non-meteorological echoes,five feature parameters including the effective reflectivity data percentage （Rz）,velocity RF （range folding） data percentage （RRF）,missing velocity data percentage （RM）,averaged along-azimuth reflectivity fluctuation （RNr,z） and averaged along-beam reflectivity fluctuation （RNa,z） are proposed.Based on the fuzzy logic method,a test pattern identification algorithm is developed,and the statistical results from all the different kinds of radar echoes indicate the performance of the algorithm.Analysis of two typical cases with heavy precipitation echoes located inside the test pattern are performed.The statistical results show that the test pattern identification algorithm performs well,since the test pattern is recognized in most cases.Besides,the algorithm can effectively remove the test pattern signal and retain strong precipitation echoes in heavy rainfall events.     

Wind erosion climatic erosivity

A physically based wind-erosion climatic factor has been derived: $$CE = \rho \int {[u^2 } - (u_T^2 + \gamma ^l /\rho a^2 )]^{3/2} f(u)du$$ where ? is the air density, a is a constant made up of other constants (von Karman, height of wind speed observation, roughness parameter), u is the horizontal wind speed, u _T is threshold wind speed, f(u) u) is a wind speed probability density function, and γ is the cohesive resistance caused by water on the soil particles. Cohesive resistance is proportional to the square of water content relative to water content at ?1500 J kg^?1. Relative water content is approximated from the Budyko dryness ratio and the Thornthwaite PE index with similar results. CE is calculable from wind speed and other generally available meteorological data, and is usable in the wind erosion equation without some of the limitations of a previously used wind erosion climatic factor.     

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.     

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 $C_{T}^2$ .     

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.