Modelling the One-Dimensional Stable Boundary Layer with an E−ℓ Turbulence Closure Scheme

The atmospheric boundary layer (ABL) model of Weng and Taylor with E−ℓ turbulence closure is applied to simulate the one-dimensional stably stratified ABL. The model has been run for nine hours from specified initial wind, potential temperature and turbulent kinetic energy profiles, and with a specified cooling rate applied at the surface. Different runs are conducted for different cooling rates, geostrophic winds and surface roughnesses. The results are discussed and compared with other models, large-eddy simulations and published field data.     

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ _w /Δ, where Λ _w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ _w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ _w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ _w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.     

Turbulent Kinetic Energy Dissipation in the Surface Layer

We estimated the turbulent kinetic energy (TKE) dissipation rate for thirty-two 1-h intervals of unstable stratification covering the stability range 0.12 ≤ −z/L ≤ 43 (z/L is the ratio of instrument height to the Obukhov length), by fitting Kolmogorov’s inertial subrange spectrum to streamwise spectra observed over a desert flat. Estimated values are compatible with the existence of local equilibrium, in that the TKE dissipation rate approximately equalled the sum of shear and buoyant production rates. Only in the neutral limit was the turbulent transport term in the TKE budget measured to be small.     

Influence of the boundary layer height on the global air–sea surface fluxes

Results from large-eddy simulations and field measurements have previously shown that the velocity field is influenced by the boundary layer height, z _i , during close to neutral, slightly unstable, atmospheric stratification. During such conditions the non-dimensional wind profile, φ _m , has been found to be a function of both z/L and z _i /L. At constant z/L, φ _m decreases with decreasing boundary layer height. Since φ _m is directly related to the parameterizations of the air–sea surface fluxes, these results will have an influence when calculating the surface fluxes in weather and climate models. The global impact of this was estimated using re-analysis data from 1979 to 2001 and bulk parameterizations. The results show that the sum of the global latent and sensible mean heat fluxes increase by 0.77 W m⁻² or about 1% and the mean surface stress increase by 1.4 mN m⁻² or 1.8% when including the effects of the boundary layer height in the parameterizations. However, some regions show a larger response. The greatest impact is found over the tropical oceans between 30°S and 30°N. In this region the boundary layer height influences the non-dimensional wind profile during extended periods of time. In the mid Indian Ocean this results in an increase of the mean annual heat fluxes by 2.0 W m⁻² and an increase of the mean annual surface stress by 2.6 mN m⁻².     

A Large-Eddy Simulation Study of Turbulent Flow Over Multiscale Topography

Most natural landscapes are characterized by multiscale (often multifractal) topography with well-known scale-invariance properties. For example, the spectral density of landscape elevation fields is often found to have a power-law scaling behaviour (with a −2 slope on a log–log scale) over a wide span of spatial scales, typically ranging from tens of kilometres down to a few metres. Even though the effect of topography on the atmospheric boundary layer (ABL) has been the subject of numerous studies, few have focussed on multiscale topography. In this study, large-eddy simulation (LES) is used to investigate boundary-layer flow over multiscale topography, and guide the development of parametrizations needed to represent the effects of subgrid-scale (SGS) topography in numerical models of ABL flow. Particular emphasis is placed on the formulation of an effective roughness used to account for the increased aerodynamic roughness associated with SGS topography. The LES code uses the scale-dependent Lagrangian dynamic SGS model for the turbulent stresses and a terrain-following coordinate transformation to explicitly resolve the effects of the topography at scales larger than the LES resolution. The terrain used in the simulations is generated using a restricted solid-on-solid landscape evolution model, and it is characterized by a −2 slope of the elevation power spectrum. Results from simulations performed using elevation fields band-pass filtered at different spatial resolutions indicate a clear linear relation between the square of the effective roughness and the variance of elevation.     

Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

A Large-Eddy Simulation Study of the Influence of Subsidence on the Stably Stratified Atmospheric Boundary Layer

The influence of the large-scale subsidence rate, S, on the stably stratified atmospheric boundary layer (ABL) over the Arctic Ocean snow/ice pack during clear-sky, winter conditions is investigated using a large-eddy simulation model. Simulations of two 24-h periods are conducted while varying S between 0, 0.001 and 0.002 ms⁻¹, and the resulting quasi-equilibrium ABL structures and evolutions are examined. Simulations conducted with S = 0 yield a boundary layer that is deeper, more strongly mixed and cools more rapidly than the observations. Simulations conducted with S > 0 yield improved agreement with the observations in the ABL height, potential temperature gradients and bulk heating rates. We also demonstrate that S > 0 limits the continuous growth of the ABL observed during quasi-steady conditions, leading to the formation of a nearly steady ABL of approximately uniform depth and temperature. Subsidence reduces the magnitudes of the stresses, as well as the implied eddy-diffusivity coefficients for momentum and heat, while increasing the vertical heat fluxes considerably. Subsidence is also observed to increases the Richardson number to values in excess of unity well below the ABL top.     

Subfilter-scale Fluxes over a Surface Roughness Transition. Part I: Measured Fluxes and Energy Transfer Rates

A wind-tunnel experiment was designed and carried out to study the effect of a surface roughness transition on subfilter-scale (SFS) physics in a turbulent boundary layer. Specifically, subfilter-scale stresses are evaluated that require parameterizations and are key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. The surface transition considered in this study consists of a sharp change from a rough, wire-mesh covered surface to a smooth surface. The resulting magnitude jump in aerodynamic roughnesses, M = ln(z ₀₁/z ₀₂), where z ₀₁ and z ₀₂ are the upwind and downwind aerodynamic surface roughnesses respectively, is similar to that of past experimental studies in the atmospheric boundary layer. The two-dimensional velocity fields used in this study are measured using particle image velocimetry and are acquired at several positions downwind of the roughness transition as well as over a homogeneous smooth surface. Results show that the SFS stress, resolved strain rate and SFS transfer rate of resolved kinetic energy are dependent on the position within the boundary layer relative to the surface roughness transition. A mismatch is found in the downwind trend of the SFS stress and resolved strain rate with distance from the transition. This difference of behaviour may not be captured by some eddy-viscosity type models that parameterize the SFS stress tensor as proportional to the resolved strain rate tensor. These results can be used as a benchmark to test the ability of existing and new SFS models to capture the spatial variability SFS physics associated with surface roughness heterogeneities.     

Simulation of the Askervein flow. Part 2: Large-eddy simulations

Large-eddy simulations of the neutrally stratified flow over the Askervein Hill were performed, to improve the knowledge of the flow obtained from field measurements and numerical simulations with Reynolds averaged Navier-Stokes (RANS) methods. A Lagrangian dynamic subgrid model was used but, to avoid the underdissipative character near the ground, it was merged with a damped Smagorinsky model. Simulations of a flat boundary-layer flow with this subgrid model showed that the turbulent vertical motions and shear stress were better resolved using grids with a stream to spanwise aspect ratio Δx / Δy = 2 than with an aspect ratio Δx / Δy = 1. Regarding the flow over the Askervein Hill, it was found that large-eddy simulations provide an acceptable solution for the mean-velocity field and better predictions of the turbulent kinetic energy in the upstream side of the hill than the model. However, as with the model, grid convergence was not achieved in the lee side and the size of the zone with reversed flow increased with the grid refinement. Nevertheless, the existence of the intermittent separation predicted with unsteady RANS in part one of this work seems unquestionable, due to the deceleration of the flow. In our opinion, a better modelling of the decelerating boundary layer in the lee side is required to improve the results obtained using equilibrium assumptions and achieve grid convergence.     

Aqueous Oxidation of Sulfur(IV) Catalyzed by Manganese(II): A Generalized Simple Kinetic Model

The reaction kinetics of S(IV) autoxidation catalyzed by Mn(II) in the pH range 3–5 typical for atmospheric liquid water, was investigated. For reactions with pH maintained constant during the reaction course, the predictions obtained by a simple integral approach cover kinetic results only for concentrations of HSO ₃ ⁻ up to 0.2 mM at pH 4.5. Thus, a generalized simple kinetic model, which can be used for predicting the reaction kinetics in wider concentration, pH and temperature ranges, was derived. This model is based on the assumption that the reaction rate is proportional to the concentration of a transient manganese-sulfito complex formed in the initial step of a radical chain mechanism. In the proposed power law rate equation

Derivation of the relationship between the Obukhov stability parameter and the bulk Richardson number for flux-profile studies

Using the relationship between the bulk Richardson numberR _z and the Obukhov stability parameterz/L (L is the Obukhov length), formally obtained from the flux-profile relationships, methods to estimatez/L are discussed. Generally,z/L can not be uniquely solved analytically from flux-profile relationships, and it may be defined using routine observations only by iteration. In this paper, relationships ofz/L in terms ofR _z obtained semianalytically were corrected for variable aerodynamic roughnessz ₀ and for aerodynamic-to-temperature roughness ratiosz ₀/z _T, using the flux-profile iteration procedure. Assuming the so-called log-linear profiles to be valid for the nearneutral and moderately stable region (z/L<1), a simple relationship is obtained. For the extension to strong stability, a simple series expansion, based on utilisation of specified universal functions, is derived.For the unstable region, a simple form based on utilisation of the Businger-Dyer type universal functions, is derived. The formulae yield good estimates for surfaces having an aerodynamic roughness of 10^–5 to 10^–1 m, and an aerodynamic-to-temperature roughness ratio ofz ₀/z _T=0.5 to 7.3. When applied to the universal functions, the formulae yield transfer coefficients and fluxes which are almost identical with those from the iteration procedure.     

Local Imbalance of Turbulent Kinetic Energy in the Surface Layer

We utilize experimental data collected in 2002 over an open field in Hanford, Washington, USA, to investigate the turbulent kinetic energy (TKE) budget in the atmospheric surface layer. The von Kármán constant was determined from the near-neutral wind profiles to be 0.36 ± 0.02 rather than the classical value of 0.4. The TKE budget was normalized and all terms were parameterized as functions of a stability parameter z/L, where z is the distance from the ground and L is the Obukhov length. The shear production followed the Businger–Dyer relation for −2 < z/L < 1. Contrary to the traditional Monin–Obukhov similarity theory (MOST), the shear, buoyancy and dissipation terms were found to be imbalanced due to a non-zero vertical transport over all stabilities. Motivated by this local imbalance, modified parameterizations of the dissipation and the turbulent transport were attempted and generated good agreement with the experimental data. Assuming stationarity and horizontal homogeneity, the pressure transport was estimated from the residual of the TKE budget.     

On the Time Evolution of the Turbulent Kinetic Energy Spectrum for Decaying Turbulence in the Convective Boundary Layer

Our focus is the time evolution of the turbulent kinetic energy for decaying turbulence in the convective boundary layer. The theoretical model with buoyancy and inertial transfer terms has been extended by a source term due to mechanical energy and validated against large-eddy simulation data. The mechanical effects in a boundary layer of height z _i at a convective surface-layer height z = 0.05z _i are significant in the time evolution of the vertical component of the spectrum, i.e. they enhance the decay time scale by more than an order of magnitude. Our findings suggest that shear effects seem to feedback to eddies with smaller wavenumbers, preserving the original shape of the spectrum, and preventing the spectrum from shifting towards shorter wavelengths. This occurs in the case where thermal effects only are considered.     

The Apsley and Castro Limited-Length-Scale $${{k-\varepsilon}}$$ Model Revisited for Improved Performance in the Atmospheric Surface Layer

The limited-length-scale k-e{k-\varepsilon} model proposed by Apsley and Castro for the atmospheric boundary layer (Boundary-Layer Meteorol 83(1):75–98, 1997) is revisited with special attention given to its predictions in the constant-stress surface layer. The original model proposes a modification to the length-scale-governing e{\varepsilon} equation that ensures consistency with surface-layer scaling in the limit of small ℓ _m/ℓ _max (where ℓ _m is the mixing length and ℓ _max its maximum) and yet imposes a limit on ℓ _m as ℓ _m/ℓ _max approaches one. However, within the equilibrium surface layer and for moderate values of z/ℓ _max, the predicted profiles of velocity, mixing length, and dissipation rate using the Apsley and Castro model do not coincide with analytical solutions. In view of this, a general e{\varepsilon} transport equation is derived herein in terms of an arbitrary desired mixing-length expression that ensures exact agreement with corresponding analytical solutions for both neutral and stable stability. From this result, a new expression for C_e3{C_{\varepsilon3}} can be inferred that shows this coefficient tends to a constant only for limiting values of z/L; and, furthermore, that the values of C_e3{C_{\varepsilon3}} for z/L → 0 and z/L →∞ differ by a factor of exactly two.     

Scaling Variances of Scalars in a Convective Boundary Layer Under Different Entrainment Regimes

For the presentation and analysis of atmospheric boundary-layer (ABL) data, scales are used to non-dimensionalise the observed quantities and independent variables. Usually, the ABL height, surface sensible heat flux and surface scalar flux are used. This works well, so long as the absolute values of the entrainment ratio for both the scalar and temperature are similar. The entrainment ratio for temperature naturally ranges from −0.4 to −0.1. However, the entrainment ratio for passive scalars can vary widely in magnitude and sign. Then the entrainment flux becomes relevant as well. The only customary scalar scale that takes into account both the surface flux and the entrainment flux is the bulk scalar scale, but this scale is not well-behaved for large negative entrainment ratios and for an entrainment ratio equal to −1. We derive a new scalar scale, using previously published large-eddy simulation results for the convective ABL. The scale is derived under the constraint that scaled scalar variance profiles are similar at those heights where the variance producing mechanisms are identical (i.e., either near the entrainment layer or near the surface). The new scale takes into account that scalar variance in the ABL is not only related to the surface flux of that scalar, but to the scalar entrainment flux as well. Furthermore, it takes into account that the production of variance by the entrainment flux is an order of magnitude larger than the production of variance by the surface flux (per unit flux). Other desirable features of the new scale are that it is always positive (which is relevant when scaling standard deviations) and that the scaled variances are always of order 1–10.     

A numerical study of the convective boundary layer

Computations of the buoyantly unstable Ekman layer are performed at low Reynolds number. The turbulent fields are obtained directly by solving the three-dimensional time-dependent Navier-Stokes equations (using the Boussinesq approximation to account for buoyancy effects), and no turbulence model is needed. Two levels of heating are considered, one quite vigorous, the other more moderate. Statistics for the vigorously heated case are found to agree reasonably well with laboratory, field, and large-eddy simulation results, when Deardorff's mixed-layer scaling is used. No indication of large-scale longitudinal roll cells is found in this convection-dominated flow, for which the inversion height to Obukhov length scale ratio –z _i /L _*=26. However, when heating is more moderate (so that –z _i /L _*=2), evidence of coherent rolls is present. About 10% of the total turbulent kinetic energy and turbulent heat flux, and 20% of the Reynolds shear stress, are estimated to be a direct consequence of the observed cells.     

Temporal and Spatial Variations of the Aerodynamic Roughness Length in the Ablation Zone of the Greenland Ice Sheet

To understand the response of the Greenland ice sheet to climate change the so-called ablation zone is of particular importance, since it accommodates the yearly net surface ice loss. In numerical models and for data analysis, the bulk aerodynamic method is often used to calculate the turbulent surface fluxes, for which the aerodynamic roughness length (z ₀) is a key parameter. We present, for the first time, spatial and temporal variations of z ₀ in the ablation area of the Greenland ice sheet using year-round data from three automatic weather stations and one eddy-correlation mast. The temporal variation of z ₀ is found to be very high in the lower ablation area (factor 500) with, at the end of the summer melt, a maximum in spatial variation for the whole ablation area of a factor 1000. The variation in time matches the onset of the accumulation and ablation season as recovered by sonic height rangers. During winter, snow accumulation and redistribution by snow drift lead to a uniform value of z ₀≈ 10⁻⁴ m throughout the ablation area. At the beginning of summer, snow melt uncovers ice hummocks and z ₀ quickly increases well above 10⁻² m in the lower ablation area. At the end of summer melt, hummocky ice dominates the surface with z ₀ > 5  ×  10⁻³ m up to 60 km from the ice edge. At the same time, the area close to the equilibrium line (about 90 km from the ice edge) remains very smooth with z ₀ = 10⁻⁵ m. At the beginning of winter, we observed that single snow events have the potential to lower z ₀ for a very rough ice surface by a factor of 20 to 50. The total surface drag of the abundant small-scale ice hummocks apparently dominates over the less frequent large domes and deep gullies. The latter results are verified by studying the individual drag contributions of hummocks and domes with a drag partition model.     

Organosulfates – A New Component of Humic-Like Substances in Atmospheric Aerosols?

Ion trap mass spectrometry (ITMS) was used to obtain further qualitative information about the chemical composition of humic-like substances (HULIS) in atmospheric particulate matter. Particles ≤10 μm (PM₁₀) were collected on quartz fiber filters for 24 h in the region of Basel (Switzerland) and extracted with water. HULIS were separated from inorganic salts by size exclusion chromatography (SEC) and detected by electrospray ionization in the negative ion mode (ESI(−)). Series of consecutive fragment ion spectra (MSⁿ) were recorded by ITMS. Full scan mass spectra of the extracts showed a mass distribution pattern characteristic for HULIS. Different molecular ions were selected from this pattern for further fragmentations. Among them the molecular ion m/z 299 was considered as representative and intensively studied. Many MS² and MS³ fragment spectra contained a fragment m/z 97 and a neutral loss of 80 u. Time-of-flight (TOF) MS and deuterium exchange experiments identified m/z 97 as hydrogen sulfate. MS² and MS³ fragment spectra supported the existence of sulfate covalently bound to HULIS. The fragmentation behavior of sulfated HULIS could be confirmed by model compounds.     

Evaluation of Haney-Type Surface ThermalBoundary Conditions Using a CoupledAtmosphere and Ocean Model

A coupled atmosphere-ocean model developed at the Institute for Space Studies at NASA Goddard Space Flight Center (Russell et al., 1995) was used to verify the validity of Haney-type surface thermal boundary condition, which linearly connects net downward surface heat flux Q to air / sea temperature difference △T by a relaxation coefficient k. The model was initiated from the National Centers for Environmental Prediction (NCEP) atmospheric observations for 1 December 1977, and from the National Ocean Data Center (NODC) global climatological mean December temperature and salinity fields at 1° ×1° resolution. The time step is 7.5 minutes. We integrated the model for 450 days and obtained a complete model-generated global data set of daily mean downward net surface flux Q, surface air temperature TA,and sea surface temperature To. Then, we calculated the cross-correlation coefficients (CCC) between Q and △T. The ensemble mean CCC fields show (a) no correlation between Q and △T in the equatorial regions, and (b) evident correlation (CCC≥ 0.7) between Q and △T in the middle and high latitudes.Additionally, we did the variance analysis and found that when k= 120 W m-2K-1, the two standard deviations, σQ and σk△T, are quite close in the middle and high latitudes. These results agree quite well with a previous research (Chu et al., 1998) on analyzing the NCEP re-analyzed surface data, except that a smaller value of k (80 W m-2K-1) was found in the previous study.     

Relating Urban Surface-layer Structure to Upwind Terrain for the Salford Experiment (Salfex)

Profiles of wind and turbulence over an urban area evolve with fetch in response to surface characteristics. Sodar measurements, taken on 22 April 2002 during the Salford Experiment in the UK (Salfex), are here related to upstream terrain. A logarithmic layer up to z = 65m was observed in all half-hour averaged profiles. Above this height the profile showed a different vertical gradient, suggesting a change in surface cover upstream. The drag coefficient varied by a factor of two over only a 20° direction change. Turbulence intensity (σ _x ) for each wind component (x) decreased with height, but the ratio suggested an underestimate of σ _u compared to previous results. Mean urban and suburban cover fraction within the source area for each height decreased sharply between z = 20 and 50m, increasing slightly above. The near-convergence of cover fractions thus occured for source areas of minimum length ≈ 2,200 m. In comparison, the mean length scale of heterogeneity L _P was calculated from surface cover data to be 1,284 m, and the corresponding mean blending height h _b was 175 m. Finally, the mean streamline angle, α, was negative and the magnitude decreased with height. An exponential fit to α for z ≤ 65m gave an e-folding height scale of 159 m. A simple relationship between this height scale and L _P was assumed, giving L _P ≈ 1,080 m, which is in reasonable agreement with the estimate from surface cover type. The results suggest that more emphasis is required on modelling and measuring surface-layer flow over heterogeneous urban canopies.