Stably Stratified Boundary-Layer Flow Over Low Hills: A Comparison of Model Results and Field Data

A linear theory of airflow over low hills andthe MSFD–STAB model are comparedwith published observations made at Cooper'sRidge, north–west of Goulburn inNew South Wales, Australia. The MSFD–STABmodel results show good agreementwith field data in weak to moderate stablystratified flow cases. The originallinear theory overpredicts the wind speed-upratio even in weakly stablecases. After some modification, the agreementis greatly improved.     

Flow Over Hills with Variable Roughness

The effect of variable roughness length upon the flow characteristics over hills is investigated. The changes considered herein cover a range of flow configurations such as the change from a forested (rough) valley with a moderately smooth hilltop to a grassy valley (smooth) with a “spiky” (rough) mountain top. The effect of moving the roughness with respect to the hill is also considered. Although many of the flow features change when the position of the roughness change is varied with respect to the hill these changes have very little impact upon the global properties used within orographic drag parametrization schemes.     

Wind-Tunnel Study Of Atmospheric Stable Boundary Layers Over A Rough Surface

Wind-tunnel simulations of theatmospheric stable boundary layer (SBL) developedover a rough surface were conducted by using athermally stratified wind tunnel at the Research Institutefor Applied Mechanics (RIAM), Kyushu University. Thepresent experiment is a continuation of the workcarried out in a wind tunnel at Colorado StateUniversity (CSU), where the SBL flows were developed over asmooth surface. Stably stratified flows were createdby heating the wind-tunnel airflow to a temperature ofabout 40–50°and by cooling the test-section floor toa temperature of about 10°. To simulate therough surface, a chain roughness was placed over thetest-section floor. We have investigated the buoyancyeffect on the turbulent boundary layer developed overthis rough surface for a wide range of stability,particularly focusing on the turbulence structure andtransport process in the very stable boundary layer.The present experimental results broadly confirm theresults obtained in the CSU experiment with the smoothsurface, and emphasizes the following features: thevertical profiles of turbulence statistics exhibitdifferent behaviour in two distinct stability regimes with weak and strong stability,corresponding to the difference in the verticalprofiles of the local Richardson number. The tworegimes are separated by the critical Richardsonnumber. The magnitudes in turbulence intensities andturbulent fluxes for the weak stability regime aremuch greater than those of the CSU experiments becauseof the greater surface roughness. For the very stableboundary layer, the turbulent fluxes of momentum andheat tend to vanish and wave-like motions due to theKelvin–Helmholtz instability and the rolling up andbreaking of those waves can be observed. Furthermore,the appearance of internal gravity waves is suggestedfrom cross-spectrum analyses.     

Large-Eddy Simulation Of Turbulent Separated Flow Over Rough Hills

Large-eddy simulations (LES) have been performed ofneutral turbulent flow over two-dimensional ridges steepenough to cause separation. Both periodic and isolated ridges havebeen considered. The results are compared with wind-tunnel observations and with the predictions of various turbulence closure models.For the periodic case the LES results are qualitatively reasonable,although the depth of the separated region appears to besensitive to the use of a distributed drag near the lower boundary.The isolated ridge results compare very favourably with the experimentaldata, with the LES performance appearing to be at least as good as that ofthe closure models.     

Large-Eddy Simulation Of Neutral Turbulent Flow Over Rough Sinusoidal Ridges

The requirements for a credible large-eddy simulation of neutral, turbulent flow over hills with an aerodynamically rough surface are discussed, in order to select a suitable case for simulation. As well as providing adequate resolution within the dynamically important inner region, obtaining a realistic upstream or undisturbed mean velocity profile is also of critical importance. A distributed drag canopy formulation has been introduced to the model to allow it to obtain such a profile while resolving very close to the rough surface. Simulations have then been performed of flow over ridges of varying heights. The results from the steepest case, which is just on the verge of separation, are compared with wind-tunnel observations. It is shown that the large-eddy simulation results are in much better agreement with the experimental data than are the results from a simple first-order mixing-length closure model. An encouraging lack of sensitivity of the simulation results to numerical resolution is also demonstrated.     

Tethered Balloon Observations Of The Nocturnal Stable Boundary Layer In A Valley

Detailed measurements of profiles of mean and turbulent variablesthrough the nocturnal stable boundary layer over a valley arepresented. Two nights of data are analysed in detail, one with only aweakly stable boundary layer and one with a strongly stable boundarylayer. The weakly stratified night shows high levels of turbulence inwhich the flow remains attached to the valley and the boundary layeracts as a single coherent layer. On the strongly stratified night, twoflow regimes are identified: attached flow, as on the weaklystratified night, and decoupled flow in which the air in the valleybecomes so dynamically stable that there is no turbulent interactionwith the mean flow aloft. Because the valley is sloping, the decoupledlower stagnant air then forms a drainage current. We find that theFroude number evaluated at the hill height, F_H = U(H)/N(H) H,diagnoses the flow regime: when F_H = 2, the flow remainsattached and when F_H 2 the flow in the valley becomesdecoupled from the flow aloft. The dynamics of the flow regimes areshown to be understandable in terms of the gradient Richardson number,which indicates the turbulent mixing. We show that the gradientRichardson number is a key parameter in diagnosing each flow regime.     

A Mixed Spectral-Integration Model for Neutral Mean Wind Flow Over Hills

A linear model for neutral surface-layer flow over orography is presented. The Reynolds-Averaged Navier-Stokes and E– turbulence closure equations are expressed in a terrain-following coordinate system created from a simple analytical expression in the Fourier domain. The perturbation equations are solved spectrally horizontally and by numerical integration vertically. Non-dimensional solutions are stored in look-up tables for quick re-use. Model results are compared to measurements, as well as other authors’ flow models in three test cases. The model is implemented and tested in two-dimensional space; the equations for a full three-dimensional version are presented.     

Aircraft-Based Measurements Of Turbulence Structures In The Katabatic Flow Over Greenland

Turbulence structures in the katabatic flow in the stable boundary layer (SBL) over the ice sheet are studied for two case studies with high wind speeds during the aircraft-based experiment KABEG (Katabatic wind and boundary layer front experiment around Greenland) in the area of southern Greenland. The aircraft data allow the direct determination of turbulence structures in the katabatic flow. For the first time, this allows the study of the turbulence structure in the katabatic wind system over the whole boundary layer and over a horizontal scale of 80 km.The katabatic flow is associated with a low-level jet (LLJ), with maximum wind speeds up to 25 m s^-1. Turbulent kinetic energy (TKE) and the magnitude of the turbulent fluxes show a strong decrease below the LLJ. Sensible heat fluxes at the lowest level have values down to -25 W m^-2. Latent heat fluxes are small in general, but evaporation values of up to +13 W m^-2 are also measured. Turbulence spectra show a well-defined inertial subrange and a clear spectral gap around 250-m wavelength. While turbulence intensity decreases monotonously with height above the LLJ for the upper part of the slope, high spectral intensities are also present at upper levels close to the ice edge. Normalized fluxes and variances generally follow power-law profiles in the SBL.Terms of the TKE budget are computed from the aircraft data. The TKE destruction by the negative buoyancy is found to be very small, and the dissipation rate exceeds the dynamical production.     

Aircraft Observations Of The Mean And Turbulent Structure Of A Shallow Boundary Layer Over The Persian Gulf

Stable internal boundary layers form when warm air isadvected over a cooler surface, a common occurrence incoastal areas. The internal boundary layer deepenswith distance along-wind, eventually reachingequilibrium with the surface and becoming a fullydeveloped marine boundary layer. We presentobservations of the late stages of internalboundary-layer evolution made bythe U.K. Meteorological Office'sC-130 Hercules research aircraft over the Persian Gulfin April 1996. Northwesterly winds brought warm dryair from the surrounding desert landmass across thecooler waters of the Gulf. Loss of heat to the surfaceresulted in the formation of a shallow, stableinternal boundary layer downwind of the coast. The aircraftmeasurements were made several hundred kilometresdownwind, by which point the original deep convectiveboundary layer had been eroded away and the internalboundary layer was well developed, effectively a newmarine atmospheric boundary layer. Throughout most ofits depth the boundary layer was statically stable anda downward heat flux of approximately 15 W m^-2was observed; however, an exceptionally strong latentheat flux, in excess of 250 W m^-2 near thesurface, was sufficient to overcome the downwards heatflux and maintain weak buoyant convection in the lower30–50% of the boundary layer.Scaling of boundary-layer turbulence statistics usinglocal similarity theory produces results in agreementwith previous studies. Because of the strong humiditycontribution to the buoyancy flux, however, care isrequired with the definition of the similarity scales.It is usual for either the sensible heat or buoyancyflux to be used in the definitions of both thetemperature and length scales; the latter being usedover water where humidity plays a significant role indetermining stability. In the present case we findthat while the buoyancy flux is appropriate in thedefinition of the length scale, the temperature scalemust be defined in terms of the sensible heat flux.     

A Case Study Of An On-Ice Air Flow Over The Arctic Marginal Sea-Ice Zone

A case study of warm air advection over the Arctic marginalsea-ice zone is presented, based on aircraft observations with direct flux measurements carriedout in early spring, 1998. A shallow atmospheric boundary layer (ABL) was observed, which wasgradually cooling with distance downwind of the ice edge. This process was mainly connected with astrong stable stratification and downward turbulent heat fluxes of about 10–20 W m^-2, but wasalso due to radiative cooling. Two mesoscale models, one hydrostatic and the other non-hydrostatic,having different turbulence closures, were applied. Despite these fundamental differences betweenthe models, the results of both agreed well with the observed data. Various closure assumptions had amore crucial influence on the results than the differences between the models.Such an assumption was, for example,the parameterization of the surface roughness for momentum (z₀) and heat (z_T). This stronglyaffected the wind and temperature fields not only close to the surface but also within and abovethe temperature inversion layer. The best results were achieved using a formulation for z₀ that took intoaccount the form drag effect of sea-ice ridges together withz_T = 0.1z₀. The stability within theelevated inversion strongly depended on the minimum eddy diffusivity K_min. A simple ad hocparameterization seems applicable, where K_min is calculated as 0.005 timesthe neutral eddy diffusivity. Although the longwave radiative cooling was largest within the ABL, theapplication of a radiation scheme was less important there than above the ABL. This was related to theinteraction of the turbulent and radiative fluxes. To reproduce the strong inversion, it wasnecessary to use vertical and horizontal resolutions higher than those applied in most regional andlarge-scale atmospheric models.     

Internal Boundary Layers: I. Height Formulae for Neutral and Diabatic Flows

The notion of an internal boundary layer (IBL) appeared in studies of local advection within the atmospheric boundary layer when air flows over a change in surface conditions. These include surface roughness, thermal and moisture properties. An ability to predict the height of the IBL interface in the atmosphere under neutral stability, accompanied by certain assumptions on the form of the mean flow parameters, have been a means of obtaining information on the velocity profile after step changes in roughness for more than half a century. A compendium of IBL formulae is presented. The approach based on the diffusion analogy of Miyake receives close attention. The empirical expression of Savelyev and Taylor (2001, Boundary Layer Meteorol. 101, 293–301) suggested that turbulent diffusion is not the only factor that influences IBL growth. An argument is offered that an additional element, mean vertical velocity or streamline displacement, should be taken into account. Vertical velocity is parameterized in terms of horizontal velocity differences employing continuity constraints and scaling. Published data are analyzed from a new point of view, which produces two new neutral stratification formulae. The first implies that the roughness lengths of adjacent surfaces are equally important and a combined length scale can be constructed. In addition new formulae to predict the height of the region of diabatic flow affected by a step change in surface conditions are obtained as an extension of the neutral flow case.     

Variability Of The Stable And Unstable Atmospheric Boundary-Layer Height And Its Scales Over A Boreal Forest

Radiosondes releases during the NOPEX-WINTEX experiment carried out in late winter in Northern Finland were analysed for the determination of the height h of the atmospheric boundary layer. We investigate various possible scaling approaches, based on length scales using micrometeorological turbulence surface measurements and the background atmospheric stratification above h. Under stable conditions, the three previously observed turbulence regimes delineated by values of z/L (L is the Obukhov length) appears as a blueprint for understanding the departures found for the suitability of the Ekman scaling based on L_E = u_/f (u is the friction velocity and f the Coriolis parameter). The length scale L_N = u_/N (where N is the Brunt–Väisälä frequency) appears to be a useful scale under most stable conditions, especially in association with L. Under unstable conditions, shear production of turbulence is still significant, so that the three scales L, L_N and L_E are again relevant and the dimensionless ratios _N = L_N/L and L_N/L_E = N/f describe well the WINTEX data. Furthermore, in the classical scaling framework, the unstable domain may also be divided into three regimes as reflected by the dependence ofu_/f on instability (z/L).     

Observations Of Nocturnal Drainage Flow In A Shallow Gully

The formation of cold air drainage flows in a shallow gully is studied during CASES-99 (Cooperative Atmosphere-Surface Exchange Study). Fast and slow response wind and temperature measurements were obtained on an instrumented 10-m tower located in the gully and from a network of thermistors and two-dimensional sonic anemometers, situated across the gully. Gully flow formed on clear nights even with significant synoptic flow. Large variations in surface temperature developed within an hour after sunset and in situ cooling was the dominant factor in wind sheltered locations. The depth of the drainage flow and the height of the down-gully wind speed maximum were found to be largest when the external wind speed above the gully flow is less than 2 m s^-1. The shallow drainage current is restricted to a depth of a few metres, and is deepest when the stratification is stronger and the external flow is weaker. During the night the drainage flow breaks down, sometimes on several occasions, due to intermittent turbulence and downward fluxes of heat and momentum. The near surface temperature may increase by 6 ° C in less than 30 min due to the vertical convergence of downward heat flux. The mixing events are related to acceleration of the flow above the gully flow and decreased Richardson number. These warming events also lead to warming of the near surface soil and reduction of the upward soil heat flux. To examine the relative importance of different physical mechanisms that could contribute to the rapid warming, and to characterize the turbulence generated during the intermittent turbulent periods, the sensible heat budget is analyzed and the behaviour of different turbulent parameters is discussed.     

Sea-Breeze Modification Of The Growth Of A Marine Internal Boundary Layer

A numerical mesoscale model is used to make a high-resolutionsimulation of the marine boundary layer in the Persian Gulf, duringconditions of offshore flow from Saudi Arabia. A marine internal boundary layer(MIBL) and a sea-breeze circulation (SBC) are found to co-exist. The sea breeze develops in the mid-afternoon, at which time its frontis displaced several tens of kilometres offshore. Between the coastand the sea-breeze system, the MIBL that occurs is consistent with a picture described in the existing literature. However, the MIBL isperturbed by the SBC, the boundary layer deepening significantly seaward of the sea-breeze front. Our analysis suggests that thisstrong, localized deepening is not a direct consequence offrontal uplift, but rather that the immediate cause is the retardation of theprevailing, low-level offshore windby the SBC. The simulated boundary-layer development can be accounted for by using a simple 1D Lagrangian model of growth driven by the surface heatflux. This model is obtained as a straightforward modification ofan established MIBL analytic growth model.     

A Comparison Of Aerosol-Layer And Convective Boundary-Layer Structure Over A Mountain Range During Staaarte '97

The temporal evolution and spatial structure of the aerosol layer (AL) height as observed with an airborne downlooking lidar over the Swiss Alps were investigated with a three-dimensional mesoscale numerical model and a particle dispersion model. Convective boundary-layer (CBL) heights were derived from the mesoscale model output, and the behaviour of surface-released particles was investigated with the particle dispersion model. While a previous investigation, using data from the same field study, equated the observed AL height with the CBL height, the results of the current investigation indicate that there is a considerable difference between AL and CBL heights caused by mixing and transport processes between the CBL and the free atmosphere. CBL heights show a more terrain-following behaviour and are lower than AL heights. We argue that processes causing the difference between AL and CBL heights are common over mountainous terrain and that the AL height is a length scale that needs to be considered in air pollution studies in mountainous terrain.     

Regional Fluxes Of Momentum And Sensible Heat Over A Sub-Arctic Landscape During Late Winter

Based on measurements at Sodankylä Meteorological Observatory the regional (aggregated) momentum and sensible heat fluxes are estimated for two days over a site in Finnish Lapland during late winter. The forest covers 49% of the area. The study shows that the forest dominates and controls the regional fluxes of momentum and sensible heat in different ways. The regional momentum flux is found to be 10–20% smaller than the measured momentum flux over the forest, and the regional sensible heat flux is estimated to be 30–50% of the values measured over a coniferous forest.The regional momentum flux is determined in two ways, both based on blending height theory. One is a parameterised method, the other represents a numerical solution of an aggregation model. The regional sensible heat flux is determined from the theory of mixed-layer growth. At near neutral conditions the regional momentum flux can be determined independently of the regional sensible heat flux. At unstable conditions the two models become coupled.The information that is needed by the parameterised blending height method and by the mixed-layer evolution method in order to derive the regional fluxes of momentum and sensible heat can be obtained from radiosonde profiles of wind speed and temperature.     

Turbulent Intensities and Velocity Spectra for Bare and Forested Gentle Hills: Flume Experiments

To investigate how velocity variances and spectra are modified by the simultaneous action of topography and canopy, two flume experiments were carried out on a train of gentle cosine hills differing in surface cover. The first experiment was conducted above a bare surface while the second experiment was conducted within and above a densely arrayed rod canopy. The velocity variances and spectra from these two experiments were compared in the middle, inner, and near-surface layers. In the middle layer, and for the canopy surface, longitudinal and vertical velocity variances () were in phase with the hill-induced spatial mean velocity perturbation (Δu) around the so-called background state (taken here as the longitudinal mean at a given height) as predicted by rapid distortion theory (RDT). However, for the bare surface case, and remained out of phase with Δu by about L/2, where L is the hill half-length. In the canopy layer, wake production was a significant source of turbulent energy for , and its action was to re-align velocity variances with Δu in those layers, a mechanism completely absent for the bare surface case. Such a lower ‘boundary condition’ resulted in longitudinal variations of to be nearly in phase with Δu above the canopy surface. In the inner and middle layers, the spectral distortions by the hill remained significant for the background state of the bare surface case but not for the canopy surface case. In particular, in the inner and middle layers of the bare surface case, the effective exponents derived from the locally measured power spectra diverged from their expected  − 5/3 value for inertial subrange scales. These departures spatially correlated with the hill surface. However, for the canopy surface case, the spectral exponents were near  − 5/3 above the canopy though the minor differences from  − 5/3 were also correlated with the hill surface. Inside the canopy, wake production and energy short-circuiting resulted in significant departures from  − 5/3. These departures from  − 5/3 also appeared correlated with the hill surface through the wake production contribution and its alignment with Δu. Moreover, scales commensurate with Von Karman street vorticies well described wake production scales inside the canopy, confirming the important role of the mean flow in producing wakes. The spectra inside the canopy on the lee side of the hill, where a negative mean flow delineated a recirculation zone, suggested that the wake production scales there were ‘broader’ when compared to their counterpart outside the recirculation zone. Inside the recirculation zone, there was significantly more energy at higher frequencies when compared to regions outside the recirculation zone.     

Stable Atmospheric Boundary Layer Over a Uniform Slope: Some Theoretical Concepts

Theoretical arguments are developed to describe the effects of a uniform slope on the development of the stably stratified atmospheric boundary layer (SBL). A maximum sustainable surface buoyancy flux exists for the SBL overlying a uniform, non-sloping surface. In this study it is shown that the SBL overlying a uniform shallow slope (with gradient of the order of 1:1000) also supports a maximum sustainable buoyancy flux, B _max, but that the value of B _max is influenced by the gradient of the slope, γ. It is demonstrated that in the limit γ → 0, results for the SBL over a horizontal surface are recovered.     

Turbulence Characteristics Of The Stable Boundary Layer Over A Mid-Latitude Glacier. Part Ii: Pure Katabatic Forcing Conditions

Observations obtained over a glacier surface in a predominantlykatabatic flow and with a distinctwind maximum below 13-m height are presented. The data werecollected using a 13-m high profilemast and two sonic anemometers (at about 2.5-m and 10-m heights).The spectra at frequencies belowthat of the turbulence range appear to deviate considerably fromthe curves obtained by Kaimal andco-workers during the 1968 Kansas experiment. The characteristicsof these deviations are compared tothe observations of others in surface-layers disturbed by anykind of large-scale outer-layer (orinactive) turbulence. In our case the disturbances arelikely to be induced by the highmountain ridges that surround the glacier. Moreover, the deviationsobserved in the cospectra seemto result from an, as yet, unspecified interaction between theinactive outer-layer turbulenceand the local surface-layer turbulence. Near the distinctwind maximum turbulence production ceasedwhile turbulence itself did not, probably the result ofturbulence transport from other levels. Consequently, we studied thelocal similarity relations using _w instead of u_* as an alternative velocity scale. Wellbelow the wind maximum, and for relatively low stability(0< Ri_g <0.2), the flow behaves accordingto well established local-scaling similarity relationshipsin the stable boundary layer. For higherstability (Ri_g > 0.2), and near or above the wind maximum, the boundary-layer structure conforms tothat of z-less stratification suggesting that the eddy sizeis restricted by the local stability ofthe flow. In line with this we observed that the sensibleheat fluxes relate remarkably well to thelocal flow parameters.     

Cases-97: Late-Morning Warming And Moistening Of The Convective Boundary Layer Over The Walnut River Watershed

Aircraft, radiosonde, surface-flux, and boundary-layer windprofiler data from the Cooperative Atmosphere Surface Exchange Study's 1997 field project, CASES-97, are combined with synoptic data to study the evolution of the vertically-averaged mixed-layerpotential temperature []and mixing-ratio [Q] onthree nearly-cloudless days from 1000 CST to 1200CST (local noon is approximately 1230 CST). This was achieved through examination of the terms in the time-tendency (`budget')equations for []and [Q]. We estimate three of the terms –local time rate of change, vertical flux divergence, andhorizontal advection. For the [Q]-budget, vertical flux divergence usually dominates, buthorizontal advection is significant on one of the three days. The [Q]-budget balances for two of the three days to within the large experimental error. For the -budget,vertical flux divergence accounts for most of the morningwarming, with horizontal advection of secondary importance.The residual in the -budget has the same sign for all three days, indicating that not all the heating is accounted for. We can balance the []-budgets to within experimental error on two of the three days by correcting the vertical-flux divergence for apparent low biases in the flux measurements of one of the aircraft and in the surface fluxes, and accounting for direct heating of the mixed layer by radiative flux divergence allowing for the effects of carbonaceous aerosols. The [];-budget with these corrections also balances on the third day if horizontal gradients from synoptic maps are used to estimate the horizontal advection. However, the corrected budget for this day does not balance if the horizontal gradient in the advection term is estimated using CASES-97aircraft and radiosondes; we suggest that persistent mesoscale circulations led to an overestimate of the horizontal gradient andhence horizontal advection.