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Water tank studies of atmospheric boundary layer structure and air pollution transport in upslope flow.. Reuten, Christian; Allen, Susan E.; Steyn, Douw G. 2007

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Water tank studies of atmospheric boundary layer structure and airpollution transport in upslope flow systemsC. Reuten,1D. G. Steyn,1and S. E. Allen1Received 2 October 2006; revised 2 February 2007; accepted 9 March 2007; published 13 June 2007.[1] Heated mountain slopes sometimes vent air pollutants out of the boundary layer overthe slope top and at other times trap pollutants in closed circulations. Field, numerical,and water tank studies of fair weather atmospheric conditions over complex terrain haveshown more complicated vertical distributions of temperature, moisture, and aerosolsthan over horizontal terrain. To study these phenomena, we analyze flow fields, densities,and dye distributions in a bottom-heated salt-stratified water tank over a 19C176 slopewith adjacent plain and plateau and compare with field and numerical model data. Verticallayering of dye results from upslope and plain-plateau circulations. The thermalboundary layer (TBL, the bottom layer up to neutral buoyancy height), coincides with thelower branches of these circulations. The return flow branches form elevated layers(EL) with properties intermediate between the TBL and environmental background. Asheating continues, the TBL rapidly entrains the ELs, leading to deeper circulationswith new ELs at greater heights. Field data suggest that successive formation andentrainment of ELs occurs at multiple scales in the atmosphere. If the aerosol loading of anEL is too high to distinguish it from the underlying TBL on lidar backscatter scans, thenboth layers and the associated closed circulation appear embedded in one deepbackscatter boundary layer. The findings suggest defining the atmospheric boundarylayer in complex terrain on the diurnal heating timescale rather than the commonly used1-hour timescale, which is more appropriate for flat terrain. We discuss conditionsleading to venting versus trapping of air pollutants.Citation: Reuten, C., D. G. Steyn, and S. E. Allen (2007), Water tank studies of atmospheric boundary layer structure and airpollution transport in upslope flow systems, J. Geophys. Res., 112, D11114, doi:10.1029/2006JD008045.1. Introduction[2] Thermally driven upslope flows play a critical role inthe transport of heat and air pollution in complex terrainduring fair weather conditions. Although they have beenstudied for over 160 years (see Atkinson [1981] for a reviewof the quantitative work until about 1980), basic questionsconcerning air pollution transport remain unanswered fordifferent reasons. Field observations often suffer fromsparse data and measurement uncertainties. Furthermore,land-use inhomogeneities, complicated topography, andlarger-scale flows disturb and interact with upslope flows[Banta, 1984; Wooldridge and McIntyre, 1986; Vergeinerand Dreiseitl, 1987; Vogeletal., 1987; Kuwagata andKondo, 1989; Blumen, 1990; Grøna˚s and Sandvik, 1999;de Wekker, 2002; Rampanelli et al., 2004; de Wekker et al.,2005; Reuten et al., 2005]. Numerical mesoscale models,because of their limited horizontal resolution, are unlikely toreproduce the small scale of upslope flows in steep complexterrain. Large-eddy simulations (LES) are more promising[Revell et al., 1996; Chow et al., 2006; Weigel et al., 2006a,2006b]. At horizontal resolutions of several hundred metersthese models still contain most turbulent kinetic energy atthe parameterized subgrid scale [Weigel et al., 2006b], butthey clearly resolve eddy structures on the scale of less than1km[Colette et al., 2003]. Schumann [1990] ran an LES ofan infinite slope under steady-state conditions producingresults in good agreement with Prandtl’s [1952] analyticalsolution. Analytical models and their numerical solutionrequire restrictive assumptions and boundary conditions[Egger, 1981; Petkovsˇek, 1982; Vergeiner, 1982; Kondo,1984; Brehm, 1986; Segal et al., 1987; Ye et al., 1987;Haiden, 1990, 2003; Ingel’, 2000]. Water tank models arelimited by their simple topography, restricted by side andend walls, and their scaling poses an additional challenge.However, a carefully designed tank can be a good scalemodel of real topography and realistic atmospheric condi-tions. Tank experiments are highly repeatable [Mitsumoto,1989] and permit measurements that are impossible in thefield. Surprisingly few water tank studies of upslope flowshave been carried out [Deardorff and Willis, 1987;Mitsumoto, 1989; Chen et al., 1996; Hunt et al.,2003]. None of these studies investigated the roleupslope flows play in the transport of air pollutants,which will be the focus in this paper. Future tank studiescould also benefit from substantial advances in experi-JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 112, D11114, doi:10.1029/2006JD008045, 2007ClickHereforFullArticle1Atmospheric Science Program, Department of Earth and OceanSciences, University of British Columbia, Vancouver, British Columbia,Canada.Copyright 2007 by the American Geophysical Union.0148-0227/07/2006JD008045$09.00D11114 1of17mental techniques (Moroni and Cenedese [2006] and Ecket al. [2005] provide good examples in convectionexperiments).[3] We designed a water tank scale model based on thenearly ideal conditions of field observations found in thework of Reuten et al. [2005]. The tank, field observations,and scaling are introduced in section 3. Experimental resultswith a particular emphasis on the transport of air pollutantsare presented in section 4 and discussed in section 5. Seibertet al. [2000] define the term ‘‘atmospheric boundary layer’’based on the dispersion of pollutants on a 1-hour timescalebut emphasize that this definition possibly requires modifi-cations in complex terrain regions. On the basis of thetank observations we suggest such a modification in thediscussion section. Conclusions are drawn in section 6.2. Methods[4] We provide an overview of the water tank andmeasurement methods (section 3.1), the field observations(section 3.3), and the scaling between water tank andatmosphere (section 3.4). Reuten [2006] and Reuten et al.[2005] contain additional details.2.1. Water Tank2.1.1. Design[5] The water tank consists of a stainless steel frameenclosing glass walls and a stainless steel bottom with plain,19C176 slope, and plateau (Figure 1). Convection is triggered inthe tank with 34 strip heaters (Watlow Mica) underneath thebottom plate with a maximum total power of about 14 kW,which can be manually controlled individually or in groupsof five to six heaters in a range from 30 to 100% of the totalpower. All water tank experiments covered in this manu-script were run with constant (in time) power supply, whichresulted in steady bottom heat flux. We tested the steadinessby plotting specific volume versus time in a well-mixednonstratified experiment and in a stratified experiment overthe flat plateau with the rest of the tank separated by aremovable wall. Good agreement with the expected specificvolume development suggests that the heat gain is steady.A control experiment with approximately sinusoidally timevarying bottom heat flux (as in the atmosphere) showedproperties very similar to the experiments analyzed here.We conclude that using a steady heat flux is not asubstantial constraint.2.1.2. Background Stratification[6] We will use the term ‘‘background stratification’’ forthe initial stratification of the water in the tank and the air inthe atmosphere to indicate the ‘‘background’’ environmentinto which the boundary layer grows. At the beginning ofeach experiment, the water was linearly salt stratified, whichwe achieved with a modification to the two-bucket method[Fortuin, 1960], described in Appendix A.2.1.3. Overview of Experiments and Measurements[7] We report results from two dye experiments, WT-Dyeand HFD-Dye, and three particle experiments, WT-Part,SP-Part, and TR-Part (Table 1). In dye experiment WT-Dye(Whole Tank), the tank was heated uniformly. The experi-ment started with a submillimeter thin layer of florescentUranine dye over the plain. A 2 cm wide and 30 cm tall lightsheet illuminated the dye through the plain’s end wall.Convection from the heated tank bottom dispersed the dye,similar to air pollutants emitted by area sources into theatmosphere.Figure 1. (a) Schematic side and (b) plan view of thewater tank. In Figure 1b the strip heaters underneath thetank bottom are numbered from 1 to 34. Their heat outputcan be controlled individually underneath the slope and intwo groups of five to six heaters each underneath plain andplateau as indicated.Table 1. Parameter Settings of Water Tank Experiments WT-Dye (Whole Tank Dye), WT-Part (Whole Tank Particle), SP-Part (ShortPlain Particle), TR-Part (Triangular Ridge Particle), and HFD-Dye (Heat Flux Decrement Dye)Parameter WT-Dye WT-Part SP-Part TR-Part HFD-DyeParticle (P) or Dye (D) experiment D P P P DBackground buoyancy frequency, sC010.379 0.379 0.379 0.342 0.567Length of plain, m 0.470 0.470 0.225 0.470 0.470Length of plateau, m 0.470 0.470 0.470 0 0.470Heat flux over plain, 10C03KmsC011.85 1.85 1.85 1.48/2.04a3bHeat flux over slope, 10C03KmsC011.85 1.85 1.85 2.59–3.70c3/1–2dHeat flux over plateau, 10C03KmsC011.85 1.85 1.85 - 3bSpatially average heat flux, 10C03KmsC011.85 1.85 1.85 3.15 3baSurface heat flux was 1.48 C2 10C03KmsC03for heaters 1–5 and 2.04 C2 10C03KmsC01for heaters 6–11 (Figure 1).bIn this early experiment, uncertainties in heat flux were very high.cSurface heat flux increased in twelve equal increments from 1.67 to 3.70 C2 10C03KmsC01from slope base to ridge.dSurface heat flux was about 3 C2 10C03KmsC03in bottom two thirds of the slope and roughly 1–2 C2 10C03KmsC01in upper third.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS2of17D11114[8] In dye experiment HFD-Dye (Heat Flux Decrement),which had lower heat flux on the upper slope, we droppedred-purpleKMnO4crystalsovertheplateauneartherightendwall(Figure1),injectedacolumnofgreenfoodcoloringovertheslopetop,andreleasedaplumeofyellow foodcoloringatthe slope base. This provided qualitative information aboutconvection and horizontal motions at different locations inthe tank.[9] In particle experiments WT-Part (Whole Tank),SP-Part (Short Plain of 22.5 cm length), and TR-Part(Triangular Ridge; additional end wall at the slope top)we measured two-dimensional velocity fields from themotion of neutrally buoyant particles using Particle ImageVelocimetry (PIV) programs for Matlab (MatPIV) developedby J. Kristian Sveen (www.math.uio.no/C24jks/matpiv/). Theparticles were made from high-temperature wax (CALWAX220) mixed at different ratios with titanium dioxide pigment,thuscoveringarangeofdensities.WemixedtheparticlesintoKodak Professional Photo-Flo 200 to reduce surface tension,added the slurry at the water surface of the filled tank, and letthe particles settle to their neutral buoyancy height. Duringthe experiments, which lasted roughly 1000 s, the particleswere illuminated as in WT-Dye. The observed velocity fieldscovered an area of approximately 40 cm width and 30 cmheight. The motion of theparticles was digitally recorded at arate of 30 frames per second and the raw video was timelapsed by a factor of three. For PIV analyses, we got bestresults by comparing every second frame of the final video.The resulting velocity fields were therefore 0.2 s apart. Weremoved turbulent variations and data gaps by determiningthe median over 20-s intervals from 100 velocity fields. Thisduration is similar to the horizontal advection time for theupslope flow and the vertical convection time of risingthermals and roughly corresponds to 10 min in the atmo-sphere (see section 3.4 below). The uncertainty of thevelocity measurements was approximately 20%.[10] Specific volume is the inverse of density. It increaseslinearly with height in water with constant positive buoyancyfrequency and therefore is comparable with potential tem-perature in the atmosphere. We determined vertical profilesof specific volume from the output of conductivity andtemperature probes by Precision Measurement Engineering,Inc., which were driven up and down by a profiler. Themanufacturer specifies a temperature accuracy of 0.05C176C, atemperature time response of 7 C2 10C03s, and a timeresponse of conductivity measurements of C03dbatapproximately 800 Hz. Uncertainties in the calibration,measurement, and conversion procedure added to theroughly 2% accuracy of salt concentration measurements.The conductivity and temperature probes consist of sensorslocated at the bottom tip of vertically installed shafts.During upward motion, the shafts drag fluid from lowerto greater heights (‘‘selective withdrawal’’ [Turner, 1973])so that the sensors at the bottom measure the conductivityand temperature of originally lower heights. During down-ward motion, the sensors take measurements of thesurrounding fluid before the fluid height is altered. Wetherefore only took measurements during the descents anddid not include the upward measurements that were underthe influence of the withdrawn water. Measurements werestarted from a prescribed maximum height, which increasedduring each experiment to account for the increasing depthof convection in the tank. When the profiler reached aheight of 4 mm above the tank bottom, it returned to a newmaximum height to start again. Profile depths increasedfrom approximately 20 to 30 cm and profile acquisitionincreased from 13 to 20 s. Returning the probes to the topposition and initialization created a 14–24 s gap betweenthe profiles. The probes were driven downward whilecontinuously acquiring data every 0.25 s at a verticalresolution of 3.5–4.0 mm. Each acquired datum consistsof the mean of eight individual measurements. Thesespecifications are roughly comparable to tethersondeprofiles 1000–1500 m deep, acquired over 10 min, witha sampling rate of 5 s, giving a vertical resolution of 20 m(see section 3.4 below for more details).2.2. Methods for Determining the BoundaryLayer Structure[11]OnthebasisofSeibertetal.[2000] it can beexpected that different methods of determining the boundarylayer structure will lead to different results. Over flathomogeneous terrain during daytime and fair weatherconditions, Seibertetal.[2000] report differences ofapproximately 10%. This is roughly equal to the uncertaintyof the field data in the work of Reuten et al. [2005] and thetank data reported here and will not be subject of this study.In this communication, we will focus on much largerdifference that can be attributed to particular flow structuresover the slope. We use two terms for the atmosphericboundary layer based on two different measurementmethods: ‘‘backscatter boundary layer’’ (BBL) and ‘‘thermalboundary layer’’ (TBL).[12] Strawbridge and Snyder [2004] describe an algo-rithm, which was used by Reuten et al. [2005] to determinethe BBL depth in the atmosphere with a Doppler lidar basedon the strength of the vertical gradient of aerosol concen-tration in the atmosphere. In the water tank we applied thesame method manually. During the experiments, the dyeoriginally released over the tank bottom forms a stronglyfluorescent BBL, which was captured every 10 s with adigital still camera and continuously with a digital cam-corder. Overshooting thermals of dye-rich water against anessentially black background form a sharp boundary thatcan be identified with an uncertainty of one pixelcorresponding to 0.2–0.3 mm in the vertical. During timesof deep entrainment of clear water down into the BBL, theboundary becomes diffuse and the uncertainty increases toseveral millimeters. This method provides information onthe average height of the BBL and the bottom and top of theentrainment layer, thus avoiding the problem of overesti-mating the BBL [Seibert et al., 2000].[13] The ‘‘thermal boundary layer’’ (TBL) is determinedfrom thermal information. For the field data in the work ofReuten et al. [2005], tethersonde measurements of temper-ature and humidity and surface measurements of tempera-ture were combined to estimate the centre height of theentrainment zone using a simple parcel method [Seibert etal., 2000]. We used a variation on the parcel method in thewater tank based on profiles of specific volume. Because ofa lack of measurements very near the tank bottom, wedetermined the top of the TBL as the centre height of theD11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS3of17D11114stably stratified entrainment zone, which was mostly fairlyshallow.2.3. Field Observations[14] The water tank is a model of an approximatelyhomogeneous 3-km wide 19C176 slope with a ridge height of760 m at Minnekhada Park in the Lower Fraser Valley,British Columbia, Canada [Reuten et al., 2005, Figure 2].During the day, aerosols are released mainly by area sourcesat the bottom of the Lower Fraser Valley and dispersed byconvective heating. The process is comparable to thedispersion of Uranine dye in tank experiment WT-Dye.We therefore will use the term BBL for both the tank’sdye layer and the atmosphere’s aerosol layer. Range-heightindicator (RHI) scans with a lidar provided information onthe BBL depth over plain and slope. Our comparisonsbetween tank and field observations will be limited to themorning hours of 25 and 26 July 2001, when synopticwinds were weak (about 2.5msC01at 850 hPa) and seabreeze and up-valley flows were not yet developed so thatupslope flows were the main transport mechanism [Reutenet al., 2005]. We focus on tank experiments of a particular‘‘test case,’’ which was designed to model field conditionsat 1100 PST (Pacific Standard Time, within 15 min of localsolar time) on 25 July 2001 (Table 2).2.4. Scaling[15] The details of the scaling are beyond the scope ofthis communication and will be reported elsewhere but arediscussed extensively in chapter 4 and section B.6 in thework of Reuten et al., [2005]. Table 1 and Table 2 providetypical values, which can be used for comparison with otherphysical scale models. We emphasize that the appropriatedefinition and critical value of the Reynolds number, forexample, require careful consideration, which are not elab-orated here.[16] We identified twelve key parameters. Six of these arecritical for achieving similarity of bulk flow features in tankand atmosphere: the height of the slope, H in units of m,instantaneous kinematic heat flux QHin K m sC01, buoyancyfrequency N in sC01, the horizontal length of the slope L inm, the kinematic energy density (total energy suppliedFigure 2. Movie frames of WT-Dye at the four times (in minutes and seconds) marked by the verticaldashed lines in Figure 3. The dye (Uranine) was originally released as a submillimeter thin layer over theentire plain and is illuminated from the left by a 2 cm wide and 30 cm tall light sheet. (The completemovie file is available as dynamic content).Table 2. Parameter Settings and Observations for Test CaseParameter AtmosphereaWater TankbTime since positive heat flux tref, s 14, 400 300Ridge height h, m 760 0.15Horizontal length of slope L, m 2200 0.43Background buoyancy frequency N,sC010.015 ± 0.001 0.38 ± 0.02Heat flux QH,KmsC010.21 ± 0.05 (1.9 ± 0.2) C2 10C03Integrated heat flux E, K m 1600 C2 400 0.56 C2 0.05TBL depth h, m 720 C2 120 0.14 C2 0.02Upslope flow velocity U,msC013.8 C2 0.5 0.005 C2 0.001Convective velocity w*=(gbhQH)1/3,msC011.8 0.0087Horizontal advection time th= L/U, s 630 25Vertical convection time tv= h/w*, s 410 16Reynolds numbercRe = hU/n 1.7 C2 1082700Rayleigh numberdRa = gDsh3/kn 1.9 C2 10174.4 C2 108aAtmospheric data are for the field site at Minnekhada Park at 1100 PST 25 July 2001. All uncertainties in this table roughly represent95% confidence intervals.bWater-tank data are for WT-Dye and WT-Part at 05:01.cHere n is molecular viscosity.dHerek is molecular diffusivity of heat; Dsis bDq in the atmosphere and Da/a0in the tank, with b coefficient of thermal expansion,q potential temperature, and a specific volume, where subscript ‘‘0’’ denotes initial surface values and D indicates increases from initialsurface values.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS4of17D11114through the surface per unit area, determined as the timeintegral of QHsince the beginning of positive heat flux) E inK m, and the buoyancy parameter gb in m sC02KC01where gis the gravitational acceleration and b the coefficient ofthermal expansion. There are three fundamental units,temperature (K), length (m), and time (s). According tothe Buckingham Pi Theorem [Buckingham, 1914], threeindependent key parameters are needed to form threenondimensional governing parameters (Pi groups). Asuitable choice of independent key parameters are the firstthree, H, QH, and N. The three Pi groups are then deter-mined by appropriately nondimensionalizing the remainingthree independent parameters. Nondimensionalized hori-zontal slope length is the aspect ratioP1¼LH; ð1ÞBy tank design, P1is equal in tank and atmosphere.Nondimensionalizing energy density givesP2¼ E C1NQH: ð2ÞThe third governing parameter is defined by nondimensio-nalizing the buoyancy parameter,P3¼ gb C1QHH2N3: ð3ÞInstantaneous heat flux and total supplied energy are thedirect physical drivers of the flows in tank and atmosphere.It is therefore more appropriate to refer to P3as non-dimensional heat flux.[17] In the water tank, surface heat flux QHis steady sothat E = QHC1 t andP2;w¼ NwC1twð4Þis essentially a nondimensional time. The subscript ‘‘w’’indicates that this equation only holds for the water tank.The expression for the atmosphere is far more complicated.We assume sinusoidally time-varying surface heat flux,QH;ataðÞ¼Qmax;aC1sinp2tatd;aC18C19; ð5Þwhere the subscript ‘‘a’’ emphasizes that this equationapplies to the atmosphere only. In (5), td,aC25 7.75 hours =27,900 s is a diurnal heating timescale such that whenpositive heat flux begins at about 0700 PST, the maximumvalue of Qmax,a= 0.289 K m sC01is reached at 1445 PST.With (5), the kinematic energy density for the atmosphere isEa¼Zta0QH;atðÞdt ¼ Qmax;atd;aC12p1 C0cosp2tatd;aC18C19C20C21ð6Þand (2) becomesP2;a¼ td;aNaC12p1 C0 cosp2tatd;aC18C19C20C21=sinp2tatd;aC18C19: ð7ÞThis expression is complex and depends on the specifictime development of heating in the atmosphere. Further-more, it is not time but rather energy density that is thephysical cause of the flow. We therefore prefer to call P2‘‘nondimensional energy density.’’[18] When tank and atmospheric values of P2and P3arematched (the aspect ratio P1is matched by design of thetank), lidar scans and tank images agree qualitatively(section 5.1). The time of similarity between water tankand atmosphere can be determined as follows. P3,wisconstant. With (5) the requirement P3,a= P3,wleads to arelationship between buoyancy frequencies Nwand Nainwater tank and atmosphere, respectively,Nwta;simC0C1¼ NababwH2wH2aQmax;aQH;wsinp2ta;simtd;aC18C19C20C21C01=3ð8Þwhere ta,simdenotes the atmospheric reference time ofsimilarity with a particular water-tank experiment withgiven QH,w. With field observations of Qmax,a, td,a, and Na,all quantities on the right-hand side of (8) are known. Hencethe buoyancy frequency required for the experiment, Nw,isfully determined by the choice of ta,sim. This value needs tobe chosen before the experiment. To achieve similarity foranother instant in time on the same day in the atmosphere,another experiment with another Nwneeds to be carried out.The time of similarity in the water tank tw,simcorrespondingTable 3. Similarity of Water Tank Experiments WT-Dye and WT-Part with the Atmosphere at Different TimesWater TankAtmosphereaND Gov. Para.bTime, min:scTime, PSTdN, sC01eP1P2P3Name03:00 0945 0.0134 2.9 68 0.0039 Midmorning05:01 1100 0.0149 2.9 114 0.0039 Late morning (test case)07:00 1205 0.0158f2.9 159 0.0039 Beginning afternoon13:00 1445 0.0166 2.9 295 0.0039 Time of maximum heatingaFor sinusoidally time-dependent heat flux where positive heat flux begins at 0700 PSTand a maximum value of 0.289 K m sC01is reached at1445 PST.bNondimensional governing parameters; tank and atmospheric values are equal.cTime (min:s) since the beginning of positive heat flux into the tank. For parameter settings see Table 1.dDetermined from (9).eBackground buoyancy frequency. Determined from (8).fRoughly corresponds to atmospheric conditions at the field site at 1205 PST 26 July 2001.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS5of17D11114to ta,simcan be derived by substituting (4) and (7) into thesimilarity requirement P2,a= P2,wand solving for tw,tw;sim¼NaNwta;simC0C1C1 td;aC12p1C0 cosp2ta;simtd;aC18C19C20C21C1 sinp2ta;simtd;aC18C19C20C21C01ð9Þwhere the notation Nw(ta,sim) emphasizes that Nwmust bedetermined through (8) as a function of ta,sim.[19] An important corollary of the last two equations is:The same experiment with initial background buoyancyfrequency Nwcan be used to check similarity with atmo-spheric observations on different field days with differentbackground buoyancy frequencies Na. Table 3 shows thatthe tank experiments WT-Dye and WT-Part representrealistic atmospheric scenarios over a long period, includingthe test case at 05:01 (min:s, time elapsed after start of heatflux into the tank).3. Results3.1. Flow Characteristics, Layering,and Regime Changes[20] We will show that mean characteristics of the water-tank flow remain unchanged for considerable periods.‘‘Regime changes’’ of the flow geometry are associatedwith substantial changes in velocity and specific-volumedistribution. In this section, we will analyze the whole-tankexperiments WT-Dye and WT-Part (Table 1) at four tanktimes, 03:00, 05:01, 07:00, and 13:00. Correspondingatmospheric conditions were calculated with (8) and (9)and are shown in Table 3.3.1.1. ‘‘Midmorning’’: 03:00[21] This early time in WT-Dye and WT-Part is similar to1045 PDT (‘‘midmorning’’) in the atmosphere for a constantbackground buoyancy frequency of 0.0134 sC01(Table 3),i.e., P2and P3in (2) and (3) are equal for tank andatmosphere. The predominant features at 03:00 in WT-Dyeare a BBL bulge over the plain near the slope and BBLdepressions at the end wall and over the lowest 10 cm of theslope (Figure 2). Over the plain, the BBL is 30–40% deeperthan predicted by an encroachment model of TBL growthoverahorizontal surface[Carson,1973],whileitagreeswiththe prediction near the left end wall (Figure 3). Notice that amuch deeper BBL than predicted was also observed in thefield (dotted line in A) at a location roughly corresponding tothe location of the open circles 13 cm from the slope base(insetinB).SeeReuten[2006,Figure4.3]formoredetailsonthe comparison between field and tank data.[22] The BBL distribution over the plain is caused by aclockwise (CW) rotating eddy near the slope base (Figure 4)and a counter clockwise (CCW) rotating eddy near the leftend wall (see dynamic content). A net flow from the CCWFigure 3. (a) Time development of backscatter boundary layer (BBL) depth (from WT-Dye) and(b) mean specific-volume increment Da (from WT-Part). The latter is the difference between averagespecific volume within the thermal boundary layer (TBL) and the original surface value at that location.The inset in Figure 3b shows the locations of the measurements. The two solid curves are predictionsfrom an encroachment model of TBL growth over a horizontal surface. The dashed vertical lines mark thetimes of the still images in Figure 2 and velocity fields in Figure 4. The dotted line in Figure 3a is basedon lidar backscatter scans over the plain near the slope base at Minnekhada Park in the morning of 25 July2001. For the conversion from atmospheric time and BBL depth to laboratory time and BBL depth, seeReuten [2006].D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS6of17D11114rotating eddy into the CW rotating eddy leads to compen-sating subsidence near the left end wall and a deep BBLover the CW rotating eddy at about x = C011 cm (Figure 5).At x = C015 cm, TBL and BBL are about 11 cm deep. Thedownflowing part of the CW rotating eddy splits into abranch joining the upslope flow and a branch closing theeddy, the latter causing a flow in the downslope directionover the plain near the slope. Mitsumoto [1989] alsoobserved the downslope flow, which persisted throughcomplete cycles of diurnal heating and cooling and wasindependent of the length of the plain.[23] From the BBL depression near the slope base to thetop, BBL depth and upslope flow depth decrease approxi-mately linearly to almost zero at the top (Figure 2 anddynamic content). Over the slope at x = 9 cm both TBL andBBL are only about 6 cm deep. On Figure 4 the upslopeflow appears shallower than the TBL, but at this early stage,only a few particles are visible at greater heights, and datacoverage is insufficient to determine upslope flow depth.Decreasing TBL depth with distance up the slope iscorroborated by mean specific volume increments at 03:00(Figure 3b), which are lower than expected over a horizon-tal surface. The slope is a transient region, where theupslope flow advects fluid with low specific volume intohigher regions. Because strongest upslope velocity occursneartheslope’smidpoint(0.5–0.6cmsC01ataboutx=20cm,Figure 4), fluid parcels overshoot near the ridge causingnegative specific volume increments. Near the slope base,specific volume in the TBL is slightly lower than expected.[24] Decreasing upslope flow depth and velocity fromslope midpoint to ridge imply decreasing mass flux andtherefore compensating detrainment of fluid from theupslope flow. If the upslope flow fills the entire TBL sucha detrainment has to occur vertically against gravity,because fluid from the upslope flow layer has a lowerspecific volume than the stratified fluid above, or laterally,adding a substantial three-dimensional (3-D) component tothe overall flow. The video (dynamic content, animation 2)supports the former process and shows no evidence for thelatter process at 03:00. The detrained fluid subsides over thelower part of the slope causing the BBL depression.[25] At the slope top, a shallow plain-plateau flow trans-ports dye toward the plateau’s end wall, where it overshootsand returns the dye above the plain-plateau flow (Figure 2).The flow in the tank is very similar to the flow in anidealized infinite series of valleys between plateaus, wherevalley bottom and plateau half-widths equal the tank’s plainand plateau lengths, respectively (Figure 6). A main differ-ence is that velocities and turbulence at the tank walls mustbe zero unlike in an infinite repetitive domain. Furthermore,Figure 4. Two-dimensional velocity fields for WT-Part corresponding to the four still images in Figure 2at the four times marked by vertical dashed lines in Figure 3. Fields are time medians over 20 s(100 individual fields) approximately centered at the indicated times of each graph. The solid curves areverticalprofilesofspecific volume(inarbitraryunits) measuredapproximatelyduringtheaveraging periodofthevelocityfieldsx=C015cmtotheleftandx=9cmtotherightoftheslopebase(atx=0cm).Alllengthand velocity scales are identical in the four graphs. A representative velocity vector of length 1 cm sC01isshown near the bottom right of each graph underneath the straight line indicating the slope surface. Thesharp spikes in some profiles are probably caused by double diffusion and not a major factor for the overallflow but helpful indicators of layer boundaries.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS7of17D11114in the real atmosphere both geometry and solar radiation arenot perfectly symmetric, permitting cross-flows and circu-lations at scales larger than those in the tank. However,since we observe strong vertical motions near the end wall,we expect the motions in the tank to be a reasonablequalitative representation of sufficiently symmetric atmo-spheric environments. In such atmospheric environments,the flow would initially be perceived as venting of aerosolsover the slope top, but by joining the plain-plateau flowcirculation, the dye returns above a growing TBL, whicheventually reentrains the dye if heating continues.3.1.2. ‘‘Late Morning’’ (‘‘Test Case’’): 05:01[26] This is the time of expected similarity of WT-Dyeand WT-Part with the atmosphere at 1100 PST 25 July 2001(Table 2 and Table 3). Qualitatively, the flow character-istics remain unchanged from 03:00 to 05:01 (Figure 2 andFigure 4).[27] The average depth of the BBL at the three locationsover the plain in Figure 3a agrees with the value expectedover a horizontal surface. From 03:00 to 05:01, the BBLdepression has weakened (Figure 2). The CW rotating eddyhas moved roughly 3 cm closer to the slope and the eddy’svelocity has slightly increased (Figure 4). At x = C020 cm,the flow from the CCW rotating eddy into the CW rotatingeddy (as sketched in Figure 5) is clearly visible. At x =C015 cm, TBL and BBL are about 16 cm deep, and at x =9 cm, TBL, BBL, upslope flow are about 8 cm deep. Asbefore at 03:00, the BBL depth over the slope decreasesapproximately linearly to almost zero at the slope top.Between x = 0 and 5 cm, however, the upslope flow depthis only about 7 cm while the BBL is almost twice as deep.In the BBL above the upslope flow, velocities are weak withsome return flow. Apparently, dye has been detrained fromthe upslope flow in the upper part of the slope and carriedinto the subsiding flow in the lower part, where it partlyfilled the BBL depression. The shallow plain-plateau flow isvisible in Figure 4 between y = 16 and 19 cm and its returnflow between y = 22 and 25 cm, which can be seen inFigure 2 as dye that has propagated horizontally from theplateau to above the midpoint of the slope.3.1.3. ‘‘Beginning Afternoon’’: 07:00[28] At 07:00, WT-Dye and WT-Part model atmosphericconditions at 1205 PST with a background buoyancyfrequency of 0.0158 sC01, hence more stable than on 25 July,but slightly less stable than on 26 July (Table 3). Flowcharacteristics begin to change.[29] The BBL depth over the plain has slightly decreasedsince 05:01 and has dropped below the value expected overa horizontal surface (Figure 3a). This is in line with adecrease of the TBL depth to roughly 13 cm at x = C015 cm(Figure 4). After 07:00, the BBL deepens again over theplain except near the end-wall (Figure 3a). Specific volumehas continued to increase approximately linearly in timeover the plain and near the slope base but has increasedrapidly over the slope near the top (Figure 3b). Thecorresponding specific volume profiles (Figure 7, top) beginto exhibit a three-layer structure at 04:22–04:39: an unstablelower layer, a weakly stable middle layer, and a stable toplayer(theinitialbackground).Thelowerlayerandthemiddlelayer are separated by a sharp spike at about ridge height (y =15 cm) probably caused by double diffusion [Reuten, 2006].At 06:47–07:07, the lower layer and the middle layer, that isthe upslope and the plain-plateau flow system, begin tomerge. At the same time over the lower part of the slope atx = 9 cm (middle) and over the plain at x =C015 cm (bottom),asimilar three-layer structure is just beginning to develop. Atthese two locations, the two lower layers merge later thanover the slope near the top (not shown in Figure 7), althoughthe plain-plateau flow system has disappeared already at07:00 (Figure 4).[30] Over the plain, TBL and BBL essentially agree. Thetop of the BBL at x = C015 cm (horizontal bars in Figure 7,determined from dynamic content) is systematically slightlyhigher than the TBL at x = C013 cm only because of thedifference in location. At 06:47–07:07, the TBL top wasslightly higher over the plain (bottom) than over the slope(middle), in agreement with the BBL top (Figure 2). TheBBL depression over the slope and the bulge over the plainhave almost disappeared, but the velocity field (Figure 4)still shows a bulge at about x = C010 cm and a deepdepression between x = 5 and 10 cm. At this stage of theexperiment, the dye has been substantially distributedthroughout the tank, and inferences on instantaneous flowfield and thermal structure from the BBL characteristics aremore difficult than at earlier times.3.1.4. ‘‘Time of Maximum Heating’’: 13:00[31] At 13:00, the water tank experiment is similar toatmospheric conditions at 1445 PST, with a backgroundbuoyancy frequency of 0.0166 sC01, which is slightly higherthan on 26 July (Table 3). The flow characteristics havechanged substantially from those at 07:00.[32]Atx=C013 cm, the BBL depth has been growingas expected over a horizontal surface (Figure 3a). Bycomparison, at x = C023 cm and C033 cm it increased slowlyuntil just before 13:00 when it increased rapidly to or nearthe expected value because the subsidence region near theFigure 5. Schematic of eddies over the plain in WT-Dyeand WT-Part from 03:00 to 07:00. ‘‘CW’’ and ‘‘CCW’’denote the clockwise and counterclockwise rotating eddies,respectively. The grey region represents the BBL.Figure 6. Mirror symmetry of water tank. The flow in thewater tank (solid lines and arrows) models perfectlysymmetric flow in an infinite array of valleys and plateausas indicated by the dashed lines and arrows.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS8of17D11114plain’s end wall narrowed, and at these two locationssubsidence was replaced by deep convection. Specificvolume at all three locations in Figure 3b has continuedto increase approximately linearly in time and at 13:00slightly exceeds the expected values over the plain and overthe lower part of the slope. The average of the specificvolume over the three locations agrees with the expectedvalue over a horizontal surface. Over the upper part of theslope, specific volume remains much smaller, indicatingthat upslope flows continue advecting fluid of lower spe-cific volume into the upper slope region. The top of theBBL slopes approximately linearly from near the plain’send wall to the plateau’s end wall (Figure 2) at an aspectratio and angle of about one third of the bottom slope angle(6C176–7C176). This agrees with Deardorff and Willis [1987], whoalso observed a sloping mixed layer top intermediatebetween horizontal and bottom slope angle.[33] The two lowest layers at x = 9 cm (Figure 7, middle)and x = C015 cm (bottom), which have begun merging at06:47–07:07, have formed a deep well-mixed TBL (about23 cm at x = 9 cm and 26 cm at x = C015 cm, Figure 4),which agrees with the BBL (Figure 2). The CW rotatingeddy is approximately 16 cm deep with its downwardvelocities exceeding 1 cm sC01, but its lower flow in thedownslope direction has disappeared (Figure 4). Theupslope flow is strong (about 1 cm sC01), shows no returnFigure 7. Vertical specific-volume profiles in WT-Part. The three graphs correspond to the locations inFigure 3b: x = C015 cm (bottom, square), x = 9 cm (middle, cross), and x = 34 cm (top, circle). Thedifference between tick marks on the x axis is 10C06m3kgC01. The profiles are horizontally offset by 2 C210C06m3kgC01to avoid overlap. The times of measurement in minutes and seconds after the beginning ofpositive heat flux, shown only in the bottom graph, apply to the corresponding profiles in the other twographs. Each profile is accompanied by the predicted specific volume profile (solid thin lines), thepredicted initial background specific volume profile (dashed thin lines), and the BBL depth averaged overthe time interval of the specific volume profiles (short horizontal bars), all relative to the plain. Specificvolume is shown as the difference from the expected initial surface value over the plain.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS9of17D11114flow, and is shallower (10–15 cm) than TBL and BBL. Thedynamic content, animation 2 reveals that the upslope flowin the center of the tank is partially compensated by a returnflow near the side walls; (Figure 4 does not show thismotion because particles near the side walls were out offocus and not illuminated and therefore automatically fil-tered in MatPIV). At the beginning of an experiment, heatconduction into the tank bottom is slow and dominated bymolecular diffusion. Because the heat conductivity of stain-less steel is much greater than that of water, the tank bottomis nearly homogeneously heated. As the flow becomes moreturbulent, heat is transported faster into the water than alongthe stainless steel bottom, and less heat is supplied to waternear the side walls. Because the entire flow in upslopedirection cannot be compensated within the weakly heatednarrow strip near the side wall, some of the flow movesagainst gravity at the right end-wall and returns above theplain-plateau flow. When lateral flows occur late in theexperiment, the tank may no longer be a good model ofthe atmosphere.3.1.5. Summary[34] The merging of layers approximately at 07:00 and13:00 in the vertical specific volume profiles corresponds toflow regime changes. Flow characteristics at 03:00 and05:01 were very similar. CCW and CW rotating eddiesoccurred over the plain (Figure 5), an upslope flow circu-lation over the slope, and a plain-plateau circulation over theslope and plateau. A large circulation filling the entire tankwidth was superimposed on top of the smaller circulations(Figure 8a).[35] At 07:00, the upper part of upslope flow circulationand the bottom part of plain-plateau circulation merged andbecame one large circulation reaching from slope base toright end wall (Figure 8b). Just before 13:00, the eddiesover the plain had disappeared and a large combinedupslope and plain-plateau flow circulation deeper than ridgeheight occurred within a deep BBL (Figure 8c). Flows inupslope direction were partially compensated laterally nearthe side walls (Figure 8d).3.2. Thermal Boundary Layer over Valley Centers[36] Subsidence observed at the plain’s end wall inWT-Dye (corresponding to the valley center of an infiniteseries of valleys between plateaus) agrees with the widelyaccepted notion that upslope flows over valley side wallscause compensating subsidence over the valley center[Whiteman, 2000]. In the tank it is plausible that subsidenceat the plain’s end wall causes a CCW rotating eddy, which inturntriggersaCWrotatingeddyneartheslope(Figure5).Byreducing the length of the plain to 22.5 cm in SP-Part, weeliminated the possibility of two eddies with a width-to-height ratio of about one. If subsidence caused the eddymotion, the only eddy over the plain in SP-Part would beCCW rotating. By contrast, our observations show a CWrotating eddy (Figure 9). The causal chain is therefore: theupslopeflowcausesaCWrotatingeddy,whichinturncausesstrongly rising motion at the valley center for a short plain orasecond(CCWrotating)eddyclosertothevalleycenterforalonger plain. In the latter case, the CCWrotating eddy causesthe familiar subsidence near the valley center. The parametersettings suggest that valleys with an aspect ratio of valleybottom width to ridge height of 2 C2 22.5 cm:14.9 cm C25 3:1exhibit strong rising motion over the valley center.[37] Colette et al. [2003] observed layering, similar toours, in their LES of two-dimensional valleys betweenmountain ranges of triangular cross section. This layering,however, could also have been the result of the initialFigure 8. Sketches of flow characteristics in WT-Dye andWT-Part (a) between 03:00 and 05:01 and (b) at 07:00;dashed arrows denote small persistent circulations; solidarrows denote a large circulation, which appears super-imposed on top of the smaller circulations. (c) Side view offlow characteristics at 13:00 and (d) plan view of C; flowsto the right are partly compensated near the lateral side wallsand partly at greater heights.Figure 9. Rising motion over a valley center. In particleexperiment SP-Part, conditions were identical to those inWT-Dye and WT-Part (Table 1) with the exception of anend wall inserted over the plain 22.5 cm from the slope(vertical line). Flow characteristics are sketched with dashedarrows (small circulations) and solid arrows (large super-imposed circulation), determined from two-dimensionalvelocity fields. The grey region outlines the BBL.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS10 of 17D11114background at the beginning of positive heat flux: a stablesurface layer topped by a neutral residual layer and a stablefree atmosphere. The authors ran experiments over a widerange of aspects ratios of valley bottom width to ridgeheight. Flow fields for a very narrow valley exhibit subsi-dence over the valley centre as expected. We speculate thatrising motion would occur at an aspect ratio of 3:1. Theclosest to this ratio in the work of Colette et al. [2003] is acase with an aspect ratio of 2:1. The authors did not showflow fields for this case so that vertical motion cannot bedirectly confirmed. However, they demonstrated that in thiscase no inversion breakup from above occurred, implying alack of subsidence. A possible explanation is that this is atransitional case between strong subsidence in a valley of anaspect ratio smaller than 2:1 and divergence in a valley withan aspect ratio of roughly 3:1.[38] Future research should test how accurately the aspectratio needs to be achieved to observe the rising motion andcompare tank with field observations. The aspect ratio maybe different for the atmosphere, where the CW rotating eddymay occur further from the slope (see below). Furthermore,past field measurements may not have been taken at thelocation of the CW rotating eddy. Unless rising motion ledto condensation, it would be unnoticed. Finally, spatiallyinhomogeneous sensible surface heat flux and imperfectvalley symmetry in the atmosphere may reduce the likeli-hood of strong rising motion.[39] Atkinson and Shahub’s [1994] three-dimensionalnonhydrostatic numerical model runs covered a wide rangeof background stabilities and valley shapes. They observedflow regime changes at background stabilities roughly anorder of magnitude smaller than stabilities in the fieldobservations in the work of Reuten et al. [2005] thatcorrespond to those in our tank experiments. For very weakstabilities, they observed strong upward motion over thevalley center. We cannot draw direct comparisons with oursteep slope angles, but the study by Atkinson and Shahub[1994] clearly demonstrates the wide range of flow charac-teristics possible even in a simple valley cross section.[40] Rampanelli et al. [2004] ran a numerical mesoscalemodel with two different two-dimensional topographies,both similar to our conditions in the tank. In neither casedid the model produce a CW rotating eddy. In one topog-raphy the valley side walls were 1 km high with a maximumslope angle of 15C176, and the valley bottom was 1 km wide.The aspect ratio of 1:1 was probably too small to supportrotating eddies over the valley bottom. In the secondtopography, a very long plain and plateau were connectedvia a slope of 3.6C176, much less than our 19C176. We will nextlook into the possible reasons for the existence of the CWrotating eddy and discuss the consequences for similaritybetween water tank and atmosphere.3.3. Backscatter Boundary Layer Bulgeand Depression Near the Slope Base[41] Lidar observations at the Minnekhada Park field sitecovering the entire morning of 25 July [Reuten et al., 2005,Figure 6] did not show a BBL bulge and adjacent depres-sion. In the atmosphere without lateral boundaries even verylight crosswinds can advect aerosols laterally into thedepression. Furthermore, as we will report elsewhere,upslope flows in the atmosphere under the conditions atMinnekhada Park are faster than those in the water tank;while that does not affect the overall qualitative agreementbetween field and tank observations, atmospheric aerosolswithin the upslope flow circulation return faster than the dyein the water tank and therefore mask the BBL depression.On a larger scale, this masking takes more time and theBBL depression can be observed more easily. de Wekker[2002] observed a BBL bulge and depression adjacent to theentire mountain range north of the Lower Fraser Valley,with a ridge height exceeding 1500 m, about twice the ridgeheight at Minnekhada Park [de Wekker, 2002, Figure 3.1].Longer distances imply longer timescales and partiallyexplain de Wekker’s observation that the BBL depressionstrengthened with time. De Wekker modeled the BBLdepression with RAMS, but the 1-km horizontal resolutionwas possibly insufficient to resolve the CW eddy motionover the plain. De Wekker concluded that the BBL depres-sion is associated with increased heating within and abovethe TBL at the slope base due to advection of warm air bythe upslope flow system. Moreover, he hypothesized thatsubsidence over the BBL depression is enhanced by hori-zontal wind divergence due to upslope flow acceleration atthe slope base. Mitsumoto [1989] speculated that the CWrotating eddy was ‘‘energetically economic.’’ We nowcombine these arguments with the water tank observations.[42] Without compensating upslope flow, a horizontalspecific-volume gradient would develop along the slope(Figure 10a). The upslope flow advects fluid of low specificvolume upwards along the slope into regions of higherspecific volume, thereby constantly reducing specific vol-ume and inhibiting TBL growth in these regions. In con-trast, advection over the plain does not cause cooling, andthe TBL grows faster there than over the slope. At 05:01 inWT-Dye, the TBL depth h over the plain is approximatelyequal to the ridge height H, and to first approximation thisleads to a TBL depth decreasing linearly from H to 0 alongthe slope (Figure 10b). Over the slope, however, a circula-tion appears superimposed on top of the inflow as sketchedin Figure 8a. The upper branch of the circulation causessubsidence W over the lower half of the slope (Figure 10c).Following Mitsumoto [1989], we speculate that indeed thedevelopment of a small circulation over the slope is ener-getically beneficial. The CCW rotating upslope flow circu-lation causes a downward drag at its left border favoring theadjacent CW rotating eddy over the plain (Figure 8a). Itremains open for future research why the four smallercirculations in Figure 8a are embedded in a larger circula-tion, although closed slope flow and plain-plateau flowcirculations without the large circulation could balance masstransport.3.4. Inhomogeneous Heating[43] In the last two sections, we presented tank observa-tions about a persistent CW rotating eddy over the plainadjacent to the slope, which was also observed by Mitsumoto[1989]. In contrast, Chen et al. [1996] did not observe theeddy over the plain, although their experiments, like those byMitsumoto [1989], used a triangular ridge and approximatelysinusoidal cycles of diurnal heating and cooling. Chen et al.[1996] injected hot water underneath the ridge top, fromwhere it flowed outward toward the end walls underneath thetankbottom.StrongventingovertheridgeintheexperimentsD11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS11 of 17D11114of Chen et al. [1996] provides evidence that there was astrong heat flux increase from end wall to ridge top. Bycontrast, Mitsumoto [1989] ensured homogeneous heat fluxby individually controlling the water temperature frominjection pipes underneath the slope. Therefore we hypoth-esize that the positive heat flux gradient from left end wall toridge top in the experiments of Chen et al. [1996], which wasnot present in the experiments of Mitsumoto [1989] and ourwhole-tank experiments, eliminates the CW rotating eddy.[44] To test this hypothesis, we ran experiment TR-Part(Table 1), in which heat flux increased by a factor of 2.5from the plain’s end wall to the removable end wall at theridge top (Figure 11). Because the plateau was cut off fromthe rest of the tank with a removable end wall, there was noplain-plateau flow. The heat flux gradient triggered longCCW rotating circulations over plain and slope (dashedarrows) and increased the strength of the upslope flow,causing overshooting over the ridge top. One would expectthat the two circulations would merge, but they remainedseparated by a high arch within the large circulation (solidarrows). We can therefore reject the hypothesis that the heatflux gradient in the work of Chen et al. [1996] destroyed theCCW rotating circulation.[45] The evidence suggests that the CCW rotating eddywas also present in the experiments by Chen et al. [1996],who reported the large circulation but not the individualCCW rotating circulations and the arch between them. Wespeculate that the authors did not report a CCW rotatingeddy because their experiments were configured to investi-gate large-scale motions: a 74 cm wide interrogation windowand particle streak photographs taken every 30 s providedless spatial and temporal resolution than our experiments.4. Discussion[46] Field observations reported by Reuten et al. [2005]raise a number of key questions: Does the boundary layerover a heated slope coincide with the TBL over flat terrainor does it have a more complicated structure? How doupslope and return flow relate to the boundary layerstructure? What are the determining parameters for ventingversus recirculation of air pollutants over heated mountainslopes? We will suggest answers to these questions in thefollowing discussion.4.1. Comparison of Field and Tank Observations[47] The explanation of BBL bulge and depression andCW rotating eddy over the plain near the slope base holdsfor atmosphere and water tank (section 4.3). A comparisonof water tank images with lidar scans roughly at the time ofsimilarity (05:01 and 1100 PST 25 July 2001, respectively)shows good qualitative agreement (Figure 12). Two minordifferences are caused by greater upslope flow velocities inthe atmosphere than in the tank. First, overshooting over theFigure 10. Schemata of TBL (gray areas), specificvolume, and flows in the water tank. (a) Withoutcompensating upslope flows, TBL depth is homogeneous.Vertical specific volume profiles for an encroachment modelare sketched for point 1 (solid line) and point 2 (dashedline). A pressure gradient exists between points 1 and 2.(b) If the TBL top was horizontal, here shown for the casewhen TBL depth equals ridge height, specific volumeprofiles over plain and slope would be identical, shown forpoints 1 and 2. (c) TBL and flows as observed in the tank:mean inflow U1into the upslope flow system near point 1,mean horizontal velocity U2in the upslope flow layer nearpoint 2, and mean subsidence velocity W between points1 and 2.Figure 11. Flow characteristics for inhomogeneous heatflux in experiment TR-Part. This experiment was designedto reproduce qualitatively tank observations by Chen et al.[1996], with their time of maximum heating correspondingroughly to 05:01 in this experiment. Distribution of heatflux underneath the tank bottom is indicated by thenumbers, which are in percentage of the maximum valueof 0.0037 K m sC01right below the ridge top. Heat fluxthrough the tank bottom was 40% for heaters 1–5, 55% forheaters6–11,andincreasedin12incrementsfrom70to100%for heaters 12–23 (Figure 1). The plateau was separated fromthe rest of the tank by a removable end wall (vertical line).Under the plateau, 70% of the maximum heat flux wassupplied to minimize the pressure gradient across theseparatingwall.Thearrowsrepresentthecirculationsat05:01.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS12 of 17D11114ridge top is stronger in the atmosphere, well documented bycumulus clouds on the lidar scans (Figures 12c and 12d).Second, the laminar-looking elevated aerosol layer rightabove the turbulent TBL at 0947 PST 25 July 2001 hadpropagated farther over the plain than the counterpart in thewater tank (Figure 12a).[48] On 26 July, background stratification was strongerthan on 25 July. At 1251 PST (Figure 12d), the BBL wasapproximately as deep as on the previous day at 0947 PST(Figure 12c), in good agreement with WT-Dye at 07:00(Figure 12b).[49] In conclusion, flow characteristics in the water tankare a good qualitative representation of atmospheric flows atMinnekhada Park during the morning. Atmospheric upslopeflows in the afternoon are substantially affected by seabreeze and up-valley flow, which will not be discussed here.4.2. Atmospheric Boundary LayerOver Complex Terrain[50] In this work, TBL depth was determined fromvertical profiles of specific volume in the tank and potentialtemperature in the atmosphere using the parcel method; theBBL was determined from images of dye concentrations inthe tank and lidar aerosol backscatter scans in the atmo-sphere. To clarify terminology, we distinguish the atmo-spheric boundary layer (ABL) from TBL and BBL. It iscommon to ‘‘define the boundary layer as the part of thetroposphere that is directly influenced by the presence of theearth’s surface, and responds to surface forcings with atimescale of about an hour or less’’ [Stull, 1988]. Seibert etal. [2000] pointed out that this definition might requiremodification in complex terrain. The requirement of suchfast response is often tacitly abandoned, even over flatterrain, for example in the case of the residual layer abovea strongly stratified nocturnal boundary layer in the winter.A sense of continuity of entrainment zone and cappinginversion from one day to the next [Stull, 1988, Figure 1.7]suggests considering the ABL as the part of the tropospherethat exchanges temperature, tracers, or moisture with theEarth’s surface within one diurnal heating cycle. Concep-tually, this definition solves a key problem over complexterrain: Venting of upslope flows over mountain ridges isvery fast and within one hour can create elevated aerosol-rich layers. These should therefore be considered part of theABL, although they may remain above the entrainmentzone for the entire day and therefore be counter to ourintuitive understanding of the ABL. On the other hand,elevated layers (EL) that merge with the TBL within onediurnal heating cycle should be considered part of the ABLeven if the merging occurs several hours later. This defini-tion of the ABL comprises all layers that exchange air withthe surface during the day. Together with inflow andoutflow by advection and venting, the ABL constitutesthe local atmospheric environment for the assessment ofair quality in complex terrain during a diurnal cycle.4.3. Multiscale Layering and the Relation of Upslopeand Return Flow to the Boundary Layer Structure[51] In the work of Reuten et al. [2005, Figure 7], fieldobservations several kilometers from the slope suggestedthat TBL and BBL were identical on the mornings of 25 and26 July 2001, when larger-scale flows were negligible. Thisis probably not representative for TBL and BBL directlyover the slope. de Wekker [2002] drew a comprehensiveconceptual picture of the ABL characteristics over complexterrain and clearly demonstrated that the BBL oftensubstantially exceeds the TBL, in particular in the after-noon. Many of the complicated ABL features investigatedby de Wekker [2002] are probably caused by ‘‘multiscalelayering,’’ a repetition of layering processes and regimechanges at increasingly larger spatial and temporal scales,which are revealed in the water tank experiments.[52] The fastest of these processes is convection, whichcreates the TBL. Without horizontal inhomogeneities, noFigure 12. Comparison of WT-Dye at (a) 05:01 and (b) 07:00 with atmospheric lidar RHI scans at(c) 0947 PST 25 July 2001 and (d) 1251 PST 26 July 2001. Figures 12a and 12c show almost the entiretank width (1.3 m) and a height of about 0.3 m. Figures 12c and 12d show a width of about 8000 m and aheight of about 1500 m. Lighter colors roughly represent higher dye/aerosol concentrations. Thefluorescent dye in Figures 12a and 12b is illuminated from the left, where dye concentrations areexaggerated. The bright areas on the right top in Figures 12c and 12d are caused by cumulus clouds. Thedark line in Figure 12d marks the BBL top. Horizontal and vertical scales of the lidar scans are adjustedto agree approximately with the scales represented by the water tank. In Figure 12d, the topography looksdifferent from Figure 12c because the azimuth angles of the two lidar scans differed by 5C176. Images inFigures 12c and 12d are adapted from Reuten et al. [2005, Figures 15 and 5].D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS13 of 17D11114other process could lead to further ABL structures. Shortsteep slopes like the one at Minnekhada Park, which wasmodeled by the tank experiments, drive upslope flows ofseveral meters per second and force a compensating returnflow over horizontal distances of only a few kilometers. Inless than 1 hour aerosols transported from near the surfaceup the slope return in an EL above the TBL. The tankexperiments show that ELs tend to have intermediatecharacteristics: aerosol concentrations and stability betweenthose in TBL and free atmosphere (Figure 7). The under-lying TBL needs less surface heating to grow into a weaklystratified EL than into the strongly stratified free atmo-sphere. In WT-Part, the TBL began merging with the EL atabout 07:00, a typical atmospheric early afternoon case(Table 3). In the atmosphere, by comparison, the differencein aerosol concentrations between TBL and EL is acomplicated function of the day’s history of emissions,advection, and entrainment. Before the merging of TBLand EL, their aerosol concentrations may become indistin-guishable. This may be the reason why both layers appear asone deep BBL in the field observations.[53] Reuten et al. [2005] speculated in their hypothesis 3that BBL and TBL were different for extended periodsduring the field observations. This is supported by the tankexperiments, in which the upslope flow layer agreed withthe TBL and the return flow layer with the EL at all times;together building up a BBL deeper than the underlyingTBL. In the lidar scans at Minnekhada Park, the TBL andthe EL within the BBL were probably indistinguishable.[54] We argued that the large BBL depressions investi-gated by de Wekker [2002] were caused by the samekinematics as in the water tank but at a scale that is similarto the Northshore Mountains as a whole rather than thesmaller individual slope at Minnekhada Park. The North-shore Mountains are approximately 100 km wide and reachan elevation of 1500–2000 m. The slope at MinnekhadaPark in a tributary valley of the Northshore Mountains isonly a few kilometers wide and 760 m high. In the watertank, multiscale layering is repetitive in time. All tankexperiments with a heated plateau caused a plain-plateauflow circulation that removed dye-rich fluid from theupslope flow circulation at the slope top and returned itabove the plain in the return flow part of the plain-plateaucirculation. Upslope and plain-plateau flow circulationmerged at approximately the same time as the TBL mergedwith the EL. At this point, the process of developing an ELabove the TBL was repeated at the larger scale of thecombined upslope plain-plateau flow circulation. Eventuallythe TBL merged with the new EL before 13:00, which issimilar to typical atmospheric settings just before the time ofmaximum heating (Table 3). By 13:00, the TBL had grownbeyond the scale of the underlying topography, which couldnot provide further horizontal inhomogeneities to continuethe multiscale layering.[55] In many real atmospheric settings, horizontal inho-mogeneities are likely to continue at increasingly largerscales, and multiscale layering is only limited by the finiteduration of the diurnal heating cycle or the depth of nearbytopography. Furthermore, inhomogeneities often occur atmore closely spaced scales and are not restricted to upslopeflows but may include along- and cross-valley flows,topographically altered synoptic winds, and flows causedby land-use variations. Such closely spaced discrete scalescause a de facto ‘‘continuum in topographic complexity andscale’’ [Whiteman, 1990]. A water tank of sufficientlysimple topography can clearly discriminate the steps inthe multiscale layering, which may be practically indistin-guishable in the atmosphere.[56] Rampanelli and Zardi [2004] developed a method offitting a piecewise smoothly connected curve to the well-mixed and entrainment layers of the ABL and applied themethod to measurements in complex terrain surrounding theTrento region, Italy. Several examples show entrainmentlayers much deeper than the underlying well-mixed layer. Aclose look at the measured profiles suggests that the authorsmay have observed several-hundred meter deep ELs, whichwere fitted within the entrainment layer. It may be worth-while investigating these data sets further by trying to fitmultiple layers with the method suggested by Rampanelliand Zardi [2004]. Bayesian model comparison could beused to decide if enough evidence is present in the data tojustify fitting of additional layers [e.g., Gregory, 2005].4.4. Venting Versus Trapping of Air Pollutants[57] The water tank is an extreme simplification of thecomplexity of the real atmosphere. This even holds fornearly ideal conditions at Minnekhada Park during themorning of 25 July 2001. Nevertheless, the detailed inves-tigations of the flows in the water tank permit conclusionsabout atmospheric flows under typically less ideal condi-tions. Essentially, local trapping of air pollution over heatedmountain slopes occurs when an EL resides over a growingTBL long enough to be entrained. The scenarios thattypically, albeit not always, support this, are now brieflydiscussed.[58] Weaker larger-scale flows lengthen the residencetime of the EL over the TBL and therefore increase thechance of entrainment.[59] Stronger sensible surface heat flux supports theentrainment of the EL by a deeper TBL. This effect ispartly offset by an increased volume into which air pollu-tants are dispersed and by a stronger upslope flow poten-tially leading to a higher EL, which decreases the chance ofentrainment.[60] Similarly, weaker stratification supports the entrain-ment of the EL by a deeper TBL. This effect could partly beoffset by the increased volume into which air pollutants aredispersed. Furthermore, the impact of background stratifi-cation on upslope flow velocity is still an open question.Numerical experiments over a wide range of stratificationsshowed regimes where the dependence of upslope flowvelocity on stratification differed substantially [Atkinsonand Shahub, 1994]. We cannot confirm this because oflarge uncertainties in field observations and a very narrowrange of background stratifications in the field data [Reutenet al., 2005] and the water tank experiments (Table 1). Theconsequences of nonlinear stratification, e.g., under a cappinginversion, are not discussed here.[61] A short plateau or no plateau increases the chancesfor trapping compared to long plateaus, because a plain-plateau flow removes a substantial fraction of the airpollutants from the upslope flow circulation into a higherEL. In addition, for a longer plateau it takes the plain-plateau circulation longer to return the air pollutants to theD11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS14 of 17D11114slope region, thereby decreasing the chance of reentrainingthem.[62] Approximately symmetric geometry, like in theperfect mirror symmetry of the tank, suppresses the possi-bility of cross flows over the ridge or to the other side of thevalley; air pollution can only escape from the surface bytransport into ELs that are not reentrained during one diurnalcycle.[63] A low ridge leads to lower EL. The smaller amountain the more likely it will recirculate rather than ventair pollutants.[64] Vergeiner [1982] hypothesized that sensible surfaceheat flux inhomogeneities, e.g., a substantial drop of heatflux along the slope surface, can lead to a flow split at theinhomogeneity and therefore a low EL. We confirmed thishypothesis in tank experiment HFD-Dye (Figure 13a). Ourtank design with individually controllable heaters under-neath the slope could be used for future research to establisha quantitative relationship between heat flux decrements andmass balance in the split flow (Figure 13b).[65] Vergeiner [1982] also hypothesized that an abruptslope angle drop, e.g., over a ledge, can lead to a flow splitsimilar to the case of a heat flux decrement (Figure 13c).This hypothesis is plausible but hard to test with our tank.[66] Finally, research should be carried out in the future toinvestigate if abrupt surface roughness changes also lead toa flow split.5. Conclusions[67] We showed observations from a bottom-heated salt-stratified water tank with a 19C176 slope and adjacent plain andplateau. Early in the experiments, these agree qualitativelywith field observations at an approximately homogeneous19C176 slope in Minnekhada Park, British Columbia, Canada.Later, three-dimensional flow characteristics in the tank andsea breeze and valley flows in the atmosphere may limitsimilarity.[68] Over the slope, advection of fluid with lower specificvolume leads to a shallow thermal boundary layer (TBL),causing in turn a clockwise rotating eddy over the plain nearthe slope. The full tank models the flow in a valley with avalley bottom to ridge height ratio of 6:1. For this aspectratio, a counter clockwise rotating eddy near the valleycenter creates subsidence over the valley center. When theaspect ratio is reduced to 3:1, the counter clockwise rotatingeddy is suppressed and strongly rising motion occursinstead.[69] Slope and plateau cause horizontal temperatureinhomogeneities, which lead to elevated layers (EL) abovethe TBL. The ELs have stability and dye/aerosol concen-trations intermediate between TBL and background. An ELis entrained into the TBL if sufficient heating continues.Before the entrainment, the backscatter of EL and TBL canbe indistinguishable, so that EL and TBL form one deepbackscatter boundary layer. The entrainment occurs rapidlyas a flow regime change. In the experiments, the upslopeflow layer agrees with the TBL and the return flow layerwith the EL.[70] We suggested defining the ABL as comprising alllayers that are in contact with surface forcings during onediurnal cycle. In particular, this definition includes pollutedELs that are entrained into the growing TBL after more thanthe commonly used 1-hour timescale. In this case, pollutantsare effectively trapped.[71] The tank experiments hint at the conditions that aretypically conducive to air pollutant trapping: weaker larger-scale flows, stronger sensible surface heat flux, weakerstratification, a short plateau or no plateau, approximatelysymmetric geometry, a low ridge, and inhomogeneities insensible surface heat flux. We also speculate that inhomo-geneities in slope angle and surface roughness can enhancetrapping. The complexity of real-world topography willtypically lead to layering, venting, and trapping in a nearcontinuum of multiple scales.Appendix A[72] In water tanks with a flat horizontal bottom, a linearstratification can be achieved with the two-bucket method[Fortuin, 1960]. We describe here the modifications wemade to that method to account for the slope in the tank.Figure 13. (a) Video frame and (b) schemata of mass fluxbreakup over the slope caused by a drop of surface heatflux in tank experiment HFD-Dye and (c) schemata ofmass-flux breakup caused by an abrupt slope angle changeabove a ledge. In Figure 13a a substantial surface heat fluxdecrement occurred in the upper third of the slope. Part of aplume of bright dye, originally released at the slope base,has been carried upslope. At about two-third of the totalslope length the flow has separated into an EL intruding intothe plain region and a residual upslope flow layer. InFigure 13b, lower and upper surface heat fluxes are denotedby QH,1and QH,2, respectively. Mass fluxes of upslope flowbelow the decrement and residual upslope flow above thedecrement are denoted by M1and M2. C is similarly toFigure 13b; mass fluxes of upslope flow below the ledgeand residual upslope flow above the ledge are denoted byM1and M2.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS15 of 17D11114[73] The experimental tank is filled at the tank bottomthrough an inlet, which is fed from a freshwater tank(Figure A1a). The freshwater tank is connected at the bottomwith a saltwater tank of the same dimensions so that bothtanks always have the same water level during the drainingprocess. The mixer in the freshwater tank mixes the water inthe freshwater tank with the saltier water supplied throughthe connection. During the filling process, the salt concen-tration in the experimental tank increases pushing previouslayers of fresher, and therefore less dense, water up.Therefore the experimental tank is filled from top to bottom.The first drainage step through the upper faucet terminateswhen the water level in the saltwater tank reaches the top ofthe solid wedge. A small amount of salt is dissolved in thesaltwater tank before continuing the filling process throughthe bottom faucet. The wedge in the saltwater tank modifiesthe volume of saltwater supplied to the freshwater tank andcompensates for the changing volume in the bottom 14.9 cmof the experimental tank. We determined the dimensions ofthe wedge and the amount of salt needed initially andbetween the first and second drainage step in a spreadsheetapplication. Figure A1b shows the specific-volume profilesat three different locations before the start of one of theexperiments described below. The volume compensation atthe height of the plateau (14.9 cm) is visible only as a smallwiggle in all three profiles, but the agreement with theexpected profile is good. Because of technical problemswith our filling tanks, we cannot avoid the weaker stratifi-cation in the bottom 3 cm. However, since the boundarylayer grows much deeper than 3 cm early in the experimentsthe weaker stratification does not seem to affect the experi-ments substantially.List of Frequently Used AcronymsABL Atmospheric Boundary LayerBBL Backscatter Boundary LayerCCW Counter ClockwiseCW ClockwiseEL Elevated LayerHFD-Dye Dye experiment with a Heat Flux Decrementabout two-thirds up the slopeLES Large-Eddy SimulationPST Pacific Standard Time (UTC-0800 h)SP-Part Particle experiment using a Shortened PlainTBL Thermal Boundary LayerTR-Part Particle experiment using a Triangular Ridge(end-wall at top of slope)WT-Dye Dye experiment using the Whole TankWT-Part Particle experiment using the Whole Tank[74] Acknowledgments. We gratefully acknowledge the support inthe Department of Civil Engineering at UBC: Greg Lawrence for providinglaboratory space for the water tank and sharing computer resources andinstrumentation; Bill Leung, Scott Jackson, and Harald Schrempp for theircontributions to designing and building the tank. We thank Ian Chan for hishelp on tank redesign, MatPIV, and several experiments. Funding supportwas provided by grants from NSERC and CFCAS to Douw Steyn andSusan Allen.ReferencesAtkinson, B. W. (1981), Meso-Scale Atmospheric Circulations, 495 pp.,Elsevier, New York.Atkinson, B. W., and A. N. Shahub (1994), Orographic and stability effectson day-time, valley-side slope flows, Boundary Layer Meteorol., 68,275–300.Banta, R. M. (1984), Daytime boundary layer evolution over mountainousterrain. Part 1: Observations of the dry circulations, Mon. Weather Rev.,112, 340–356.Blumen, W., (Ed.) (1990), Atmospheric Processes Over Complex Terrain,323 pp., Meteorol. Monogr. 23, Am. Meteorol. Soc., Boston, Mass.Brehm, M. (1986), Experimentelle und numerische Untersuchungen derHangwindschicht und ihre Rolle bei der Erwa¨rmung von Ta¨lern, Ph.D.thesis, 150 pp., Ludwig-Maximilian-Univ., Mu¨nchen, Germany.Buckingham, E. (1914), On physically similar systems; illustrations of theuse of dimensional equations, Phys. Rev. Lett., Second Series, IV, 345–376.Carson, D. J. (1973), The development of a dry inversion-capped convec-tively unstable boundary layer, Q. J. R. Meteorol. Soc., 99, 450–467.Chen, R.-R., N. S. Berman, D. L. Boyer, and H. J. S. Fernando (1996),Physical model of diurnal heating in the vicinity of a two-dimensionalridge, J. Atmos. Sci., 53, 62–85.Chow, F. K., A. P. Weigel, R. L. Street, M. W. Rotach, and M. Xue (2006),High-resolution large-eddy simulations of flow in a steep alpine valley.PartI:Methodology,verificationand sensitivitystudies,J. Appl.Meteorol.Climatol., 45, 63–86.Colette, A., F. K. Chow, and R. L. Street (2003), A numerical study ofinversion-layer breakup and the effects of topographic shading in idea-lized valleys, J. Appl. Meteorol., 42, 1255–1272.Deardorff, J. W., and G. E. Willis (1987), Turbulence within a barocliniclaboratory mixed layer above a sloping surface, J. Atmos. Sci., 44, 772–778.Figure A1. (a) Schematic side view of the filling tanksetup and (b) typical initial specific volume profiles. InFigure A1a the mixer is inside the freshwater tank reachingclose to the bottom. The solid wedge fills the entire width ofthe saltwater tank. Both tanks are connected via a hoseon the bottom. The ‘‘experimental tank inlet’’ releases thewater from the freshwater tank at the bottom ofthe experimental tank. The top faucet stops draining whenthe water level in the saltwater tank reaches the top of thewedge. In Figure A1b the three vertical profiles weremeasured before the start of experiment SP-Part in onesynchronous descent of three conductivity and temperatureprobes over three different locations (plain, slope near base,and slope near ridge). We made minor adjustments to matchthe profiles near the tank bottom. The straight thin diagonalline shows the expected profile.D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS16 of 17D11114de Wekker, S. F. J. (2002), Structure and morphology of the convectiveboundary layer in mountainous terrain, Ph.D. thesis, 191 pp., Dep. ofEarth and Ocean Sci., Univ. of Brit. Columbia, Vancouver, B.C., Canada.de Wekker, S. F. J., D. G. Steyn, J. D. Fast, M. W. Rotach, and S. Zhong(2005), The performanceofRAMS in representingthe convective boundarylayer structure in a very steep valley, Environ. Fluid Mech., 5,35–62.Eck, S., M. S. Kharicha, A. Ishmurzin, and A. Ludwig (2005), Measure-ment and simulation of temperature and velocity fields during the coolingof water in a die casting model, Mater. Sci. Eng. A, 413, 79–84.Egger, J. (1981), On the linear two-dimensional theory of thermally inducedslope winds, Beitr. Phys. Freien Atmos., 54, 465–481.Fortuin, J. (1960), Theory and application of two supplementary methods ofconstructing density gradient columns, J. Polymer Sci., XLIV, 505–515.Gregory, P. (2005), Bayesian Logical Data Analysis for the PhysicalSciences, 488 pp., Cambridge Univ. Press, New York.Grøna˚s, S., and A. D. Sandvik (1999), Numerical simulations of localwinds over steep orography in the storm over North Norway on October12, 1996, J. Geophys. Res., 104, 9107–9120.Haiden, T. (1990), Analytische Untersuchungen zur konvektivenGrenzschicht im Gebirge, Ph.D. thesis, 140 pp., Univ. Wien, Austria.Haiden, T. (2003), On the pressure field in the slope wind layer, J. Atmos.Sci., 60, 1632–1635.Hunt, J. C. R., H. J. S. Fernando, and M. Princevac (2003), Unsteadythermally driven flows on gentle slopes, J. Atmos. Sci., 60, 2169–2182.Ingel’, L. K. (2000), Nonlinear theory of slope flows, Izv. Russ. Acad. Sci.Atmos. Oceanic Phys., 36, 384–389.Kondo, H. (1984), The difference of the slope wind between day and night,J. Meteorol. Soc. Jpn., 62, 224–232.Kuwagata, T., and J. Kondo (1989), Observations and modeling of ther-mally induced upslope flows, Boundary Layer Meteorol., 49, 265–293.Mitsumoto,S.(1989),A laboratoryexperimentontheslopewind,J. Meteorol.Soc. Jpn., 67,565–574.Moroni, M., and A. Cenedese (2006), Penetrative convection in stratifiedfluids: Velocity and temperature measurements, Nonlinear ProcessesGeophys., 13, 353–363.Petkovsˇek, Z. (1982), Ein einfaches Modell des Tages-Hangwindes,Z. Meteorol., 32, 31–41.Prandtl, L. (1952), Essentials of Fluid Dynamics, 452 pp., Blackie Acad.and Prof., New York.Rampanelli, G., and D. Zardi (2004), A method to determine the cappinginversion of the convective boundary layer, J. 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Gryning, S. Joffre, A. Rasmussen, and P. Tercier(2000), Review and intercomparison of operational methods for the deter-mination of the mixing height, Atmos. Environ., 34, 1001–1027.Strawbridge, K. B., and B. J. Snyder (2004), Planetary boundary layerheightdeterminationduringPacific2001usingtheadvantageofascanninglidar instrument, Atmos. Environ., 38, 5861–5871.Stull,R.B.(1988),AnIntroductiontoBoundaryLayerMeteorology,670pp.,Springer, New York.Turner, J. S (1973) Buoyancy Effects in Fluids, 368 pp., Cambridge Univ.Press, New York.Vergeiner, I. (1982), Eine energetische Theorie der Hangwinde, paper pre-sented at 17 Internationale Tagung Alpine Meteorologie, Berchtesgarden1982, Ann. Meteorol. NF, 19, 189–191.Vergeiner, I., and E. Dreiseitl (1987), Valley winds and slope winds–Observations and elementary thoughts, Meteorol. Atmos. Phys., 36,264–286.Vogel, B., G. Adrian, and F. Fiedler (1987), MESOKLIP-Analysen dermeteorologischen Beobachtungen von mesoskaligen Pha¨nomenen imOberrheingraben, 369 pp., Inst. fu¨r Meteorologie und Klimaforschungder Univ. Karlsruhe, Karlsruhe, Germany.Weigel, A. P., F. K. Chow, M. W. Rotach, R. L. Street, and M. Xue (2006a),High-resolution large-eddy simulations of flow in a steep alpine valley.Part II: Flow structure and heat budgets, J. Appl. Meteorol. Climatol., 45,87–107.Weigel, A. P., F. K. Chow, and M. W. Rotach (2006b), On the nature ofturbulent kinetic energy in a steep and narrow Alpine valley, BoundaryLayer Meteorol., 123, 177–199.Whiteman, C. D. (1990), Observations of thermally developed wind sys-tems in mountainous terrain, in Atmospheric Processes Over ComplexTerrain, Boston Meteorol. Monogr., vol. 23, edited by W. Blumen, pp. 5–42, Am. Meteorol. Soc., Boston.Whiteman, C. D. (2000), Mountain Meteorology: Fundamentals andApplications, 376 pp., Oxford Univ. Press, New York.Wooldridge, G. L., and E. L. McIntyre (1986), The dynamics of the pla-netary boundary layer over a heated mountain slope, Geofizika, 3, 3–21.Ye, Z. J., M. Segal, and R. A. Pielke (1987), Effects of atmospheric thermalstability and slope steepness on the development of daytime thermallyinduced upslope flow, J. Atmos. Sci., 44, 3341–3354.C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0C0S. Allen, C. Reuten, and D. Steyn, Department of Earth and OceanSciences, University of British Columbia, 6339 Stores Road, Vancouver,BC, Canada V6T 1Z4. (creuten@eos.ubc.ca)D11114 REUTEN ET AL.: WATER TANK STUDIES OF UPSLOPE FLOWS17 of 17D11114

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