{"Affiliation":[{"label":"Affiliation","value":"Science, Faculty of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."},{"label":"Affiliation","value":"Earth, Ocean and Atmospheric Sciences, Department of","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","classmap":"vivo:EducationalProcess","property":"vivo:departmentOrSchool"},"iri":"http:\/\/vivoweb.org\/ontology\/core#departmentOrSchool","explain":"VIVO-ISF Ontology V1.6 Property; The department or school name within institution; Not intended to be an institution name."}],"AggregatedSourceRepository":[{"label":"AggregatedSourceRepository","value":"DSpace","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","classmap":"ore:Aggregation","property":"edm:dataProvider"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/dataProvider","explain":"A Europeana Data Model Property; The name or identifier of the organization who contributes data indirectly to an aggregation service (e.g. Europeana)"}],"Campus":[{"label":"Campus","value":"UBCV","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","classmap":"oc:ThesisDescription","property":"oc:degreeCampus"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeCampus","explain":"UBC Open Collections Metadata Components; Local Field; Identifies the name of the campus from which the graduate completed their degree."}],"Creator":[{"label":"Creator","value":"Reuten, Christian","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/creator","classmap":"dpla:SourceResource","property":"dcterms:creator"},"iri":"http:\/\/purl.org\/dc\/terms\/creator","explain":"A Dublin Core Terms Property; An entity primarily responsible for making the resource.; Examples of a Contributor include a person, an organization, or a service."}],"DateAvailable":[{"label":"DateAvailable","value":"2010-01-16T20:37:53Z","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"edm:WebResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"DateIssued":[{"label":"DateIssued","value":"2006","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/issued","classmap":"oc:SourceResource","property":"dcterms:issued"},"iri":"http:\/\/purl.org\/dc\/terms\/issued","explain":"A Dublin Core Terms Property; Date of formal issuance (e.g., publication) of the resource."}],"Degree":[{"label":"Degree","value":"Doctor of Philosophy - PhD","attrs":{"lang":"en","ns":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","classmap":"vivo:ThesisDegree","property":"vivo:relatedDegree"},"iri":"http:\/\/vivoweb.org\/ontology\/core#relatedDegree","explain":"VIVO-ISF Ontology V1.6 Property; The thesis degree; Extended Property specified by UBC, as per https:\/\/wiki.duraspace.org\/display\/VIVO\/Ontology+Editor%27s+Guide"}],"DegreeGrantor":[{"label":"DegreeGrantor","value":"University of British Columbia","attrs":{"lang":"en","ns":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","classmap":"oc:ThesisDescription","property":"oc:degreeGrantor"},"iri":"https:\/\/open.library.ubc.ca\/terms#degreeGrantor","explain":"UBC Open Collections Metadata Components; Local Field; Indicates the institution where thesis was granted."}],"Description":[{"label":"Description","value":"Flows up heated slopes are an elementary component of thermally-driven flows in complex terrain and play a fundamental role in the transport of air pollutants. Our understanding of upslope flows is still incomplete because of the difficulty of carrying out field measurements in complex terrain, the sensitivity of upslope flows to external disturbances, and the difficulty of resolving topographic details in numerical models. In this dissertation I study upslope flows by combining field observations and water-tank experiments. Field observations at a 19\u00b0 slope showed strong upslope flows of 4 m s\u207b\u00b9 in the lower half of the backscatter boundary layer (BBL), determined from lidar scans of aerosol backscatter. A return flow in the upper half of the BBL nearly compensated the upslope volume transport which suggests a trapping of air pollutants in a closed slope flow circulation. I built a bottom-heated water tank with a 19\u00b0 slope between a plain and a plateau and, using time-dependent scaling, I develop mathematical idealisations of the water tank and the field site. Field and tank observations of non-dimensional thermal boundary layer (TBL) depth agree within 20%. An analysis of the data with probability theory demonstrates that non-dimensional upslope flow velocities in atmosphere and water tank have significantly different functional dependencies on the governing parameters. I demonstrate that the tank flows are fluid-dynamically smooth and explain the similarity violation by a fluid-dynamic feedback: in the water tank, roughness length strongly decreases with increasing upslope flow velocity; by contrast the atmospheric flows were fluid-dynamically rough and roughness length was approximately constant. Flows in the water tank show a persistent eddy with near-surface flows in downslope direction over the plain adjacent to the slope. I argue that the eddy is a result of a TBL depression in the lower part of the slope caused by upslope-flow advection of dense fluid. Water tank experiments suggest that the eddy can cause strongly rising motion over a valley centre for a ratio of about three between valley width and ridge height. In experiments with a plateau length exceeding roughly half the ridge height, independent plain-plateau and upslope flow circulations developed. The upslope flow layer in the water tank agreed with the TBL; the return flow returned dye originally injected over the plain in an elevated layer above the TBL and underneath the plain-plateau flow. When the dye concentrations in TBL and elevated layer became sufficiently similar both layers appeared as one deep BBL. As heating continued two regime changes occurred. First, the TBL merged with the elevated layer, and the upslope flow formed one large circulation with the plain-plateau flow. In a subsequent regime change, the TBL merged with a new elevated layer formed by the large circulation. Upslope flows in the atmosphere are likely to exhibit regime changes at multiple scales. Conditions conducive to re-entrainment of air pollutants are: symmetric topography; weak stratification and larger-scale flows; strong sensible surface heat flux; low ridge height; short plateau; sensible surface heat flux decrements over the slope; and abrupt slope-angle decrements.","attrs":{"lang":"en","ns":"http:\/\/purl.org\/dc\/terms\/description","classmap":"dpla:SourceResource","property":"dcterms:description"},"iri":"http:\/\/purl.org\/dc\/terms\/description","explain":"A Dublin Core Terms Property; An account of the resource.; Description may include but is not limited to: an abstract, a table of contents, a graphical representation, or a free-text account of the resource."}],"DigitalResourceOriginalRecord":[{"label":"DigitalResourceOriginalRecord","value":"https:\/\/circle.library.ubc.ca\/rest\/handle\/2429\/18458?expand=metadata","attrs":{"lang":"en","ns":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","classmap":"ore:Aggregation","property":"edm:aggregatedCHO"},"iri":"http:\/\/www.europeana.eu\/schemas\/edm\/aggregatedCHO","explain":"A Europeana Data Model Property; The identifier of the source object, e.g. the Mona Lisa itself. This could be a full linked open date URI or an internal identifier"}],"FullText":[{"label":"FullText","value":"Scaling and Kinematics of Daytime Slope Flow Systems by Christian Reuten Diplomphysiker, University of Goettingen, 1993 A THESIS S U B M I T T E D I N P A R T I A L F U L F I L L M E N T OF T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R OF P H I L O S O P H Y in T H E F A C U L T Y OF G R A D U A T E S T U D I E S (Atmospheric Science) T H E U N I V E R S I T Y OF B R I T I S H C O L U M B I A March 2006 \u00a9 Christian Reuten, 2006 Abstract Flows up heated slopes are an elementary component of thermally-driven flows in com-plex terrain and play a fundamental role in the transport of air pollutants. Our understanding of upslope flows is still incomplete because of the difficulty of carrying out field measure-ments in complex terrain, the sensitivity of upslope flows to external disturbances, and the difficulty of resolving topographic details in numerical models. In this dissertation I study upslope flows by combining field observations and water-tank experiments. Field observations at a 19\u00b0 slope showed strong upslope flows of 4 m s\"1 in the lower half of the backscatter boundary layer ( B B L ) , determined from lidar scans of aerosol backscatter. A return flow in the upper half of the B B L nearly compensated the upslope vol-ume transport which suggests a trapping of air pollutants in a closed slope flow circulation. I built a bottom-heated water tank with a 19\u00b0 slope between a plain and a plateau and, us-ing time-dependent scaling, I develop mathematical idealisations of the water tank and the field site. Field and tank observations of non-dimensional thermal boundary layer (TBL) depth agree within 20%. A n analysis of the data with probability theory demonstrates that non-dimensional upslope flow velocities in atmosphere and water tank have significantly dif-ferent functional dependencies on the governing parameters. I demonstrate that the tank flows are fluid-dynamically smooth and explain the similarity violation by a fluid-dynamic feed-back: in the water tank, roughness length strongly decreases with increasing upslope flow velocity; by contrast the atmospheric flows were fluid-dynamically rough and roughness length was approximately constant. Flows in the water tank show a persistent eddy with near-surface flows in downslope di-rection over the plain adjacent to the slope. I argue that the eddy is a result of a T B L depres-sion in the lower part of the slope caused by upslope-flow advection of dense fluid. Water-tank experiments suggest that the eddy can cause strongly rising motion over a valley centre for a ratio of about three between valley width and ridge height. In experiments with a plateau length exceeding roughly half the ridge height, independent plain-plateau and upslope flow circulations developed. The upslope flow layer in the water i i tank agreed with the T B L ; the return flow returned dye originally injected over the plain in an elevated layer above the T B L and underneath the plain-plateau flow. When the dye concentra-tions in T B L and elevated layer became sufficiently similar both layers appeared as one deep B B L . As heating continued two regime changes occurred. First, the T B L merged with the ele-vated layer, and the upslope flow formed one large circulation with the plain-plateau flow. In a subsequent regime change, the T B L merged with a new elevated layer formed by the large circulation. Upslope flows in the atmosphere are likely to exhibit regime changes at multiple scales. Conditions conducive to re-entrainment of air pollutants are: symmetric topography; weak stratification and larger-scale flows; strong sensible surface heat flux; low ridge height; short plateau; sensible surface heat flux decrements over the slope; and abrupt slope-angle decrements. 111 Table of Contents Abstract ii Table of Contents iv List of Figures vii List of Tables xi List of Symbols xii List of Constants xvii List of Abbreviations xviii Preface ; xix Acknowledgements xx 1 Introduction 1 1.1 Research Motivation, Goal, and Questions 1 1.2 The Basic Mechanism of Upslope Flows 3 1.3 Review of Previous Investigations 4 1.3.1 Return F low Above the C B L or N o Return F low 5 1.3.2 Return F low Below the C B L 7 1.4 Research Approach and Outline of Thesis 9 2 Field Observations during Pacific 2001 12 2.1 Experimental Layout and Methods 12 2.1.1 Location, Topography, and Period of Observations 12 2.1.2 Synoptic Weather 14 2.1.3 Instrumentation 15 2.2 Observations of Closed Slope Flow Systems versus Mountain Venting 16 2.2.1 Convective Boundary Layer Height 17 2.2.2 Slope Flow System versus Convective Boundary Layer 22 2.2.3 Volume Transport 24 2.2.4 Impact of Larger-Scale Wind Systems 25 2.3 Discussion and Conclusions 29 2.3.1 Hypothesis 1: Impact by Larger-Scale F low Systems 29 iv 2.3.2 Hypothesis 2: Internal Dynamics of Slope F low System 33 2.3.3 Hypothesis 3: Thermal Boundary Layer and Backscatter Boundary Layer are Different 33 2.3.4 Conclusions 33 3 Scaling and Idealisations 35 3.1 Introduction 35 3.2 Atmospheric and Water-Tank Idealisations 37 3.3 Buckingham P i Analysis 44 3.3.1 P i Groups in the Atmospheric Idealisation 44 3.3.2 P i Groups in the Water-Tank Idealisation 46 3.3.3 Similarity between Atmospheric and Water-Tank Idealisations 48 3.4 Hypotheses for the Atmosphere 50 3.4.1 C B L Depth and Potential Temperature 51 3.4.2 Upslope F low Velocity 60 3.5 Hypotheses for the Water Tank 71 3.5.1 C B L Depth 71 3.5.2 C B L Specific Volume 72 3.5.3 Upslope F low Velocity 73 3.6 The Relation Between Atmospheric and Water-Tank Reference Time 74 3.7 Summary and Conclusions 79 4 Physical Scale Modeling 81 4.1 Introduction 81 4.2 Experimental Layout and Methods 82 4.3 Testing the Scaling Hypotheses 84 4.3.1 C B L Depth 85 4.3.2 C B L Specific Volume 88 4.3.3 Upslope F low Velocity 92 4.3.4 Discussion of the Similarity Violation of Upslope Flow Velocity 100 4.3.5 Conclusions on the Similarity between Atmosphere and Water Tank 111 4.4 F low Characteristics and Regimes 112 4.4.1 Flow Characteristics of the Test Case 112 4.4.2 Layering and Regime Changes in the Test Case 122 4.4.3 Summary of the Test Case 126 4.4.4 Impact of the Left End Wal l : Hypothesis on C B L Rising in a Valley Centre. 128 4.4.5 C B L Bulge and Depression near the Foot of the Slope 130 4.4.6 Inhomogeneous Heating 132 4.5 Discussion and Conclusions 134 4.5.1 Conclusions on Flow Characteristics and Regimes 134 4.5.2 Relation between Upslope Flow System and Atmospheric Boundary Layer.. 137 4.5.3 Trapping versus Venting of A i r Pollution 142 5 Summary of Conclusions and Recommendations for Future Research 150 v 5.1 Summary of Conclusions 150 5.2 Recommendations for Future Research 152 References 155 Appendix A : Rigorous Derivation of the Prandtl Model 162 Appendix B : Scaling 172 B . 1 Derivation and Discussion of Upslope Flow Velocity Hypotheses 172 B.2 Empirical Analysis 189 B.3 Hypothesis Comparison and Parameter Estimation Using Probability Theory 199 B.4 Two Atmospheric Test Cases and Their Corresponding Water-Tank Experiments 210 B.5 A Strategy for Scaling 214 B . 6 Scaling of other Non-dimensional Quantities 216 Appendix C : Physical Scale Modelling 224 C. 1 Technical Design of the Water Tank 224 C.2 Heating 225 C.3 Fi l l ing the Tank with Salt-Stratified Water 227 C.4 Measurement of Specific Volume 229 C.5 Tracer Dispersion 235 C.6 Measurement of Velocity 236 C.7 Determining the Heat Flux into the Tank 240 C.8 Conversion of Probe Voltages to Specific Volume 244 C.9 Production of Neutrally-Buoyant Particles 257 C I O Entrainment Coefficient over the Heated Plateau 259 C . l 1 Empirical Analysis of Maximum Upslope Flow Velocity 261 vi List of Figures Figure 1.1: Map of the Lower Fraser Valley ( L F V ) , Canada 1 Figure 1.2: High-level diagram of the mechanism of upslope flows (adapted from Atkinson, 1981) 3 Figure 1.3: Scenarios of upslope flow systems 4 Figure 1.4: Schematics of research approach 10 Figure 1.5: Photograph of the water tank 11 Figure 2.1: Contour plot of Minnekhada Park (see Figure 1.1) 13 Figure 2.2: Synoptic charts for July 25 (a and b) and July 26 (c and d), 2001, at 1700 PDT. .14 Figure 2.3: B B L depth above M S L at different times on July 25, 2001 18 Figure 2.4: Tethersonde profiles superimposed on a R A S C A L R H I scan 19 Figure 2.5: Potential temperature profile determined from tethersonde ascent and descent....20 Figure 2.6: Time development of the entrainment zone of the T B L and the B B L on July 25 (a) and July 26 (b), 2001 21 Figure 2.7: Time-height section of the along-slope component of the horizontal wind vectors above the Doppler sodar for July 25, 2001 22 Figure 2.8: A s Figure 2.7 but for July 26, 2001, and without error bars 23 Figure 2.9: Comparison of upslope flow and return flow depths with C B L depth 24 Figure 2.10: Along-slope Volume transport for the morning of July 25, 2001 25 Figure 2.11: Hourly measurements of wind speed, wind direction, relative humidity, and temperature at Vancouver International Airport ( Y V R ) and Abbotsford Airport ( Y X X ) for July 25-26, 2001 27 Figure 2.12: Time-height sections of the horizontal wind vector above the Doppler sodar for the morning of July 25, 2001 30 vn Figure 2.13: A s Figure 2.12 but for July 26, 2001 30 Figure 2.14: R A S C A L R H I scans for July 25, 1047 P D T (top) and July 26, 1053 P D T (bottom) 32 Figure 3.1: Concept map of the scaling 36 Figure 3.2: Topography at the field site and atmospheric and water-tank idealisations 38 Figure 3.3: Diagram of quantities in an encroachment model of the C B L in the atmospheric idealisation 52 Figure 3.4: Comparison of field observations and A l predictions of C B L mean potential temperature increment 56 Figure 3.5: Comparison of field observations and A l predictions of C B L depth 59 Figure 3.6: Joint probability distribution of unknown constant factor and standard deviation of background noise for different upslope flow velocity hypotheses 65 Figure 3.7: Joint probability distribution p^m^m^Dj)' of the exponents in upslope flow velocity hypothesis for the atmosphere 70 Figure 3.8: Diagram of quantities in an encroachment model of the C B L in the W T I 72 Figure 3.9: Water-tank buoyancy frequency Nv required to achieve similarity of the tank experiment with the atmosphere at atmospheric reference time tatjm 75 Figure 3.10: Relationship between atmospheric background buoyancy frequency Na and time of similarity taitm for a given water-tank experiment 77 Figure 4.1: Schematic of the water tank 83 Figure 4.2: C B L growth over the plain ...86 Figure 4.3: Non-dimensional C B L depth comparison of field and tank observations 88 Figure 4.4: Comparison of field and tank observations of C B L mean specific volume increment a 89 .v,w Figure 4.5: Vertical profiles of the (plain-parallel) x-component of velocities in the water tank : 93 v m Figure 4.6: Joint probability distribution of unknown constant factor and standard deviation of background noise for different upslope flow velocity hypotheses in the water tank 97 Figure 4.7: Joint probability distribution m2\\D,l) of the exponents in upslope flow velocity hypothesis for the water tank and comparison with atmosphere, plotted using two different scales 98 Figure 4.8: Comparison of fitted upslope flow velocity hypotheses with tank observations in N D form 99 Figure 4.9: Satellite view of Minnekhada Park field site 103 Figure 4.10: Parameter representations of exponents of roughness length in the gravity-current hypothesis 107 Figure 4.11 (next two pages): Modell ing Pacific 2001 in the water tank 113 Figure 4.12 (next page): Vertical specific volume profiles in test case W T 2 123 Figure 4.13 (next page): Sketch of flow characteristics in test case W T 2 126 Figure 4.14: C B L rising over valley centre 129 Figure 4.15: Mechanics of C B L depression and CW-rotating eddy 132 Figure 4.16: F low characteristics for inhomogeneous heat flux 133 Figure 4.17: Comparison of water tank dye experiments with atmospheric R A S C A L R H I scans 135 Figure 4.18: Video frame of mass flux break-up over the slope 147 Figure 4.19: Schemata of mass flux break-up caused by a surface heat flux decrement 148 Figure 4.20: Schemata of mass-flux break-up caused by an abrupt slope-angle decrement.. 149 Figure Appendix I: Upslope flow without convective turbulence 176 Figure Appendix II: Schemata for derivation of horizontal pressure gradient 178 Figure Appendix III: Vertical profile of normalized time average o f normalised upslope flow velocity and fitted Prandtl profile for July 25, 2001, 0850-1230 P D T 182 ix Figure Appendix IV: Multiple regression of N D maximum upslope flow velocity UmiK* as function of n 2 o and n 3 o 193 Figure Appendix V : Multiple regression of N D maximum upslope flow velocity U^* as function of YI2a and n 3 u ' = n 3 J n i Q 196 Figure Appendix V I : Comparison of fitted upslope flow velocity hypotheses with field observations in N D form 198 Figure Appendix VII : Comparison of fitted upslope flow velocity hypotheses with field observations in dimensional form 199 Figure Appendix VIII: Schematics of closed-channel flow 220 Figure Appendix I X : Schematic side view of tank. (Not to scale.) 225 Figure Appendix X : Plan view of strip heater arrangement. (Approximately to scale.) 226 Figure Appendix X I : Side view of strip heater installation underneath the tank bottom 227 Figure Appendix XI I : Schematic of filling tanks 228 Figure Appendix XIII : Background stratification of test case 230 Figure Appendix X I V : Hysteresis caused by selective withdrawal by C T probes 231 Figure Appendix X V : Double-diffusive convection 232 Figure Appendix X V I : Circulations in water tank 233 Figure Appendix X V I I : Temperature and salinity in double-diffusive convection 234 Figure Appendix X V I I I : Salt fingers caused by double-diffusive convection 235 Figure Appendix X I X : Heating of a well-mixed freshwater tank 242 Figure Appendix X X : Time series of the median of the three probes in a heated and wel l -mixed freshwater tank 243 Figure Appendix X X I : Tank observations of the C B L growth over flat terrain for two different stratifications 260 Figure Appendix X X I I : Multiple linear regression of N D water-tank maximum upslope flow velocities 262 List of Tables Table 3.1: Independent parameters in atmospheric idealisation (Al ) and water-tank idealisation (WTI) 44 Table 3.2: Summary of P i groups in atmospheric idealisation (Al ) and water-tank idealisation (WTI) ; 47 Table 3.3: Independent water-tank quantities before and after applying the scaling and similarity constraints 50 Table 4.1: Overview of water-tank experiments used for upslope flow velocities analyses.... 94 Table 4.2: Similarity between water-tank and atmospheric idealisation 116 Table Appendix I (next two pages): Two test cases extracted from a spreadsheet to facilitate Buckingham P i analysis 211 xi List of Symbols Special Notations: a b w CO 5 A Latin Symbols: A \\> K M c d d [m] d, W D Dw [m] D~w [m] E [Km] E f^ c^^ water vapor Fr, 8 \\jn s~2 J g.s Gr h [m] K [m] H Suffix denoting turbulent perturbations Subscript denoting atmospheric quantities Subscript denoting background quantities Subscript denoting water-tank quantities Superscript denoting the j t h hypothesis (when using probability theory) Prefix denoting finite differences Prefix denoting non-turbulent perturbations of background quantities; denoting step length in summation Entrainment coefficient, Qtop\/QH Horizontal cross-sectional inner area of the water tank Inner surface area of the water-tank bottom Characteristic buoyancy in Chen et al. (1996) Constant coefficient or correction factor Julian day Characteristic depth in gravity current Individual datum Statement on the data (when using probability theory) Water depth over the plain in the tank Mean water depth in the tank Kinematic thermal-energy \/ heat density J Water vapour created during phase change Internal Froude number Gravitational acceleration Reduced buoyancy scale Grashof number C B L depth C B L depth predicted for zero entrainment (,4 = 0 ) Hypothesis (when using probability theory for hypothesis testing) x i i H [m] Ridge height Hf [m] Total height of the fluid right above the gravity-current front \/ Statement on background information (when using probability theory) Ieff \\A\\ Effective (measured) current through heaters lg Briggs logarithm (to base 10), i.e. lg = log 1 0 In Natural logarithm (to base e), i.e. In = log,, L \\m\\ Horizontal length of the slope Lh [m] Length of the plain in the water tank LD \\m\\ Diagonal length of the slope L \\m\\ Latent heat associated with phase change Lt [m] Length of the plateau in the water tank m [?] Slope of linear fit curve (units dependent on particular data) m [kg] Mass M ^ m s - 1 ] Kinematic mass flux m Negative normalised insolation vector (unit vector pointing towards the sun) n [m] Slope-normal coordinate in rotated coordinate system n Slope surface normal vector (unit vector perpendicular to slope sur-face) N [ V 1 J Buoyancy frequency p \\jigm~x s~2] Pressure p(H\\l} Conditional probability that H is true, given that I is true Pw \\W~\\ (Electrical) power supplied to heaters underneath the tank bottom Pr Prandtl number q m 3 J Kinematic thermal energy \/ heat q [ j ] Dynamic thermal energy \/ heat Q * ^ m ^ ' j Kinematic net radiative surface heat flux \/ power density QF m 51\"1 J Kinematic latent heat flux \/ power density QG ^ f f l ^ ' j Kinematic molecular conductive flux \/ power density into the ground QH [K m ] Kinematic net sensible surface heat flux \/ power density Q,* [ \/ C m s - 1 ] Kinematic longwave radiative surface heat flux \/ power density finax m s ~ ] ] Maximum kinematic net sensible surface heat flux \/ power density Qtop \\Kms~]~\\ Kinematic heat flux added to C B L by entrainment at the top x i i i Q yJm 2 J Dynamic thermal-energy\/heat density QH \\w m~2 J Dynamic net sensible surface heat flux \/ power density Q \\jV m~2 J Dynamic net radiative surface heat flux \/ power density r Ratio of observed and predicted C B L depth, Hs\/Hp Ra Rayleigh number Re Reynolds number RiQ Overall Richardson number Ro Rossby number s [w] Slope-parallel coordinate in rotated coordinate system t [5] Time td [s] Time to maximum heating (diurnal heating time scale) t [s] Time of onset of sea breeze propagation at the coastline (relative to the beginning of positive heat flux) tt [s] Time to transition to sea breeze at a location inland (relative to onset time t at the coastline) (UTC [N] Time in hours U T C T [K] Temperature TQ [K] Surface (screen) temperature Ts [K] C B L temperature scale Tv [K] Virtual temperature U [ms'1^ x component of velocity U0 s'] J Predicted fictitious maximum upslope flow velocity at surface UVU2, U3 \\jn s~l ] x, y, z component of velocity, respectively UChen \\jn s~x J Max imum upslope flow velocity from Chen hypothesis Ue \\m s~x J Expected true maximum upslope flow velocity after application of no-slip condition at the surface <7exp [m s~l J Expected maximum upslope flow velocity Ufit \\_m s'] ] Fitted maximum upslope flow velocity Ufric \\jn s~] ] Maximum upslope flow velocity from friction hypothesis UCrm s~l J Predicted nose velocity in gravity-current flow UHunl \\jn s~l J Maximum upslope flow velocity from Hunt hypothesis UM [w s'1 ] Vertically-averaged (mean) upslope flow velocity i [ \/ m a x \\m s~] 1 Predicted maximum upslope flow velocity xiv U\u00bbbs \\_ms ' ] Observed upslope flow velocity Up \\_m s'] ] Propagation speed of sea breeze (sum of sea breeze and synoptic wind speed) Us \\jn s'{ J Slope-parallel component of velocity Us \\jn s~] J Characteristic velocity scale USchu s'1 J Maximum upslope flow velocity from Schumann hypothesis V s'] J y component of velocity V [m3, J Volume Veff [V] Effective (measured) voltage of A C power supply W \\jn s~l ] z component of velocity Wn j^ m J Slope-normal component of velocity Ww [m] Interior width of the water tank x,, x 2 , x 3 [m] x, y, z component of location, respectively x [m] x coordinate in Cartesian coordinate system; distance inland from the coastline X - {x 1 5 . . . ,x n } Generic place holder for a set of data x ( , i = \\,...,n y [m\\ y coordinate in Cartesian coordinate system and cross-slope coordi-nate in slope coordinate system z [w] z coordinate (height) in Cartesian coordinate system Greek Symbols: aQ w ^rrr1 kg~] J Specific volume at water surface aD w [w3 kg~l J Specific volume difference between top and bottom of water asw [m 3 Ag~'J C B L mean specific volume increment in water tank B J Coefficient of volumetric expansion ya [K m'] J Environmental lapse rate for potential temperature in atmosphere yw ^m2 kg'] ~^ Environmental lapse rate for specific volume in water tank 8^ Kronecker delta sjJk Epsilon tensor Ga [K] Potential temperature in the atmosphere 9sa [K] C B L mean potential temperature increment in the atmosphere 6V [K] Virtual potential temperature xv K [m2 s~] J Kinematic molecular thermal diffusivity y: ^ g f f l \" ' j \" ' j Dynamic viscosity v \\jn2 s~] ] Kinematic molecular viscosity n, i t h P i group p [&gm~ 3 ] Density Ti\/ i \" 2 ] Viscous stress tensor cp [\u00b0] Slope angle Q. [ V ] i t h component of angular velocity of the Earth's rotation xv i List of Constants This is a list of parameters that I assumed constant in the thesis to simplify calculations or to make a problem solvable. The values are collected from and cross-checked between Glick-man (2000), Gobrecht (1974), Kuchling (1979), Serway and Beichner (2000), Stull (1988), Stull (2000), Weast (1978-79). a0tW = 1\/998.23 m3 kg~x Specific volume of freshwater at 20\u00b0C Ba = 0.003674 K~x Coefficient of thermal expansion of air 20\u00b0C Bw = 2.6 x 10~4 K~x Coefficient o f thermal expansion o f freshwater 25\u00b0C Ca = 1006 Jkg-'K'1 Specific heat of dry air at sea level at 20\u00b0C Cw =4179.6 Jkg'xK'x Specific heat of water at 25\u00b0C Ds = \\.5x\\0'9m2 s~x Diffusivity of N a C l salt at molarities 0.01-0.1 Td = 9.8xl0~ 3 Km~ x Dry adiabatic lapse rate g = 9.8\/7?. s~2 Gravitational acceleration at sea level at mid-latitudes KA - 2.11 x 10~5 m2 s'x Kinematic molecular thermal diffusivity of dry air at sea KW = 1.45 x 10~7 m2 s'x Kinematic molecular thermal diffusivity of water at 25\u00b0C Lf = 0.334 x l 0 6 y A ^ - 1 Latent heat of freezing (energy released during freezing) Ls = - 2 . 8 3 x l 0 6 J kg'] Latent heat of sublimation (energy required for sublimation) Lv = -2.50 x 10 6 J kg'] Latent heat of vaporization (energy required for vaporization) va -1.52 x 10\" 5 w 2 s~\\ Kinematic molecular viscosity of dry air at sea level pressure at 20\u00b0C vw - 8 . 9 x l 0 \" 7 m 2 s~x Kinematic molecular viscosity of water at 25\u00b0C ( \u00ab \u00b1 1 0 % for + 5 \u00b0 C ) R = 287.053 J K'] kg'1 Gas constant for dry air pa = 1.204 kg m~3 Density of dry air at sea level pressure and 20\u00b0C pw = 997.O kg m'3 Density of freshwater at 25\u00b0C Wm'2 pa-Ca=\\2\\\\ r Heat capacity of dry air at 20\u00b0C Kms , Wm~2 pw . Cw = 4.167 x 10 r Heat capacity of freshwater at 25\u00b0C Kms~ xv i i List of Abbreviations 2 - D Two-dimensional 3 - D Three-dimensional A l Atmospheric idealisation A M S American Meteorological Society B B L Backscatter Boundary Layer C B L Convective Boundary Layer C C W Counter clockwise C F C A S Canadian Foundation for Climate and Atmospheric Sciences C W Clockwise G V R D Greater Vancouver Regional District L E S Large-Eddy Simulation L F V Lower Fraser Val ley L S T Local standard time lidar light detection and ranging M S L (Above) Mean Sea Level N D Non-dimensional N S E R C Natural Sciences and Engineering Research Council o f Canada PDF Probability density function P D T Pacific Daylight Time PIV Particle image velocimetry P M Particulate matter R A S C A L Rapid Acquisition SCanning Aerosol Lidar RHI Range height indicator sodar sound detection and ranging T B L Thermal boundary layer T K E Turbulent kinetic energy WTI Water-tank idealisation xvm Preface Parts of this dissertation were published in Reuten et al. (2005). Section 1.3 \"Review of Previous Investigations\" is an extension of the literature review written by my. Section 2.1 \"Experimental Layout and Methods\" is basically unchanged. Dr. Kev in Strawbridge contrib-uted the paragraph on the lidar. Paul Bovis wrote the synoptic weather analysis and obtained from Michel Jean at the Canadian Meteorological Center the original analysis charts, on which I based Figure 2.2. Furthermore, he provided the inset to Figure 1.1. Paul Jance helped me generate the topographic map in Figure 1.1 and Dr. Pascal Haegeli created the topographic map o f Figure 2.1. Sections 2.2 \"Observations of Closed Slope F low Systems versus Moun-tain Venting\" and section 2.3 \"Discussion and Conclusions\" were originally written by me and for this dissertation extended by additional analyses and a link to the remainder of the thesis. Dr. Kev in Strawbridge contributed the lidar scans in Figure 2.14 and Figure 2.4 and all backscatter boundary layer height data used in this dissertation. Paul Bovis pre-processed the tethersonde data, and provided final temperature, moisture, and wind data in Microsoft Excel format. I pre-processed the sodar data, carried out all further data analysis, and created the remaining figures. xix Acknowledgements First I would like to express my gratitude to my thesis supervisors Douw Steyn and Susan Al len for their financial and intellectual support. Beyond the dissertation research Douw Steyn has been an invaluable mentor in my professional growth and very supportive of my volunteer activities at U B C . Susan Al l en has spent endless hours with me pondering over technical challenges with the water tank and many of the interesting questions that surfaced during the research. I am grateful to Lome Whitehead for his co-supervision and financial support at the be-ginning of my dissertation. In particular I appreciate his understanding and encouragement when I decided to \"follow my heart\" and change the thesis topic. .1 am indebted to the mem-bers of my Ph.D. committee, Roland Stull and Han van Dop, for providing very important feedback on my progress and the thesis manuscript. I also greatly appreciated Noboru Yone-mitsu's help and inspiring discussions. I wish to thank Greg Lawrence for providing the laboratory space for the water tank and sharing computer resources and instrumentation. The water tank was built in the workshop in the Department of C i v i l Engineering at U B C : B i l l Leung built the mechanical parts and Scott Jackson the electrical and electronic components. Workshop supervisor Harald Schrempp generously allocated workshop time for the \"fish-tank project\", and his experience was of tremendous help particularly during the design stage. I thank Ian Chan for endless shared hours in the laboratory for re-designing and re-building the tank, re-writing parts of MatPIV, and running experiments, which often needed more than two hands. Funding support for this study was provided by grants from N S E R C and C F C A S to Douw Steyn and Susan Al l en and also by Environment Canada under the Pacific 2001 project. I would like to thank K e v i n Strawbridge and Paul Bovis (Environment Canada) for their col-laboration in Reuten et al. (2005). Permissions for the setup of field instrumentation were granted by the Greater Vancouver Regional District ( G V R D ) and the City of Port Coquitlam. A l Percival ( G V R D ) , M r . Bernie Buttner ( G V R D ) , and M r . Geoff Y i p (City of Port Coquit-lam) were of great help for the setup of instrumentation and on-site support. xx Several people have contributed to the dissertation in various ways. Phi l Gregory in the Department of Physics and Astronomy at U B C taught me the use of probability theory to ana-lyse data. Miche l Jean (Canadian Meteorological Center) provided the synoptic analysis charts on which Figure 2.2 was based. Paul Jance and Pascal Haegeli in the Department of Geography at U B C helped me create Figure 1.1 and Figure 2.1. Furthermore, I wish to ac-knowledge all those people, whose names I forgot to mention here but who may have contrib-uted to this dissertation by sharing their ideas and opinions. Finally, in many respects having a dad or husband, who pursues a Ph.D., is different from having one, who works on a regular job. I would like to thank my children Serena and Sebas-tian and my wife Shan for putting up with the less pleasurable differences. xxi 1 Introduction 1.1 Research Motivation, Goal, and Questions The Lower Fraser Valley ( L F V ) , British Columbia, Canada is characterised by a shallow maritime boundary layer, a valley geometry that narrows towards the interior, steep slopes rising over 1000 m above the adjacent plain, and tributary valleys (Figure 1.1). The L F V shares some of these characteristics with other places like Los Angeles, Santiago, and Athens, all notorious for their air-pollution problems. 124\u00b0W 123\u00b0W 122\u00b0W 49\u00b0N 0 Kilometres 25 \\ Canada TAT^^ \\ \\ Vancouver Island \/ J \/ 21. 49\u00b0N 124\u00b0W 123\u00b0W Longitude 122\u00b0W Figure 1.1: Map of the Lower Fraser Valley (LFV), Canada. Shown are the locations of Vancouver International Airport (YVR), Abbotsford Airport (YXX), and site of slope flow observations in Minnekhada Park (black rectangle). White areas are water surfaces; shades of grey indi-cate contour intervals of 0-500 m, 500-1000 m, etc. The dashed triangle approximates the shape of the LFV. The black star in the inset shows the location of the LFV within British Columbia (B.C.) and Canada. (Based on Fig. 1 in Reuten et al, 2005) 1 In the case of the L F V the main source of air pollution is traffic near the coast at the Strait of Georgia. During summer under fair-weather conditions, ozone precursors and particulate matter are carried downwind toward the interior into rural areas where ozone levels reach a maximum (Steyn et al., 1997), significantly impairing the relatively large portion of the popu-lation that is performing physical work outdoors (Brauer and Brook, 1997). Upslope flows play a particularly important role in the dispersion of air pollution at places like Vancouver, Los Angeles and Mexico City. In Whiteman's (2000) overview of air pollu-tion dispersion in mountainous terrain it is assumed that upslope flows vent air pollutants out of the boundary layer into the free atmosphere. I w i l l demonstrate in this thesis that this is not always the case, that air pollution can be trapped or recirculated within the boundary layer. Some investigators have come across the possibility of air-pollution recirculation without paying attention to it while most investigators have either not observed it or simply excluded the possibility in their models. The possibility of a recirculation challenges the simple concept of an upslope flow filling the convective boundary layer ( C B L ) over a heated slope and opens up an array of questions. It is the goal of this dissertation to provide new insights into the kinematics of daytime slope flow systems by addressing these questions: Is the boundary layer over a heated slope identi-cal to the C B L over flat terrain or does it have a more complicated structure? How do upslope and return flow relate to the boundary-layer structure? Is there a continuous transition be-tween the two extremes of recirculation and venting or are there two distinct regimes? What are the determining parameters? The simple conceptual model presented in section 1.2 below is fairly representative of our current understanding of upslope flows; yet, it does not answer any of these questions. In sec-tion 1.3 I w i l l review previous investigations against the questions. After 160 years of re-search on upslope flows our understanding is still incomplete. The approach I have taken to answer those questions above is laid out in section 1.4. 2 1.2 The Basic Mechanism of Upslope Flows During fair-weather conditions mountain slopes often exhibit upslope flows of air during the day and downslope flows during the night. The following high-level explanation for up-slope flows is based on Atkinson (1981) (Figure 1.2). Figure 1.2: High-level diagram of the mechanism of upslope flows (adapted from Atkinson, 1981).
0\u00b0 up to a critical angle the heat island flow persists, now interacting with a slope flow. Above the critical angle there is only one convection cell and the slope wind is \"Prandtl-like\", with only weak return flows occurring above the C B L . Defining the C B L depth Hs as the thermal boundary layer depth for
2 m s\"1. The thickness of the resolved vertical layers in our parameter settings was 50 m at heights 110-310 m and 30 m at all other heights between 20 and 1000 m. Each averaging cycle lasted approximately 20 minutes. The airflow components were determined by integrat-ing all backscatter spectra over the entire 20-minute cycle. Due to the remoteness of the M i n -nekhada site and because no obstacles were near the sodar's beam, background noise or echo corrections were not necessary. I used the entire available pulse frequency range of 1650-2750 Hz . To optimise the signal-to-noise ratio (SNR), I operated the sodar in full multi-beam mode, i.e. one pulse sent vertically and one simultaneous pulse pair sent at 29\u00b0 and 22\u00b0 from the vertical for each of the four directions east, west, north, and south. The circle around the sodar location in Figure 2.1 indicates the horizontal spread of the pulse beams at the mean maximum C B L height. During daytime, high S N R occurred throughout the entire C B L . Above the entrainment zone the S N R was mostly low, a known effect which has been used by other investigators (e.g. Neff, 1990) to estimate the height of the C B L . Because the effect was inconsistent in our observations I did not use the S N R to determine C B L height. Sodar meas-15 urements were continuous except for approximately 1 minute of system integration at the end of each averaging cycle and manual adjustments of parameter settings a few times each day, which typically caused interruptions of a few minutes. At a nearby site on the adjacent plain (Figure 2.1) Kev in Strawbridge operated a R A S C A L (Rapid Acquisition SCanning Aerosol Lidar) to measure the backscatter of particulate matter (see Strawbridge and Snyder, 2004). Lidar data were obtained over a 12-km range at a resolu-tion of 3 m along the beam axis and a scan speed of 0.2\u00b0 per second. Each R H I (range height indicator) scan took about 5.5 minutes to acquire and covered an elevation range from 3\u00b0 to 70\u00b0 above the horizon. R H I scans were performed continuously at four different azimuth an-gles, every fourth scan passing over the sodar (solid line in Figure 2.1). Paul Bovis flew a tethered balloon near the lidar with a standard meteorological package (AIR IT53 A H ) to measure temperature, wind speed, wind direction, and specific humidity. For the two time periods presented here, the morning of July 25 and the daytime of July 26, 2001, I used a total of 3 ascents and 16 descents. About one half of all flights took approxi-mately 15-20 minutes per ascent or descent with a vertical resolution of roughly 10 m. The remaining flights carried additional instrumentation so that each ascent or descent took ap-proximately 30-40 minutes and the vertical resolution was roughly 5 m. The maximum height of most flights exceeded 1000 m M S L . 2.2 Observations of Closed Slope Flow Systems versus Mountain Venting The results are presented in three steps. In the first step I show how I used the lidar data to establish the top of the C B L based on the agreement between the lidar backscatter boundary layer ( B B L ) and the thermal boundary layer (TBL) . Lidar R H I scans intersected the beam range of the sodar at a height from 130 m to 1000 m M S L . Dr. Kev in Strawbridge used the algorithm detailed in Strawbridge and Snyder (2004) to determine the top of the B B L , which can be identified as a highly scattering, i.e. aerosol-rich, layer. After smoothing the raw back-scatter data, the algorithm determines the height of the largest gradient in the backscatter pro-file around a first threshold estimate of the B B L depth. To verify the algorithm I visually es-16 timated from lidar scans instantaneous values of the mixed layer depth zi, which ranged from approximately the bottom to the top of the entrainment layer. The time or horizontal averages zi are a measure for the mean mixed-layer depth at the midway point o f the entrainment zone and agree well with the output of the algorithm. When available and of sufficient quality I used my surface temperature measurements at the sodar site and vertical potential temperature profiles from Paul Bovis ' s tethersonde flights to determine the T B L depth as the neutral buoyancy height of near-surface air parcels (parcel method). In some cases this alone was inconclusive and I consulted vertical profiles of rela-tive humidity (RH) to verify where R H dropped quickly and compared with an earlier or later tethersonde flight. Even over flat terrain there w i l l be some disagreement between B B L and T B L depth when determined as explained above. This is not of great concern for the investigation in this disser-tation. A s long as the fairly large error bars overlap I w i l l assume that B B L and T B L depths are equally representative measures of the C B L depth. O f interest are only discrepancies, which are clearly identifiable as layering of one boundary-layer characteristics within the other, for example a thermal layering within the B B L . The second section shows the vertical wind profiles I obtained with the Doppler sodar at the foot of the mountain slope. In the third section I present estimates of the mass transport over the slope. The final section contains an analysis of larger scale flows (synoptic winds, sea breeze, and valley flows) and their potential impact on the slope flow observations. 2.2.1 Convective Boundary Layer Height When I compared the T B L and B B L a number of problems arose, exemplified by Figure 2.3 and Figure 2.4. Firstly, the horizontal position of the tethersonde is at -500 m relative to the lidar, and the lidar never scanned over the tethersonde position. From Figure 2.3 it is ap-parent that the B B L depth does not remain constant over the slope, a phenomenon that has been demonstrated by previous investigators such as Vogel et al. (1987) and de Wekker (1997). Our observations confirm previous observations that the B B L follows the underlying topography early in the day but becomes more horizontal as the B B L grows deeper. As a measure for the B B L height I averaged the minimum and maximum B B L heights over the 0 17 to 2500 m range of the lidar R H I scans for July 25. Over this horizontal range the B B L height is over flat ground, since the slope is more than 2500 m from the lidar. The B B L height de-termined with this method was in good agreement with point measurements of the B B L height above the sodar. For July 26 I therefore used the point measurements to simplify the analysis. 1200 E. 1000 a> > 800 600 ro CD W CD > O < \u2022\u00a7> 400 X 200 1041 1001 ^ 0928 ^ ^ ' v - ^ 0 8 5 2 ^ ^ ~ s - \/ \" \" - \" ~ ~ 1000 200 2000 3000 4000 5000 0 1000 2000 3000 4000 5000 6000 Horizontal Distance from Lidar (m) Figure 2.3: BBL depth above MSL at different times on July 25, 2001. The four curves in the upper panel represent with increasing line width the BBL depth for 0852, 0928, 1001, and 1041 PDT, respectively. Similarly the lower panel shows BBL depth at 1053, 1136, 1219, and 1304 PDT. I smoothed the data with a 21-point uniform moving average, corresponding to averaging over a horizontal range of approximately 60m. The grey area shows the topography. Notice the slight differences in topography between the two panels due to different scanning angles. (Based on Fig. 6 in Reuten et al, 2005) 18 Secondly, it proved very difficult to determine T B L heights from the tethersonde data be-cause of large variations in moisture and temperature measurements and an ambiguous en-trainment zone at the top of the C B L , which contains a mixture of C B L air and free tropo-spheric air. In many cases I could only succeed by interpolating between those tethersonde profiles where the T B L heights were clearly expressed. I supplemented the tethersonde data by using surface temperature measurements, which I took irregularly at the sodar site, to de-termine the neutral buoyancy height of surface air parcels. 7 Moisture (g\/kg) 9 11 ' ' 1 ' 293 Potential Temperature (K) 297 0 500 1000 1500 2000 2500 Horizontal Distance from Lidar (m) Figure 2.4: Tethersonde profiles superimposed on a RASCAL RHI scan. The white solid line shows potential temperature and the white dashed line shows specific humidity measured with a tethersonde on July 26, 2001 from 1314-1355 PDT. The RASCAL RHI scan was taken on July 26, 2001 at 1350-1353 PDT. Lighter shades of grey correspond to greater aerosol loading. The bold dark line at the top of the light grey aerosol layer indicates the top of the BBL. The tethersonde profiles were smoothed by application of a seven point, binomially weighted moving average. (Based on Fig. 5 in Reuten et al., 2005) It is possible that the advective processes over the slope affected the vertical profiles of potential temperature and moisture even as far as 3500 m away from the slope, making it more difficult to interpret the data. For example, a tilting of the potential temperature profile from the vertical within the T B L similar to the one in Figure 2.4 was anticipated by Prandtl in 1942 and demonstrated by Schumann (1990) in his large-eddy simulation. The potential tem-perature profile in Figure 2.4 was determined from an ascent sounding and the tilting could be 19 the result of non-stationarity during the time it takes the tethersonde to rise; that this was not the cause is demonstrated by the same tilting seen in the descent sounding immediately fol-lowing the one in Figure 2.4 (Figure 2.5). 293 294 295 296 297 Potential Temperature (K) Figure 2.5: Potential temperature profile determinedfrom tethersonde ascent and descent. Potential temperature soundings on July 26, 2001 (smoothed by application of a seven point, binomially weighted moving average) determined from a tethersonde ascent from 1314-1355 PDT (dashed line, same as solid line in Figure 2.4) and a descent from 1355-1431 PDT (solid line). Thirdly, lidar scans required only a few minutes while the tethersonde flights typically took 40 minutes. During the morning hours the boundary layer height changed greatly within 40 minutes. In the afternoon, on the other hand, the boundary layer height remained fairly constant in time but often exceeded the maximum elevation of the tethersonde flights. The increase of moisture with height above 800 m (Figure 2.4) is unlikely to be a measurement error. It could be that a return flow advected air of higher moisture content horizontally from above the mountain plateau onto the adjacent plain. I w i l l revisit this point in the next section. Despite the difficulties in determining the T B L , Figure 2.6 shows good agreement be-tween the T B L and the B B L . Because of this agreement I decided to make use of the more abundant and precise lidar data to establish the relationship between the slope flow system and the C B L , and I equated the C B L with the B B L . 20 J 1 1 I I I I I I I I I I I L 600 i -E, 500 - | C I 400-O | 300 < .5> 200 X 100 i 0 0 0 0 9 0 9 0 0 July 25, 2001 o ~ i \u2014 i \u2014 i \u2014 ' \u2014 i \u2014 ' \u2014 i \u2014 i \u2014 i \u2014 i \u2014 i \u2014 ' \u2014 r 0840 0900 0920 0940 Local Time (PDT) T i r 1000 0900 1100 1300 1500 Local Time (PDT) 1700 1900 Figure 2.6: Time development of the entrainment zone of the TBL and the BBL on July 25 (a) and July 26 (b), 2001. Grey areas show the entrainment zone of the TBL, open circles show the BBL, and the error bars show the maximum range of overshooting thermals and entrainment of the BBL. For July 26, I showed the error bar at only one of the open circles to avoid overloading the figure. Note the difference of time and height scale between (a) and (b). In the morning of both days, I could determine the lower and upper limit of the entrainment zone. However, after 1100 PDT on July 26, the top and sometimes also the bottom of the entrainment zone exceeded the maximum elevation of the tethersonde flights. In these cases, the grey area shows the range from the bottom of the entrainment zone to the maximum flight elevation, while the cross-hashed areas extend from the maximum flight elevation to the upper limit of the scale. The maximum flight elevations of the tethersonde rangedfrom less than 600 m to more than 1000 m. (Based on Fig. 7 in Reuten et al, 2005) 21 2.2.2 Slope Flow System versus Convective Boundary Layer In this section I relate sodar measurements of wind speed to C B L estimates from lidar measurements at the foot of the mountain slope. Figure 2.7 shows a time-height section of the horizontal along-slope components of the wind velocity over a 4-hour morning period on July 25, 2001. After 0850 P D T , an upslope wind gradually strengthened to about 3-5 m s\"1 as it grew to a depth of approximately 500 m by late morning. During the same period, a return flow of approximately equal strength and depth was observed above the upslope flow layer. Initially the return flow occurred above the ' C B L , but when the C B L had reached a depth of about 500 m at 0930 P D T , the return flow occurred within the C B L , and the depth of upslope flow layer and the return flow layer aloft were each approximately half the depth of the C B L . The C B L stopped growing at about 1130 P D T and maintained a depth of about 1000 m until observations ended at 1230 PDT. Local Time (PDT) 0900 1000 1100 1200 i . i-7 , , r,-:-, r, i . . \u2022. r. . . - i . . . i . . . i . . . . |-.<.\u00ab\u00abr . . . . . -2 0 2 -2 0 2 -2 0 2 -2 0 2 -2 0 2 -2 0 2 0 2 Wind Velocity (m s\"1) Figure 2.7: Time-height section of the along-slope component of the horizontal wind vectors above the Doppler sodar for July 25, 2001. Positive values (grey shading) are upslope flows, negative values are return flows. Inner tick marks on the hori-zontal axis show 1 m s~' intervals. Open circles show the CBL depths as determined from lidar measurements. The error bars show the range of overshooting thermals and entrainment within the horizontal range of the scanning cone of the sodar (circle in Figure 2.1). (Based on Fig. 8 in Reuten et al, 2005) 22 On July 26 (Figure 2.8) observations are less conclusive. A comparison with Figure 2.7 shows that both C B L and upslope flow grew more slowly. It took until about 1500 P D T for the C B L to reach its maximum depth of about 1100 m. A t 1050 P D T a return flow started, at first above the C B L and then, after 1110 PDT, within the C B L . The C B L depth at that time was about 600 m, slightly more than the 500 m on July 25, when the return flow occurred underneath the C B L top. Local Time (PDT) 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Wind Velocity (m s\"1) Figure 2.8: As Figure 2.7 but for July 26, 2001, and without error bars. (Based on Fig. 9 in Reuten et al, 2005) A direct comparison of the top of the upslope flow and the return flow with the top of the C B L for both days is shown in Figure 2.9. For July 25, the top of the upslope flow scatters around the dashed line indicating half the height of the C B L . The top of the return flow scat-ters along the solid line indicating the height of the top of the C B L . For July 26, morning measurements initially show the top of upslope and return flow both exceeding the C B L depth. From late morning until evening the situation is comparable to that of the morning of July 25. 23 C B L Depth (m M S L ) C B L Depth (m MSL) Figure 2.9: Comparison of upslope flow and return flow depths with CBL depth. Top of the upslope flow (circles) and the return flow (triangles) plotted versus CBL depth for July 25 (left) and July 26, 2001 (right). The time (in PDT) of each measurement is shown next to the data points. Data for the top of the return flow are missing usually when the value exceeded the 1000-m vertical range of the Doppler sodar and in some cases because of a weak sodar signal above the CBL. The dashed and solid line represent half of and the full CBL height, respectively. (Based on Fig. 10 in Reuten et al, 2005) 2.2.3 Volume Transport The volume transport in the along-slope direction per lateral distance across the slope is given by lu(z)dz\u00abYu(zj)^j o y=i where U (z) is the upslope flow velocity at height z and Hs is the C B L depth. I divided the C B L into n layers, where t h e \/ h layer has a depth of A z y . is the average slope wind component in the \/ h layer. For July 25, the volume transport appears unbalanced and unsteady over short periods of time (Figure 2.10). However, averaged over the entire morning period, the volume transport of the downslope flow (446 m 2 s\"1) balanced 89% of the volume transport of the upslope flow 24 (502 m 2 s\"1). The discrepancy of 56 m 2 s\"1 is within the range of uncertainties in the data. No volume transport is shown for July 26 because it is obvious from Figure 2.8 that the volume transport of upslope and return flow was unbalanced. -2000 0850 0950 1050 Local Time (PDT) 1150 Figure 2.10: Along-slope Volume transport for the morning of July 25, 2001. The upper solid curve shows upslope volume transport (positive) and the lower solid curve downslope volume transport (negative). The dashed line represents the sum of both. (Based on Fig. 11 in Reuten et al, 2005) 2.2 A Impact of Larger-Scale Wind Systems One hypothesis for the recirculation observed on July 25 is advection of larger-scale flows into the slope flow system. Referring back to Figure 1.1 there were three larger-scale wind systems that could modify the daytime slope flow system: synoptic-scale winds, sea breeze, and valley winds, which I w i l l explain first individually in the following sections before dis-cussing their impact on the slope flow system in the discussion section. Synoptic Winds The 850-hPa charts for July 25-26, 2001, and the nearest three soundings in Quillayute, Port Hardy, and Kelowna showed westerly to north-westerly winds of 2.5-5 m s\"1 at about 1500 m M S L . The surface charts and the few available sodar measurements above the surface layer for night-time and early morning indicate west-south-westerly C B L winds of roughly 2 m s . 25 Above 500 m both sodar and tethersonde showed a change of wind direction from south-erly to westerly winds with increasing altitude early in the night from July 25 to July 26, in approximate agreement with synoptic weather charts. Hourly wind measurements at Vancou-ver International Airport ( Y V R ) and Abbotsford Airport ( Y X X ) indicate west-north-westerly synoptic surface winds as w i l l be shown in the following section on the sea breeze. The dis-crepancies between the different data may be due to differences in forced channelling of the synoptic flow. Sea Breeze From Figure 1.1 one expects a westerly sea breeze at the measurement site in Minnekhada Park. Figure 2.11 shows hourly measurements of wind direction, wind speed, temperature and relative humidity for July 25-26 for Y V R and Y X X . Y V R is located right at the east coast of the Strait of Georgia. Y X X lies approximately 30 km inland from the ocean to the south-west, which is similar to Minnekhada Park's 35-km distance from the ocean to the west. Both air-ports are sufficiently far away from the mountains enclosing the L F V to rule out any slope and valley flows at these two locations. 26 360 270 180 h 360 270: 180 ~ 0000 0600 1200 1800 0000 0600 1200 1800 2400 PDT I July 25 ! July 26 ! Date 0000 0600 1200 1800 0000 0600 1200 1800 2400 PDT I July 25 I July 26 I Date 289 a 0000 0600 1200 1800 0000 0600 1200 1800 2400 PDT I July 25 I July 26 I Date 0000 0600 1200 1800 0000 0600 1200 1800 2400 PDT I July 25 I July 26 I Date Figure 2.11: Hourly measurements of wind speed, wind direction, relative humidity, and temperature at Van-couver International Airport (YVR) and Abbotsford Airport (YXX) for July 25-26, 2001. 'YVR-Wind' and 'YXX-Wind' show wind speed (solid curves, left vertical axes) and wind direction (dashed curves, right vertical axes). 'YVR-Thermal' and 'YXX-Thermal' show relative humidity (solid curves, left verti-cal axes) and temperature (dashed curves, right vertical axes). Gaps are missing data. (Based on Fig. 12 in Reuten et al, 2005) Because there was an onshore synoptic wind, I could not see a sea breeze front in the data and had to look for a time period of transition to an observable sea breeze. The data from Y V R in the night and early morning of July 25 show west-north-westerly synoptic wind with no indication of a land breeze. A t about noon on July 25, the wind started shifting to the ex-pected westerly sea breeze direction. This minor shift was accompanied by a very weak tem-perature decrease and relative humidity increase between 1100 and 1200 P D T , while wind speed decreased from about 7 m s\"1 in the late morning to about 2 m s \" 1 in the evening. Data for Y V R on the following day were easier to interpret. In the late evening of July 25, winds shifted to the south-easterly land breeze direction. The land breeze ceased between 0700 and 27 0900 P D T on July 26 and was temporarily replaced by a north-westerly wind. Toward noon, the direction changed slowly to the westerly sea breeze direction with a wind speed of ap-proximately 4 ms\" 1 . The temperature and relative humidity data for Y V R on July 26 partly support this picture. Between 1100 and 1200 P D T , temperature briefly dropped while relative humidity remained constant. Surprisingly, the strongest signals for a sea breeze in the tem-perature and relative humidity data occur between 1600 and 1700 P D T on both July 25 and 26, 2001. Unfortunately, the wind data provide inconsistent information on the sea breeze. In contrast to Y V R , Y X X further inland showed a decaying weak easterly land breeze be-tween 0700 and 0900 P D T on July 25. A slightly stronger north-westerly synoptic wind of about 2.5 m s\"1 replaced the land breeze until about noon. Between 1200 and 1400 P D T winds adjusted to the south-westerly sea breeze direction at Y X X with speeds of about 5 m s \" 1 . A t average wind speeds of 5-7 m s\"1 between Y V R and Y X X the sea breeze must have started about 1.5 hours earlier in Y V R than in Y X X , which is in good agreement with the identification of a sea breeze transition between 1100 and 1200 P D T at Y V R . Wind data for Y X X on July 26 did not clearly show evidence of a transition to sea breeze. A n increase of relative humidity and a brief slowing down of the daytime temperature increase between 1200 and 1300 P D T , however, suggest an air mass change associated with a sea breeze initiation, in reasonable agreement with the transition time at Y V R . In conclusion, I estimate the time of a transition to sea breeze for our measurement site at Minnekhada Park at approximately 1200-1300 P D T on both days, July 25-26. The direction of the sea breeze was westerly with strengths of approximately 5 m s\"1 and 3 m s\"1 on July 25 and 26, respectively, based on the assumption of a west-north-westerly synoptic wind of about 2 m s\"1 at the two airport stations. These observations are in good agreement with the sea breeze climatology of the L F V in Steyn and Faulkner (1986). Valley Winds Up-valley winds were expected to start several hours after the onset of the upslope flow and fi l l the entire C B L (Whiteman, 2000). The local topography at Minnekhada Park (see Figure 1.1 and Figure 2.1) suggests that up-valley winds should come from the south-west. Since the wind measurements were made at the edge of the valley mouth it is not clear to what degree valley winds were noticeable. I w i l l discuss this further in section 2.3. 28 2.3 Discussion and Conclusions On the first day of observations, July 25, 2001, we observed daytime slope flow systems with a two-layer structure. The bottom half of the C B L was filled with strong upslope flows, while the upper half of the C B L was filled with an equally strong return flow (Figure 2.7-Figure 2.9). Individual 20-minute intervals of wind measurements differed strongly from each other. However, the time-averaged mass transport for the entire morning of July 25 showed an approximate balance between upslope flow and return flow within the C B L . The mass bal-ance and the lidar scans, which did not show any venting of air pollutants out of the C B L , suggest a closed slope flow circulation, which trapped air pollutants within the C B L . In the following sections I discuss three hypotheses for the trapping. 2.3.1 Hypothesis 1: Impact by Larger-Scale Flow Systems The insets in Figure 2.12 and Figure 2.13 show the direction of the larger-scale wind sys-tems. Both days showed a complex interplay of slope wind systems and larger-scale flows. As with previous analyses the data for July 25 are easier to interpret than for July 26. Only near the surface does the horizontal wind vector indicate pure upslope winds until approximately noon, when most likely an up-valley wind started steering the horizontal wind vectors clock-wise (Whiteman, 2000). This influence of the up-valley wind started later at lower altitudes within the upslope flow layer. Above the upslope flow layer, winds were approximately west-erly. This cannot be a sea breeze, because the sea breeze started only after 1200 P D T (section 2.2.4). 29 0900 1000 1100 1200 1300 Local Time (PDT) Figure 2.12: Time-height sections of the horizontal wind vector above the Doppler sodar for the morning of July 25, 2001. Open circles with error bars represent the CBL depth as determined from the lidar scans above the sodar (also shown in Figure 2.7) and grey areas represent upslope flow. Inset shows the expected directions of upslope flow (UpS), up-valley flow (UpV), synoptic wind (Syn), and sea breeze (Sea). North is up. Also compare with Figure 1.1 and Figure 2.1. Notice that upslope and up-valley flows are not exactly perpendicular because the slope is at the mouth of the valley. (Based on Fig. 13 in Reuten et al., 2005) 0800 0900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000 Local Time (PDT) Figure 2.13: As Figure 2.12 but for July 26, 2001. (Based on Fig. 14 in Reuten et al, 2005) 30 I cannot give a conclusive explanation for the observed wind directions but suspect a su-perposition of the synoptic wind with an upslope flow in the bottom part of the C B L and with a return flow in the upper part of the C B L . A n y northerly synoptic wind on the order of l m s - ' could have caused a measurable net mass transport in the return flow direction. Dur-ing the morning hours an up-valley flow is added to the wind system, which slowly penetrates downwards from the centre of the C B L . In the afternoon (see Figure 2.13) the wind system seems dominated by the up-valley wind, without a strong contribution from the sea breeze. On July 26, 2001, we also observed return flows within the C B L , but they occurred much later in the day and did not balance the upslope flows. It is likely that venting of air pollutants occurred earlier on that day. Figure 2.14 shows a short and thin layer of strong aerosol back-scatter over the ridge top about 6 km north of the lidar site on July 25 at 1047 P D T (upper panel). In contrast, the lower panel shows a longer and much deeper layer of strong aerosol backscatter moving over the ridge top on July 26 at a similar time in the morning. Also notice layers of strong aerosol backscatter and smooth appearance moving south toward the lidar from above the ridge top on both days. These layers are merging with the deep C B L on July 25 while they are clearly separated from the much shallower C B L on July 26. These observations challenge the explanation that synoptic winds alone caused the trap-ping on July 25 because synoptic winds were of similar strength and direction on both days. The main difference between the two days was the growth of the C B L , which was slower on the second day, caused by stronger background stratification and probably large-scale subsi-dence. This suggests that the internal dynamics of the slope flow system played at least a par-tial role in the observed trapping. 31 100 2 3 4 5 Distance from L i d a r (km) 10 2 3 4 5 Distance from L i d a r (km) Figure 2.14: RASCAL RHI scans for July 25, 1047 PDT (top) and July 26, 1053 PDT (bottom). The black areas represent the mountain slope as determined by the scanning lidar \"ground\" returns. The CBL can be identified visually as the turbulent layer of elevated particulate matter concentrations up to approxi-mately 1000m (top) and 500m (bottom). Cumulus clouds are present on July 25 about 8km from the lidar at an altitude of approximately 1700m. The logarithmic grey scale represents the relative backscatter ratio at 1064nm (lighter shades represent high aerosol concentrations; darker shades represent low aerosol concentrations). (Based on Fig. 15 in Reuten et al, 2005) 32 2.3.2 Hypothesis 2: Internal Dynamics of Slope Flow System In this hypothesis a return flow occurs within the C B L under particular conditions as part of the internal dynamics of the slope flow system. For example, Chen et al. (1996) found in their water-tank experiments for a two-dimensional ridge that the flow properties depended only on a non-dimensional (ND) quantity Gc, the ratio of ridge height and C B L depth far from the slope. Their results suggest that closed slope flow circulations within the C B L occur when Gc is below a critical value of Gc \u00ab 0.6 - 0 . 7 . This value differs greatly from our observed values for July 25, Gc \u00ab 2.6, and July 26, Gc \u00ab 1 . 4 . The possible reasons for the differences wi l l be revisited in chapter 4 after the scaling. 2.3.3 Hypothesis 3: Thermal Boundary Layer and Backscatter Boundary Layer are Different This hypothesis includes the possibility that the B B L may be composed of sub-layers, for example a C B L in contact with the heated ground and an elevated mixed layer separated from the underlying C B L by a temperature jump. In such a scenario, the upslope flow fills the ground-based C B L and the return flow recirculates pollutants in the downslope direction within the elevated mixed layer. To test this hypothesis a detailed analysis of vertical varia-tions of aerosol concentrations within the B B L and a comparison with the T B L structure would be required. Unfortunately, the uncertainties in the tethersonde observations did not allow me to determine the internal structure of the T B L . In chapter 3, I w i l l revisit the hy-pothesis in the context of physical scale modeling, which permits detailed measurements of the B B L and the T B L . 2.3.4 Conclusions The review of previous studies in section 1.3 showed that in most cases return flows either did not occur or were rather weak and occurred above the C B L . Kuwagata and Kondo (1989) gathered information from several field studies and summarized the relation of the upslope flow depth to the C B L depth in their Fig. 4. A l l measurements of the top of the upslope flow, except for the one at Azuma Takayu, scattered near the diagonal representing the top of the C B L . In comparison, Figure 2.9 in this thesis showed upslope flow depths scattering near the 33 dashed line representing half the depth of the C B L , providing more evidence that strong re-turn flows can occur within the C B L . We performed the measurements during fair-weather conditions. Under these conditions, predominantly westerly synoptic winds and the sea breeze advect air pollution, generated mainly near the coastline, towards the east (Steyn and Faulkner, 1986). During the advection, photochemical processes generate high concentrations of ozone. The fate of primary and sec-ondary pollutants is of particular importance in the suburban and rural areas east of the main source area of pollution where a high percentage of the population works outdoors. Most pre-vious observations at other locations showed upslope flows filling the entire C B L . As a con-sequence, air pollutants were vented into the free atmosphere above the mountain ridge. In contrast, our observations on July 25, 2001, suggest that air pollutants can remain trapped in closed slope flow circulations. I speculate that these observations are at least partially internal to the dynamics of the slope flow system, albeit supported by synoptic winds opposing the upslope flow. It is impos-sible with our field data to test the hypothesis that the T B L and the B B L are different or that the T B L exhibits a more complex structure over steep slopes than over flat terrain. For the remainder of this thesis I w i l l investigate this hypothesis with the help of water-tank experi-ments. In chapter 3 I w i l l develop the scaling that w i l l allow me to draw comparisons between field and water-tank observations (chapter 4). 34 3 Scaling and Idealisations 3.1 Introduction Scaling has been used for hundreds of years as a powerful tool in applied mathematics and engineering and is often interpreted differently by different investigators (Barenblatt, 2003). The central goal of scaling in this thesis goes back to Tolman's (1914) principle of similitude requiring that two universes of different scales are exactly similar. Tolman postulated the principle \"as a temporary criterion for the correctness of physical theories\", hence as a screen-ing tool 1 . Generalising Tolman' (1914) work, Buckingham (1914) developed the formalism of dimensional analysis, which is well explained in Barenblatt (2003) and which I w i l l follow in this chapter. I strongly emphasize here what this scaling is not meant to be: Often, scaling is used to es-timate the relative magnitude of terms in the governing equations. Smaller terms are neglected and the governing equations may then be easier to solve numerically or analytically. Based on this use of scaling and often limited to steady state, previous investigators achieved an order-of-magnitude agreement between atmospheric and water-tank observations. B y contrast, I set a more stringent goal: to use the water tank as a quantitative scale model of the atmospheric upslope flows observed in Minnekhada Park. This goal is closely linked to Tolman's principle of similitude i f we interpret the atmosphere and the water tank as two dif-ferent universes. Major improvements over previous investigations are necessary to achieve this goal. Firstly, a clear concept map needs to be developed to connect mathematical models with real physical systems (water tank and atmosphere). Secondly, I w i l l need to apply scaling as dimensional analysis using the Buckingham P i theorem to determine the non-dimensional 1 As an interesting digression into modern physics, Dr. Han van Dop pointed out to me that the combination of fundamental constants in our universe is probably scale invariant and therefore violates Tolman's principle of similitude. 35 governing parameters. Thirdly, time dependence needs to be explicitly included in the analy-sis. To develop the concept map, recall the schematics of my research approach (Figure 1.4 on page 10). The goal is to establish a quantitative link between observations in the atmosphere and in the water tank by means of scaling. This requires the introduction of two mathematical idealisations, one each for the atmosphere and the water tank, which I w i l l call the 'atmos-pheric idealisation' (A l ) and the 'water-tank idealisation' (WTI), (Figure 3.1). In the context of scaling, these idealisations are models, a term which I w i l l avoid in this context because of its sometimes confusing and inconsistent usage. For example in 'numerical model' the separa-tion between the mathematical idealisation and the physical, i.e. numerical, experiment is not possible and in 'physical scale model' it is not clear i f one means the mathematical model of the experimental apparatus or the physical apparatus itself. A l and W T I and their independent variables are introduced in section 3.2. Field Data \u2022 Atmospheric Similarity ^ p. Water Tank Data \u00ab Tank Observations 4 Predictions Idealisation Idealisation \u2022 Predictions Observations Figure 3.1: Concept map of the scaling. Scaling has to be carried out between each pair of neighbouring boxes. Field and tank observations provide data to develop atmospheric and water-tank idealisations, respectively. In return, the two idealisations can be used to predict other quantities in the real atmosphere and water tank. Central is the similarity over many or-ders of magnitude between atmospheric idealisation and water-tank idealisation. With regards to the second improvement, the use of dimensional analysis, the concept map Figure 3.1 clearly shows that three steps are required to carry out the scaling: first between real atmosphere and A l (section 3.3.1), second between real water tank and WTI (section 3.3.2), and finally by requiring similarity in the bulk behaviour of A l and W T I (section 3.3.3). From A l and additional assumptions, hypotheses on dependent quantities can be derived and tested with field observations (section 3.4). Requiring similarity between A l and WTI , I w i l l derive from the W T I testable hypotheses or predictions for water-tank experiments (sec-tion 3.5), which wi l l be checked in chapter 4. The third improvement is dropping the assumption of steady state. Surface heating in the atmosphere is roughly sinusoidal with time, while heating of the tank bottom is constant. I 36 account for this difference in surface heating in the scaling, but this raises the issue of a com-mon reference time in A l and WTI , which wi l l be addressed in section 3.6. Appendix B con-tains additional material on scaling. In this chapter, quantities specific to the atmosphere w i l l be distinguished by a subscript 'a ' from water-tank specific quantities, which wi l l carry subscript ' w ' . If a quantity applies generally to atmosphere and water tank the subscript w i l l be dropped. M y hope was to achieve similarity between the two systems within the uncertainty of the field observations (about 20%) at any given point in time in the interval from the beginning of positive heat flux to maximum heat flux - not, however, simultaneously at every point in time. This would have allowed the use of tank experiments to quantitatively model field ob-servations reported in the previous chapter. Water-tank experiments are repeatable and permit more measurements than field studies to investigate, for example, the hypothesis that thermal boundary layer and backscatter boundary layer are different (section 2.3.3). This goal was not fully achieved, the primary reasons being the complexity of the atmospheric flow, great un-certainties and insufficient range in atmospheric upslope flow velocity measurements, and violation of the scaling laws caused by molecular effects in the water tank. These reasons wi l l be discussed in this and the following chapter. 3.2 Atmospheric and Water-Tank Idealisations The topography of the A l is infinite in cross-slope direction and consists of an infinite pe-riodic array of plains at mean sea level ( M S L ) with half length Lba= 2400 m (3.1) and plateaus at Ha= 160m MSL (3.2) with half length Lta= 2400 m (3.3) separated by slopes with a horizontal length of 37 La =2201 m (3.4) (Figure 3.2, A). 800 jjj 600 f 200 -8000 - A V \\ \\ A 2Lt,a \\ \\ \\ - \\ \/ \/ H a f \\ \\ \/ \\ - \\ , r W 2Lb,a i i 1 r \u20224V : \u2022 \u2022\u2022 I\"' -4000 4000 Distance from Sodar (m) B 8000 .S 7T.._._ Figure 3.2: Topography at the field site and atmospheric and water-tank idealisations. A: The solid line shows the vertical cross-section of the slope at Minnekhada Park as seen from the sodar in the direction of the steepest slope (dashed line in Figure 2.1 on page 13). The dashed line represents the idealised periodic topography. B: The solid box encloses the water-tank domain. The end walls impose a mirror symmetry shown by a schematic flow pattern within the tank (solid arrows) and the imaginary mirrored flow outside the tank (dashed arrows). For comparison, the dotted box encloses the domain to be used with numerical models with wrap-around symmetry. Notice that horizontal and vertical axes do not have the same scale. In the corresponding WTI, A , W = V =0-470 m; Hw =0.149 m, and L... = 0.433 m (3.5) (3.6) (3.7) (Figure 3.2. B). The tank width is 38 Ww= 0.431m. (3.8) Notice the underlying assumption that in both A l and WTI , the slope angle (p = 19\u00b0, i.e. the aspect ratio Lw\/Hw = 2.90. In other words, horizontal and vertical lengths scale identically between A l and WTI . I w i l l briefly return to this assumption in section 3.3. Lhw and Lt w are constraints originating from the finite dimensions of the tank. The tank's end walls impose the symmetry indicated by the schematic flow patterns inside and outside of the water-tank do-main (Mitsumoto, 1989), i f heat loss and additional friction between end wall and fluid is negligible (a mirror or even-parity symmetry) (Figure 3.2. B) . I chose Lba and Lta in (3.1) and (3.3) such that A l and W T I are geometrically similar, i.e. ^ = ^ a n d (3.9) h J y3 - 1 0 , (B.10) is a function of momentum roughness length z0 a and \"thermal\" roughness length zQT a , Monin-Obukhov length L,a (negative for unstable conditions), surface layer depth hK a , and C B L depth ha. k \u00ab 0.4 is the von Karman constant. The rough estimate Ta - 1 0 was sug-gested by Hunt et al. (2003). I w i l l now discuss some characteristics of (B.8). 1. Hunt et al. (2003) derived their hypothesis for small slope angles, but they argued that the assumption that buoyancy drives the flow and determines the turbulence in the C B L holds for cp < 20\u00b0 so that the slope at Minnekhada Park falls within the range of validity. I am not aware of any other assumptions in Hunt's et al. deriva-tion that would exclude the 19\u00b0 slope angle at Minnekhada Park. 2. In the derivation of (B.8), Hunt et al. (2003) assumed that C B L depth and upslope flow layer depth are identical. Our field observations on July 25, by contrast, show that the upslope flow filled only the bottom half of the C B L (Figure 2.9, page 24). 3. Hunt et al. (2003) assumed that the environmental stratification above the upslope flow layer is undisturbed, which is unrealistic because the return flow advects nearly neutral fluid over the upslope flow layer. 173 4. The latter problem is related to the assumption that a return flow underneath the ridge top w i l l only occur underneath an inversion (scenario 1 in Hunt et a l , 2003). In the absence of an inversion and an opposing synoptic flow (scenario 3 in Hunt et al., 2003), Figure 2 in Hunt et al. (2003) suggests that the authors assumed a deep unidirectional flow extending from the plain over the slope to the plateau without a return flow. 5. In the hypothesis by Hunt et al. (2003), the upslope flow velocity is assumed inde-pendent of height within the mixed layer and is essentially equal to (only slightly smaller than) the maximum upslope flow velocity, which occurs in the surface layer. In contrast, our observations in Figure 2.7 (page 22) and Figure 2.8 (page 23) show that the vertical profile of upslope flow velocity, following a Prandtl pro-file, decreases from its maximum value at a height approximately one quarter of the upslope flow depth to zero at the top of the upslope flow layer. 6. The dependence of the constant of proportionality, Ta, on its arguments is only known to an order of magnitude. Furthermore, none of the arguments is known better than an order of magnitude; this includes the C B L depth, because Hunt et al. (2003) did not considered that the C B L is much shallower over the upper part of the slope than the lower part. 7. The dependence o f Ta on surface roughness for momentum and heat challenges the assumption that non-dimensional (ND) maximum upslope flow velocity de-pends only on IT,, F I 2 a , and n 3 a , (3.68), because surface roughness was ne-glected in the scaling. Moreover, it may be impossible to achieve the same ratio of momentum and \"thermal\" roughness length in atmospheric idealisation (Al ) and water-tank idealisation (WTI) because of the different fluid properties. 8. Monin-Obukhov theory was derived from field observations over flat terrain. It may not be valid over sloping terrain at all or require different empirical constants. Even i f valid, Monin-Obukhov length and surface layer depth could be functions of upslope flow characteristics like speed and depth so that Ta would not be a con-stant. A l l these cases could violate the assumption Ta ~ 10. 174 9. Proportionality between upslope flow velocity and convective velocity scale is physically reasonable, because the convective heating of the C B L seems to drive the upslope motion. It is instructive at this point to have a closer look at a water-tank experiment 5. Figure Appendix I clearly shows that in the water-tank upslope flows were fully developed before the onset of turbulent convection. It may well be that a change of the driving mechanism occurs in the water tank when convec-tion begins, but the problem of explaining the upslope flow without the presence of convection remains. Figure Appendix I also provides strong arguments against Hunt's et al. (2003) assumption that the upslope flow layer is identical to the heated layer: the heating over the slope has at most reached a depth of a few mi l -limetres above the surface (through molecular diffusion of heat) whereas the up-slope flow layer is about 4 cm deep. More information on this experiment is pro-vided in chapter 4. 5 Background information on the water tank can be found in section 4.2. 175 Figure Appendix I: Upslope flow without convective turbulence. This photograph of a dye experiment shows almost the entire plain and the bottom third of the slope, a total width of about 60 cm. Horizontal and vertical lengths are shown to scale. The photograph was taken 30-40 s after the heating was turned on. Convection is about to begin as can be seen by a few white bulges over the plain near the slope. The upslope flow is already fully developed, well visualised by the dye carried along the slope. The dye was originally injected as a thin layer (\u00ab1 mm) over the plain. The stream of dye also roughly outlines the vertical profile of the upslope flow velocity. The upslope flow layer has a depth of about 4 cm. Because mean and maximum upslope flow velocity are essentially equal in Hunt's et al. (2003) hypothesis, the predicted maximum upslope flow velocity (B.8)-(B.10) is UmAxa - 1 0 ( s m p - g p a h a Q H , f*\\2.\\ms-x (B. 11) where the value holds for 1200 P D T on July 25, (B.1)-(B.6). Because of the logarithm and cubed root in (B.10), Ya depends only weakly on its parameters. Therefore, substantial modi-fications to the parameters of Ta in (B.10) are required to fit UmMa to the observed velocity Uohxa \u00ab ( 3 . 8 \u00b1 0 . 3 ) m 5 - 1 . Despite the attempts by Hunt et al. (2003) to derive the coefficient Ya from first principles it remains essentially an unknown parameter, which needs to be de-termined by fitting the hypothesis to the data. I therefore define the 'Hunt hypothesis' of maximum upslope flow velocity for atmosphere and water tank by UHun,^cHu\u201e,(gj3hQH)y\\ (B.12) 176 Upslope Flow Velocity Hypotheses by Chen et al. (1996) Chen et al. (1996) derived an upslope flow velocity \"scale\" for atmosphere and water tank from a balance between horizontal advection and pressure gradient term. I present a modified derivation here, applicable for atmosphere and water tank, in which I retain a factor of 2, which Chen et al. (1996) dropped in their derivation. The hydrostatic pressure difference can be determined from the Navier-Stokes equation for vertical acceleration, i.e. from (A. 16) \/dt ^ \/ dXj P o P o dxi \/ dXj ^L = - g . A p , (B.14) dz where A denotes departures from the hydrostatic background values. Denoting background values with subscript 'b ' , AP = P-Pb (B.15) and Ap = p - P b . (B.16) Substitution of the last two equations into (B.14), noting that the background is in hydrostatic balance, and using the definition of specific volume, (3.12), gives dP dPb dP 1 + - U L = - g . p - g . p b ^> = _ g . p = _ g . _ (B.17) dz dz dz a Let z e [0 ,z ( o \/ J ] , where zlop = Dw for the water tank and zlop =