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Gap winds in a fjord : Howe Sound, British Columbia Jackson, Peter L. 1993

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GAP WINDS IN A FJORD: HOWE SOUND, BRITISH COLUMBIAByPeter L. JacksonB. Sc. (hons.) (Physical Geography focus Climatology/Meteorology)A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinTHE FACULTY OF GRADUATE STUDIESGEOGRAPHYWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIA1993© Peter L. Jackson, 1993In presenting this thesis in partial fulfilment of the requirements for an advanced degree atthe University of British Columbia, I agree that the Library shall make it freely availablefor reference and study. I further agree that permission for extensive copying of thisthesis for scholarly purposes may be granted by the head of my department or by hisor her representatives. It is understood that copying or publication of this thesis forfinancial gain shall not be allowed without my written permission.GeographyThe University of British Columbia2075 Wesbrook PlaceVancouver, CanadaV6T 1Z1Date:c-11 Z^/ 67 3AbstractGap, outflow, or Squamish wind, is the cold low level seaward flow of air through fjordswhich dissect the coastal mountain barrier of northwestern North America. These flows,occurring mainly during winter, can be strong, threatening safety, economic activity andcomfort.Howe Sound gap winds were studied using a combination of observations and severaltypes of models. Observations of winds in Howe Sound showed that gap wind strengthvaried considerably along the channel, across the channel and vertically. Generally, windsincrease down the channel, are strongest along the eastern side, and are below 1000 mdepth. Observations were unable to answer all questions about gap winds due to datasparseness, particularly in the vertical direction. Therefore, several modelling approacheswere used.The modelling began with a complete 3-dimensional quasi-Boussinesq model (CSURAMS) and ended with the creation and testing of models which are conceptually simpler,and more easily interpreted and manipulated. A gap wind simulation made using RAMSwas shown to be mostly successful by statistical evaluation compared to other mesoscalesimulations, and by visual inspection of the fields. The RAMS output, which has veryhigh temporal and spatial resolution, provided much additional information about thedetails of gap flow. In particular, RAMS results suggested a close analogy between gapwind and hydraulic channel flow, with hydraulic features such as supercritical flow andhydraulic jumps apparent. These findings imply gap wind flow could potentially berepresented by much simpler models. The simplest possible models containing pressuregradient, advection and friction but not incorporating hydraulic effects, were created,iitested, and found lacking. A hydraulic model, which in addition incorporates varyinggap wind height and channel geometry, was created and shown to successfully simulategap winds.Force balance analysis from RAMS and the hydraulic model showed that pressuregradient and advection are the most important forces, followed by friction which becomesan important force in fast supercritical flow. The sensitivity of gap wind speed to variousparameters was found from sensitivity tests using the hydraulic model. Results indicatedthat gap wind speed increases with increasing boundary layer height and speed at thehead of channel, and increasing synoptic pressure gradient. Gap wind speed decreaseswith increasing friction, and increasing boundary layer height at the seaward channelend. Increasing temperature dilterences between the cold gap wind air and the warmerair aloft was found to increase the variability of the flow — higher maximum but lowermean wind speeds.iiiTable of ContentsAbstract^ iiList of Tables^ viiiList of FiguresAcknowledgment^ xix1 Introduction 11.1 Motivation ^ 31.2 Objectives 41.3 Approach ^ 71.3.1^Field measurements ^ 71.3.2^Numerical and analytical modelling ^ 72 Gap winds around the world — a review of the literature 92.1 Nomenclature and classification ^ 92.2 Observations and studies of gap winds in western North America^ 102.3 Bora winds ^ 182.4 Theoretical work on severe downslope winds ^ 202.5 Numerical modelling studies ^ 232.5.1^Numerical modelling of the bora ^ 233 Observational program 25iv3.1 Introduction  ^253.1.1 Geographic Setting  ^263.2 Surface observations  ^323.2.1 Summary of surface wind data ^  343.3 Vertical profiles  ^373.3.1 Summary of vertical profile data  ^383.4 Synoptic observations for the case studied  ^453.4.1 Synoptic scale features  ^453.5 Summary of observational program ^  504 Numerical modelling: RAMS strategy and configuration^514.1 Introduction ^ 514.1.1 Modelling strategy  ^544.2 RAMS configuration ^ 55),)4.2.1 Model parameters  554.2.2 Grids and nesting  ^564.2.3 Initial data and boundary conditions  ^584.2.4 Terrain  ^605 Numerical modelling: RAMS results^ 675.1 Comparison of RAMS output with observations ^  695.1.1 Quantitative evaluation of model performance  695.1.2 Qualitative evaluation - time series  ^785.1.3 Qualitative evaluation - vertical profiles  ^855.1.4 Qualitative evaluation - surface winds  ^905.1.5 Summary of simulation problems ^  925.2 Analysis of model output ^  965.2.1 Horizontal cross sections  ^975.2.2 Vertical cross sections ^  1015.2.3 Froude number analysis  1165.3 Summary of numerical modelling results ^  1235.4 RAMS momentum balance ^  1255.4.1 Results ^  1255.4.2 Implications  1316 Simple analytic models^ 1346.1 Theory ^  1356.2 Results — comparison with observations and RAMS output ^ 1386.3 Discussion ^  1447 Hydraulic channel flow: an analog to gap wind^ 1457.1 Hydraulic theory ^  1457.1.1 Hydraulic flow regimes ^  1497.1.2 The energy equation  1547.1.3 The hydraulic jump ^  1557.2 The hydraulic model  1577.2.1 Method of solution — hydmod ^  1607.3 Results ^  1637.3.1 Rectangular channel ^  1657.3.2 Howe Sound — realistic and modified channel ^ 1877.4 Discussion and summary ^  2018 Summary of conclusions 2048.1 Questions answered ^  204vi8.2 Significance ^  2128.3 Recommendations and future work ^  214Appendices^ 215A RAMS description^ 216A.1 Model formulation  216B Hydmod data^ 226Glossary^ 230Bibliography^ 233viiList of Tables2.1 Green Island relative outflow percentages (Beal, 1985)  ^123.1 Summary of surface station data during field season, October 1987 to April1988 ^334.1 Grid structure of RAMS ^  575.1 Stations and areal weights used in statistical evaluation of RAMS simulation. 715.2 RAMS modelled and observed wind evaluation statistics spatially averagedover all stations and over the 31 hours of simulation.  ^725.3 RAMS modelled and observed temperature evaluation statistics spatiallyaveraged over all stations and over the 31 hours of simulation.  ^777.1 Values used in hydmod runs and sensitivity tests for the rectangular channe1.1657.2 Values used in hydmod runs and sensitivity tests for modified channel. . . 1907.3 Values of parameters used in hydmod simulations. Times are PST  197B.1 Cross sectional areas below the given height, along the "real" channel.Heights are from 100 to 1000 m. Area is x10 6 m3^  226B.2 Cross sectional areas below the given height, along the "real" channel ^Heights are from 1100 to 2000 m. Area is x10 6 m3. ^ 227B.3 Cross sectional areas below the given height, along the modified channel ^Heights are from 100 to 1000 in. Area is x10 6 m3^  228viiiB.4 Cross sectional areas below the given height, along the modified channel.Heights are from 1100 to 2000 m. Area is x106 m3. ^ 229ixList of Figures1.1 Visualization of gap wind flow superimposed on oblique view of topographyin southern Howe Sound ^32.1 Location map of northwestern North America^  173.1 Topography of Howe-Sound region, showing meteorological stations usedin the study^  303.2 Location map of Howe- Sound region. ^  313.3 Wind rose diagrams for October 1987 until April 1988. Concentric ringsare frequency in 10 % increments. ^  363.4 Down-channel component of the Daily maximum wind at Watts Point(WAT) and AlRsonde flights during the field season. ^ 393.5 Composite of AlRsonde observed profiles of a) wind, and b) potentialtemperature at Squamish town for case 1 (January). ^ 423.6 Composite of AlRsonde observed profiles of a) wind, and b) potentialtemperature at Squamish town for case 2 (February)^ 433.7 Composite of AlRsonde observed profiles of a) wind, and b) potentialtemperature at Squamish town for case 3 (March). ^ 443.8 a) 50 kPa chart for January 29, 1988 04:00 PST. b) Sea level pressurechart for January 29, 1988 10:00 PST.  ^473.9 a) 50 kPa chart for January 30, 1988 04:00 PST. b) Sea level pressurechart for January 30, 1988 10:00 PST.  ^483.10 a) 50 kPa chart for January 31, 1988 04:00 PST. b) Sea level pressurechart for January 31, 1988 10:00 PST.  ^494.1 Location and grid spacing of the four RAMS grids used.  ^624.2 RAMS grid 1 after smoothing and adjustment. ^  634.3 RAMS grid 2 after smoothing and adjustment.  644.4 RAMS grid 3 after smoothing and adjustment. ^  654.5 RAMS grid 4 after smoothing and adjustment.  665.1 Time series of observed and modelled: a) wind direction, b) wind speed,and c) standard deviation of wind speed; averaged over 12 stations at eachtime during the simulation.  ^735.2 Comparison of observed and modelled wind as time series of a) total,systematic, and unsystematic components of the Root Mean Squared Dif-ferences; and b) the Index of Agreement^  745.3 Time series of observed and modelled: a) temperature, b) standard devi-ation of temperature; averaged over 12 stations at each time during thesimulation.  ^765.4 Comparison of observed and modelled temperature as time series of a)total, systematic, and unsystematic components of the Root Mean SquaredDifferences; and b) the Index of Agreement. ^  775.5 Time series of surface observations and RAMS model output for SquamishAirport (SQA) and Squamish Town (SQT) ^  795.6 Time series of surface observations and RAMS model output for WattsPoint (WAT) and Defence Island (DEF) ^  805.7 Time series of surface observations and RAMS model output for BrunswickPoint (BRU) and Finisterre Island (FIN)  ^81xi5.8 Time series of surface observations and RAMS model output for LookoutPoint (LOO) and Ragged Island (RAG)^  825.9 Time series of surface observations and RAMS model output for PortMellon (MEL) and Langdale (LAN) ^  835.10 Time series of surface observations and RAMS model output for MountHarvey (HAR) and Deeks Peak (DEE) ^  845.11 a) AlRsonde observed profile at Squamish town, 16:00 PST January 301988; b) RAMS generated vertical profile at same time and location as a)^865.12 a) AlRsonde observed profile at Squamish town, 23:30 PST January 301988; b) RAMS generated vertical profile at same time and location as a)^875.13 a) AlRsonde observed profile at Squamish town, 6:00 PST January 311988; b) RAMS generated vertical profile at same time and location as a)^885.14 a) AlRsonde observed profile at Squamish town, 10:00 PST January 311988; b) RAMS generated vertical profile at same time and location as a) 895.15 Surface winds at 3 hour intervals: a) January 30 14:00 PST; b) January30 17:00 PST; c) January 30 20:00 PST; d) January 30 23:00 PST. . .^935.16 Surface winds at 3 hour intervals: a) January 31 02:00 PST; b) January31 05:00 PST; c) January 31 08:00 PST; d) January 31 11:00 PST. . .^945.17 Surface winds at 3 hour intervals: a) January 31 14:00 PST; b) January31 17:00 PST; c) January 31 20:00 PST.  ^955.18 RAMS level 4 (279 m) winds at 3 hour intervals: a) January 30 14:00 PST;b) January 30 17:00 PST; c) January 30 20:00 PST; d) January 30 23:00PS   985.19 RAMS level 4 (279 m) winds at 3 hour intervals: a) January 31 02:00 PST;b) January 31 05:00 PST; c) January 31 08:00 PST; d) January 31 11:00PS   99xi i5.20 RAMS level 4 (279 m) winds at 3 hour intervals: a) January 31 14:00 PST;b) January 31 17:00 PST; c) January 31 20:00 PST^ 1005.21 Location of down-channel and down core directions  1025.22 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 14:00 PST. The down-channel wind component as a vectorsuperimposed on contours of potential temperature, is above a plot of theFroude number  1045.23 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 17:00 PST. The down-channel wind component as a vectorsuperimposed on contours of potential temperature, is above a plot of theFroude number  1055.24 Vertical Cross section oriented along the main channel of Howe Sound for^January 30 20:00 PST    1065.25 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 23:00 PST    1075.26 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 02:00 PST    1085.27 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 05:00 PST    1095.28 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 08:00 PST. ^  1105.29 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 11:00 PST    1115.30 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 14:00 PST^  1125.31 Vertical Cross section oriented along the main channel of Howe Sound for.January 31 17:00 PST. ^  1135.32 Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 20:00 PST    1145.33 Vertical Cross section oriented along the core of strongest winds for Jan-uary 30 23:00 PST^  1155.34 Vertical Cross section oriented along the core of strongest winds for Jan-uary 31 11:00 PST^  1165.35 Froude number at 3 hour intervals: a) January 30 14:00 PST; b) January30 17:00 PST c) January 30 20:00 PST; d) January 30 23:00 PST^ 1195.36 Froude number at 3 hoUr intervals: a) January 31 2:00 PST; b) January31 5:00 PST; c) January 31 8:00 PST; d) January 31 11:00 PST^ 1205.37 Froude number at 3 hour intervals: a) January 31 14:00 PST; b) January31 17:00 PST; c) January 31 20:00 PST. ^  1215.38 Vertical plot of down-channel (DC) wind speed and momentum tendenciesfor January 31 11:00 PST, at the horizontal location -143.875 km^ 1275.39 Vertical plot of horizontally averaged down-channel (DC) wind speed andabsolute value of down-channel momentum tendencies for January 31 11:00PST^  1295.40 Vertical plot of horizontally averaged cross-channel (CC) wind speed andabsolute value of cross-channel momentum tendencies for January 31 11:00PST^ 1305.41 Horizontal plot of down-channel velocity and down-channel momentumtendency, vertically averaged below 679 m for January 31 11:00 PST. . . 1315.42 Horizontal plot of cross-channel velocity and cross-channel momentum ten-dency, vertically averaged below 679 m for January 31 11:00 PST^ 132xiv6.1 Visualization of Friction model. ^  1396.2 Comparison of observed down-channel winds with winds calculated from:RAMS simulation; Friction model; and the Bernoulli equation for January30 23:00 and January 31 05:00. ^  1426.3 Comparison of observed down-channel winds with winds calculated from:RAMS simulation; Friction model; and the Bernoulli equation for January31 11:00 and January 31 17:00. ^  1437.1 Definition sketch for airflow in a channel^  1487.2 Longitudinal profiles of channel flow height through various features.^1537.3 Schematic illustration of h versus specific energy for a particular flow con-dition (after Henderson (1966))^  1557.4 Forces acting on a slab of air on either side of a hydraulic jump ^ 1567.5 Simplified flow chart for hydmod. ^  1627.6 Gap wind flow for rectangular channel with "most likely" input parame-ters. a) Height of gap wind; b) Gap wind speed^  1677.7 Gap wind flow for rectangular channel with "most likely" input parame-ters. a) Froude number; b) Force balance components. ^ 1687.8 Sensitivity of mean and maximum gap wind speed to changes in h o (initialgap wind height) for a rectangular channel with one contraction. . . . . 1697.9 Sensitivity of mean and maximum gap wind speed to changes in h f (gapwind height at end of channel) for a rectangular channel with one contraction. 1697.10 Sensitivity of mean and maximum gap wind speed to changes in u 0 (initialwind speed) for a rectangular channel with one contraction. ^ 1707.11 Sensitivity of mean and maximum gap wind speed to changes in : if: (ex-ternal pressure gradient) for a rectangular channel with one contraction^ 170xv7.12 Sensitivity of mean and maximum gap wind speed to changes in g' (effec-tive gravity) for a rectangular channel with one contraction. ^ 1717.13 Sensitivity of mean and maximum gap wind speed to changes in C (dragcoefficient) for a rectangular channel with one contraction. ^ 1717.14 Gap wind flow for rectangular channel showing subcritical regime, withho = 300 m. a) Height of gap wind; b) Gap wind speed. ^ 1737.15 Gap wind flow for rectangular channel showing subcritical regime, withho = 300 in. a) Froude number; b) Force balance components. ^ 1747.16 Gap wind flow for rectangular channel showing predominantly supercriti-cal regime, with r = 0.013 Pa m -1 . a) Height of gap wind; b) Gap windspeed. ^  1757.17 Gap wind flow for rectangular channel showing predominantly supercriti-cal regime, with s = 0.013 Pa m -1 . a) Froude number; b) Force balancecomponents^  1767.18 Gap wind flow for rectangular channel showing entirely supercritical regime,with cs 0.02 Pa m -1 . a) Height of gap wind; b) Gap wind speed. . . . 1777.19 Gap wind flow for rectangular channel showing entirely supercritical regime,with -di-, 0.02 Pa m -1 . a) Froude number; b) Force balance components. 1787.20 Gap wind flow for rectangular channel showing influence of downstreamcontrol on flow, with hf = 1050 m. a) Height of gap wind; b) Gap windspeed. ^  1797.21 Gap wind flow for rectangular channel showing influence of downstreamcontrol on flow, with hf = 1050 m. a) Froude number; b) Force balancecomponents^  1807.22 Gap wind flow for rectangular channel showing effect of small frictionaldrag, with C = 0.001. a) Height of gap wind; b) Gap wind speed. . . . . 181xvi7.23 Gap wind flow for rectangular channel showing effect of small frictionaldrag, with C 0.001. a) Froude number; b) Force balance components. . 1827.24 Gap wind flow for rectangular channel showing effect of small effectivegravity due to a difference in potential temperature between the layers of1° C. a) Height of gap wind; b) Gap wind speed.   1837.25 Gap wind flow for rectangular channel showing effect of small effectivegravity due to a difference in potential temperature between the layers of1° C. a) Froude number; b) Force balance components.   1847.26 Gap wind flow for rectangular channel showing effect of large effectivegravity due to a difference in potential temperature between the layers of19° C. a) Height of gap'wind; b) Gap wind speed  1857.27 Gap wind flow for rectangular channel showing effect of large effectivegravity due to a difference in potential temperature between the layers of19° C. a) Froude number; b) Force balance components.   1867.28 Topography of Howe-Sound region, showing locations of cross sections andof artificial "wall" along western side used to reduce channel width. . . . 189^7.29 Gap wind flow for "realistic channel" using "most likely" input parameters ^a) Height of gap wind; b) Gap wind speed^   1917.30 Gap wind flow for "realistic channel" using "most likely" input parameters ^a) Froude number; b) Force balance components. ^  1927.31 Gap wind flow for "modified channel" using "most likely" input parame-ters. a) Height of gap wind; b) Gap wind speed^  1937.32 Gap wind flow for "modified channel" using "most likely" input parame-ters. a) Froude number; b) Force balance components. ^ 1947.33 Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 30, 23:00 PST^ 195xv ii7.34 Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 05:00 PST ^1957.35 Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 11:00 PST ^1967.36 Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 17:00 PST ^1967.37 Sensitivity of mean and maximum gap wind speed to changes in h o (initialgap wind height) for modified channel. ^  1977.38 Sensitivity of mean and maximum gap wind speed to changes in h f (gapwind height at end of channel) for modified channel. ^ 1987.39 Sensitivity of mean and maximum gap wind speed to changes in u 0 (initialwind speed) for modified channel^  1987.40 Sensitivity of mean and maximum gap wind speed to changes in 2 (ex-ternal pressure gradient) for modified channel^  1997.41 Sensitivity of mean and maximum gap wind speed to changes in g' (effec-tive gravity) for modified channel^  1997.42 Sensitivity of mean and maximum gap wind speed to changes in C (dragcoefficient) for modified channel. ^  200A.1 Arakawa type C grid stagger used in the model^  221xv ii iAcknowledgmentMany people and organizations helped to make this study possible.I would like to thank the Atmospheric Environment Service of Environment Canadawhich: gave me unpaid leave of absence to undertake this project; provided personalfunding for one year via their "Postgraduate scholarship in Atmospheric Science"; fundedpart of this research via science subvention grants to my supervisor; made data availablefrom Pam Rocks, Alta Lake, and Point Atkinson; allowed installation of an electronicbarometer at Alta Lake; purchased AlRsondesTM that were used in vertical soundings;lent a meteorological theodolite to track the AlRsondesTM; provided pibal lights to enabletracking of AlRsondesTM at night; and were generally supportive of my research efforts.I wish to thank the following organizations who also funded this work: The NaturalScience and Engineering Research Council (NSERC) provided personal funding for twoyears via their "NSERC Postgraduate Scholarship" and for half a year via a ResearchAssistantship from my supervisor's operating grant. Also NSERC funded much of theoperating costs of this research via grants to my supervisor. The Isaac Walton KillamMemorial Trust provided one year of personal support via its Pre-Doctoral Fellowship.The UBC Geography Department provided personal funding through several TeachingAssistantships. The U.S. National Center for Atmospheric Research (NCAR), providedsupercomputing resources for numerical modelling. (NCAR is funded by the U.S. Na-tional Science Foundation.)I thank the following organizations which provided or helped to acquire data: CanadaCoast Guard allocated use of a hovercraft for installation, removal and servicing of surfaceobserving stations at Ragged Island, Defence Island, and Finisterre Island. B.C. Ministryxixof Transportation and Highways provided station data from their weather stations alongthe eastern shore of Howe Sound (Mount Strachan, Deeks Peak, Alberta Creek, andMount Harvey). B.C. Ministry of the Environment provided data from their stations atSquamish and Langdale, and allowed installation of electronic barometers at these sites.I would like to thank the following people or groups who allowed use of their propertyfor observing station locations: The Squamish Nation allowed stations on their landsat Defence Island and in the Squamish River valley. B.C. Hydro allowed installationof a station on the Daisy Lake Dam. B.C. Telephone Company installed and serviceda station on their microwave tower at Watts Point. B.C. Rail permitted location of astation near their railway right of way at Brunswick Point. Howe Sound Pulp and Paperallowed a station near their pulp mill at Port Mellon. Hood Point Holdings allowed astation on Finisterre Island.The following people assisted this project in various ways: Sheryl Tewnion, a stu-dent assistant helped with some station data processing during and after the field pro-gram. John Hogg of University Computing Services wrote a custom visualization program(Windview) which helped make sense of RAMS output. Patricia Chalk of The Universityof Western Ontario Geography Department, Cartography Section, drafted some of thelocation maps and schematic diagrams. Roger Pielke of the Atmospheric Science Depart-ment at Colorado State University provided the numerical model (RAMS), and helpedacquire significant computing resources on the CRAY supercomputers at NCAR for thisproject. Craig Tremback and Bob Walko of CSU were extremely helpful and generouswith their time and knowledge in helping with the use of RAMS, during a four monthstay at CSU and afterwards. The faculty and staff of the Geography Department at TheUniversity of Western Ontario, accomodated completion of the final stages of this thesis.I would very much like to thank Douw Steyn, my graduate supervisor, for beingsupportive of my research and graduate program in terms of funding, intellectual supportxxand advice, for taking care of administrative detail, for knowing when to give advice andwhen not to, and for letting me "get on with it" in my own way.Finally I thank my family: Tessa and Ian Jackson, my children, for "putting upwith dad and his thesis"; and Chris (Olson) Jackson, my wife, paid and unpaid researchassistant, and companion who has helped me with this work in countless ways and hassomehow managed to live with me while I struggled through it.xxiChapter 1IntroductionIf the surface of Earth were smooth and homogeneous, climate (averaged weather) wouldvary by latitude only. It is apparent that the northwest coast of North America is neitherflat (it is a mountain chain dissected by fjords) nor of homogeneous surface type (havingboth land of varying surface roughness, and water). Since the detailed expression ofclimate depends on the local configuration of surface types, it consequently displays avariety of climates. One of the most striking winter wind regimes affecting the fjords ofwestern North America, is gap, outflow or, colloquially, Sguamish l wind.Outflow wind is the movement of cold, dry air at low levels from the interior of thecontinent to the coast. A major barrier to this motion, especially if the air is stable, is theCoast Mountain chain. Thus, low level air will preferentially flow through major valleys,and over lower mountain passes, to coastal inlets. This will generally occur whenevera pressure gradient is directed from the interior to the Coast. Under certain conditionsoutflow winds can be very strong and damaging. For example surface winds of 51 mwith higher gusts were recorded near Portland Inlet in northern British Columbia 2 onJanuary 10 1969 (Beal, 1985), while on January 14 1950, Abbotsford, in the lower Fraservalley, had seven hours of gap winds in excess of 26 m s -1 (Tyner, 1951b).'All three terms: gap, outflow, and Squamish wind are closely related and will be used inter-changeably in the thesis. The term Squamish wind seems to be come from the geographic place name"Squamish" which is the name of both a town at the head of Howe Sound, and of the native peopleswhose ancestral lands cover the area. The term Squamish wind is generically applied to similar windsin other fjords along the British Columbia coast (Schaeffer, 1975)'NOTE: place names used in the thesis can be found in figures 2.1, 3.1 and 3.21Chapter 1. Introduction^ 2In British Columbia, the conditions creating the most intense gap winds occur duringwinter when a strong arctic anticyclone builds over the interior of the province (Tyner,1950; Tyner, 1951a; Tyner, 1951b). In this situation arctic air, which cools and deepensin the interior, is partially contained by the Coast Mountains which separate it fromrelatively warm, moist, air on the coast. The difference in temperature, humidity, andhence density, on either side of the mountain barrier results in a large pressure gradient,oriented perpendicular to the mountain barrier. As a result, and because cold denseair on a slope will accelerate under the influence of gravity, strong low level winds candevelop through inlets and valleys. This is depicted schematically in figure 1.1 which isan oblique view of Howe Sound with the axes of strong outflowing air indicated by heavyarrows. Figure 1.1 is a composite from observations and numerical model output. Theonset of strong outflow is often accompanied by passage of an arctic front onto the coast.Although air moving down slope is dynamically warmed due to adiabatic compression, itis still cold relative to the maritime air it is displacing. When this situation at the surfaceis combined with outflowing winds at mid levels, (which results in both a lee trough dueto the mountains and a thermal trough due to the warm ocean) the pressure gradientand gap wind strength are further enhanced.Strong outflow can also occur without an arctic outbreak - usually as the result ofa deep cyclonic centre approaching the coast. While gap winds can occur whenever sealevel pressure is greater inland than on the coast, the preceding paragraph describes aconceptual model of an intense outflow event. A goal for this research will be to validateand quantify the conceptual model of gap wind flow.Chapter 1. Introduction^ 3Figure 1.1: Visualization of gap wind flow superimposed on perspective view of topogra-phy in southern Howe Sound. View is from south, looking north-northeastwards. Verticalexaggeration is 10.1.1 MotivationThe effects of strong outflow wind can be dramatic: extreme wind chill, storm to hurricaneforce winds, crop damage, and blizzard conditions with visibility near zero in blowingsnow or dust. High winds are hazardous to aircraft because of severe low level turbulence,and to shipping because of potential severe icing and sea state (Atmospheric ResearchIncorporated, 1986). Strong outflow in winter results in "snow belts" on the east coastsof Vancouver Island and the Queen Charlotte Islands as the cold air acquires moisture,and becomes unstable from the warm ocean. The moist, unstable air when forced toChapter 1. Introduction^ 4rise up the eastern slope, can form clouds and snow. Episodes of strong gap winds canresult in widespread power outages due to wind-blown trees knocking down electric powerlines (The Vancouver Sun, 1989a; The Vancouver Sun, 1989b). When these winds areassociated with extreme cold, the result is large power consumption, and severe damageto transportation, property, domestic water supplies, etc. (North Shore News, 1989;The Vancouver Sun, 1989c).While the effects of strong but relatively rare outflow events can be dramatic, it isalso important to understand less dramatic more frequent outflow events of moderateintensity. In narrow valleys and fjords, such as those dissecting British Columbia's CoastMountains, significant winds can only occur either as inflow (up-valley) or outflow (down-valley). Outflow is the dominant direction in winter (Jackson and Steyn, 1992; Steynand Jackson, 1990), so that understanding its characteristics is an important part ofunderstanding the wind climatology of fjords in the region.Present forecast techniques employed by Atmospheric Environment Service (AES)meteorologists using surface pressure prognoses are able to provide some guidance onoutflow onset and duration. If an observation exists with which to calibrate the forecast,the range of intensity at a point can also be estimated. However, very little is knownabout the detailed spatial and temporal variability of the flow, or about its intensity,with any accuracy. By studying outflow winds, improved analysis and forecasts of theonset, duration and intensity of the flows, as well as their spatial and temporal variabilitywill be possible.1.2 ObjectivesGap winds are an expression of the internal flow dynamics controlled by an interac-tion between external forcing parameters (synoptic weather conditions) and the internalChapter 1. Introductionboundary conditions (terrain) within an inlet or valley. Questions to be studied concern-ing these winds are divided into two groups which are listed below. The first is a seriesof questions about the detailed nature and characteristics of gap winds. The second isquestions concerned with external parameters which cause and control the wind flow.Characteristics of gap windshorizontal outflow structure:• Where does the maximum wind speed occur?• How do changes in internal boundary conditions (topography, valley slope, rough-ness and width) affect the flow?• What are the effects of obstacles such as islands, on outflow winds?• How does flow vary temporally / diurnally? Are there wave-like (periodic in spaceor time) fluctuations?vertical outflow structure:• What is the depth of outflowing air, and how does it vary along a fjord?• Where is the vertical speed maximum? How does the height of the speed maximumvary along the fjord?• What is the vertical temperature structure? Does an inversion mark the top of theoutflowing air?• Is it possible to extrapolate results from the study of one fjord to others? Is itpossible to separate the phenomena from their internal boundary conditions?Chapter 1. Introduction^ 6Reaction of flow to external boundary conditionsBased on the conceptual model described previously, by analogy with downslopewindstorms (see for example Clark and Peltier (1984), Durran and Klemp (1987), Klempand Lilly (1975), Peltier and Clark (1983), Smith (1985)), from the work done on gapwinds in Alaska (Lackmann and Overland, 1989; Macklin, Overland and Walker, 1984;Macklin, 1988; Macklin, Bond and Walker, 1990), from the work done on a closely relatedphenomenon called the Bora in Croatia (Klemp and Durran, 1987; Smith, 1987; Yoshino,1976a) and from local studies of related wind flow patterns (Mass and Albright, 1985;Overland and Walter, 1981; Reed, 1981; Reed, 1931), it is possible to make several generalstatements about external pararneters that are thought to affect gap winds. These are:direction and magnitude of horizontal surface pressure gradient; temperature contrastbetween the cold air inland and the warmer maritime air on the coast; geostrophic windvelocity at mountain top level; depth of cold air in interior (height of inversion); verticalwind profile — presence of critical layers and regions of wind reversal. These are outlinedin more detail in the literature review presented in chapter 2.The following questions provide a framework for assessing the importance of the abovecontrols:• Are these the important external parameters for gap winds?• What is the relative importance of each?• Are there other important external parameters?• Are there threshold values which these parameters must exceed for the flow to beginor to be maintained?• How do external forcing parameters affect flow characteristics?Chapter .1. Introduction^ 7• Which parameters are most important?1.3 ApproachA three-pronged approach was employed to fulfill these objectives and answer the pre-vious questions: field measurements, numerical modelling using a mesoscale model, andanalytical / numerical modelling using simpler models. Field measurements and numeri-cal model output provide answers to questions about the internal dynamics and structure.Numerical and analytical modelling provide answers to questions about the influence ofexternal parameters.1.3.1 Field measurementsTo better understand gap wind characteristics in Howe Sound, a field measurement pro-gram was mounted. The program consisted of a network of surface stations and a seriesof vertical soundings. The surface stations continuously monitored and recorded wind,temperature, and pressure, providing information on the horizontal structure of outflownear the surface. The vertical soundings provided information about the vertical struc-ture at one location during selected outflow events. The data obtained from the fieldwere used to examine the synoptic setting and mesoscale structure of a gap wind event.1.3.2 Numerical and analytical modellingA numerical mesoscale model was used to simulate the detailed structure of the flow,and validated against observations. If the model simulates the flow adequately, thenmodel output can be used to determine horizontal and vertical flow structure. The useof numerical models to examine detailed flow structure can be extremely informative,since the horizontal and vertical resolution is much greater than that of the observationalChapter 1. Introduction^ 8network. Numerical model output is used to suggest analytic and simpler numericalmodels representing simplifications of the equations of motion.Once analytical, or a simple numerical model has been created and verified, it willbe used to determine the sensitivity of the flow to external parameters. To do this,all external boundary conditions will be held constant at some typical value, exceptone which will be varied through a range of values for each computation. This willbe done successively for the major forcing parameters which are included in the simplemodel. Thus it will be possible to judge the sensitivity of analytical model output (eg.wind speed) to external forcing parameters. Sensitivity analyses using a simple model ispreferred to the "brute force" method of performing multiple computations with the full3D model for several reasons:• computational costs required to perform many simulations is prohibitive.• simple models are much easier to manipulate.• interpretation of primitive equation numerical model output is often very difficult,whereas interpretation of the results from a simpler set of equations is often clearerand more scientifically satisfying.Chapter 2Gap winds around the world — a review of the literature2.1 Nomenclature and classificationBefore reviewing the literature concerning gap winds and other similar local winds,nomenclature and terminology will be defined. Gap winds have been loosely definedas resulting from a balance between the horizontal pressure gradient, and inertia (accel-eration). Overland and Walter (1981) have described gap winds as:^dv^1 dP^v— dx^p dx(2.1)where x is aligned along the channel, v is the down-channel wind speed, p is air density,and t' is the channel-parallel pressure gradient. This represents a balance betweenacceleration and horizontal pressure gradient.Therefore, by applying the name "gap" to Squamish wind a statement is made aboutthe process which accounts for it. In previous studies (Macklin, Lackmann and Gray,1988; Macklin, Bond and Walker, 1990; Overland and Walter, 1981), the term "gapwind" has been applied to winds in horizontal channels in situations where the horizontalpressure gradient is oriented along the channel. While this is the case for Howe SoundSquamish winds, the effect of changing channel elevation may be important over land.Gap winds are related to a class of downslope winds, typified by the "bora" of Croa-tia. Bora winds, unlike gap winds, are not constrained horizontally by channel walls.Changes in elevation, as cold air flows down steep slopes, is an important source of ki-netic energy for bora winds. Several classification schemes have been developed to better9Chapter 2. Gap winds around the world — a review of the literature^10understand and describe bora winds. The first scheme, originally developed by Benevant(1930), classified boras by synoptic type as follows: Anticyclonic — high pressure inland;Cyclonic — low pressure over the sea; and Mixed — a combination of the first two. Thenext classification scheme, proposed by Paradi2 (1957) and Paradi2 (1959), consideredthe relative importance of pressure gradient and temperature contrast across the DinaricAlps. Yoshino (1976b) proposed a scheme with six different classifications based on therelative positions of anticyclonic and cyclonic centres.Bora winds are closely related to fan winds, like the Chinooks of Alberta. The maindifference between the two, seems to be that fOhn winds are relatively warm, whereasbora winds are relatively cold. Classification becomes difficult when the wind is relativelycold at one part of the slope and relatively warm at another (Jurec, 1981). Bora andfan winds in turn are related to "downslope windstorms", which occur when air flowingover a mountain barrier develops a large amplitude lee wave, resulting in very strongwinds at the foot of the lee slope. Processes accounting for downslope windstorms arestill under active research, although a consensus is developing (Atkinson (1981), Smith(1987)) which states that hydraulic theory, or some derivative of it, can explain all ofthese phenomena.2.2 Observations and studies of gap winds in western North AmericaSome of the earliest studies of strong outflow in British Columbia were conducted byTyner (1950, 1951a, 1951b), who first used the term "Squamish" in scientific literatureto refer to gap winds in Howe Sound. He reported strong outflow through the inlets andvalleys along British Columbia's coast frequently coincide with an arctic outbreak. Thisoccurs during winter when an arctic anticyclone builds a cold stable airmass over theinterior. The outbreak is often "triggered" by falling pressures on the coast due to theChapter 2. Gap winds around the world — a review of the literature^11passage of a cyclone to the south (Tyner, 1950) . In a study of outflow through PortlandInlet during the 1949-1950 winter, Tyner (1950) reported 46 percent of recorded windswere outflow, and 38 percent of these were gale force (greater than 34 knots). He alsonoted that outflow winds persisted up to 30 km offshore, and usually had a depth of 1000m although depths as high as 2500 m had been observed (Tyner, 1951a). He reportedsmall pressure ridges at the mouths of the inlets during outflow events and postulatedthe size of the ridges is related to outflow strength. However no mention is made of howthe pressure field is resolved at that scale.A study of several very intense arctic outbreaks was made by Tyner (1951b). Itreported at Abottsford, on January 25 to 26 1950 there were 15 hours of 35 knot outflowwinds with a peak gust of 61 knots, with 61 knot winds also observed in Howe Sound.During another outbreak, Abottsford had seven hours of wind in excess of 52 knots and50 year record minimum temperatures were set all over southern British Columbia (manyof which still stand).A more recent report, Schaeffer (1975), studied wind records for Squamish from 1969to 1972. It found that outflow winds occur mainly in December and January, oftenpersisting for 3 to 5 days with speeds commonly reaching 35 knots gusting up to 60knots. Outflow episodes occurred an average of twice a month during December andJanuary.Patrick (1980), while studying a gap wind event with uniform pressure gradient acrossthe Coast Mountains, examined a visual satellite image which depicted low cloud andfog being pushed offshore by outflow winds. Using this, and a topographic map, hepostulated that wide, low elevation valleys allowed easiest flow of air from the interiorto the coast. Thus, outflow would occur first in Portland Inlet and Douglas Channel,followed by the Fraser Canyon. As the depth of cold air increased over the interior,Skeena valley, Dean Channel, Burke Channel, Knight Inlet, Bute Inlet, Howe Sound andChapter 2. Gap winds around the world — a review of the literature^12Observed Northeasterly Winds>35 knots >50 knotsOctober 5.5% .05%November 11.5% .11%December 19.6% 1.6%January 15.1% 2.9%February 13.1% .81%March 4.3% .20%Table 2.1: Green Island relative outflow percentages (Beal, 1985)Harrison Lake would also record strong outflow (see figure 2.1 for locations).A climatological study of outflow winds (Beal, 1985) at Green Island (located atthe mouth of Portland Inlet — figure 2.1) using data from 1909 to 1983 found outflowwind speeds were distributed as shown in table 2.1. Outflow occurs most frequently inDecember and January, and gale force outflow at these times is common. Peak outflowwas measured at 99 knots with higher gusts on January 10 1969. During December 1977and January 1978, 32 consecutive days of outflow had winds greater than 35 knots.A mesoscale study of an outflow event through the Fraser Valley, on February 13 1980(Overland and Walter, 1981), used an instrumented aircraft, 8 meteorological buoys, andfour upper air sounding stations in addition to the existing meteorological network, tostudy gap wind in southern Strait of Georgia and in Juan de Fuca Strait. A core of 30 to35 knot winds whose border was sharply defined by wind shear and by large temperatureand moisture gradients was observed. This was arctic air pouring out of the Fraser Rivervalley. By plotting the arrival time of cold air, it was shown that a narrow core of airmoved rapidly from the Fraser River valley through Bellingham to Victoria. The air thenspread into the Juan de Fuca Strait and the central Strait of Georgia. The wind velocityin the core of cold air remained constant while the core spread horizontally and verticallyChapter 2. Gap winds around the world — a review of the literature^13as arctic air "filled up" the southern Strait of Georgia. Winds below 2000 m came fromnortheast with a maximum speed at 700 m elevation. The outflowing air had a largecross isobaric component, with the pressure gradient acting to increase momentum inthe core of strong winds (the jet). Overland and Walter (1981) postulated that an eddyfeature at the mouth of Juan de Fuca Strait may have been caused by a hydraulic jump.Another study using the same data (Faulkner, 1980), reported a dry adiabatic lapse rateup to 800 in indicating strong mechanical mixing, and a maximum observed speed of 40knots.There have been several cases of outflow winds examined in the Northwestern UnitedStates (Cameron (1931), Cameron and Carpenter (1936), Reed (1981), and Mass andAlbright (1985)). Reed (1981) examined a strong "bora like" outflow event with windspeeds over 50 knots in Western Washington. The strongest winds flowed through theStampede Pass and Columbia Gorge which are the least obstructed passages through theCascade Mountains. He found the strong winds resulted from a large pressure gradient(12 mb per 100 km, or .012 Pa m -1 ) which existed between a strong anticyclone inlandand a deep cyclone offshore. This large pressure gradient was sustained because themountain barrier separated cold air inland from warm air on the coast. The mountainchain also acted to restrict low level subsidence warming inland, which further increasedthe temperature contrast. The measured wind speeds were consistent with analytictheory (the Bernoulli equation, discussed later). Reed (1981) calculated that air flowingover higher passes would have lower speeds and would not be cold enough to penetratethe coastal inversion. Although the cause of acceleration was the large pressure gradient,it was enhanced by kinetic energy resulting from the loss of potential energy as the airmoved down the slope.A Central American example of strong outflow winds has been observed in southernMexico - near the Gulf of Tehuantapec. Hurd (1929) reported observations of strongChapter 2. Gap winds around the world — a review of the literature^14northerly winds in a polar outbreak through a topographic gap in the Sierra MadreMountains. Other examples of the blocking effect of mountains on low level winds occurin Alaska (Schwerdtfeger (1975), Mitchell (1956)).Macklin, Lackmann and Gray (1988) describe the wind field and force balance outsidethe topographic gap for two gap wind events in Alaska, using low-level aircraft data aswell as routine observations. Gap winds were 750 — 1100 m in depth, and no hydrauliceffects were observed. The flow was ageostrophic (down the pressure gradient) in the"jet" but tended toward geotriptic balance (a balance between pressure gradient force,Coriolis force, and friction) beyond one Rossby radius of deformation from the coast. TheRossby radius of deformation gives the e-folding distance for geostrophic adjustment inthe vicinity of a barrier (Mass, Albright and Brees (1986), Bannon (1981)), and in thecase of flow within a neutrally stratified boundary layer surmounted by an inversion, isdefined as:R = (g'h)f(2.2)where(STOP — OBOT)g^x^ (2.3)OBOTis the effective or reduced gravity; h is boundary layer depth; f is the Coriolis param-eter; 'hop is the potential temperature above the inversion; and °Boy. is the potentialtemperature in the neutral layer below the inversion.Lackmann and Overland (1989) discuss a gap wind event through the relatively wideShelikof Strait, Alaska, also using low-level aircraft data. Momentum and equivalentpotential temperature budgets found the following:• temperature and inversion height differences accounted for cross strait pressuregradients.Chapter 2. Gap winds around the world — a review of the literature^15• along strait winds diverged, however the inversion height increased due to entrain-ment of air from aloft.• pressure ridging occurred along the right side of the flow at the end of the straitdue to geostrophic adjustment in which the Coriolis force turns wind to the right,resulting in convergence along the right side of the channel. This increases theinversion height and therefore the surface pressure. It can occur if the duration ofthe flow exceeds the time scale for geostrophic adjustment (104 seconds ti 3 hours).• a sharp transition occurs at the channel exit when the channel width is less thanthe Rossby radius.• pressure gradient force is the largest component of the along channel momentumbudget, accounting for 180% of the observed acceleration. Vertical entrainmentand surface friction are the retarding forces that equally account for the difference.• events with large potential temperature changes across the inversion and less shear,show the most acceleration because the effect of entrainment in decelerating theflow is reduced.• along channel winds were generally in geostrophic balance, which was favoured bythe large width of the channel, and its northerly location.Macklin, Bond and Walker (1990) analysed a gap wind event near Prince WilliamSound, Alaska, in which the gap wind "jet" flowed over open ocean after it had left theconstraining fjord. A 0.2 KPa ridge of high pressure was observed slightly to the rightof the jet. The gap wind was relatively constant at 500 m in depth. A momentumbudget analysis corroborated previous findings that the pressure gradient force was mostimportant, being opposed by surface friction, and to a lesser extent by entrainment.Chapter 2. Gap winds around the world — a review of the literature^16These Alaskan aircraft case studies, while very informative, were concerned withthe structure and dynamics of gap winds over open ocean, or through the wide ShelikofStrait, which parallels the coast. They did not examine the structure of gap winds withinthe topographic gap itself. They found that wind acceleration could be explained as abalance between pressure gradient, surface drag, and entrainment, and that geostrophicadjustment of the wind and mass field occurred when the duration of the flow approached104 seconds 3 hours).Chapter 2. Gap winds around the world — a review of the literature^17Figure 2.1: Location map of northwestern North America.Howe Sound region box is enlarged in figure 3.2Chapter 2. Gap winds around the world — a review of the literature^182.3 Bora windsBora winds have been documented frequently in European scientific literature since themid-nineteenth century (Yoshino, 1976b). The name "bora" was originally given to thedownslope winds of the northeastern Adriatic coast from Croatia to Trieste, Italy. Otherdownslope winds which have been studied are the bora near Novorossiysk on the BlackSea's northeastern coast, the "mistral" of Mediterranean France (Pettre, 1982), bora-like winds at Novaya Zemlya in the Russian Arctic, and outflow winds in the Salt andBols fjords of northern Norway; as well as bora-like winds reported near Lake Baykal,Crimean Peninsula, coast of Sea of Okhotsk, Central Sardinia, and Bulgaria (Jureec(1981), Yoshino (1976b)).The most intensely observed and studied wind of this type is the bora on the north-eastern Adriatic coast. This coastline is topographically somewhat similar to the BritishColumbian coastline, as a mountain range (the Dinaric Alps) near the coast separates thecoastal zone from an elevated inland plateau. One significant difference is the Adriaticcoast lacks long, narrow, steep sided fjords which dissect British Columbia's coastline.Bora winds can occur at any time of the year but, as in British Columbia, they arestrongest in winter when they are associated with an arctic outbreak (Jureec, 1981).This occurs when a strong anticyclone lies over eastern Europe, often in conjunctionwith a cyclonic circulation in the Mediterranean. In this situation, a pressure gradientis directed across the Dinaric Alps and allows arctic air to move across Hungary wherethe Dinaric Alps partially block the flow. Arctic air then deepens and eventually spillsthrough passes onto the coast (Jureec (1981), Yoshino (1976b), Smith (1985)).Of the studies conducted by the Yugoslav and Japanese researchers, only one wasbased on a specially collected data set (Yoshimura, Nakamura and Yoshino, 1976). Therest of the studies relied on routinely collected data or non- meteorological indicatorsChapter 2. Gap winds around the world — a review of the literature^19such as wind shaped trees (Yoshino et al., 1976).The following summarizes salient features of bora winds in Croatia:• strongest winds occur during winter and at night (Jureec, 1981)• generally 10 "bora days" occur per month each winter (Yoshino, 1972)• most bora winds last 12 to 20 hours but can last as long as 10 days (Yoshino, 1969)• anticyclonic bora winds affect a localized area, but a cyclonic bora has widespreadstrong winds (Jureec, 1981)• bora winds are strongest at coastal stations except for the very highest mountainstations (Yoshimura, 1976)• wind velocities greater than 30 knots are frequent in winter (Yoshino, 1969)• the strongest bora wind reported was a gust to 95 knots in February 1929 at Trieste(Yoshino, 1975)• a stable layer usually exists at mountain top level — 1500 to 2000 m above sealevel (Yoshino, 1976a)• bora wind velocity increases as the stability of the air increases (Yoshimura, Naka-mura and Yoshino, 1976)• maximum bora depths are 2000 to 3000 m (Jureec, 1981)• at the onset of strong bora winds, temperatures often rise and then fall (Yoshimura,Nakamura and Yoshino, 1976)• bora winds are usually cold (Yoshino, 1976a)Chapter 2. Gap winds around the world — a review of the literature^20• there have been frequent observations of fan wall clouds, lee wave and rotor cloudsover the mountain tops during bora eventsNovorssiysk on the Black Sea (Yoshino, 1975), averages 54 bora days per year withwinds often reaching 45 knots and occasionally 60 knots. At Salt Fjord Norway, sim-ilar winds have been observed, with Mook (1962) noting the wind speed was directlyproportional to the pressure gradient. Many known features of British Columbia's out-flow winds are similar to those observed in bora-like winds in other parts of the world.Bora-like winds are possible where a mountain range separates two contrasting airmasses.Although bora-like winds are commonly observed, there has been no detailed study ofthe flow structure or its temporal and spatial variability – in any environment whichremotely resembles a British Columbian fjord.2.4 Theoretical work on severe downslope windsTheoretical work related to gap winds has studied periodically occurring windstorms inthe lee of the Colorado Front Range Mountains. Although a concensus is forming in theliterature (Atkinson (1981), Smith (1987)) that various winds which occur downstreamfrom major mountain barriers are all members of the mountain lee wave family and canbe described by hydraulic shallow water theory, there are significant differences betweengap winds and lee slope windstorms:• Most observations of lee slope windstorms indicate strong, uniform flow aloft whichresult in large amplitude stationary lee waves. These lee waves have horizontalwavelengths of 50 to 100 km and propagate vertically until reaching a critical levelwhere breaking occurs. Conversely, outflow wind, is essentially a low level flow. Itis forced by large low level horizontal pressure gradients created when a mountainbarrier partially blocks cold inland arctic air from reaching the coast. The presenceChapter 2. Gap winds around the world — a review of the literature^21of large amplitude lee waves accompanying gap wind has not been observed (Massand Albright, 1985).• Previous North American west coast gap wind studies, (Overland and Walter(1981), Mass and Albright (1985), and Macklin, Lackmann and Gray (1988)) indi-cate strong winds persist over relatively long horizontal distances. Strong lee windsobserved in Colorado however, have small horizontal length scales which is relatedto their lee wave forcing.• Previous lee slope wind studies have considered the flow to be 2-dimensional — theflow of air over an infinitely wide mountain barrier. Conversely, outflow wind isfundamentally 3-dimensional as it originates through mesoscale gaps in mountainbarriers and is modulated and controlled by valleys and inlets through which theair flows.Despite these differences, many controlling factors considered important for lee slopewinds are also felt important for outflow. These are: large scale sea level pressure gra-dients across the mountain barrier, moderate flow normal to the barrier at mountaincrest level, and a stable layer near mountain crest level upstream of the barrier. Notingthese similarities and differences, a brief review of previous downslope wind studies willbe made.Three mechanisms have been proposed to account for strong lee slope wind devel-opment. The first mechanism, based on hydraulic theory, was first proposed by Long(1954), and used by Houghton and Kasahara (1968), Houghton and Isaacson (1968),and Arakawa (1968,1969). The theory proposed by Smith (1985) is similar, except theatmosphere is presumed to have constant stratification rather than layers separated bya density interface. The Smith (1985) work was extended by Smith and Sun (1987) toChapter 2. Gap winds around the world — a review of the literature^22incorporate Long's model. The flow of air over a mountain is modelled by fluid flow-ing over a barrier using shallow water equations. Strong winds occur on the lee slopewhen the fluid (air) goes from subcritical flow upstream, to supercritical flow over themountain, becoming subcritical again downstream as kinetic energy dissipates in a tur-bulent hydraulic jump. When applied to the atmosphere, the main weaknesses of thistheory are that it doesn't allow continuous stratification, or vertical propagation of en-ergy above either the free surface or rigid lid upper boundary condition. However thistheory is attractive because of its simplicity, and its apparent inclusion of important fea-tures observed in downslope windstorms. Work by Durran (1986), suggests that verticalpropagation of energy plays only a minor role in strong lee slope wind development whichappears to be the case for gap wind, but is a departure from other lee slope wind theories.A strong inversion typically present over arctic air in an outflow event, resembles the stepchange in density represented by water in the shallow water equations, indicating thatthis theory may be applicable to gap winds.The second mechanism thought to account for Colorado downslope windstorms (Klempand Lilly, 1975) is the amplification of linear vertically propagating gravity waves, bywaves reflected off the tropopause (or some other layer where the Scorer parameter,(Scorer, 1949) changes rapidly). The wave amplitude is determined by the superpositionof these upward and downward propagating modes and will depend upon whether ornot the atmosphere is "tuned" to constructive interference. As this theory is linear, itsapplicability to large amplitude waves has not been determined (Durran, 1986).The third mechanism proposed (Clark and Peltier (1977,1984), Peltier and Clark(1979, 1983)), suggests large amplitude waves and downslope winds occur after a devel-oping wave breaks. The area of wave breaking creates a critical layer with strong mixingand wind reversal. This self-induced critical layer traps and reflects upward propagat-ing waves resulting in resonance and strong surface winds. A comprehensive review ofChapter 2. Gap winds around the world — a review of the literature^23downslope winds can be found in Durran (1990).Due to the differences between gap winds produced on the West Coast of NorthAmerica and lee slope windstorms in Colorado, the applicability of lee slope wind stormtheories to outflow wind phenomenon is unknown. In particular, the presence of largeamplitude lee waves during outflow events has not been observed. Rather, previousstudies, (Overland and Walter (1981), Mass and Albright (1985), and Reed (1981)), havefound an approximate ageostrophic balance between pressure gradient and inertia.2.5 Numerical modelling studiesMost numerical model work has been involved in simulating lee slope windstorms inthe Colorado Front Range Mountains, (Clark and Peltier (1977,1984), Peltier and Clark(1979, 1983), Klemp and Lilly (1975, 1978), Lilly and Klemp (1979), Durran (1986),Klemp and Durran (1987), Durran and Klemp (1983, 1987), and others). The subsetconcerned with modelling outflow-like winds is fairly small.2.5.1 Numerical modelling of the boraKlemp and Durran (1987), performed a series of 2-dimensional numerical simulations ofthe Croatian bora using idealized topography and initial and boundary conditions. Theyperformed a number of sensitivity analyses to determine how well shallow water theorycould represent the bora, finding that wave overturning within the cold air was responsiblefor strong lee slope flow, and that it resembled hydraulic flow produced both by shallowwater theory and by their simulations in which wave overturning was suppressed. Klempand Durran (1987) also found strong lee slope response even when the flow was notinitially forced. In one simulation, the model was initialized with cold air on the inlandside of the mountains and no wind. Thus, horizontal thermal inhomogeneity createdChapter 2. Gap winds around the world — a review of the literature^24the pressure gradients which generated the flow. Their results agreed quite well withobservations. By comparing the assumed fundamental mechanisms behind severe leeslope winds in the Croatian bora and the Colorado lee slope windstorms, Klemp andDurran (1987) postulate that despite flow differences, the mechanisms producing thestrong wind are fundamentally the same. This supports the notion that the essentials,if not the details of severe lee slope winds may be embodied in simple hydraulic theory(despite its simplifications and limitations).Chapter 3Observational program3.1 IntroductionTo better understand outflow characteristics in Howe Sound, a field measurement pro-gram was mounted from October 1987 until April 1988. Nine surface-based stationswere installed. The location of these stations, and those of other agencies, are shown infigure 3.1. Each station recorded hourly values of wind speed and direction and temper-ature; some stations also recorded surface pressure. Additionally, a series of 18 upper airsoundings were made during several outflow events.The station locations were chosen with the following goals in mind:• to maximize horizontal flow structure information.• to sample the entire Howe Sound region, from the mountain pass at Whistler, tothe mouth of the fjord.• to sample the wind across and along the fjord.• to locate anemometers where they were exposed to outflow winds, and where theirmeasurements were representative of winds in the area.This last goal was often difficult to attain, given the nature of the terrain. Islands, whilebeing useful anemometer sites, also pose problems by perturbing the flow.The data averaging time was another factor considered in planning the observationalprogram. If data are averaged over too long a time interval, details of temporal variation25Chapter 3. Observational program^ 26will be lost. On the other hand, if data are averaged over a very short time interval prac-tical problems arise: data must be downloaded more frequently and will be voluminous.More frequent data retrieval was not feasible as several of the sites (RAG, DEF, FIN)were inaccessible except by boat, hovercraft or air. As a compromise, an averaging timeof one hour was chosen which also matched the observation frequency of other agencies.Since the time scale of a typical gap wind event is a few days, this observing frequencywas felt sufficient to resolve important temporal variations. The standard deviation ofspeed and direction were retained so that not all of the higher frequency wind informationwas lost.3.1.1 Geographic SettingOutflowing air originates on British Columbia's interior plateau northeast of the CoastMountains. During its path to the coast, relatively dense cold air spills over lower moun-tain passes and is channelled by valleys. Thus, the topographic setting — width, depth,and roughness of valleys, and elevation of passes — is important in determining outflowcharacteristics.Twenty kilometres northwest of Vancouver British Columbia, is a glacial valley whichdissects the Coast Mountains (figure 3.1 and 3.2). The "wet" part of the valley is a fjordnamed Howe Sound. Shaped like a twisted 2-dimensional funnel, the fjord's "cone" (20km across) opens south-southwestwards onto the Strait of Georgia, and its "tube" (5km wide) points north-northeast, ending at the town of Squamish. Coast mountains oneither side of Howe Sound, rise steeply to 1200 - 2000 m above sea level, over horizontaldistances of about 5 km. The funnel "cone" contains many small islands. A perspectiverepresentation of Howe Sound's topography underlies the schematic illustration of gapwinds in figure 1.1.Entering the head ("tube") of Howe Sound at the town of Squamish, is the SquamishChapter 3. Observational program^ 27River which divides 10 km north of the town. The western fork retains the name"Squamish River", and is in a comparatively broad, low elevation valley. The valleyends abruptly 50 km to the north-northwest without becoming a mountain pass. A trib-utary of the Squamish River, the Elaho, continues on to the northwest and eventuallycrosses the Coast Mountains, but at a high elevation of 900 m. The eastern fork, theCheakamus River, has a valley which is more rugged and at higher elevation in its lowerreaches than the Squamish River valley. The Cheakamus valley gradually rises to a sig-nificant mountain pass (Whistler) at 640 m elevation, about 50 km north-northeast of thefork. On either side of each of these valleys, mountains of the Coast range rise sharplyto elevations in excess of 2200 m.George Vancouver, who became the first European to visit Howe Sound during hisexplorations in June 1792 (Vancouver, 1798), described it as follows:"Quitting point Atkinson and proceeding up the sound ... we made a rapidprogress, by the assistance of a fresh southerly gale, attended with darkgloomy weather that greatly added to the dreary prospect of the surroundingcountry. The low fertile shores we had been accustomed to see, though latelywith some interruption, here no longer existed: their place was now occupiedby the base of the stupendous snowy barrier, thinly wooded and rising fromthe sea abruptly to the clouds; from whose frigid summit, the dissolving snowin foaming torrents rushed down the sides and chasms of its rugged surface,exhibiting altogether a sublime, though gloomy spectacle, which animatednature seemed to have deserted ...... We had scarcely finished our examinations when the wind became exces-sively boisterous from the southward attended with heavy squalls and torrentsof rain.Chapter 3. Observational program^ 28... About nine o'clock (we) landed for the night near the west point of entranceinto the sound, which I distinguished by the name of Howe's Sound in honorof Admiral Earl Howe."The Howe Sound/Squamish/Whistler area (hereafter referred to as the Howe Soundregion) is the most populated and heavily used fjord in British Columbia. The town ofSquamish is a major transportation centre where containers are unloaded from shipsfor railway transport eastwards. There are two major pulp and paper mills on thewestern shores of Howe Sound, one at Wood Fibre 7 km southwest of Squamish, andthe other at Port Mellon further south (figure 3.2). As a consequence, tugboats towinglog booms are common. The waters of Howe Sound are used extensively for recreation,by boaters, windsurfers, scuba divers, and commercial and recreational fishermen. Themountains, especially along eastern Howe Sound and near the Cheakamus valley, containmany parks and recreational areas used extensively all year by hikers and campers fromnearby Vancouver. Whistler and Blackcomb mountains at the town of Whistler (figure3.2), are world renowned ski facilities.Although outflow winds occur through most valleys dissecting the coastal mountainchain of western North America, the Howe Sound region was chosen for this detailedstudy because:• gap winds occur with a fairly high frequency and strength.• anemometers can be placed where they are well exposed and fairly representativeof wind in the surrounding area.• it is accessible for instrument deployment and maintenance, and downloading ofdata as well as for vertical profile sampling.Chapter 3. Observational program^ 29• Howe Sound is relatively heavily used and populated, increasing the usefulness ofthis study.• it is fairly typical of other British Columbia fjords facilitating possible extrapolationof results.• several surface weather stations are already in place and supplement data fromthose deployed for this study.The main disadvantage in using the Howe Sound region is that the frequency and strengthof outflow events are reduced in comparison to northern fjords.10 KM• A.E.S.■M.O.E.• M.T.H.*U.B.C.NChapter 3. Observational program^ 30Figure 3.1: Topography of Howe-Sound region, showing meteorological stations used inthe study. Solid contour is the coastline. Dashed contours are at 300, 900 and 1800 melevation. Abbreviations can be found in the Glossary.VANCOUVER•Lätidihg.Roint AtkinsonEnglishBayBOWEN.ISLAND:PAISLEYISLANDSTRAIT OF GEORGIAChapter 3. Observational program^ 31Figure 3.2: Location map of Howe-Sound region.Chapter 3. Observational program^ 323.2 Surface observationsSurface observations were made at the stations shown in figure 3.1 during the course ofthe field program. Table 3.2 lists the types of measurements recorded at each station.University of British Columbia (UBC) and B. C. Ministry of the Environment (MOE)data were one hour averages (except pressure which was instantaneous). AtmosphericEnvironment Service (AES) and B. C. Ministry of Transportation and Highways (MTH)data were recorded each hour, but averaged over a shorter time. Wind measurements atmost stations were made at 10 m above ground level, except where indicated below. Toobtain representative wind measurements, sites were selected where the influence of nearfield surface roughness elements (trees, rocks, hills etc.) was minimized. However, thiswas not always possible.The surface data were from four agencies:• AES — provided data from Alta Lake (ALT), Squamish Airport (SQA), Pam Rocks(PAM) and Point Atkinson (ATK). ALT and SQA are staffed 13 hours daily. PAMis an automatic buoy transmitting 24 hourly observations daily. During this fieldprogram, PAM data were intermittent. ALT, SQA and PAM gave hourly obser-vations of wind, temperature, dew-point temperature, surface pressure, visibility,cloud and weather. ATK, a Canadian Coast Guard manned lighthouse, providedwind observations every three hours. It is closed for the 01:00 PST observationtime (09:00 UTC). Wind sensors at ALT, SQA and ATK are mounted at 10 inabove ground level. PAM's wind sensor is about 1.5 m above sea level. The winddata from these stations are a two minute average ending at the observation time.The largest wind speed variation greater than 5 knots above the average, for theperiod ten minutes prior to the observation time, is reported as a gust speed.Chapter 3. Observational program^ 33station agency elevation W ' T TD 1^P comments# obs. / dayAlta L.^(ALT) AES 658 m 13 13 13 24 closed at nightSquamish A.^(SQA) AES 52 m 13 13 13 13 heavy treesPam Rocks^(PAM) AES 0 m 24 24 24 24 buoyPt. Atkinson^(ATK) AES 9 m 7 — — — 3 hourlySquamish Town (SQT) MOE 3 m 24 24 — 24 roof of bldg.Langdale^(LAN) MOE 12 m 24 24 — 24 Ferry gantryDeeks Peak^(DEE) MTH 1280 m 24 24 — —Mt. Harvey^(HAR) MTH 1560 m 24 24 — —Mt. Strachan^(STR) MTH 1420 m 24 24 — —Alberta Cr.^(ALB) MTH 670 m 24 24 — —Daisy L. (DAI) UBC 380 m 24 24 — — on damSquamish R.^(SQR) UBC 34 m 24 24 — 24 in swampWatts Pt.^(WAT) UBC 260 m 24 24 — — on^wave towerDefence I.^(DEF) UBC 3 m 24 24 — —Brunswick Pt.^(BRU) UBC 18 m 24 24 — — side of slopePort Mellon^(MEL) UBC 3 m 24 24 — 24Finisterre I.^(FIN) UBC 21 m 24 24 — —Lookout Pt.^(LOO) UBC 4.6 m 24 24 — 24Ragged I.^(RAG) UBC 12 m 24 24 — —Table 3.1: Summary of surface station data during field season, October 1987 to April1988. See glossary for abbreviations.• MOE — provided Hourly averaged wind and temperature data for automatic sta-tions at Squamish townsite (SQT) and Langdale (LAN). The SQT wind obser-vations are taken from a 5 m mast mounted on a 2 story provincial governmentbuilding in the town of Squamish. The anemometer height is about 15 in aboveground. The LAN wind observations are from a 13.7 m mast mounted on top ofa 12 in gantry at the B.C. Ferry terminal, for a total instrument height of 25.7 inASL. The wind data are one hour averages.Chapter 3. Observational program^ 34• MTH — provided data for Deeks Peak (DEE), Mount Harvey (HAR), Mount Stra-chan (STR) and Alberta Creek (ALB), located on ridges along the east shore ofHowe Sound. All are automatic stations with hourly averaged observations of windand temperature at 10 m AGL.• UBC — installed nine stations for the purposes of this study: Daisy Lake (DAI),Squamish River (SQR), Watts Point (WAT), Defence Island (DEF), BrunswickPoint (BRU), Port Mellon (MEL), Finisterre Island (FIN), Lookout Point (LOO),and Ragged Island (RAG). All wind measurements, except LOO and WAT wereat 10 m AGL. The LOO station used a 6 m mast. The WAT wind sensor wasmounted at 15 m AGL on a pole extending 1.8 m from the side of a B.C. TelephoneCompany Microwave tower. The DAI 10 m mast was mounted at the base of theDaisy Lake Dam. Thus the total instrument elevation above the dam was 6.75 m.All wind data are one hour averages.3.2.1 Summary of surface wind dataThe wind data for the period of the field program are summarized by wind rose diagrams,in figure 3.3. These diagrams are representations of the frequency of wind occurrenceby direction, in various wind speed classes. Frequency is the radial coordinate in 10%increments. The "arms" of the rose point in the direction from which the wind is coming.The speed class is indicated by the thickness of the "arm" — increasing thickness meanshigher speed. Speed classes are in increments of 2 m s -1 from 0 to 20 m s'. It should beemphasized these are not long-term wind roses, but the results of just one winter season.The exception is Mount Strachan which is a summary of wind data from the winters of1985/86 and 1986/87, and does not include the field season.Several interesting features can be noted from the wind roses. In Squamish andChapter 3. Observational program^ 35Cheakamus river valleys, north of Howe Sound, surface winds are frequently light andmostly bidirectional. This bidirectionality is a consequence of topographic channelling.Light winds are partially a consequence of greater surface roughness when compared withsurface roughness over the sea to the south. Near Squamish, topographically inducedbidirectionality is again apparent. Here, the frequency of stronger winds, particularlyfrom the northern to eastern quadrants, is much greater. This indicates the importanceof gap wind events in the winter time wind climatology (at least for this year). Bidi-rectionality is less apparent at Defence Island, as the fjord widens so that topographicchannelling is decreased. The wind roses from stations in western Howe Sound, Port Mel-lon and Langdale, show bidirectionality and a high frequency of northerly light winds.Both of these wind roses also show a large frequency of light northwesterly winds, dueto katabatic drainage flow down the western slopes of Howe Sound. The Pam Rocksand Finisterre Island wind roses, show bidirectionality and a high frequency of strongnortherly winds indicating the relative importance of gap winds here. The wind rose forRagged Island, in the less topographically constrained southern end (mouth) of HoweSound, is not bidirectional, but shows a high frequency of northeasterly winds. MountStrachan on a mountain ridge along the eastern side of Howe Sound and above the to-pographic channelling, has a wind rose showing frequent strong easterly winds, as doesPoint Atkinson which is "around the corner" from the mouth of Howe Sound.DEFENCE ISLAND BRUNSWICK POINTSQUAMISN RIVER DAISY LAKE ALTA LANE SDUAMISH TOWN SCHIANISH RIRPCGRTPAM ROCKSMOUNT STRACHINRAGGED ISLAND FINISTEFtRE ISLAND POINT ATKINSON LOOKOUT POINT36Chapter 3. Observational programFigure 3.3: Wind rose diagrams for October 1987 until April 1988. Concentric rings arefrequency in 10 % increments.Chapter 3. Observational program^ 373.3 Vertical profilesWhile the surface network described in the previous chapter gave a reasonable picture ofthe horizontal details of surface wind flow, it said nothing about the vertical structureof wind and temperature. Consequently, during gap wind events, vertical soundings ofwind, temperature and moisture were made from the Squamish River delta at the headof Howe Sound, just south of the town of Squamish (figure 3.2). This was accomplishedusing an AIRsondeTM system which consisted of the following components:• a helium balloon which carried the instrument package aloft.• an AIRsondeTM instrument package which included: an electronic aneroid barome-ter, a "dry" thermistor, a "wet" thermistor (for dry- and wet- bulb temperature),and a radio transmitter to send this information to the ground station. These in-struments were contained in a styrofoam case shaped like a propeller. The wholepackage rotated as it ascended, ventilating the temperature sensors located at theends of the propeller "blades".• the AIRsondeTM ground station which received and decoded the radio signal fromthe AIRsondeTM, placing the data on cassette tape.• the meteorological theodolite used to visually track the balloon and instrumentpackage.In total, eighteen AIRsondeTM flights were made during four gap wind events. The date ofeach flight superimposed on a plot of the down-channel component of the maximum dailywind at Watts Point (WAT) shown in figure 3.4, indicates that most of the significantgap wind events were sampled.The altitude of AIRsondeTM observations was determined by converting the pressuremeasured by the barometer, to a height using the hydrostatic equation. The meanChapter 3. Observational program^ 38horizontal wind between two levels was found by locating the balloon at two times,subtracting the two horizontal locations to find a distance, and then dividing by thetime interval to find the velocity. The balloon location was found by combining theelevation and azimuth angles from a theodolite with the balloon elevation from the on-board barometer. The expected accuracy of theodolite derived wind velocity, AU, is equalto the square root of 2 times the error in horizontal location divided by the observingtime interval:AU = ./2-AX T (3.1)AX can be found as a function of the balloon elevation angle, 0, the balloon altitude, H,and the error in estimating the balloon elevation angle, AO, by simple trignometry as:AX = H tan AOThis results in the following expression for the expected error in theodolite / barometerderived wind speed measurements:AU = H tan AOAT sin 2 0 (3.3)Since the balloon is carried downwind from the theodolite location, errors in theodoliteazimuth angle do not contribute significantly to computed wind velocity errors and wereleft out of the error analysis. For values of H below 2000 m, using typical values of 0 (30°)and a pessimistic AO of .5° (the smallest resolvable angle increment on the theodolite usedwas .1°) the maximum estimated wind velocity error is 2.5 m s -1 . If a more optimisticAO value of .2° is used, the maximum wind velocity error below 2000 m is 1.0 msin 2 0(3.2)3.3.1 Summary of vertical profile dataComposite vertical profiles of wind and potential temperature (0) from the three casesrepresented by groups of solid triangles in figure 3.4 are shown in figures 3.5, 3.6, andChapter 3. Observational program^ 39Figure 3.4: Down channel component of the Daily maximum wind at Watts Point (WAT)and AlRsonde flights during the field season. Times of AlRsonde flights are indicatedby triangles. AlRsonde flights represented by solid triangles are included in compositeprofiles.3.7. In each of these figures, four profiles of 0 are plotted, and 500 in layer mean u andv wind components averaged over all four flights are shown. The dashed crosses indicate± 1 standard deviation from the mean wind. The wind representation is a hodograph:the wind at the indicated level "blows" from the centre of the hodograph to the plottedpoint.All three composite hodographs show a northeasterly wind maximum below 1250in, winds decreasing above this level, and usually increasing again above 2250 in butfrom another direction. Case 1, January 30-31, (figure 3.5) is examined in more detailthrough the rest of the thesis. This hodograph shows peak northeasterly winds in the500 — 1000 m layer (labelled 750 in figure 3.5a) which decrease to near zero, and thenincrease and become northwesterly above 2250 m. A similar pattern is shown in theChapter 3. Observational program^ 40hodograph for case 2, February 23 — 24 (figure 3.6a), except that winds above 1750 mbecome light southeasterly. The case 3, March 15 — 16 (figure 3.7), hodograph also showsrelatively strong northeasterly winds below 1750 m which increase above 2250 m, froma northeasterly direction.The composite potential temperature profiles all show evidence of a neutral or lessstable layer below 1000 m, and indicate another neutral or less stable layer between about1200 and 2200 m. The neutral layer below 1000 m is mechanically well mixed, whereasthe top of the elevated less stable layer indicates the upper boundary of the outflowingcold air from the interior. This is confirmed by the hodographs. The strongest outflowingwinds in each case are located below about 1000 m, and the winds below about 2200m are distinct from those above, having different directions and speeds. The separationof the two near neutral or less stable layers seems to be due to nocturnal radiationalcooling of the surface, the effects of which are mixed by mechanical turbulence only intothe lowest 1000 m. This separation is much less distinct in the afternoon soundings (seefigures 3.5b and 3.7b), where surface radiational cooling is offset by solar radiation whichheats the surface resulting in thermal / mechanical mixing penetrating the full depth ofthe outflowing air.The potential temperature profile for case 1 (figure 3.5b) shows a lower, nearly neu-trally stratified layer (below about 1000 m) which cools with time. This diurnal coolingis due to nocturnal radiant energy losses at the surface, but could also be attributedto increased advection of cold air from the interior source region, or katabatic drainagedown the fjord sides (which is also driven by nocturnal radiational cooling of the sur-face). The lower layer is surmounted by a stable layer which underlies another less stablelayer extending to about 2500 m. The upper and lower near neutral layers are almostindistinct in the late afternoon sounding. The vertical profiles of potential temperaturefor case 2 (figure 3.6b), show very little change over time. Since all soundings were madeChapter 3. Observational program^ 41in the early morning (eliminating diurnal effects), little change in cold air advection isindicated. The potential temperature profiles indicate a layer of relatively low stabilitybelow 800 m, and another between 1200 and 2000 m. These would be connected byconvective thermal mixing in the afternoon to form one deep layer. The case 3 potentialtemperature profiles (figure 3.7b) show an initially neutral layer below 2600 m in the lateafternoon. Overnight the bottom of this layer cools while the upper part warms, and itdecreases in height to about 2000 m, with a distinct layer below 1000 m forming. Thediurnal behaviour is similar to that observed in the case 1 vertical profiles (figure 3.5).This confirms the hypothesis that two less stable layers observed on most profiles becomeone during daytime due to convective mixing from instability caused by solar radiationabsorbed by the surface, and are separated again at night due to surface radiant energylosses which cool the layer below 1000 m.16:10 PST Jan. 30, 198823:30 PST Jan. 30, 19886:00 PST Jan. 31, 19889:30 PST Jan. 31, 1988OOOO00• coEC 0o 0cri^(NIw>OOO -Chapter 3. Observational program^ 4217)Ca)C00.E0U0.••• ..^.^..... .^.^...•..^• .•.^..• •12502250• •^•2750•...3250..... 3750-10^-5^0^5^10U component (m/s)a)Ob)265 270 275 280 285 290Potential Temperature (K)Figure 3.5: Composite of AlRsonde observed profiles of a) wind, and b) potential tem-perature at Squamish town for case 1 (January). Winds are 500 m averages. Flight timesare: January 30 1988 16:10 and 23:30 PST; and January 31 1988 6:00 and 9:30 PST. Thedashed crosses indicate +1 standard deviation from the mean wind.0OOo>0OO6:50 PST Feb. 23, 19888:30 PST Feb. 23, 19887:40 PST Feb. 24, 19889:50 PST Feb. 24, 1988 Chapter 3. Observational program^ 43a)CE000nso...-10^-5^0^5^10U component (m/s)a)b275 280 285 290 295 300 305Potential Temperature (K)Figure 3.6: Composite of AIRsonde observed profiles of a) wind, and b) potential tem-perature at Squamish town for case 2 (February). Winds are 500 m averages. Flighttimes are: February 23 1988 6:50 and 8:30 PST; and February 24 1988 7:40 and 9:50PST. The dashed crosses indicate +1 standard deviation from the mean wind.a).• . 17po• :• s . '•• -.^tiso•• • .^. .225o..• 250^32.50O17ia)c 0E0Ob)17:30 PST Mar. 15, 198800:15 PST Mar. 16, 19887:15 PST Mar. 16, 198810:55 PST Mar. 16, 1988OOOOChapter 3. Observational program^ 44-10^-5^0^5^10U component (m/s)275 280 285 290 295 300 305Potential Temperature (K)Figure 3.7: Composite of AlRsonde observed profiles of a) wind, and b) potential tem-perature at Squamish town for case 3 (March). Winds are 500 m averages. Flight timesare: March 15 1988 17:30 PST; and March 31 1988 0:15, 7:15 and 10:55 PST. The dashedcrosses indicate *1 standard deviation from the mean wind.Chapter 3. Observational program^ 453.4 Synoptic observations for the case studiedThe two previous sections described and summarized mesoscale surface and AIRsondeTMobservations made during the course of the field program. Synoptic scale features formthe meteorological backdrop in which mesoscale outflow winds develop. This section willdescribe the synoptic scale observations for the event studied in detail in the rest of thethesis — January 30 to February 2, 1988. Detailed mesoscale observations for this eventare described in chapter 5 where they are compared to numerical model results.3.4.1 Synoptic scale featuresThe synoptic setting for January 30 to February 2 is typical of moderate gap windevents along the west coast of North America. A ridge at 50 kPa (figures 3.8a - 3.10a)builds offshore, increasing its amplitude, while a deep 50 kPa trough in the interiorintensifies. This configuration aloft results in north to northeasterly airflow and coldair advection over the coastal zone. Associated with this pattern aloft, a large areaof surface high pressure forms to the east of the upper level ridge over Alaska, Yukonand Northern British Columbia (figure 3.8b). Surface radiational cooling in this highpressure zone helps to further decrease the temperature, increasing the air density andsurface pressure. As the upper level ridge (figures 3.8a to 3.10a ) increases in amplitudeto the north and moves eastward, the surface high pressure zone moves southward in theinterior of British Columbia (figures 3.8b to 3.10b). Cold low level air associated withthe surface high pressure area is partially trapped over the interior plateau by the CoastMountains, allowing the large surface pressure gradient (figure 3.10b) to form across theCoast Mountains. An arctic front located in a surface trough of low pressure separatesthe leading edge of cold arctic air associated with the area of high surface pressure, fromthe warmer air which it is displacing. The passage of this front marks the onset of outflowChapter 3. Observational program^ 46wind through the fjords dissecting the Coast Mountains.In a study of a much stronger outflow wind episode, Jackson (1993) found an initiallysimilar synoptic scale setting. However in that case, a 50 kPa low like that seen in figure3.8a, continued to deepen and move south of Vancouver Island, placing the region innortheasterly flow aloft, resulting in much stronger gap winds. In the present case, theupper level low propagated to the east (rather than southwards down the coast), hencesignificant northeasterly flow aloft never developed over the coastal zone, and the gapwind strength through the fjords was less.Chapter 3. Observational program^ 47a)b)Figure 3.8: a) 50 kPa chart for January 29, 1988 04:00 PST. b) Sea level pressure chartfor .January 29, 1988 10:00 PST. For a), heights are in metres. For b) pressure is inmillibars (1 mb = .1 kPa).Chapter 3. Observational program^ 48a)b) Figure 3.9: a) 50 kPa chart for January 30, 1988 04:00 PST. b) Sea level pressure chartfor January 30, 1988 10:00 PST. For a), heights are in metres. For b) pressure is inmillibars (1 mb = .1 kPa).Chapter 3. Observational program^ 49a)b) Figure 3.10: a) 50 kPa chart for January 31, 1988 04:00 PST. b) Sea level pressure chartfor January 31, 1988 10:00 PST. For a), heights are in metres. For b) pressure is inmillibars (1 mb = .1 kPa).Chapter 3. Observational program^ 503.5 Summary of observational programThe observational program, comprising continuously recorded hourly surface observationsat several stations, and vertical profiles at select times during gap wind events, was ableto help answer only some of the important questions about gap winds sought in thiswork. This is discussed further in chapter 5 in relation to model validation. The fieldprogram itself however was a qualified success. There were very little data lost fromthe surface network, and nearly all of the gap wind events during the program weresampled with AlRsondesTM. The wind and temperature data seemed reliable, however thebarometric data from the stations with electronic aneroid barometers appeared unreliable.AIRsondeTM wind measurements made by visually tracking the balloon were prone toerror, and difficult to make at night.There were no strong gap wind events during the field season, so that a moderateevent was chosen for analysis and modelling. The spatial resolution of data, as wellas the temporal resolution of vertical data made analysis of detailed flow structure (forexample hydraulic effects discussed later) impossible. There were not enough gap windevents sampled to be able to use observations to answer questions about interactionsbetween the flow and external boundary conditions. However, despite these difficulties,the observations provide the most detailed analysis to date of gap winds in Howe Sound,and are very useful for model validation.Chapter 4Numerical modelling: RAMS strategy and configuration4.1 IntroductionEnvironmental fluid dynamics are inherently non-linear. As such the only way of re-alistically modelling detailed environmental flows (except in a few idealized cases), iswith a numerical model (or possibly a physical scale model). Such a model consists ofa set of differential equations — the Navier Stokes equations (or close approximations tothem), which due to their non-linearity, must be solved numerically. This can be done bydefining variables on a rectangular grid (in one, two or three dimensions), using variablesat neighbouring space locations to give spatial derivatives, and using variables at neigh-bouring time locations to give temporal derivatives allowing the system to be steppedforward in time.Using a 3-dimensional numerical model to examine detailed flow structure can beextremely informative, since vertical and horizontal model resolution is typically muchgreater than that of an observational network. In this study, the application of a 3-dimensional mesoscale numerical model provides detailed information about gap wind.This information would otherwise be impossible to obtain without the prohibitively ex-pensive use of aircraft. Model output, because it represents a dynamically balancedrealization of the flow in which all the important terms of the primitive equations aredefined, allows important forces to be diagnosed by reconstructing terms in the primi-tive equations. Because a numerical model represents nature by a computer code, it is51Chapter 4. Numerical modelling: RAMS strategy and configuration^52possible to perform numerical "experiments" with it, which cannot be done in nature.These experiments, or sensitivity tests, can be performed by varying initial and bound-ary conditions and noting changes in the flow which ensue. Because of computationalconstraints, this was not done with the full 3-dimensional numerical model in the presentstudy. Rather, a simpler model was used for sensitivity experiments, which are describedin chapter 7.Models can give useful information, but they must first be validated by compari-son with observations, or possibly with an analytic solution to an ideal linearized case.Conclusions based on poor modelling results are dubious. A model may not produce arealistic simulation for several reasons:• incomplete or inaccurate parameterization of sub grid scale effects• errors or inadequacies in the numerical schemes used in the model to solve thespatial and temporal differential equations• coding errors in the model• user errors resulting from incorrect application of the model• incorrectly specified boundary or initial conditions• non-optimal choices of model parameters and optionsTo validate the model, the episode (described in section 3.4) for which surface andAIRsondeTM observations are available was chosen for simulation. This is the first time amesoscale numerical model, incorporating actual topography and observations as initialand boundary conditions, has been applied to this class of atmospheric flow. Technicalobstacles, stemming from the large range of atmospheric and topographic horizontallength scales which are important for gap winds, make realistic simulations difficult.Chapter 4. Numerical modelling. RAMS strategy and configuration^53Gap winds are mesoscale phenomena since they occur through, and are enclosed by,narrow gaps in mountain barriers. Evidence from numerical and analytical modelling(chapters 5 and 7) indicates that internal structure of gap flow is governed by small scalehydraulics which are intimately linked to small scale topography. However, gap windsoccur because the fjords are relatively long, providing a path for air to flow through amuch larger scale mountain range. The atmospheric precursors (boundary conditions)to a gap wind event, occur at synoptic scales in the atmosphere – scales of hundreds tothousands of kilometres. Thus there are three horizontal scales of importance:• valley width of order 1-10 km• valley length (mountain width) of order 100 km• synoptic scale atmospheric boundary conditions of order 1000 kmThis range of scales presents a problem for a numerical model. To resolve small scalefeatures of the flow, grid spacing (distance between adjacent nodes in the model grid)must be small. To contain and model the atmospheric, and to a lesser extent topographic,boundary conditions of the flow, the horizontal domain must be large. This implies alarge number of grid points and a small time-step which is computationally expensive.These technical difficulties are surmounted by using a nested model – one which hasgrids with fine resolution (small horizontal grid spacing, domain size, and consequentlytime step) nested within coarse resolution grids (larger horizontal grid spacing, domainsize and time step). For this study, a model with four nested grids is used. Anotherway these difficulties are overcome, is by effectively "nesting" the largest model gridinto a much larger scale (hemispheric) forecast model (Canadian Meteorological CentreFinite Element Model — CMC FEM), and allowing the time dependent lateral boundaryconditions of the mesoscale model to be "nudged" to match those of the larger scalemodel.Chapter 4. Numerical modelling: RAMS strategy and configuration^54The 3-dimensional, mesoscale numerical model capable of gap wind simulations, andchosen for this study is the Colorado State University Regional Atmospheric ModellingSystem (CSU RAMS). RAMS was applied to the case described in section 3.4 for whichobservational data from the field program were available. For a description of RAMSrefer to appendix A.4.1.1 Modelling strategyRAMS was used to simulate a moderate gap wind event for which surface and AIRsondeTMdata are available because:• the data can be used to validate the model and assess its applicability for this classof wind flow by comparing model output with observations• once validated, the model output can be used to describe detailed features of gapwind flow• validated model output can be used to find the forces important in gap wind flow• model output can suggest simpler models (analytic or numerical) which would beeasier to interpret and apply to forecast and analyse gap wind eventsImplicit in the above progression is the assumption that successful model validation atthe scale of the observing network (stations are 10's of kilometres apart) leads to realisticresults on the smaller scales contained in the model (1.25 km horizontal spacing on grid4). Because the atmosphere is a non-linear system, it could be argued that this would notbe the case for simplistic, linear models. However, RAMS is not a simple, linear model.RAMS is a 3D quasi-Boussinesq model incorporating the important non-linearities ofatmospheric flows, so that validation at a slightly larger scale should indicate a degree ofrealism at the scale of the model resolution.Chapter 4. Numerical modelling: RAMS strategy and configuration^55The event chosen for simulation had the strongest surface winds of any during thefield program for which AIRsondeTM vertical soundings were available. It is a moderategap wind event — there were no strong events during the course of the field program. Inthe years following the field program, there have been a few extreme events, which couldhave been chosen for simulation (Jackson, 1993). However in those events, the surfacenetwork and AIRsondeTM data were not available for model verification, so the presentcase, for which verification data were available, was chosen. In future studies, it wouldbe worthwhile to simulate an extreme event.The simulation was started several hours before the onset of outflow, and continuedfor a total of 40 hours, which was less than the life span of the outflow event. It wasable to contain the onset of the event, but not the termination, which is a more gradualfeature. This was due primarily to a limitation in the computer resources available.4.2 RAMS configurationRAMS is a very versatile mesoscale model. It is capable of operating in two or threedimensions; in one or several nested grids; in hydrostatic or non-hydrostatic mode; andwith or without topography, to mention just a few of the possible options. In thischapter the RAMS configuration used for this study will be described. A more detaileddescription of the model, and of the parameters used in this simulation is provided inappendix A.4.2.1 Model parametersThe important parameters and options of RAMS used in these simulations are listedbelow:Chapter 4. Numerical modelling: RAMS strategy and configuration^56non-hydrostatic; horizontally variable initial conditions and time dependent lateral bound-ary conditions; moisture as a passive tracer (no clouds, cloud forming or precipitationprocesses - gap winds are dry); rigid lid upper boundary condition (no other choice possi-ble with horizontally variable fields and non-hydrostatic equations); solar and terrestrialradiation permitted on all grids (computed every 540 seconds); semi-implicit acousticmodel; second order leapfrog (horizontal) advection and second order forward (vertical)advection; five grid levels in the soil ranging down to 1 m below the surface; surfaceroughness length of 1 m over land (dominant vegetation type is coniferous forest withrocky terrain giving high form drag)and computed from wind speed over water.4.2.2 Grids and nestingAll grids in the model use the Arakawa type C grid stagger. Four grids were nested tobring the grid spacing from 60 km (required to efficiently resolve the synoptic scale) to1.25 km (required to effectively resolve the fjord topography). Four are necessary becausegrid size ratios between neighboring grids greater than 4:1 can result in problems withwave and energy reflection at the grid boundaries (Walko, 1988).The RAMS nesting scheme implements two-way interaction as described by Clarkand Farley (1984). Briefly, at the boundaries of a fine grid, values are interpolated fromthe coarse grid in which it is nested, whereas in the grid interior, fine mesh values areaveraged to replace the coarse mesh value which they surround. The grid spacing, numberof grid points, total size, and time step of each of the four grids used in this simulationare shown in table 4.1. The location and horizontal extent of each grid is shown in figure4.1.Grid 1, with a horizontal extent of 1440 by 1740 km is just large enough to containthe synoptic atmospheric boundary conditions to gap wind flow. The grid spacing of 60km is able to resolve ocean, Coast Mountains, Interior Plateau and Rocky Mountains (seeChapter 4. Numerical modelling: RAMS strategy and configuration^57grid AX (km) Nx Size W-E (km) Ny Size N-S (km) AT sec1 60 25 1440 30 1740 902 20 26 500 35 680 453 5 42 205 46 225 154 1.25 38 46.25 58 71.25 5Table 4.1: Grid structure of RAMSfigure 4.2). Topographically, the valleys dissecting the Coast Mountains are unresolved,so that gap winds are not modelled.Grid 2, encompasses an area of 500 by 680 km, and is not large enough to contain thesynoptic scale atmospheric forcing. At 20 km grid spacing, it can only crudely resolvemajor valleys dissecting the Coast Mountains. Gap winds are not adequately representedon this grid (see figure 4.3)Grid 3, extends 205 by 225 km horizontally. The 5 km grid spacing can resolve thelarger scale features of major valleys - see figure 4.4. Gap winds can be resolved on grid3, although not in great detail.Grid 4, with a horizontal extent of 46.25 by 71.25 km, must rely on intergrid commu-nication from coarser grids at its lateral boundaries for synoptic scale information. The1.25 km grid spacing (see figure 4.5) is sufficient to resolve the major terrain features ofHowe Sound, and can represent gap winds in some detail.Vertically, all grids had the same 30 levels, with vertical grid spacing starting at 100m at the surface, and stretching by a factor of 1.15 for each successive level above thesurface to a maximum separation of 1000 m. This results in vertical levels at the followingelevations (in metres) for thermodynamic points (where variables other than velocity aredefined) in the grid stagger:Chapter 4. Numerical modelling: RAMS strategy and configuration^580, 100, 215, 347.25, 499.338, 674.238,875.373, 1106.679, 1372.680, 1678.581, 2030.367, 2434.921,2900.159, 3435.183, 4050.460, 4758.029, 5571.733, 6507.493,7507.493, 8507.493, 9507.493, 10507.493, 11507.493, 12507.493,13507.493, 14507.493, 15507.493, 16507.493, 17507.493, 18507.493.These levels are for grid points with a surface elevation of 0 m, for other grid points,the terrain following or "sigma-Z" coordinate scheme (Gal-Chen and Somerville, 1975)transforms the vertical elevation according to the following formula:(z — zs )* = H((H — z3)) (4.1)where z* is the height of a particular grid point in the terrain following coordinate system;z s is terrain elevation at that grid point; z is the untransformed vertical coordinate; andH is the height of the model top at which the z* coordinate surface becomes horizontal(ie. 18507.493 m in this case).4.2.3 Initial data and boundary conditionsRAMS initial fields are horizontally variable (as opposed to horizontally homogeneous).Thus initial gradients are allowed to vary horizontally across the domain. This is animportant feature of RAMS, allowing it to provide realistic pre-gap wind initial condi-tions. The data used to initialize (and provide lateral boundary conditions for) RAMSgrid 1 were interpolated from the 0 hour prognosis of the CMC FEM. This dataset incor-porates real data (surface data, aircraft observations, radiosonde profiles, satellite data,etc.) with previous CMC FEM runs to produce a dynamically balanced dataset. This ispreferred over straight interpolation of real data, as there is less likelihood of the initialand boundary data producing errors (spurious waves for example) in the simulation.Chapter 4. Numerical modelling: RAMS strategy and configuration^59As well as allowing horizontally variable initial conditions, RAMS permits time-dependent lateral boundary conditions. This means that fields on the lateral boundaryof grid 1 are nudged (Davies, 1976) toward the time interpolated values obtained fromCMC FEM output. The CMC FEM data used for this purpose were at 6 hour intervals.The nudging procedure is weighted so that a weight of 1.0 means at that grid point, theCMC FEM data are matched; a weight of 0.0 means the CMC FEM data are ignoredand the RAMS modelled field is accepted completely; and a weight between 0.0 and1.0 means there is some balance between the CMC FEM data and the RAMS modelledfield. The nudging was applied 12 grid points from the edges of grid 1 with the followingweights:0.8,^0.8,^0.8,^0.8,^0.8,^0.7,^0.7,^0.6,^0.5,^0.5,^0.3,^0.2.The number and value of weights used was large. It was found in test runs with smallweights that RAMS had difficulty accurately simulating the large scale features on grid 1— there were spurious gradients (in perturbation pressure and vertical velocity) createdin areas where nudging ended. Because of the grid communication scheme (where finemesh values overwrite the corresponding coarse mesh values, except at the edge of thefine mesh), the use of large weights across grid 1 results in the direct effects of the nudgingbeing felt on the lateral boundaries of grid 2, and not at all directly on grid 4.Interpolation of CMC FEM data to RAMS initial fieldsThe CMC FEM data were obtained at 2° latitude by 2° longitude spacing at the following11 pressure levels (kPa):100, 85, 70, 50, 40, 30, 25, 20,^15,^10, 5.The following were specified at each of these levels on the horizontal grid: U wind compo-nent, V wind component, potential temperature, geopotential height, and mixing ratio.Chapter 4. Numerical modelling: RAMS strategy and configuration^60Additionally, over the ocean, sea surface temperature was provided.To create a RAMS initial field, CMC FEM data were first vertically interpolatedonto 40 isentropic levels with the horizontal spacing still the original 2° latitude by 2°longitude. The terrain elevation was found for each horizontal location by interpolationfrom a 0.5° latitude by 0.5° longitude terrain dataset obtained from NCAR. The finalstep was to horizontally interpolate all of the fields (including terrain) to model grid 1,creating RAMS initial fields.4.2.4 TerrainDue to the importance of interaction between small scale topography and the atmo-sphere for gap wind flows, representation of topography in the model which resolves theimportant small scale topographic features was critical. One problem with the data in-terpolation procedure described above is the terrain goes from a resolution of .5° to 2°(matching the CMC FEM data spacing). It is then interpolated to the 60 km resolutionof grid 1. Usually in the RAMS initialization procedure, terrain for other grids is theninterpolated from grid 1 terrain. This results in terrain on all grids having an effectiveaccuracy of 2°. In order to circumvent this problem, and achieve the best possible ter-rain representation on all grids, high resolution terrain data were inserted at run timefor grids 2, 3, and 4. Grid interaction meant that special care had to be taken to adjustterrain elevations on all grids. On the boundaries of a fine grid, the meteorological fieldsare interpolated from the next coarser grid. This means the terrain on the boundariesof a fine grid must also be interpolated from the coarse grid. The fields in the interiorof a coarse grid which overlays a fine grid are replaced by averages of the surroundingfine grid field values. This means the terrain in a coarse grid interior which overlays afine grid must be the average of the terrain elevations of the surrounding fine grid points.If these adjustments are not made, dynamic imbalances in the model result, causingChapter 4. Numerical modelling: RAMS strategy and configuration^61spurious results and model "blow-up". To avoid this, a terrain adjustment procedurewas followed to adjust the prepared terrain data files making them acceptable to RAMS'nesting scheme.Terrain preparationThe terrain for grid 1 of the model was obtained as previously described, from a .5°dataset interpolated to 2° and then to 60 km (the spacing on grid 1). The terrain datafor the other grids were obtained from an Energy Mines and Resources 1 km dataset.These data were interpolated (using a 2D cubic spline) to 1.25 km, and averaged usinga 25 point (5 X 5) binomial filter to 5 km, and 20 km. The raw 1.25 km, 5 km, and 20km, terrain files were then filtered using a 2D fast Fourier transform to place the data inwavelength domain where all wavelengths less than 4 AX (5 km for grid 4) were removedusing a ramp filter. An inverse fast Fourier transform then placed the data back in thespace domain. These files were then adjusted according to the procedure outlined in theprevious section to allow the grid nest interaction to function properly. The resultingcontoured model terrain can be seen in figures 4.2 to 4.5 for grids 1 to 4 respectively.Tests using other averaging / smoothing / filtering schemes were made, however themodel was quite sensitive to the way in which the terrain is smoothed. In particular, ifthere is much variation at wavelengths less that 20X, then numerical errors grow, ruiningthe simulation.Chapter 4. Numerical modelling: RAMS strategy and configuration^62Figure 4.1: Location and grid spacing of the four RAMS grids used.Chapter 4. Numerical modelling: RAMS strategy and configuration^63Figure 4.2: RAMS grid 1 after smoothing and adjustment. Contour interval is 100 in.Chapter 4. Numerical modelling: RAMS strategy and configuration^64Figure 4.3: RAMS grid 2 after smoothing and adjustment. Contour interval is 100 in.Chapter 4. Numerical modelling. RAMS strategy and configuration^65Figure 4.4: RAMS grid 3 after smoothing and adjustment. Contour interval is 100 m.Chapter 4. Numerical modelling: RAMS strategy and configuration^66Figure 4.5: RAMS grid 4 after smoothing and adjustment. Contour interval is 100 in.Chapter 5Numerical modelling: RAMS resultsThe synoptic context of the case chosen for simulation using RAMS was described insection 3.4. This chapter provides a mesoscale description of the event while comparingobserved data with RAMS output.Several test runs were made (starting from run A), prior to the run presented here. Itwas found that modelled flow evolution was sensitive to the way in which the terrain wasaveraged, the amount of nudging applied to the time varying lateral boundary conditionson grid 1, and the time of day at which the run was initialized. The model runs fromA to Y were incremental improvements in the simulation as errors were eliminated,better methods of terrain averaging and smoothing were developed, and different waysof applying lateral boundary conditions were tried. Most of the earlier runs were of shortduration.The run described here, (run X), was initialized on grids 1 and 2 starting at 04:00 PSTJanuary 30, 1988. After one hour of simulation, grid 3 was added. After a further hourof simulation, grid 4 was added. The model output presented is from hour 10 to hour40 of the simulation (January 30, 14:00 PST to February 1, 20:00 PST). The simulationended at hour 40. The model output were saved at 15 minute intervals, however resultsare shown at 3 hour intervals.Most earlier runs were initialized 12 hours later than the initialization of run X (ie. at16:00 PST January 30, 1988 rather than at 04:00 PST). The runs initialized at this latertime in some cases had better flow representation, especially in the southern part of Howe67Chapter 5. Numerical modelling: RAMS results^ 68Sound, but were unable to simulate the flow reasonably for more than 10 hours. This isthought to be related to initialization of fields on fine grids in complex terrain. In theprocess of initializing fine grids, fields are interpolated from the next coarser grid onto thefine grid. This may result in small errors in the fine grid initial fields (due to differencesin terrain elevation between grids) which can subsequently grow and contaminate thesimulation. By starting a simulation at the beginning of nightfall (in the earlier runs forexample), the model is in a cooling mode with a trend towards increasing atmosphericstability. Any errors near the ground would therefore be unable to dissipate by turbulentmixing and possibly grow during the simulation. There was evidence in support of thishypothesis from several earlier runs, which showed a tendency to pool unrealistically coldair in topographic bowls, especially on grid 3. This resulted in pockets of very stableair which continued cooling and could not be penetrated by the ambient airflow. Thisproblem did not occur when the model was initialized at 0400 PST. By starting thesimulation in the early morning hours, it is expected that errors of this type, arisingfrom the interpolation of fields onto finer grids will be "mixed out" by turbulence asparameterized solar radiation heats the model ground.Comparisons of modelled versus actual data are both qualitative and quantitative,encompassing visual comparisons of time-series, vertical profiles, and horizontal plots aswell as statistical analyses of surface wind and temperature means, standard deviations,root mean square deviations and an index of agreement. The purpose of comparison isto show whether or not RAMS is able to produce a reasonable simulation of a gap windcase, and to validate the use of model output for more in depth analysis of gap wind flow.In depth analysis of RAMS output includes the presentation and discussion of verticalcross sections of wind and potential temperature, and horizontal Froude number plots.Chapter 5. Numerical modelling: RAMS results^ 695.1 Comparison of RAMS output with observationsOutput from RAMS is compared with surface and AIRsondeTM observations for theJanuary 30, to February 2, 1988 event. Directly comparing actual data with model outputmust be carefully considered, since they represent two different kinds of data. Surfaceobservations are hourly averages of wind and temperature at a point 10 m above ground.Near-field local influences on the wind in particular are critically important (although siteselection criteria tried to minimize this). RAMS wind (to which the surface observationsare compared) is the instantaneous wind in a box which is 100 m high by 1.25 km oneach side. Thus the terrain resolution is only 1.25 km (it has been filtered so that actualresolution is even coarser). Consequently, near-field local influences on the wind are notincorporated.AIRsondeTM observations are a vertically tilted atmospheric profile since the heliumballoon is advected downwind as it lifts the instrument package. With an average ascentrate of 1000 m in 300 seconds, this corresponds to a downwind shift of about 1 to 3horizontal grid points (depending on the wind speed) per 1000 m of ascent. AIRsondeTMobserved temperatures are instantaneous, and winds are layer averages. The RAMSoutput to which this is compared is layer averages of wind and temperature in onevertical column near the balloon release point. This horizontal shift in the AIRsondeTMprofile is likely to make little difference, especially since largest displacements will occurat highest elevations where the wind is relatively constant and uninfluenced by terrain.5.1.1 Quantitative evaluation of model performanceRAMS surface wind and temperature fields are compared with observed data using sta-tistical measures recommended by Willmott (Willmott, 1981; Willmott, 1982; Willmottet al., 1985), and applied by Steyn and McKendry (1988) and Ulrickson and Mass (1990).Chapter 5. Numerical modelling: RAMS results^ 70Willmott suggests the following parameters be used for quantitative evaluation of modelperformance:• Observed and modelled means and standard deviations;• Total, systematic, and unsystematic root mean squared differences (RMSD, RMSD S ,RMSDu) between observed and modelled fields. These are defined as (Willmott etal., 1985):RMSD =RMSDS =RMSDU =^N ^N^I • 5E wilPi - oi ri E w i^i=i^i=i^  ^N^1 ' 5E wilPi - oi l2/ E w ii.i^i=i^[N ^,,^N^I • 5EwilPi — PiriEwiL :1^i.i(5.1)(5.2)(5.3)where P, is the predicted and 0, is the observed value; N is the number of stations;Pi is the ordinary least squares estimate of P (P, = a + b0, where a, b are the inter-cept and slope); w i represents the areal weight for each station, and is proportionalto the fraction of the total area that station represents.• The Index of Agreement, d, (d 2 in Willmott et al. (1985)) which is defined as:Nd = 1 — RMSD 2/ [E wi(lPi — 01+10i — 01) 21^(5.4)where O is the weighted mean of the elements contained in 0:N^NO = E wioi/ E w i^(5.5)i=iin the application of these statistics to wind, 0 and P are considered as vectors,and the appropriate vector arithmetic is used.Areal weights for each station are found using the Thiessen polygon technique (Thiessen,1911). Only 12 stations with continuous hourly records in the southern 3/4 of the domainChapter 5. Numerical modelling: RAMS results^ 71ALC BRU DEE DEF FIN HAR LAN LOO MEL RAG SQT WAT8 12 8 22 15 10 19 22 30 16 25 20Table 5.1: Stations and areal weights used in statistical evaluation of RAMS simulation.were used for statistical evaluations. Stations in the northern part of the domain eitherdidn't have continuous records (SQA) or were not well enough situated for representativewind measurements (SQR), so were not included. The stations and their weights areshown in table 5.1, and the locations can be found in figure 3.1.According to the interpretations of Willmott, total RMSD represents the total differ-ence between model and observations. The systematic component (RMSD s ) representsmodel linear bias, whereas the unsystematic component (RMSD u ) represents model pre-cision. The Index of Agreement, d (a dimensionless number), is a measure of the relativeerror of the model, with a range of 0.0 (for no agreement) to 1.0 (for perfect agreement).Figures 5.1a-c show observed and modelled direction, speed, and standard deviationof wind for 31 hours of simulation, averaged over the twelve stations listed in table 5.1.Simulated directions are slightly more easterly than observed in the first part of thesimulation. Average simulated wind speeds show an increasing trend which is not seen inthe observations. Modelled winds are less than observed until 11:00, January 31, whenthey become similar to observed speeds. They become greater than observed wind speedsnear the simulation end. The observed standard deviation of wind velocity is greater thanmodelled by about 2 m s' during most of the simulation. This is likely due to sub-gridscale effects upon the observed wind unresolved in the model. Figures 5.2a and b showwind RMSD and Index of Agreement. Until about 11:00 January 31, the RMSD is near 6s -1 , most of which is systematic, due to the difference between observed and modelledmeans shown in figure 5.1b. The Index of Agreement lies between 0.5 and 0.6 during thisChapter 5. Numerical modelling: RAMS results^ 72Direction Speed Std. Dev. RMSD RMSDS RMSDu d(°N) (m s-1) (m s-i) (m s-i) (m s-i) (m s-i) (_)observed 42.3 6.1 3.7 6.3 5.2 3.5 .59modelled 60.8 4.9 2.3Table 5.2: RAMS modelled and observed wind evaluation statistics spatially averagedover all stations and over the 31 hours of simulation.time. Between 11:00 and 13:00 on January 31, when observed and modelled mean windspeeds are similar, the systematic RMSD becomes small with the total RMSD mainlycomprised of the unsystematic component. The Index of Agreement at this time peaksat 0.83. The RMSD becomes larger again after this time, as the systematic componentagain becomes large when average modelled winds become greater than observed. Theaverages of wind, standard deviation, RMSD, and Index of Agreement over the entiresimulation are shown in table 5.2. The RMSD's are large compared to the mean windspeed, partly because they are found using observed and modelled wind as vectors (notjust as speed values).Similarly, the modelled and observed temperatures averaged over twelve stations, arecompared for the 31 hours of simulation. Averages and standard deviations of observedand modelled temperature are shown in figures 5.3a-b. Modelled temperatures start andend somewhat cooler than observed, but show a similar trend. Observed and modelledstandard deviations are virtually identical. Figure 5.4a presents the total, with thesystematic and unsystematic components of Root Mean Squared Deviation (RMSD) fortemperature. The total RMSD, comprised mostly of the unsystematic part, representingrandom deviations, is fairly constant at between 1.5 and 3 K. However, between 11:00and 13:00, January 31, (the times when the wind field simulation is most accurate) thesystematic RMSD becomes very small and the total RMSD also decreases. The Indexof Agreement for temperature during the course of the simulation, remains high (greaterS0^observedA^modelledg EN •w.3^: ea f&A As AA.^ • -°,0 0- 'a o - •^6., A .,6, A.A A.A.6A 00000-:0,4 y<r!,-(D0.0000U000.00a0^observedA^modelled,000.00 0.0, oaAAAa ao 000 0 00 Aqeao00 Pc)°a-A P.A.A.A pAAL A-A3^o -fAAL_^ 0.0 n 0 0 0 00.0 a° 0.0 -;,AA \o.ayooo co2oPcleAz 6\A AA A \AA^dKA0^observedA^modelledo -3^•Chapter 5. Numerical modelling: RAMS results^ 7318^0 6^12^18Time: January 30 - 31 1988 (PST)18^0 6^12^18Time: January 30 - 31 1988 (PST)18^0 6^12^18Time: January 30 - 31 1988 (PST)Figure 5.1: Time series of observed and modelled: a) wind direction, b) wind speed, andc) standard deviation of wind speed; averaged over 12 stations at each time during thesimulation.a)b)c)^0 ^RMSD total^A^RMSD systematic+^RMSD unsystematicp C,pz:\ zaa000pA n,, so2 2 CA° \ooPA.A.2222o`^A ,+-4-A :A^Ap0^0/^AOA A\ \+++++^++++ 4..\ \O. ^/2IVE,-1-4\+,+-+ ±.4++.+ ±/^+++ \A.A A^AfAN2 -Chapter 5. Numerical modelling: RAMS results^ 74a)18^0^6^12^18Time: January 30 - 31 1988 (PST)b)1.00.6-0.4O.& 000oo^\zo/ \000-^\ o ,0 00c .00^o\^)3oo^000^oo o\o'00020.0-18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.2: Comparison of observed and modelled wind as time series of a) total, sys-tematic, and unsystematic components of the Root Mean Squared Differences; and b)the Index of Agreement.Chapter 5. Numerical modelling: RAMS resultsthan 0.8). Averages of temperature, standard deviation, RMSD and index of agreementover all stations for the whole 31 hours of simulation are shown in table 5.3.As Willmott provides little guidance on values of d which represent "good" or "poor"simulations, the above statistics are compared to those found in other mesoscale simula-tions — Steyn and McKendry (1988) (hereafter SM88) and Ulrickson and Mass (1990)(hereafter UM90). Both SM88 and UM90 applied a hydrostatic predecessor to RAMS(described in Mahrer and Pielke (1977a), Mahrer and Pielke (1977b), Mahrer and Pielke(1978), McNider and Pielke (1981)), to simulate summertime seabreeze circulations inthe complex terrain of Vancouver (SM88), and Los Angeles (UM90). While thermallyforced seabreezes occurring under light synoptic conditions are considerably different fromgap winds, there were no more similar simulations with appropriate evaluation statistics,available for comparison. While the SM88 and UM90 simulations are in complex terrain,the winds are not as severly constrained by topography as gap winds in Howe Sound.Given these considerations, statements about the relative veracity of the different modelsare not valid. However, at least the RAMS evaluation results can be placed in somecontext.SM88 used identical statistics to evaluate wind and temperature fields, except they didnot apply different spatial weights to the observations, and used data from 24 stations, asopposed to 12 stations used here. Their domain was about twice as large as the portionof the RAMS grid 4 terrain validated here however. SM88 had a wind field Index ofAgreement, d which ranged between .41 and .61, with a mean value of .51 over 24 hours ofsimulation. RAMS run X, over 31 hours of simulation had d for wind ranging between .42and .83, with a mean of .59. The SM88 temperature field Index of Agreement, d, rangedbetween .11 and .74, with a mean of .34. RAMS run X had a mean d for temperature of.88, with a range of .75 to .96. UM90 also used the Willmott recommended statistics toevaluate the simulated windfield. They found d ranging between .4 and .75 (but did notcv • Lkao,otsAA A ° °Rg -0^observedA^modelled-@e0 0 acoChapter 5. Numerical modelling. RAMS results^ 76report a mean value). They did not evaluate temperature in their simulation.Despite difficulties in making direct comparisons, the RAMS gap wind simulation per-forms statistically better than SM88 and UM90 mesoscale seabreeze simulations. Thereare problems with the RAMS simulation, especially in the southern part of the domainfor much of the time which will be discussed subsequently, however the relatively goodstatistical evaluation lends confidence to further interpretations of model output.a)18^0^6^12^18Time: January 30 - 31 1988 (PST)b) •A AA .A0 OA .0^ic 0-ob A 48-0 Cr— 46-pko 0`1 0 0^Ll 'A ■0•K 0 0^.L1•.0 0000^observedA^modelled0 -3^18^0 6^12^18Time: January 30 - 31 1988 (PST)Figure 5.3: Time series of observed and modelled: a) temperature, b) standard deviationof temperature; averaged over 12 stations at each time during the simulation.,60 0 0 RMSD totalA RMSD systematicA\n + RMSD unsystematic\--\60 00`10-k._)-,/-i-.-F+ ±:CPQ‘P:99'"99.9.(P'^Z16,++-a)coccChapter 5. Numerical modelling: RAMS results^ 7718^0^6^12^18Time: January 30 - 31 1988 (PST)b) 1.0-0.8.-0.00000006-00000^0 0 '0000000' 0O^0000.6-00.40.20.018^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.4: Comparison of observed and modelled temperature as time series of a) total,systematic, and unsystematic components of the Root Mean Squared Differences; and b)the Index of Agreement.Temperature Std. Dev. RMSD RMSDS RMSD d(°C) (°C) (°C) (°C) (°C) (-)observed -1.3 3.4 2.3 1.5 1.7 .88modelled -2.3 3.4Table 5.3: RAMS modelled and observed temperature evaluation statistics spatially av-eraged over all stations and over the 31 hours of simulation.Chapter 5. Numerical modelling: RAMS results^ 785.1.2 Qualitative evaluation — time seriesTime series of temperature and down-channel wind components were constructed fromthe actual surface observations, and from RAMS model output. These are shown fromfigure 5.5 to figure 5.10. The general conclusion to be drawn from these comparisonsis that RAMS seems to simulate the flow (and temperature) best, both in magnitudeand time response, in the northern and middle part of the region (figures 5.5, 5.6, 5.7a),however the simulation is not nearly as good in the south (figures 5.7b and 5.8a).In the northern and middle parts of the domain, observations and model output showdown-channel winds increasing and temperatures dropping in the afternoon and eveningof January 30. This trend continues until the afternoon of January 31 when winds begindecreasing and temperatures begin increasing at most stations. RAMS, in most placesdoesn't simulate the decrease in wind speed at the end of the simulation particularlywell, tending to maintain the same speed or increase it slightly. Timing of the gap windonset, especially in middle of the domain is quite good (see figures 5.6b and 5.7a). Theten hours of simulation prior to those shown in figures 5.5 to 5.10, had light winds.Observations in the southern part of the domain do not compare favourably withRAMS model output (see figures figure 5.7b and 5.8a). Observed winds here are strongest,whereas modelled winds are weak. Reasons for this are discussed in more detail subse-quently.U)U)CCC0tztU)U)Ev)• 0Ea)b)- observed wind^ rams model winiti3^a^- observed temperaturerams model temperature.........^..................^...- observed temperaturerams model temperatureChapter 5. Numerical modelling: RAMS results^ 7918^0 6^12^18Time: January 30 - 31 1988 (PST)Squamish Airport18^0 6^12^18Time: January 30 - 31 1988 (PST)- observed windrams model wind3^18^0 6^12^18Time: January 30 - 31 1988 (PST)Squamish Town18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.5: Time series of surface observations and RAMS model output for SquamishAirport (SQA) and Squamish Town (SQT)a)afcb)U)0aEI-0— observed wind^ rams model wind— observed temperaturerams model temperature.. . .^.. . . .31–^— observed wind-- rams model windChapter 5. Numerical modelling: RAMS results^ 8018^0^6^12^18Time: January 30 - 31 1988 (PST)Watts Point18^0 6^12^18Time: January 30 -311988  (PST)18^0^6^12^18Time: January 30 - 31 1988 (PST)Defence Island— observed temperature---- rams model temperature18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.6: Time series of surface observations and RAMS model output for Watts Point(WAT) and Defence Island (DEF)a)CDCCCs_c9C0o.?-CDE0b)observed windrams model wind- 3^1.................... ...- observed temperature---- rams model temperatureobserved windrams model wind9,CsE0U?0- observed temperature-- rams model temperatureChapter 5. Numerical modelling. RAMS results^ 8118^0^6^12^18Time: January 30 - 31 1988 (PST)Brunswick Point18^0^6^12^18Time: January 30 - 31 1988 (PST)18^0^6^12^18Time: January 30 - 31 1988 (PST)Finisterre Island18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.7: Time series of surface observations and RAMS model output for BrunswickPoint (BRU) and Finisterre Island (FIN)0o0Csa v?EU)C5aCCCs_c9Ca0L)Cr)a)b)- observed temperaturerams model temperatureChapter 5. Numerical modelling: RAMS results^ 82- observed windrams model wino,18^0^6^12^18Time: January 30 - 31 1988 (PST)Lookout Point............ - observed temperaturerams model temperature18^0^6^12^18Time: January 30 - 31 1988 (PST)- observed windrams model wind11^18^0 6^12^18Time: January 30 - 31 1988 (PST)Ragged Island18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.8: Time series of surface observations and RAMS model output for LookoutPoint (L00) and Ragged Island (RAG)183^ _18^0 6^12Time: January 30 - 31 1988 (PST)Port Mellona)— observed wind---- rams model wind.• ...^........................— observed temperature-- rams model temperature1818^0^6^12Time: January 30 - 31 1988 (PST)Langdale1831^18^0 6^12Time: January 30 - 31 1988 (PST)b)— observed temperature----  rams model temperatureU)CaCCCs0C— observed wind--- rams model windChapter 5. Numerical modelling: RAMS results^ 8318^0^6^12^18Time: January 30 - 31 1988 (PST)aI-Figure 5.9: Time series of surface observations and RAMS model output for Port Mellon(MEL) and Langdale (LAN)a) U)CCsCCaCa00U)0b)c 0C0SCCsE0cJL'f7)— observed wind------^rams model wind3^— observed temperaturerams model temperature3^Chapter 5. Numerical modelling: RAMS results^ 8418^0 6^12^18Time: January 30 - 31 1988 (PST)Mount Harvey18^0 6^12^18Time: January 30 - 31 1988 (PST)— observed wind---- rams model wind31 -18^0^6^12^18Time: January 30 - 31 1988 (PST)Deeks Peak---— observed temperature— rams model temperature18^0^6^12^18Time: January 30 - 31 1988 (PST)Figure 5.10: Time series of surface observations and RAMS model output for MountHarvey (HAR) and Deeks Peak (DEE)Chapter 5. Numerical modelling: RAMS results^ 855.1.3 Qualitative evaluation — vertical profilesFigures 5.11 to 5.14 show observed and modelled hodographs and vertical profiles ofpotential temperature at Squamish. The potential temperature profiles are quite closeto those observed, both in value and shape. An elevated stable layer below about 2800m above ground marks the top of outflowing air. A lower, mechanically mixed neutrallayer near the surface about 1000 m deep is the region of strongest flow. Both observedand modelled hodographs show different speeds and directions below the stable layerthan above it. Winds are stronger and more northeasterly in the outflowing layer. Inthe last vertical sounding shown, figure 5.14, the vertical profile shape is similar, howeverobserved temperatures are several degrees cooler near the surface.• • ......... • • •379584b)-10^-5^0^5^10^15^270^275^280^285^290U component (m/s) Potential Temperature (K)a)O00.1-171OChEcO 0▪ 0.1NLIJOOCa)CEO10^-5^0^5^10^15U component (m/s) Potential Temperature (K)265 270 275 280 285 290Ca)C0E0OOOOOCr)C00Ca 0> 0• C‘IOOOOChapter 5. Numerical modelling: RAMS results^ 86Figure 5.11: a) AIRsonde observed profile at Squamish town, 16:00 PST January 301988; b) RAMS generated vertical profile at same time and location as a)0a)a)00EO0E0caAa)0000000000000 •00E00U)oChapter 5. Numerical modelling: RAMS results^ 87 -10^-5^0^5^10U component (m/s)15^265 270 275 280 285 290b)Potential Temperature (K)-10^-5^0^5^10^15^265^270^275^280^285^290U component (m/s) Potential Temperature (K)Figure 5.12: a) AIRsonde observed profile at Squamish town, 23:30 PST January 301988; b) RAMS generated vertical profile at same time and location as a)•C'a0E00$•- •1486sa18-5^0^5^10^15-1007/7-Ca)CO0E00U)-10^-5^0^5^10^15Chapter 5. Numerical modelling: RAMS results^ 880)a)a)EC0a)U component (m/s)000•zr000O0OO00 0 •265 270 275 280 285 290Potential Temperature (K)a)b)U component (m/s)270 275 280 285 290Potential Temperature (K)Figure 5.13: a) AlRsonde observed profile at Squamish town, 6:00 PST January 31 1988;b) RAMS generated vertical profile at same time and location as a)a)11)0a)U)0cEL 0O' ; 2981'.1.2177^.^'. 07^:x.. I/^5;1,00 :' --------N.'''s-'"---......_._.__I^. •685^. • .'^'.316 .1 -0Ec oo 0oCtlO000Chapter 5. Numerical modelling: RAMS results^ 89OOO0EOU000E clocoI> oo012)^CVL1.1O00-10^-5^0^5^10^15U component (m/s)265 270 275 280 285 290Potential Temperature (K)b)-10^-5^0^5^10^15^265^270^275^280^285^290U component (m/s) Potential Temperature (K)Figure 5.14: a) AIRsonde observed profile at Squamish town, 10:00 PST January 311988; b) RAMS generated vertical profile at same time and location as a)Chapter 5. Numerical modelling: RAMS results^ 905.1.4 Qualitative evaluation — surface windsFigures 5.15 to figure 5.17 show modelled winds as vectors from the second model level at3 hour intervals during the course of the simulation. These can be interpreted as averagesover the 1.25 km by 1.25 km by 100 in high first grid in the model. Only one quarter ofthe model grid points are shown so that vector tails are 2.5 km apart. Observed surfacewinds are superimposed in bold with the vector heads terminating in a •, on the vectorplots of modelled winds.The modelled winds in 5.15a, show light flow everywhere before the onset of gapwinds. As time progresses, down-channel wind speeds increase until the flow becomesfully developed through the fjord (figures 5.16 and 5.17). Observations suggest the flow issomewhat lighter than simulated in the north, and considerably stronger than simulatedin the south. This can only partially be explained by near-field influences of surroundingtopographic and roughness elements on the observations.The general horizontal pattern of gap flow increasing down the fjord from north tosouth matches observations and the conceptual model of gap winds in Howe Sound.Acceleration along the channel observed near the simulation end, is also verified by ob-servation and theory. The simulation's horizontal wind field, while not exactly matchingobservations (especially in the south early in the simulation), seems to capture the mainflow features of the gap wind event. RAMS shows an initial pulse of gap wind devel-oping by January 31, 23:00 PST (figure 5.15d), decreasing slightly after that, and thenincreasing and becoming fully developed after January 31, 11:00 PST (figure 5.16d).As made apparent by the time series comparison, the simulation was quite successfulin northern and central parts of Howe Sound, but there were simulation problems in thesouth. The vector plots give a clearer picture of the possible reasons for the differences.Initially, easterly flow across the southern part of the domain in the model was muchChapter 5. Numerical modelling: RAMS results^ 91stronger than indicated by observations. The core of strong modelled northeasterly windsin southern Howe Sound in figures 5.15 and 5.16 is more northeasterly than observed, withthe axis cutting diagonally across Gambier Island to the western side of Bowen Island,rather than being confined to the main channel between Bowen Island and the easternwall as observations, particularly from Finisterre Island (FIN), suggest (see figure 3.2 forlocations). This is likely due to stronger than observed modelled easterly winds south ofHowe Sound, and at elevation over Howe Sound. This would result in enhanced transfer ofeasterly momentum downward into the outflowing air in Howe Sound, deflecting the coreof strong winds into a northeasterly rather than a northerly orientation. Grid 3 (the 5 kmgrid in which grid 4 is nested), level 3 (layer between 100 and 215 in) winds, (not shown)clearly show the strong modelled winds across the south of the domain originating in theFraser valley. In figure 5.17 the model's easterly winds across the south have decreasedand modelled gap wind flow in the south more closely resembles flow observed 12 to 18hours before (see figures figure 5.7b and 5.8a for example). Enhanced modelled easterlyoutflow from the Fraser River valley would also lead to an increased cold air height at themouth of Howe Sound. According to hydraulic theory, which will be discussed in moredetail in chapter 7, this also would result in decreased gap winds near and upstream ofthe mouth of Howe Sound.It appears the reason modelled flow is stronger and more easterly than observedacross the south is related to terrain resolution, particularly of the Fraser valley in itspath through the coast mountain barrier (referred to as the Fraser Canyon). The FraserCanyon is resolved but not fully contained on grid 3 (figure 4.4), but is partially resolvedon grid 2 (figure 4.3) where it is the only passage through the Coast Mountain barrier thatis resolved. This means low level air on grid 2 can only flow out the Fraser valley. Sincegrid 2 provides boundary conditions to grid 3 and grid 3 provides boundary conditions togrid 4 via the grid interaction scheme, this would result in a spuriously large amount of airChapter 5. Numerical modelling: RAMS results^ 92flowing out of the Fraser Valley. Attempts were made to solve this problem by increasingthe horizontal extent of grid :3, both northwards (so the Howe Sound - Cheakamusvalley could be fully resolved from the coast to the interior plateau), and eastwards (sothe Fraser valley could be better resolved). Although this did result in an improvedsimulation compared to earlier runs where grid 3 was of a smaller horizontal extent, theproblem was not completely solved. To eliminate this problem entirely, grid 3 wouldlikely need a horizontal extent the size of grid 2, resulting in prohibitively large computermemory and cpu time requirements. Since this problem only appears after several hoursof simulation, it is difficult (ie. computationally expensive) to find the minimum size ofgrid 3 required by making tests using successively larger grid :3 sizes.5.1.5 Summary of simulation problemsAs discussed previously, there were two major problems thought to contribute to simu-lation errors.• The first was related to the simulation start time and initialization of fine grids incomplex terrain. When the simulation was started at 16:00 PST, the model was ina cooling and stabilizing phase, and initially small, near surface temperature errorsdue to the initialization of fine grids grew with time. This problem disappearedwhen the model was initialized at 4:00 PST instead.• The second problem, which wasn't satisfactorily resolved, is the lighter and moreeasterly than observed gap wind across the south of the domain. This seems to berelated to terrain representation and resolution in the model. The Fraser Canyonis the only cross mountain channel resolved on grid 2 resulting in too much gapflow from the Fraser valley. Grid 3 was enlarged to better resolve other valleys asChapter 5. Numerical modelling: RAMS results^ 93a)^b)c)^d)Figure 5.15: Surface winds at 3 hour intervals: a) January 30 14:00 PST; b) January30 17:00 PST; c) January 30 20:00 PST; d) January 30 23:00 PST. Observed winds areindicated in bold with vectors that terminate in a •. The spacing between vector tailsrepresents 16 in s-1.t/ 19 794/4 /^/ / / 1I^1 1 • /^/ /'''''^•^o s•• •^• ,^I.^.^„ .^• _— / /9,94 N ^1• I I ^  / /• 1^N. /• •'''''^„^•^•^.............^.^•^." 1- ••-49-29-N - • / /9 '194 / 4 /^/ / / / /^" / / / I ^1 I / J / /• -^; -^• •- ■ ■^/^• \ • , „, //^N.^•^\^\^•• /• •^•• •^I^r ^1 1 /•/ • /9 0 • 1 /^• • //^•^• ••^••••• I^• • /,^•^•-49 29 .1,1 •  Chapter 5. Numerical modelling: RAMS results^ 94a)^ b)c)^ d)Figure 5.16: Surface winds at 3 hour intervals: a) January 31 02:00 PST; b) January31 05:00 PST; c) January 31 08:00 PST; d) January 31 11:00 PST. Observed winds areindicated in bold with vectors that terminate in a •. The spacing between vector tailsrepresents 16 in s-1.Chapter 5. Numerical modelling: RAMS results^ 95a)^ b)Figure 5.17: Surface winds at 3 hour intervals: a) January 31 14:00 PST; b) January 3117:00 PST; c) January 31 20:00 PST. Observed winds are indicated in bold with vectorsthat terminate in a •. The spacing between vector tails represents 16 mChapter 5. Numerical modelling: RAMS results^ 96well as the Fraser Canyon, but this was only partially successful, and limited bycomputing resources available.Some features of an earlier run (run R, not shown), in which these errors had not yetdeveloped, are worth mentioning. Run R, was initialized at 16:00, January 31 1988, 12hours after run X. Consequently, the first problem described in the preceding paragraph,led to serious simulation errors after about 10 hours of simulation. These errors (toocold near the ground) however occurred on grid 3, quite a distance from the region ofinterest and did not seem to influence the simulation on grid 4 before this time. Thesecond problem (too much airflow through the Fraser Canyon), which occurred after 6 to8 hours of simulation, had not yet developed. Consequently, there is a period of time fromhour 3 (after the model had properly initialized on all grids) to hour 7 (before the errorshad time to develop) in the run R simulation, when simulated flow is closer to observedin the domain south near a time of maximum outflow. At this time, run X which wasstarted 12 hours before, showed weak winds in the south due to the second problem,above. Despite an improved flow representation in the domain south, the overall windverification for the entire domain did not show improvement over run X.Despite these problems with flow representation in the south for part of the simulation,RAMS produced a gap wind simulation which qualitatively resembled observations overthe rest of the domain. A statistical assessment of model performance showed that theRAMS gap wind simulation was as good or better than other mesoscale wind simulationswhich were available for comparison.5.2 Analysis of model outputA very useful application of numerical model output, especially in situations where (gen-erally expensive or impossible to obtain) complete data coverage is unavailable, is to useChapter 5. Numerical modelling: RAMS results^ 97model output to provide a detailed analysis. In this study, while a reasonably densesurface observation network was in place, the density and frequency of vertical soundinginformation was sparse. To extend observations and gain further insight into flow details,horizontal and vertical cross sections will next be presented and discussed.5.2.1 Horizontal cross sectionsFigures 5.18 to 5.20 are vector representations of run X winds from grid 4 in vertical level4, at 3 hour intervals from January 30 1400 PST to January 31 17:00 PST. Level 4 of themodel represents the layer between 215 and 347 m AGL, in terrain following coordinates.Superimposed on four of these plots are winds from the nearest AIRsondeTM time andelevation. These figures can be compared with figures 5.15 to 5.17 which show windsin the first hundred metres of the atmosphere. One should note however, that vectorsize is scaled differently in the two sets of figures - the lower layer wind has a maximumvector size (equal to the distance between the starting points of two adjacent vectors) of16 m s -1 , while level 4 winds have a maximum vector size of 20 m s -1 . The two sets offigures are similar, with initially light flow on January 30 14:00 developing into a pulseof stronger gap flow by 23:00 (figure 5.15d and 5.18d), decreasing slightly after that, andthen increasing again and becoming fully developed after January 31 11:00 PST. Thewinds on level 3 are also strong and easterly across the south, which seems to inhibitstrong wind development there and divert it diagonally across Gambier and Bowen Islandrather than down the main channel on the east side of the Sound.Chapter 5. Numerical modelling: RAMS results^ 98a) b)c)^ d)Figure 5.18: RAMS level 4 (279 m) winds at 3 hour intervals: a) January 30 14:00 PST;January 30 17:00 PST; c) January 30 20:00 PST; d) January 30 23:00 PST. Thespacing between grid points indicates 20 my94,N,^•^11.•••• •/^•^•• j^•• 1^•^ f9 "/ • • /^//1•"1///////////1••••1/1•//rrr•///// •\\NI `/////••/1//• •\\\ I,/•'/////1'/ ,^\ \ ` ••\\ 'I1^1^• Si^•/^• • / /•9 .-21 -N^f %929 -N - / //////•\^•^• • /Chapter 5. Numerical modelling: RAMS results^ 99a)^ b)c)^d)Figure 5.19: RAMS level 4 (279 m) winds at 3 hour intervals: a) January 31 02:00 PST;b) January 31 05:00 PST; c) January 31 08:00 PST; d) January 31 11:00 PST. Thespacing between grid points indicates 20 m .Chapter 5. Numerical modelling: RAMS results^ 100a) b)Figure 5.20: RAMS level 4 (279 m) winds at 3 hour intervals: a) January 31 14:00 PST;January 31 17:00 PST; c) January 31 20:00 PST. The spacing between grid pointsindicates 20 mChapter 5. Numerical modelling: RAMS results^ 1015.2.2 Vertical cross sectionsVertical cross sections of potential temperature and down-channel component of windhave been prepared in valley-following coordinates. The valley-following coordinate sys-tem follows the main channel centre along the eastern side of Howe Sound. The modeldata used are from grid points which lie closest to the main channel axis. Interpolationof data between grid points to more closely follow the channel centre line seemed unnec-essary given the density of model data points on grid 4. The exact path chosen for themain channel is indicated by the heavy solid line in figure 5.21. In the along channel vs.z (elevation) plane, wind nearly parallels isentropes (contours of potential temperature).This gives important flow information — whether it is descending or ascending, andwhether layers are becoming thinner or thicker. The isentropes also give atmosphericvertical stratification and stability information.Figures 5.22 to 5.32 show vertical cross sections of the down-channel and verticalcomponents of wind as vectors, superimposed on contours of potential temperature atthree hour intervals, for the lowest 2.6 km of the model domain (the first 13 levels of themodel). The wind vector angle from the horizontal (but not the vector magnitude) isscaled to match the vertical exaggeration of the plots. Below the vertical cross sectionsare line plots of Froude number along the down-channel axis. The Froude number iscalculated from RAMS output, and will be described later. At most times one can notea clearly marked layer below 1.5 km elevation where air is less stable, and down-channelwind component is larger than above this elevation. As the simulation progresses, struc-ture in the layer below 1.2 km elevation becomes more distinct, and a core of outflowingair begins to form (figure 5.24). By January 30 23:00 PST (figure 5.25), a distinct jet ofoutflowing air bounded by the descending 273 K isentrope with maximum down-channelspeeds of more than 10 in s -1 has formed below 1 km elevation. At this time, layers ofChapter 5. Numerical modelling: RAMS results^ 102Figure 5.21: Rams grid 4 contoured terrain with heavy solid line indicating the channelcentre line used in down-channel vertical profiles. The dashed line indicates the downcore direction used in some vertical profiles.Chapter 5. Numerical modelling. RAMS results^ 103increased stability also observed in the vertical profile (figure 5.12) are apparent above1 km elevation. At the termination of this jet (near the down-channel (y) coordinate ofbetween -150 and -160 km in figure 5.25), a zone of rapid deceleration and wind rever-sal is co-located with ascending isentropes. This resembles a hydraulic transition fromsubcritical to supercritical flow (in the zone of descending isentropes), which becomessubcritical again at a hydraulic jump (in the zone of ascending isentropes). While hy-draulic theory is most commonly applied to two layer flow problems involving liquidssuch as water in a channel, enough apparent similarity exists between numerical modeloutput and the flow of water in a channel, to suggest than application of hydraulic theoryto this class of phenomenon would yield useful results. In fact hydraulic theory which hasbeen previously used to account'for related severe downslope windstorms (Long, 1954),is presently enjoying a resurgence in popularity (Durran, 1986). This will be discussedin more detail in the following section describing the Froude number analysis, and inchapter 7.After January 30 23:00 PST, the flow intensity becomes somewhat less, and thenincreases once again reaching a maximum by January 31 11:00 PST (figure 5.29), witha core speed of more than 15 m s -1 at about 200 m elevation. At this time, there is asecond descending layer which has formed to the north with down-channel winds of morethan 11 m s -1 . This feature continues to develop at 14:00 PST (figure 5.30), becomingthe dominant feature by 17:00 PST (figure 5.31), and apparently propagating across theentire domain by the end of the simulation at 20:00 PST as shown in figure 5.32.Above 1.5 km elevation, the winds are no longer strongly channelled by topography,so that the valley following coordinate system is not an appropriate frame of reference.Because of this, small changes in the wind direction can result in changes in the downchannel wind component which are not representative of wind speed changes. Thisaccounts, at least in part, for the large variation in the down channel wind component-160.00^- 150.00^-140.00^-130.00^-120.00^-110.00^-100.v I km )Chapter 5. Numerical modelling: RAMS results^ 104--..^., ._ .. • — a__ .,,...0--,--1 4'284 --...'^.^---:---------- ----^\1.58-^:::^--,-----------728° . '---   ^, -E_le—^_-----------' - r^.,.-,,---N^1 0 ..0_,_..,,_--s.---: . -^ 276 ------..--2?6- -_I' ^.--------%  .2_"1b—-170.003 ,2.52 -ca)-oz01.51 ^-L 0.50 ^-170Figure 5.22: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 14:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number.The horizontal spacing between vector tails represents 11 m s'. Vertical exaggerationis 10X.32.521.51P_IJ-^0.50-170 -160 -150 -140 -130 -120 -110 -100Chapter 5. Numerical modelling: RAMS results^ 105EN-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.v Ikm)Figure 5.23: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 17:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number.The horizontal spacing between vector tails represents 11 m s -1 . Vertical exaggerationis 10X.Chapter 5. Numerical modelling: RAMS results^ 106-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.v Ikm)3 ^2.521.51 ^2u_^0.50 I^-170^-160^-150^-140^-130^-120^-110^-100Figure 5.24: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 20:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.-130.00^-120.00 -110.00^-100..^_^r ^1,),^r) T-^-170.00^-160.00^-150.00^-140.00y (km )-100-120^-1103 ^2.5 -2 -a)c^1.5 -1 —0.5 -0 I^-170 -160^-150^-140^-1303 . 00-_-284 .1.50-•6276.0.5E284-276 .1^I^1 1 11 1 1 1 1 1 1 11Chapter 5. Numerical modelling: RAMS results^ 107Figure 5.25: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 30 23:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.E-170.00^-160.00^-150.00^-140.00^-130.00^-120.001, ( km)32.521.5I^I^I^1 1.1^I^I^1^I^11 1 -110.00^-100.-160^-150^-140^-130^-120^-110^-1001 ^0.5 -0 ^-170Chapter 5. Numerical modelling: RAMS results^ 108Figure 5.26: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 02:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.3.00-2.5&,_2801.576,N^1 . 00-276^ •2 6• 72.-ry• _^•^.1^t -170.00^-160.00^-150.00^-140.00VI km )I^1^1^1 j^111 1111f ,-110.00^-100.-130.00^-120.0032.5E^21.512LL^0.50-170 -160 -150 -140 -130 -120 -110 -100Chapter 5. Numerical modelling: RAMS results^ 109Figure 5.27: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 05:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.Chapter 5. Numerical modelling: RAMS results^ 110-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.V lkm) 3 ^2.5  -21.510.5 -0 ^-170 -160^-150^-140^-130^-120 -110^-100Figure 5.28: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 08:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.-150.00 -140.00V (km)EN11111111111,^1-110.00^-100.-170.00^-160.00 -130.00^-120.003Cr) 2.5E 2a) 1.57:37010.50-170 -160 -150 -140 -130 -120 -110 -100Chapter 5. Numerical modelling: RAMS results^ 111Figure 5.29: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 11:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s'. Vertical exaggeration is 10X.2.52.03.00-205^ 001.5;^ —?)6...,"^/ 1 1,1:11,'1 . 0^,^".r^...,/^.-- 4:2> / I ,^/^72. , ,/ / /— ./ "-. : / / / 1 /^"...-- / /0.5^ A/Z.- /^///'-/'-',.----.---,.-•^.•,^ , m w ".„NChapter 5. Numerical modelling: RAMS results^ 112-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.y^IIsm )3Z13 2.5E 21.501Ii 0.5j-170 -160 -150 -140 -120 -110 -100Figure 5.30: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 14:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s -1 . Vertical exaggeration is 10X.32.521.510.50-170 -160 -150 -140 -130 -120 -110 -100Chapter 5. Numerical modelling: RAMS results^ 1133.00—EN2.507_1.00—/ --.4-...y:/. .--- ...„....._ ..,......._ -.. '''.—.....—0.50= 1 ."-/ ..--^\ 1^./^../..---'--"-- ..."' ,s4\ ./'.... ‘ / ^ .,^ .-.. , /^*---.----.--“--.... \\'...^/^.'0.0 .^■,'...—^.---.--..---'--/•"— •\'''''''.. '-- .—t/1-1-1--a 1 (IT—170.00^—160.00^—150.00^—140.00y Ikm),J I I 11^1 I i.11111111 ,—110.00^—100.—130.00^—120.00Figure 5.31: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 17:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s-1 . Vertical exaggeration is 10X.3Zr) 2.5E 2a) 1.5730LL 0.50-170 -160^-150^-140^-130^-120^-110^-100Chapter 5. Numerical modelling: RAMS results^ 114-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.v Ikm)Figure 5.32: Vertical Cross section oriented along the main channel of Howe Sound forJanuary 31 20:00 PST. The down-channel wind component as a vector superimposed oncontours of potential temperature, is above a plot of the Froude number. The horizontalspacing between vector tails represents 11 m s'. Vertical exaggeration is 10X.Chapter 5. Numerical modelling: RAMS results^ 115above this elevation, which can be seen in the vertical cross sectionsSince the core of strong winds, in this simulation, is not directly along the mainchannel in the southern part of the domain, vertical profiles of potential temperatureand down core wind component were computed and contoured for January 30, 23:00 PST(figure 5.33) and January 31, 11:00 PST (figure 5.34). In this case "down core" is thesame as down-channel except in the south where the core cuts diagonally across Gambierand Bowen Islands. The "down core" path is shown by the heavy dashed line in figure5.21. The figures showing the "down core" wind and temperature profiles are very similarto "down channel" plots of the same time, except as expected the zone of strong windsextends further south.-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.y 1km)Figure 5.33: Vertical Cross section oriented along the core of strongest winds for January30 23:00 PST. Down-channel wind component as a vector superimposed on contours ofpotential temperature. The horizontal spacing between vector tails represents 11 mVertical exaggeration is 10X.Another interesting feature which can be seen in the vertical cross sections is a markedChapter 5. Numerical modelling: RAMS results^ 116-170.00^-160.00^-150.00^-140.00^-130.00^-120.00^-110.00^-100.y (km)Figure 5.34: Vertical Cross section oriented along the core of strongest winds for January31 11:00 PST. Down-channel wind component as a vector superimposed on contours ofpotential temperature. The horizontal spacing between vector tails represents 11 in s'.Vertical exaggeration is 10X.diurnal change in the structure and character of outflowing air. During the night, noctur-nal surface cooling and consequent atmospheric stabilization near the ground, possiblycombined with hydraulic effects discussed in the following section, results in a decrease inthe depth of the mechanically mixed surface-based neutral layer to about 800 m elevation(see figures 5.24 to 5.29). As solar radiation heats the ground during the day, convectionmixes the low level momentum to a greater depth increasing the depth of the surfacebased neutral layer to about 1200 m (figures 5.30 to 5.31).5.2.3 Froude number analysisBecause there are indications that gap wind flow in Howe Sound is similar to the hydraulicflow of water in a channel, Froude numbers from RAMS output were computed andplotted. The Froude number is dimensionless and defined as the ratio of fluid speed toChapter 5. Numerical modelling: RAMS results^ 117the speed of a gravity wave traveling on the fluid interface. In the water analogy, the fluidspeed is the current, and the gravity wave speed is that of a long surface water wave. Ingap winds, the fluid speed is the mean wind speed in the layer of outflowing air, and thegravity wave speed is that of a gravity wave traveling along the "interface" defined by thestable layer which surmounts the outflowing air. An assumption is made that this stablelayer can be approximated by a step change in temperature, which is the simplest wayof treating the problem. By referring to figures 5.24 to 5.29 a distinct stable layer canbe seen. A more complete treatment would consider the air as a continuously stratifiedfluid (Smith, 1985; Smith and Sun, 1987) rather than a fluid of two distinct layers.The Froude number is defined as:F =V 'h^(5.6)gwhere: F is the Froude number; U is the mean speed of outflowing air; g' is the effectiveor reduced gravity defined by:OTOP OBOTg^ X g^ (5.7)OBOTg is gravitational acceleration, 9.8 m s -2 ; °Top is the potential temperature at the topof the stable layer; OgoT is the average potential temperature in the lower (outflowing)layer; h is the height of the outflowing layer and is the layer over which U is averaged.To compute h from RAMS output, it is found as the height from the ground to theinflection point in the 0 vs. Z profile (ie. maximum in 70-d2e - which is where the slopeof 0 vs. z changes most rapidly) where potential temperature begins increasing withheight. This leads to an arbitrary definition of Froude number which forces a two layerstructure on a continuously stratified fluid. This definition of Froude number is used inhydraulic modelling discussed in chapter 7. It is expected that there will be error in theseautomatically computed Froude numbers, so that they should be interpreted and usedas an index only.Chapter 5. Numerical modelling: RAMS results^ 118Flows with Froude number less than 1.0 have gravity wave speed greater than thefluid speed and are termed subcritical. In this case information (disturbances in the flow)can propagate both up and downstream as gravity waves. Flows with Froude numbergreater than 1.0 have fluid speed greater than gravity wave speed and are supercritical.In this case information can only propagate downstream. Flows with Froude numbersequal to 1.0 are critical. In this case the gravity wave speed equals the fluid speed. Theflow has markedly different characteristics depending upon whether it is sub- super- orcritical. In particular, according to hydraulic theory discussed in more detail in chapter7, strongest gap winds will be associated with a supercritical flow regime. Plots of Froudenumber are shown below the vertical cross sections in figures 5.22 - 5.32. Horizontal plotsof Froude numbers are computed and displayed at three hour intervals in figures 5.35 to5.37. In these figures, areas with Froude number greater than .5 are enclosed by a dashedline, whereas areas which are supercritical are shaded. Light cross-hatched areas haveFroude numbers between 1.0 and 2.0, whereas heavy cross-hatched areas have Froudenumbers greater than 2.0.Initially (figure 5.35a-c) only some areas over high terrain are supercritical. Howeveras the gap flow develops (figure 5.35d) patches of supercritical flow, north of Squamish,and downstream of Gambier and Bowen Island begin to form. There is then a decrease inthe extent of supercritical flow in Howe Sound around January 31, 2:00 to 5:00 PST exceptfor the flow across the southern part of the Sound which is due to the too-strong easterlyflow from the Fraser valley. Corresponding to the increase in gap wind flow apparent infigures 5.16d — 5.17 and figures 5.29 — 5.32, there is an increase in the supercriticalarea oriented along the main channel and diagonally across Gambier and Bowen Islandsafter January 30, 23:00 PST (shown in figures 5.36d and 5.37). This corresponds tothe area of strong gap wind flow shown in figure 5.16d and 5.17. In comparing Froudenumber plots with the vertical cross section plots in shown in figures 5.22 to 5.32 it canc)Chapter 5. Numerical modelling: RAMS results^ 119a)^ b)Froude number from RAMS - January 30. 1400 PST Froude number from RAMS - January 30. 1700 PSTFroude number from RAILS - January 30. 2000 PST Froude number from RAMS - January 30. 2300 PSTFigure 5.35: Froude number at 3 hour intervals: a) January 30 14:00 PST; b) January30 17:00 PST c) January 30 20:00 PST; d) January 30 23:00 PST.Dashed line encloses regions with Froude number greater than .5. Light cross hatchedareas have Froude numbers between 1.0 and 2.0. Heavy cross hatched areas have Froudenumbers greater than 2.0.Chapter 5. Numerical modelling: RAMS results^ 120a)^ b)Froude number from RAMS - January 31. 0200 PST Froude number from RAMS - January 31. 0500 PSTd)Froude number from RAMS - January 31. 0500 PST Froude number from RAMS - January 31. 1100 PSTFigure 5.36: Froude number at 3 hour intervals: a) January 31 2:00 PST; b) January 315:00 PST; c) January 31 8:00 PST; d) January 31 11:00 PST.Shading as in figure 5.35.Chapter 5. Numerical modelling: RAMS results^ 121a)^ b)Froude number from RAMS - January 31, 1400 PST Froude number from RAMS - January 31, 1700 PSTc)Froude number from RAMS - January 31,2000 PSTFigure 5.37: Froude number at 3 hour intervals: a) January 31 14:00 PST; b) January31 17:00 PST; c) January 31 20:00 PST.Shading as in figure 5.35.Chapter 5. Numerical modelling: RAMS results^ 122be seen that zones of supercritical flow correspond to regions of descending isentropesand accelerating flow in the vertical cross sections. This is expected from the definitionof Froude number. High Froude numbers across the south of many of these figures arefrom strong easterly flow originating in the Fraser valley, and not related to Howe Soundgap wind.The Froude number analysis of RAMS output shown in figures 5.35 to 5.37 anddiscussed above, indicates a close relationship between gap wind intensity and the Froudenumber. This lends support to the notion that the essence of gap winds may be containedin hydraulic theory, which is a great simplification to the 3D quasi-Boussinesq systemmodelled by RAMS.Chapter 5. Numerical modelling: RAMS results^ 1235.3 Summary of numerical modelling resultsThis chapter has quantitatively and qualitatively compared observations with RAMSmodel output for the case under consideration. The results show that RAMS is capableof producing a plausible gap wind simulation which matches conceptual theory and toa somewhat lesser extent, observations. Modelled surface temperature over the entiredomain, and wind in the northern and central part of the domain are most similarto observations both in magnitude and temporal trend. Modelled vertical profiles ofpotential temperature and wind at Squamish, were very close to observations. Problemswith simulated wind in the south were thought to be due to inadequate resolution of majorvalleys and fjords (except the Fraser valley) on grid 2. This resulted in a concentration ofoutflow through the grid 2 Fraser valley and consequently via the grid interaction scheme,stronger than observed modelled easterly wind across the southern grid 4 domain. Thisgave modelled winds a larger than observed easterly component and accounts for the poorcomparison with observations for part of the simulation in this region. The increasedmodelled gap wind depth which would result from enhanced cold air flow through theFraser valley, could also account (from hydraulic theory) for lighter than observed windsnear the mouth of Howe Sound.Following the evaluation of performance, further analysis of RAMS output was car-ried out to extend observations particularly in the vertical, to improve understandingof gap winds. Vertical cross sections of wind and potential temperature showed threeclearly marked layers: the first, a zone of strongest gap wind flow below about 1 km withneutral stability due to mechanical mixing; the second, a zone of less strong gap windand increased stability from about 1 to 2.5 km ; and the third, ambient air above 2.5km, a stable zone uninfluenced by the gap flow below. Vertical cross sections indicated apossible analogy between gap winds, and the hydraulic flow of water in a channel. ThisChapter 5. Numerical modelling: RAMS results^ 124led to discussion of horizontal contours of Froude number computed from RAMS output.Froude numbers showed areas of supercritical flow located in zones of strongest gap windswhich develop downwind of major obstacles (such as Gambier Island) and channel con-strictions. This agrees well with hydraulic theory and will be discussed more in chapter7. The RAMS modelling has also illustrated the technical difficulties in simulating a realflow of this kind which spans several topographic and atmospheric scales — all of whichmust be resolved. For this kind of simulation, accurate (but appropriately smoothed)representation of the fine scale topography, including all fjords and passes is critical.Chapter 5. Numerical modelling: RAMS results^ 1255.4 RAMS momentum balanceNumerical models such as RAMS which solve a major subset of the full Navier-Stokesequations (ie. the quasi-Boussinesq equations), produce dynamically balanced synthetic"data" at very high spatial and temporal resolution. If a model produces credible simu-lations of a phenomenon, the synthetic data can be used in lieu of real data to providea more complete analysis and understanding of the phenomenon, as has been done withRAMS model output. In addition, the model can be used to extract the forces whichmake up the individual components of the momentum equation. It is these forces whichact to accelerate or decelerate wind, and hence account for its spatial and temporal vari-ation. This chapter will describe and discuss the down- and cross-channel components ofthe momentum tendency in a valley-following vertical slice. A partial motivation for thisis to aid creation and justification of simpler models, by indicating the relative impor-tance of the various forces and by providing an indication of which of them can thereforebe ignored.5.4.1 ResultsThe RAMS momentum equation (equation A.8) which is described in more detail inappendix A, is reproduced here,1^2a poui p000 &bur'at^a Ox73^ 4ADV(po u i )+ poTURB(ui)+( 000' + 1.61ry — rT)ai3 Eij3fui65This equation gives the momentum tendency, as found in the model, and has six compo-nents. The components are the:Chapter 5. Numerical modelling: RAMS results^ 1261. total momentum tendency, (the acceleration) which is a consequence of the othertendencies or forces.2. tendency due to pressure gradient force.3. tendency due to advection of momentum.4. tendency due to parameterized sub-grid scale turbulent diffusion.5. tendency of vertical velocity due to buoyancy.6. tendency due to Coriolis acceleration.The horizontal down- and cross- channel components of the above tendencies (except 5,which is for vertical velocity), were found in a vertical slice which followed the axis of themain channel in Howe Sound. This was done by transforming the horizontal componentsfrom Cartesian (east, north) components to down- and cross-channel components. Thelocation of this valley-following slice is shown in figure 5.21, and was the same used todisplay vertical cross sections of other RAMS fields in section 5.2.2. The down-channeldirection is defined as tangent to the valley-following vertical slice, while the cross-channeldirection is perpendicular. The time selected was January 31 at 11:00 PST, which is nearthe time when RAMS surface wind field was found to agree best with observations (seefigure 5.2). Thirty-six time steps of the model were made (for a total of 180 seconds),at each of which the five tendencies were extracted. The tendencies shown are averagesof these thirty-six values. The use of average values was not strictly required as thetendencies changed little over time, so that use of any one set of the thirty-six wouldhave given a similar result.Figure 5.38 is a vertical plot of the down-channel wind and momentum tendencycomponents at the horizontal location of -143.875 km. Total velocity tendency whichdif  advCarpgftotChapter 5. Numerical modelling: RAMS results^ 127is relatively small, is the sum of the other tendencies. The most important term ispressure gradient force which is balanced primarily by advection, and at low levels alsoby diffusion (friction). These three terms were found to be dominant in other verticaltendency profiles as well (not shown). Figure 5.39 is a vertical plot of down-channel wind0^5^10^15^20^-.01^-.005^0.0^.005^.01DC wind (m/s) DC wind tendency (m/s^2)Figure 5.38: Vertical plot of down-channel (DC) wind speed and momentum tendenciesfor January 31 11:00 PST, at the horizontal location -143.875 km.pgf - tendency due to pressure gradient force; adv - tendency due to advection; dif -tendency due to parameterized turbulent diffusion; tot - the actual total tendency dueto all of the others; cor - tendency due to Coriolis effect.and absolute value of the down-channel momentum tendencies, horizontally averaged overthe slice. Because some tendencies, most notably pressure gradient force and advection,fluctuate greatly on either side of zero in the horizontal, averaging the actual valuesChapter 5. Numerical modelling: RAMS results^ 128results in partial cancellation which under represent their relative importance. This iscorrected by looking at average absolute values of tendencies in order to get a pictureof the relative importance of each. The dominant terms, especially near the surface arepressure gradient, advection and diffusion. The importance of diffusion decreases above1000 m, becoming first similar in magnitude to, and eventually smaller than, the Coriolisand acceleration term. Figure 5.40, showing the cross-channel wind and absolute valueof the cross-channel momentum tendencies, gives a similar picture. Pressure gradient,advection and diffusion are the dominant forces in the gap wind below about 1000 melevation. The Coriolis force becomes equal in magnitude to advection and pressuregradient above 2500 m, while diffusion tends to zero. This is expected since the frictionaldrag exerted by the surface (the dominant source of diffusion in the model) decreasesaway from it.Figure 5.41 is a horizontal plot of down-channel wind and tendencies, vertically av-eraged below 679 m and not including the first level. The first level is excluded, as it isset equal to level 2 in the model formulation. Clearly pressure gradient force, balancedby advection and to a lesser extent diffusion, are most important. Coriolis force and thetotal tendency are much smaller by comparison. There are large horizontal fluctuationsin pressure gradient force and advection tendencies, with one being a mirror image of theother. Areas where the wind speed is increasing down the channel are marked by positivepressure gradient force tendencies, and by negative advection tendencies. The pressuregradient force is acting to increase the speed down the channel, explicitly resulting in anegative advection tendency. Figure 5.42 which is a horizontal plot of cross-channel windand tendencies vertically averaged below 679 m, gives a similar picture. Diffusion be-comes an important force when the winds are strong. The large fluctuations in pressuregradient force indicate that this force is not solely the result of a steady synoptic pressuregradient, but that hydraulic pressure gradients due to fluctuating gap wind depth areChapter 5. Numerical modelling: RAMS results^ 1290^2^4^6^8^10 12DC wind (m/s)0.0^0.001^0.002^0.003^0.004abs DC wind tendency (m/(s*s))Figure 5.39: Vertical plot of horizontally averaged down-channel (DC) wind speed andabsolute value of down-channel momentum tendencies for January 31 11:00 PST.Legend is the same as in figure 5.38.Ec0>a)w-- pgf^ advdiftotCOrChapter 5. Numerical modelling: RAMS results^ 130CD0^2^4^6^0.0^0.001^0.002^0.003^0.004CC wind (m/s) abs CC wind tendency (m/(s*s))Figure 5.40: Vertical plot of horizontally averaged cross-channel (CC) wind speed andabsolute value of cross-channel momentum tendencies for January 31 11:00 PST.Legend is the same as in figure 5.38.---- tot- cor \\^\- pgf^ adv ^difChapter 5. Numerical modelling: RAMS results^ 131important. In summary, pressure gradient force, balanced by advection, and to a lesserextent, by diffusion, are the dominant forces in this gap wind simulation.-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 5.41: Horizontal plot of down-channel velocity and down-channel momentumtendency, vertically averaged below 679 m for January 31 11:00 PST.Legend is the same as in figure 5.38.5.4.2 ImplicationsThe important forces for gap winds simulated by RAMS, are pressure gradient, advection,and to a lesser extent, parameterized turbulent diffusion. The influence of Coriolis forceOn down-channel momentum tendency is, as expected, small. The flow was in near steadystate, so the total tendency also was small.These findings can be used to aid creation of simpler models. Such models should, ata minimum, contain the pressure gradient force, and advection. Turbulent diffusion or6-3-6Chapter 5. Numerical modelling: RAMS results^ 132-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 5.42: Horizontal plot of cross-channel velocity and cross-channel momentum ten-dency, vertically averaged below 679 m for January 31 11:00 PST.Legend is the same as in figure 5.38.Chapter 5. Numerical modelling: RAMS results^ 133friction, while of lesser importance, could also be included. Pressure gradients are dueto horizontal variation in pressure at a constant elevation. Pressure varies horizontallybecause the weight of the atmosphere above a horizontal plane changes. This is dueto horizontal variations in air density, caused mainly by temperature variations. Insearching for simpler models of gap wind flow, two approaches will be taken. The first,expanded upon in chapter 6, is to consider gap wind flow of constant depth, so thathorizontal pressure gradient at the surface is due to different atmospheric weights abovethe gap wind (ie. the pressure gradients are synoptically imposed). The second, andmore realistic, described in chapter 7 is to allow synoptically imposed pressure gradients,but also to permit the depth of gap wind flow to vary, which also results in horizontalpressure gradients, and is analogous to hydraulic channel flow.Chapter 6Simple analytic modelsThe use of a full 3-dimensional mesoscale model for diagnosis and forecasting gap windsroutinely is not practical. This is because a 3D mesoscale model capable of realisticallysimulating such an event, would take too long to execute on even the fastest computerspresently available. In addition, the technical expertise required to use such a modelwould make implementation in a.forecast office difficult. Thus it would be useful to findsimpler models to simulate the flow. While simple models will not be capable of producingdetailed comprehensive simulations, they may be able to provide enough information tobe useful. Overland and Walter (1981), Reed (1981), and Mass and Albright (1985) madesuccessful use of the Bernoulli equation to explain strong gap, and downslope-like winds.Toward this, the first step is the elucidation and testing of the simplest analyticmodels possible. When considering the flow of air in a channel such as Howe Sound, itis possible to derive very simple analytic relations to describe the wind, by eliminating"small" terms from the momentum equation and either ignoring or finding a suitableparameterization for surface friction. In this chapter, two such models are developed andcompared to observations and RAMS simulation output. The usefulness and applicabilityof these models are discussed. This provides impetus to the development of a morecomprehensive model in chapter 7.134Chapter 6. Simple analytic models^ 1356.1 TheoryThis section presents the momentum equation and make several simplifications to it inorder to apply it to wind flow in a channel of constant elevation. The derivation followsthat of Jones (1985), except that here an analytic solution for the wind speed is found,whereas Jones used numerical methods. The momentum equation in vector notation is:dI7 VP — 1 dr^ fk x V dz+ --dt^p p31^2^ 4(6.1)where: 17 is the vector wind, t is time, p is air density, P is pressure, f is the Coriolisparameter, k is a unit vector directed upwards, and T is the eddy stress. In this equation:term 1 is the Lagrangian acceleration (ie. the acceleration following the flow); term 2 isthe pressure gradient force, term 3 is the Coriolis force, and term 4 is friction. In orderto simplify this equation the following assumptions will be made:• The channel is straight, and aligned along the x direction.• Term 3, the Coriolis term can be ignored. As the wind is topographically con-strained by the channel, geostrophic adjustment is inhibited. This is supported bythe fact that velocity tendency due to the Coriolis effect was found to be small inthe chapter 5.4 force balance analysis (see figures 5.38 — 5.42).• The friction term (4) can be parameterized using a drag coefficient parameterizationafter Deardorff (1972).The surface stress, 7, = pu* can be set equal to CDu 2 , where CD is a drag coefficientand u is the 10 m wind speed. According to Deardorff (1972), if h is the height of thePlanetary Boundary Layer (in this case the neutral layer of gap wind flow), and r = 0Chapter 6. Simple analytic models^ 136at z h, then the friction term, 4, can be approximated:1 dr —1 Ts —CDU2 (6.2)p dz^p hwhich assumes the drag is exerted throughout the boundary layer. Under neutral andstable conditions, 6.2 is a poor approximation because the stress doesn't increase linearlywith height. Deardorff (1972) modified this equation to incorporate stability:1 dr —Cu 2p dz^hC = cCD c = 1 for unstable conditionsc = 2.8 for neutral and stable conditionsTherefore equation 6.1 can be simplified to:du^d ( u2 1^Cu2dt^dx k 2 h—1 dPwhere = --p dxThe balance between pressure gradient, friction and acceleration represents a geotripticwind. Implicit in the formulation is that u in the friction term, which is meant to be a 10m wind, is the same as u in the acceleration term, which is an average speed over depthh. If friction is neglected altogether, the result is a form of the Bernoulli equation:du d (u 2 ) —1 dPdt^p dx^ (6.5)which can be integrated to give:U2 UO2 AP=^— (6.6)where u 0 is the initial speed, AP is the pressure difference between the end point andthe initial point, and u is the Lagrangian velocity. For u 0 = 0 this reduces to:—2APu=p(6.3)(6.4)(6.7)Chapter 6. Simple analytic models^ 137This result describes the flow neglecting rotation, friction and changes in elevation andwill be called the "Bernoulli" model. Incorporating friction, equation 6.4 can be solvedanalytically. This is done by substituting 0 = 12 into 6.4 which results in:2dc4,^2Cdx^hwhich has a solution:u 2^rah^-2Cx= = 2C + Ae hOne can find A, by letting u u0 at x 0, resulting in:9^-2CxU =^0,6 --)e h^ (6.10)C^Cwhich is the "Friction" model. For u0 = 0 this simplifies to:h /^-2Cxu=^h (6.11)after a long time in a long channel, this reduces to:u= C (6.12)which represents the upper boundary of steady state speed.To see that the above solution reduces to the Bernoulli equation in the limit as C^0,one can rewrite the Bernoulli equation (equation 6.7) in terms of the horizontal pressuregradient as:u = V2yx^ (6.13)The Friction model (equation 6.11)is:(6.8)(6.9)L. — e h-2CxU (6.14)Chapter 6. Simple analytic models^ 138which in the limit as C ---* 0 is indeterminate (= 96 ). To resolve this, L'hospital's rule isapplied:-2Cxhu 2 =^- e-2C x HMG litc lirn u 2^h71^dCC-40 OldCeC h )u 2^2xh(6.15)(6.16)(6.17) u = V2qx (6.18)which is the same as the Bernoulli result.The Friction model (equations 6.10 and 6.11) is visually depicted in figure 6.1 showingwind speed as a function of distance down-channel and boundary layer height over dragcoefficient, h/C, for a pressure gradient of .005 Pa The Friction model neglectsEarth's rotation, pressure gradients resulting from channel elevation changes, and changesin outflow depth. The effects of varying channel cross section - width constrictions andexpansions - are also not included in the formulation. This model represents a balancebetween friction, an externally imposed pressure gradient, and acceleration.6.2 Results - comparison with observations and RAMS outputIn order to assess the two simple analytic models - Bernoulli and Friction - comparisonswith observations and RAMS output will be made for four times during the episode. Thetimes chosen span the RAMS simulation at six hour intervals. They are (PST): January30, 23:00; January 31, 05:00; January 31, 11:00; and January 31, 17:00. The stations usedfor comparison from north to south are: Squamish Airport (SQA), Squamish townsite(SQT), Watts Point (WAT), Defence Island (DEF), Brunswick Point (BRIJ), FinisterreIsland (FIN), and Lookout Point (LOO).The Friction and Bernoulli models have modest input data requirements. The BernoulliChapter 6. Simple analytic models^ 139Figure 6.1: Visualization of Friction model. Wind speed along channel is representedon the vertical axis as a function of distance down channel and boundary layer heightdivided by drag coefficient (h / C). A pressure gradient of .005 Pa m -1 (5 mb / 100 km)is used.model only needs a horizontal pressure gradient (change in pressure between two points),and a down-channel wind speed at the channel head. In addition to these, the Frictionmodel needs an estimate of boundary layer height (h), and drag coefficient (C).There was some difficulty in estimating the horizontal pressure gradient at specifictimes. A mean pressure gradient found from a synoptic weather map central to all fourtimes gave a value of .004 Pa m'. The pressure gradient found by using the reduced sealevel pressure at SQR and LOO, was between .002 and .003 Pa m -1 , while that foundusing SQT and LOO gave values between .0083 and .0092 Pa m -1 . The higher pressuresChapter 6. Simple analytic models^ 140observed at SQT could be due in part to the presence of a deeper layer of cold air over SQTthan SQR. A simple hydrostatic calculation indicates that a 4 ° temperature differenceover a depth of 1000 m could account for this, however the surface temperatures areslightly colder at SQR. It was found that the calibration of the electronic barometers usedat these stations changed between the beginning and end of the field season. The pressuredata were subsequently found using a linearly variable calibration, which assumes thebarometer calibration changed gradually and at a constant rate over the field season.This may not be the case, and could at least account in part for the difference. Becauseof this uncertainty, results using both values of horizontal pressure gradient at each timeare shown. The starting down-channel wind speeds were found from the average of windsat Squamish Airport and Daisy Lake. The initial velocity and pressure gradients usedare shown in table 7.3.The boundary layer height, h, was found by inspecting the vertical profiles in figure3.5 and lie between 500 and 900 m. A mean value of 800 in was chosen as appropriate.The drag coefficient, C, is more difficult to estimate, in part because it is smaller overwater than over land. Garratt (1977) in a review of drag coefficients over oceans andcontinents, suggested the following be used for neutral flow over water:C = .51 x 10 -306 (6.19)where u is the 10 m wind speed. This results in a value of .0015 for winds of 10 m s'andassumes that wave action is fully developed. This is not the case during gap wind eventswhen sea state is fetch limited, so actual drag coefficients over water would be less. Overland, form drag due to uneven topography, as well as frictional drag are important. Anaverage value suggested over land is C = .01 which corresponds to a roughness length,z0 of .2 m (Garratt, 1977). A value of C higher than .01 over land could be appropriatein Howe Sound due to the rugged terrain and aerodynamically rough vegetation.Chapter 6. Simple analytic models^ 141An appropriate drag coefficient for Howe Sound is likely somewhere between the valuesfor land and water (between .001 and .01), since the sides of the fjord are aerodynamicallyrough land, while the bottom is relatively smooth water interspersed with frictionallyrough islands. Drag coefficients are formulated for 10 m winds, while the wind speedused is a layer average. Thus, drag coefficient values should be less, since layer meanwind speed is greater than the 10 m wind. These estimates result in h / C values possiblyranging from 5 — 90 x 104 , with a value of 10 5 being chosen as most appropriate.Figures 6.2 and 6.3 compare observed down channel wind speeds with those calculatedfrom the RAMS simulation, Bernoulli model, and Friction model. In these figures and insubsequent similar figures, the flow is from right to left (north to south) and the horizontalcoordinate matches that of RAMS vertical cross section plots. Two lines are plotted foreach model, one for output from the pressure gradient between Squamish River (SQR)and Lookout Point (LOO), and the other for output from the pressure gradient betweenSquamish Town (SQT) and LOO.The Bernoulli model, which should represent the upper bound of wind speed, is higherthan observed everywhere, and much higher than observed in the large pressure gradientscenario. It shows a monotonic increase in speed along the channel. The Friction model,which also shows a monotonic increase and mostly higher than observed wind speeds, iscloser to observations than the Bernoulli model due to the inclusion of friction. The lowerpressure gradient scenario (based on pressure differences between SQR and LOO), bestmatches the observations. Neither model is able to represent decreases in wind speedalong the channel. Inclusion of variable drag coefficients over land and water would haveresulted in slightly flatter curves from the starting point at horizontal coordinate -100to -126 (over land) in figures 6.2 and 6.3, producing a somewhat better agreement withobservations.0 -30•25 •201510•5•..................................................................................... ..........-^":".••••-,.....:::---obsRAMSF-SQRF-SQTB-SQRB-SQT.-- ........................................b)30 •25 •2015105obsRAMSF-SQRF-SQTB-SQRB-SQT•-•-a........-.... ...... .,Chapter 6. Simple analytic models^ 142a)January 30, 23:00 PST-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)January 31, 05:00 PST,......,.....■...■....■. ■.. ..... ...■....... . ..... ...... ...... . ...... ............^:'"".S................^.."...■.. ....................... ......,"......... .................-- - • , .. . .. . .. . .....--... ..•".^..... ...... .•• •...-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 6.2: Comparison of observed down-channel winds with winds calculated from:RAMS simulation; Friction model; and the Bernoulli equation for January 30 23:00 andJanuary 31 05:00.The boundary layer height divided by drag coefficient (h / C) value for the frictioncalculation is 10 5 . The line labelled "obs" is observed data; "RAMS" is RAMS modeloutput; the prefix "F-" is output from the Friction model; the prefix "B - " is output basedon the Bernoulli model; the suffix "SQR" means the SQR — LOO pressure gradient wasused; and the suffix "SQT" means the SQT — LOO pressure gradient was used.0 obsRAMSF-SQRF-SQTB-SQRB-SQT'^•• . - • • „a)3025E 20-0 1510a50January 31, 11:00 PSTb)E302520151050Chapter 6. Simple analytic models^ 143-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)January 31, 17:00 PSTobs^ RAMS•■■  F-SQRF-SQTB-SQR- B-SQT•• • •^•• •^•^•• •-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 6.3: Comparison of observed down-channel winds with winds calculated from:RAMS simulation; Friction model; and the Bernoulli equation for January 31 11:00 andJanuary 31 17:00.Legend as in figure 6.2.Chapter 6. Simple analytic models^ 1446.3 DiscussionTwo simple models of wind flow in a channel have been presented which result fromsimplifications to the momentum equation. The Bernoulli model is the balance betweenhorizontal pressure gradient and acceleration, while the Friction model also includesfriction. Neither model explicitly includes horizontal pressure gradients resulting fromvariable gap wind depth or channel base elevation, or horizontal variations in channelcross section. Both models show a monotonic increase in wind speed, and winds mostlystronger than observed.These models would be most applicable in constant elevation channels of relativelyuniform cross section, where hydraulic effects, such as transitions between subcriticaland supercritical flow, do not occur. The minimal ability of these models to accuratelyrepresent gap winds in Howe Sound (with both accelerating and decelerating winds alongthe channel), implies that they do not fit the traditional gap wind classification. Infact, Howe Sound gap winds violate several assumptions implicit in these models. Themodel described in chapter 7 will relax the most limiting assumptions to include pressuregradients resulting from changes in channel elevation and gap wind depth, to incorporatevariations in channel cross section along the fjord, and therefore to implicitly include thehydraulic effects which were observed in the RAMS simulation.Chapter 7Hydraulic channel flow: an analog to gap windOne goal of this research is to find models of gap wind flow which are both computa-tionally and conceptually simpler than 3-dimensional mesoscale numerical models. In-vestigations using simple analytic models with fixed boundary layer heights and channelbase elevations (chapter 6) point out their inadequacy in representing anything but hy-draulically subcritical, monotonically increasing, down-channel flow. Since gap winds area low level flow of dense air, constrained horizontally by fjord walls, and vertically by aninversion, they would seem to resemble the flow of water in a channel. Moreover, resultsfrom numerical modelling show similarities between gap wind flow and hydraulic flow(chapter 5): descending, supercritical flow in zones of strong wind; sharply ascendingflow where wind rapidly becomes light and subcritical. For these reasons, it seems thathydraulic channel flow theory is a potentially useful analog to gap wind flow.This chapter will describe basic hydraulic theory and extend it to include synopticpressure gradients and friction. The model thus created will then be applied to airflow inrectangular and realistic channels, and compared with observations. Finally, the modelwill be used to test the sensitivity of gap wind to initial and boundary conditions.7.1 Hydraulic theoryHydraulic theory has been used extensively for many years (often in a civil engineeringcontext) to study the flow of water in open channels. The developments described in thissection follow closely those which can be found in classical hydraulics textbooks, such145Chapter 7. Hydraulic channel flow: an analog to gap wind^ 146as Henderson (1966), except that here gravity (g) is replaced by effective (or reduced)gravity (g') to account for the different densities of water and air; a different formulationfor friction is used; and an externally imposed synoptic pressure gradient is included(something which is clearly of minor importance when considering the flow of water).Simplified atmospheric applications of hydraulics (which only considered inviscid flowthrough rectangular channels and no synoptic pressure gradient) can be found in thestrong katabatic wind theory of Ball (1956) which has been applied by Arakawa (1968),and Pettre (1982) to strong wind flow in valleys. Pettre (1982) studied the "Mistral" —a low level flow similar to gap wind which occurs through the RhOne valley in France.He applied hydraulic theory for a rectangular channel of constant elevation with noexternal pressure gradient or friction, and used it to interpret wind observations alongthe valley. He found that observed strong flow occurred downwind of the major horizontalcontraction in the valley, which was in agreement with hydraulic theory. A sharp decreasein wind speed near the end of the valley was attributed to a hydraulic jump. Aircraftobservations of wind and potential temperature corroborated the hydraulic interpretationof the winds. Pettre (1982) provides a precedent for the application of hydraulic theoryto phenomena like gap wind. The assumptions implicit in the extension of hydraulics togap wind, will be discussed after the theory is developed.Consider two layer incompressible channel flow with the upper, less dense (p2 ) fluidat rest, while the lower moving fluid of higher density (p i ) is relatively shallow (height h).Assume flow in the lower layer is parallel to the ground and constant in the cross-channeland vertical directions, so it varies only in the down-channel direction. This is meant tobe analogous to gap winds' lower, nearly neutral layer of strongest winds surmounted bya stable layer. Further assume the hydrostatic approximation holds, and the time andlength scales are sufficiently small that Earth's rotation can be ignored. Let the channelbe aligned along the x direction with the configuration and variables shown in figure 7.1,Chapter 7. Hydraulic channel flow: an analog to gap wind^ 147and assume the flow is steady-state (it- = 0). The steady-state assumption is supportedby RAMS results in which the total velocity tendency was shown to be small (section5.4).With these assumptions, the momentum equation is:du^,dh^,de 1 dP 1 drdx +9 dx +g dx^dx^dz °1^2^3^4^5(7.1)where u is down-channel speed; h is thickness of the lower layer; P is large scale pressureat the top of the layer; e is the channel elevation; T is the eddy stress; g' (p1pip2) x g =(92 - 9i ) x g is reduced gravity; and p is air density. In equation 7.1: term 1 is velocityadvection; term 2, is a horizontal pressure gradient force due to a gradient in the thicknessof the dense air; term 3, is a horizontal pressure gradient force due to changes in valleybottom elevation; term 4, is an external pressure gradient force imposed at the top of thesystem (alternately referred to as a "synoptic pressure gradient"); and term 5, is friction.The equation of continuity in the outflowing air is:Q = uA = uhb = constant_ Q dQ 0dx^dxwhere A is channel cross sectional area, b is mean width, and Q is total discharge whichis conserved along the channel.If one divides equation 7.1 by g', and uses continuity to replace u by g the resultingequation is:^Q 2  dA dh de^1 dP^1 dr— 09' A3 dx + dx + dx + gip dx g' p dzwhere, by the chain rule:dA d(hb) -dh^dbdx^dx^dx + - dx(7.2)(7.3)(7.4)(7.5)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 148Figure 7.1: Definition sketch for airflow in a channel.If one defines the channel slope, So as positive "down hill", then cd-t- = —So . If the externalpressure gradient is defined as a "slope", Sp, and made positive for decreasing pressuredPalong x, then —gi1 p —dz. = —Sp. The momentum equation can now be written:hQ 2 d7)^1 dz(17-(1^^Q2  -b)dh = Sp + So + g'A 3 dx g'p—g'A3 dx(7.6)The Froude number as before is defined as:F =  ^ (7.7)fg'hChapter 7. Hydraulic channel flow: an analog to gap wind^ 149If friction is parameterized as in chapter 6, then the momentum equation can finally bewritten:dh^P h dr)(1 — F2)—dx =Sp + So^b dx C F2 (7.8)This equation lies at the heart of the hydraulic model. It is similar to standard hy-draulics treatments (for example Henderson (1966)) except that gravity has been replacedby reduced gravity, an external pressure gradient is included, and friction is parameter-ized as discussed in chapter 6. Despite its apparent simplicity, the equation can describe avariety of complex flow situations. It incorporates pressure gradients which are externallyimposed, pressure gradients due to changing channel elevation, and pressure gradientsdue to changing boundary layer depth. It can incorporate friction, and channels of vari-able cross section. This equation relaxes many of the most limiting assumptions of theanalytic models described in chapter 6. This will be discussed further in section 7.2.As discussed in chapter 5, Froude number determines the flow regime: if the Froudenumber is less than 1, flow is subcritical; if the Froude number is greater than 1, flowis supercritical; and if it is equal to 1, flow is critical. Since the Froude number is theratio of fluid speed to wave speed, supercritical flow means that fluid travels faster thangravity waves on the fluid interface. Therefore, in supercritical flow, fluid disturbancescan only propagate downstream — no "information" can propagate upstream, so that it iscontrolled by upstream conditions. Supercritical flow is directly analogous to supersonicflow in gases with Mach number greater than 1. In subcritical flow which is controlledby downstream conditions, information can propagate both up and downstream.7.1.1 Hydraulic flow regimesEquation 7.8 permits solutions of different characteristics depending upon whether theflow is sub- or supercritical, and the sign of the right hand side of the equation (ie.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 150the steepness of the channel and pressure slope compared to friction and the amount ofhorizontal contraction). At each location along the fjord, it is possible to find the criticaldepth, h,, the depth at which the flow at that location would be critical (F = 1). This isfound by setting the Froude number to 1 in equation 7.7 and solving for h c . For channelsof rectangular cross section, this is simply h, = 13/ -112 (after Henderson (1966)). Forg' A 2non-rectangular channels, this will in general have to be found iteratively since A is anon-constant function of h. The critical speed can also be defined as the speed when theflow is critical: ti c = which can be found directly once h, is known.If the flow depth is below the critical depth, then the speed will be greater than thecritical speed and the flow will be supercritical with a Froude number greater than 1,and vice-versa for subcritical flow. It is the occurrence of supercritical flow which createsthe strongest winds in a channel.In channels of constant slope and cross section it is possible to define a flow state calleduniform flow (Henderson, 1966), in which state the fluid thickness is constant = 0),and the pressure and channel slope terms are exactly balanced by friction (since withconstant cross section the contraction term — F2 h cil;^•in equation 7.8 is zero):dxSP+So=CF 2 (7.9)Uniform flow could really only exist for long channels of uniform slope, roughness andcross section. The flow in such a channel would asymptotically tend toward uniform flow.It can be seen that if the channel is horizontal (S0 = 0), and since Sp = lig7 (with thepressure gradient force, = _ip r. as in chapter 6), the condition of uniform flow reducestou^i1 hCwhich is the same as equation 6.12 and was the result found in the friction model afterthe flow had evolved over a long time (as t --+ oo). Uniform flow will have a certain(7.10)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 151depth, Ito , called the uniform depth, that can be determined for a given location bysolving equation 7.9, which in general must be solved iteratively. Locations where thetotal slope, ST (= Sp + S0 ), is zero or negative, have undefined uniform depths. Eventhough gap wind flow in natural channels is probably never uniform, (the channel crosssection varies so the contraction term on the right hand side of equation 7.8 is non-zero)the concept of uniform flow along with that of critical flow, is useful in understandingpossible hydraulic flow regimes in channels where variations in cross section are negligible.Situations where the total slope, ST, is greater than the friction term for critical flow,must have supercritical uniform flow and therefore a uniform height, It o , less than thecritical height, II,. Such slopes are called "steep". Situations where the total slope, ST,is less than the friction term for critical flow, must have subcritical uniform flow andtherefore a uniform height, h o , greater than the critical height, h.,. Such slopes are called"mild". If the total slope equals the friction term for critical flow, then the flow is critical,and the slope is called "critical". Flows with total slopes that are horizontal, or adversecannot have uniform flow (since friction and opposing slopes would eventually decreasethe wind speed to zero, giving infinite uniform height)(Henderson, 1966).It is difficult to apply equation 7.8 where the flow crosses transitions between sub-and supercritical, since several of the terms become zero, making large or infinite. Anadditional complication is that equation 7.8 does not incorporate the loss of momentumand energy which occurs in a turbulent hydraulic jump. This will be treated later byconsidering conservation of momentum.The concept of controls is a very important one in hydraulic theory. A control is achannel feature that fixes the flow in its locality. A control can act to force subcriticalflow upstream and supercritical flow downstream, when flow becomes critical at thecontrol. A control is the only location where the flow can transit from subcritical tosupercritical. The reverse transition, however, from supercritical to subcritical, whichChapter 7. Hydraulic channel flow: an analog to gap wind^ 152occurs as a hydraulic jump does not in general occur at a control, although its locationis determined by a control further downstream (Henderson, 1966).Whether or not a feature will act as a control, depends on both the boundary condi-tions (pressure slope, terrain slope, amount of horizontal contraction, and friction), andthe flow itself (discharge, speed and depth). Under certain flow conditions a feature mayact as a control while under other conditions it will not. If a feature acts as a control, thenthe right hand side of equation 7.8 will change signs from negative to positive. This canoccur when the slope changes from "mild" to "steep", or near the location of maximumhorizontal contraction. The reverse change, from positive to negative, may result in ahydraulic jump, although this will usually occur further downstream. A fixed boundarylayer height at the channel terminus, like a reservoir, acts as a control on upstream flow.Figure 7.2 shows schematic examples of gap wind through the above features in flowsituations where they do and do not act as controls. In river channel hydraulics otherfeatures such as weirs, flumes and sluice gates may also act as controls.subcritical features act as controlshydraulic jumpsupercritical supercriticalP1subcriticalmild slope subcriticalsteep slopeChapter 7. Hydraulic channel flow: an analog to gap wind^ 153contractionfixedendpointsubcritical - no controlsU "'"••••••■- P1mild slopesteep slopecontractionfixedendpointP2 supercritical - no controlssteep slopecontractionfixedendpointFigure 7.2: Longitudinal profiles of channel flow height through various features that: doact as controls; don't act as controls because the flow is too slow and deep (subcritical);and don't act as controls because the flow is too fast and shallow (supercritical)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1547.1.2 The energy equationThe momentum equation gives considerable qualitative channel flow information, andcould also be used in a numerical integration to find it quantitatively. The traditionalapproach in hydraulics however is to use an integrated form of the momentum equation.This is a statement of conservation of energy and a form of the Bernoulli equation. Theenergy equation can be found by starting with the equation of momentum (equation 7.1),dividing it by g' and making the substitution for the friction term of equation 6.3 andthe pressure slope defined before, resulting in:u du dh de^Cue+ + — P ^ =0g' dx dx dx^g'hThis equation is now integrated along x:(7.11)20 ( u h e) = (Sp — CF 2 )Ax^(7.12)where the left hand side is the change in total energy along x (the change in "head"), andthe right hand side contains the factors causing the total energy to change (friction, andexternal pressure gradient). The over bar denotes an average over the horizontal intervalAx. This equation is the one used in the "step method" to be discussed later to find theflow between control points. The first two terms on the left hand side of equation 7.12define the flow "specific energy":uE = 2— + h^ (7.13)2g'That this equation is actually a cubic in h, can be easily seen in the case of a rectangularchannel where Q uhb with b the width. If u 2 is replaced by h+ 2/7 , then the result ish3 — Eh 2 + 29 2b2 = 0. This equation has generally three roots, of which one is negative andcan be ignored. The two positive roots represent different values of h at which the flowcan have the same specific energy. This can be seen in figure 7.3 which depicts h versusChapter 7. Hydraulic channel flow: an analog to gap wind^ 155E for a particular discharge and width. Flows through valleys of varying cross sectionare represented by a family of such curves. The two heights possible for a given dischargeare called "alternate" heights. The smaller h value is for supercritical flow, while thelarger is for subcritical flow. At the minimum in E, there is only one positive root, at thecritical height, It,. A similar analysis could be used for non-rectangular channels, exceptthat in general the roots must be found iteratively.Figure 7.3: Schematic illustration of h versus specific energy for a particular flow condi-tion (after Henderson (1966)).7.1.3 The hydraulic jumpWhen flow transits from super- to subcritical in a hydraulic jump, there is considerableenergy loss due to turbulence. This energy loss is not represented on the right handside of equation 7.12, so the equation breaks down and cannot be used to find the flow.Instead, a technique utilizing conservation of momentum principles can be used on eitherside of a hydraulic jump (Henderson, 1966).chapter 7. Hydraulic channel flow: an analog to gap wind^ 156Consider the slab of air containing a hydraulic jump in the channel depicted in figure7.4. Ignoring the frictional drag of the channel which is a minor term compared to theP2hydraulic jumpFH1P1FH2Figure 7.4: Forces acting on a slab of air on either side of a hydraulic jumpenergy lost in the hydraulic jump, the change in momentum across the slab must equalthe difference in hydrostatic forces acting on each face of the slab:A(Q Pu) = Q Pu2 — Q Pui (7.14)= FH -- FH2 (7.15)where F H is the hydrostatic force acting on the face of each end of the slab. The hy-drostatic thrust is equal to the mean pressure due to the weight of air times the crosssectional area:F H = (7.16)where h is the height of the centroid of cross sectional area A. If the slab under consid-eration was large, we would also need to consider an addition to the hydrostatic thrustby externally imposed pressure gradients and an additional force due to the mass of theslab on a slope. However, we are only interested in the case when the length of theslab is small — just large enough to contain the jump, which in the present treatment isconsidered to be vertical. Additionally we assume that the pressure on top of the coldair layer is the same on either side of the jump. Equating the change in momentum toChapter 7. Hydraulic channel flow: an analog to gap wind^ 157the difference in forces, after some manipulation results in the following:Q2^Q2g l A2^g'Ai^+ A2h2 ^ + Alhi) = 0 (7.17)This equation can be solved iteratively for the two heights on either side of the jump (h 1and h 2 ), which are called "conjugate heights". For rectangular channels it can be solveddirectly, leading to the well known hydraulic jump equation (Henderson, 1966):2-47 =^+ 8F? - 1)where F1 is the upstream Froude number.(7.18)7.2 The hydraulic modelWith an equation for conservation of energy (equation 7.12) which is applicable on ei-ther side of a transition from sub- to supercritical flow, and conservation of momentum(equation 7.17) which is applicable on either side of a transition from super- to subcriticalflow, it is possible to construct a model describing the flow of a relatively dense fluid (inthis case cold air) underlying less dense fluid (in this case warm air) in a channel. Theequations and definitions used are repeated here for clarity.The energy equation:h e) (Sp — CF 2 )0xThe hydraulic jump equation:Q2^g/A1Q2g f^ + A2h2 ^ +^) 0A  where:SP - —dP = the externally imposed pressure gradient (expressed as a slope)g p dxC = a frictional drag coefficient(7.19)(7.20)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 158F = ^ = the Froude number-Vg'hh = the height of fluid (gap wind) above ground levele. = the elevation of the valley floor above some datumQ = uA = uhb the total discharge of fluid (gap wind), which is assumed to be conservedalong the channelu = the mean velocity in the fluid (depth averaged gap wind speed)— ^ x g — (82B 01) x g = reduced gravityp = the fluid (air) densityA = the cross sectional area, which is a function of x and h= h= the mean channel widthThe input data required to solve the above equations are:• Q, the discharge of outflowing air.• a tabulation of cross sectional area, A, for various heights at various horizontallocations along the channel• e, the elevation of the channel floor at various horizontal locations along the channel• 01 , 02 , the potential temperature of the lower and upper air layers• the externally imposed horizontal pressure gradient along the channel• C, drag coefficient values at horizontal locations along the channel• h f , the height of gap wind at the end of the channelThe model described by the above equations relaxes the most limiting assumptionsof the analytic models described in chapter 6 by including parameters such as: varyingchannel elevation and cross section; externally imposed pressure gradients; friction; andChapter 7. Hydraulic channel flow: an analog to gap wind^ 159variations in the height of gap wind. There remain however, a number of assumptionsimplicit in the hydraulic model itself, as well in its extension to gap winds. The hydraulicmodel (even as applied to water) is only valid where the flow is steady in time, graduallyvarying in space, 1-dimensional, and on slopes which are not too steep. Thus transientphenomena such as waves are not incorporated. Flows which are rapidly varied in spacesuch as hydraulic jumps and drops, are constructed by the superposition of graduallyvarying sections.The extension of hydraulics to gap wind adds other assumptions. The gap wind shouldbear some resemblance to water — a clearly marked lower, more dense layer surmounted bya definite inversion. The hydraulic model does not incorporate entrainment of air fromabove, or any other interactions with overlying air (other than an externally imposedpressure gradient) such as transport of momentum. This could be a problem in caseswhere lower level air is not clearly of different density than the air above. Velocity inthe hydraulic model is a layer mean velocity which is assumed to be constant acrossthe entire channel (1-dimensional). In fact, as observations and RAMS simulations haveshown, velocity is not constant across the channel, with certain regions having greatlyenhanced flow. This can be the case in river channels as well, and its affect on the heightprofile incorporated by multiplying the velocity head term (--u2 ) in the energy equation by2.9 1a velocity coefficient, a, which varies between 1.1 and 2.0, according to Hoggan (1989).This correction was felt to be small and of unknown validity for gap wind, so was notused. In any case the correction only applies to the fluid depth, not its velocity. It isassumed that energy losses due to channel sinuosity are negligible. There are empiricalways to account for this in river hydraulics, but these were not tried.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1607.2.1 Method of solution — hydmodThe energy equation is solved over finite steps, in an upstream direction (usually) forsubcritical flow, and in a downstream direction (always) for supercritical flow. This iscalled the "step method" in classical hydraulics. The equation is always solved in reachesbetwecn control points, with a complete solution for the entire fjord being comprised ofthe superposition of solutions over individual reaches. For subcritical flow, the influenceof downstream control points can extend upstream through other control points as far asnecessary. Likewise, supercritical flow resulting from an upstream control point, can ex-tend downstream through other control points if necessary. The hydraulic jump equationis used to determine the location of a hydraulic jump in reaches where there is supercrit-ical flow from an upstream control point, and subcritical flow from a downstream controlpoint. In the model it is possible for subcritical flow from a downstream control pointto extend "influence" upstream far enough to "drown" an upstream control point whichcreated supercritical flow, resulting in no supercritical flow, and no hydraulic jump. Aflow diagram of the model created as part of this work to solve these equations, calledhydmod, is shown in figure 7.5.The terrain data (C, e, and A at 100 m intervals of h from the ground to 2000 mabove ground) are input along the valley at regular intervals (every 2500 in in this case).Since the input intervals are too coarse to solve the energy equation accurately, dataare interpolated horizontally using cubic splines to the much higher resolution (62.5 m)model spacing. At high resolution horizontal locations, cubic splines are computed forcross sectional area (A) as a function of height, giving A at any height for any horizontallocation along the fjord. Once initial data have been input and interpolated to themodel resolution, the model: computes critical and uniform flow at all points; finds allpotential control points; computes sub- and supercritical flow up and downstream fromChapter 7. Hydraulic channel flow: an analog to gap wind^ 161each potential control point assuming critical flow at the control point; solves the actualflow (which may or may not become critical at any control point); and finally outputs /plots the results. The model is coded in FORTRAN 77, while the plotting and analysismodule is in S+.It was necessary to make a few somewhat arbitrary assumptions in creating the hy-draulic model. Hydmod uses the initial height and speed of gap wind only to computethe discharge. Uniform height and speed are used as the actual initial conditions. This isbecause incorrect specification of height and speed could create initial conditions whichare physically unrealistic resulting in an incorrect simulation. For example if the specifiedinitial conditions made the flow subcritical and deeper than the uniform height, then theflow depth would increase in height as though the flow were into a "reservoir". The crosssectional area above 2000 m, or above the highest terrain in each cross section, is assumedto be rectangular. This can be justified by considering that if the gap flow reaches thisheight, then it is probably flowing over the mountains on either side of the fjord as well,so the air itself provides a kind of lateral boundary. None of the simulations made hadflow depths as great as this.solve section-driver which decides what kind offlow occurs in a section and callsthe appropriate subroutine.0111.41p.step-solves energy equationone horizontal stepsub sup-flow transits fromsub- to super- criticicalat control pointsub sub-flow is and remainssubcritical throughcontrol pointsup_sup-flow is and remainssupercritical throughcontrol pointdriver-driver for entire model-interpolates and prepares input data-calls all major subroutinescn_flow-computes critical and uniform flowat all model pointscontrol_points-finds all potential control points(width contractions and slopetransitions)solve Grit-driver which finds sub- and super-critical flow up and downstream fromeach control point assuming itbecomes critical at the control pointjump-a hydraulic jump mayoccur upstream of thecontrol pointoutput-outputs results to filesplotting/ analysis-Splus routines foranalysis and displayof outputChapter 7. Hydraulic channel flow: an analog to gap wind^ 162Figure 7.5: Simplified flow chart for hydrnod.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1637.3 ResultsHydmod is used to simulate gap winds in both a "realistic" representation of the HoweSound fjord, and in an idealized rectangular channel with one horizontal contraction.The purpose of tests using a rectangular channel are to check the model's veracity, andto elucidate the role of various initial and boundary conditions.Hydmod can test the sensitivity of the flow to various parameters. The external pa-rameters which can be tested are: synoptic pressure gradient; height and speed of gapwind at the start of the channel (ie. variations in discharge); height of gap wind at thechannel exit; and effective gravity, which is a function of the difference in potential tem-perature between the upper and lower layers. In addition the effect of internal parameterscan be tested: the frictional roughness of the fjord; and the configuration of the channelitself. In order to test the sensitivity of the flow to various parameters, most probablevalues, and the likely range of each must be specified. This is straightforward for someparameters, and more difficult for others.The average observed value of synoptic pressure gradient is 0.004 Pa m -1 from thesea level pressure analysis shown in figure 3.10b and will be used as the most probablevalue, while a likely range would be from 0.0 to 0.02 Pa m -1 . The observed average gapwind initial height value of 800 m will be used as the most probable value, while a likelyrange would be from 150 to 1500 m. These values will also be used for gap wind height atthe channel exit. An average observed gap wind speed at the head of the fjord of 5 in s -1will be used as the most probable value, while a range of 1 m s -1 to 15 in s -1 is chosen asmost likely. An estimated drag coefficient value of 0.01 (chapter 6) will be used as mostprobable, with a range of 0.001 - 0.02 chosen as likely. The average observed potentialtemperature in the gap wind layer of 267 K will be used as the most probable values.The likely range in potential temperature difference between upper and lower levels isChapter 7. Hydraulic channel flow: an analog to gap wind^ 1641 to 20 K. The maximum value of 20 K is from observations of a very severe gap windevent by Jackson (1993). The most probable value chosen for the potential temperatureof the upper layer in the rectangular channel tests is in the middle of this range — 277 K.The most probable input values and likely range used for the rectangular channel testsare summarized in table 7.1.In the plots which follow, a force balance analysis of the hydraulic model output hasbeen carried out. To facilitate comparison with RAMS, the hydmod force balance hasbeen made as compatible as possible with that of the RAMS simulation. The forces aredefined as follows, by multiplying equation 7.1 by —1:du ,dh ,de 1 dP 1 dr—u— -g - - g dx dx — —dz --= 0 (7.21)dx dx  1 2 3 4 5where the terms are velocity tendencies caused by: 1 - advection; 2 - pressure gradientdue to changing height; 3 - pressure gradient due to changing channel elevation; 4 -external pressure gradient; and 5 - friction. A direct comparison of forces is difficult forseveral reasons. It is difficult to separate the horizontal pressure gradient term in RAMSinto elevation, gap wind height, and external pressure gradient components. The RAMSforce balance analysis was a vertical average in the fixed layer below 679 m, whereas thehydmod forces pertain to the entire gap wind layer. Also, in hydmod the Coriolis force isnot represented, and the total tendency is zero by definition.Sensitivity tests are carried out for both the rectangular and realistic channel in thefollowing way. All input parameters are held constant at the most likely value, except onewhich is varied through the probable range in ten increments. The results are summarizedin plots of maximum and mean gap wind versus the input parameter which was variedso that sensitivity of the wind to that parameter can be assessed.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 165Input Variable most likely value probable rangehoinitial height800 m 150 - 1500 mh fending height800 m 150 - 1500 muoinitial speed5 m s' 1- 15 m s -1dpclspressure gradient0.004 Pa m -1 0.0 - .02 Pa m-101lower pot. temp.267 K 267 K02upper pot. temp.277 K 268 - 287 KCdrag coefficient.01 .001 - .02Table 7.1: Values used in hydmod runs and sensitivity tests for the rectangular channel.7.3.1 Rectangular channelThe rectangular channel used to test the model and help assess the importance of initialand boundary conditions is 50 km in length and 5 km in width. In the centre of thechannel there is a width contraction to 3 km. The channel is horizontal, although theeffect of varying external pressure gradients is like "tilting" it. The effect of the horizontalwidth contraction is similar to that of a terrain elevation maxima which is effectively avertical contraction.Figures 7.6 and 7.7 show flow height, speed, Froude number, and force balance com-ponents along the channel for a hydmod simulation with the most likely input dataparameters (flow is from right to left). The incoming subcritical flow speed increasesand height decreases as it nears the contraction where the flow transits to supercriti-cal. Downstream of the contraction, the flow is supercritical for a short distance beforeChapter 7. Hydraulic channel flow: an analog to gap wind^ 166transiting to subcritical in a hydraulic jump. The subcritical flow downstream of the con-traction is determined and controlled by the gap wind depth at the end of the channel.The peak wind speed is located in the supercritical zone immediately downstream of thecontraction. The shape of the Froude number (figure 7.7a) and wind speed plots (7.6b)are similar and opposite in character to the gap wind height plot (7.6a). This followsdirectly from the definition of Froude number. In this (figure 7.7b) and subsequent forcebalance analysis plots, lines labelled "advection" and "friction" are components of accel-erations due to advection and friction. The lines labelled "pgf elevation", "pgf height",and "pgf external" represent components of acceleration from horizontal pressure gra-dient forces due to: channel elevation changes, gap wind height changes and externallyimposed pressure gradients, respectively. The force balance analysis plot (7.7b) clearlyshows the largest forces within the contraction are the pressure gradient force due tohorizontal gradient of gap wind height, and advection which opposes it. Friction and theexternal pressure gradient force are smaller. The main force balance is between heightpressure gradient and the external pressure gradient in subcritical flow away from thecontraction. This agrees qualitatively with the RAMS force balance analysis presented inchapter 5.4 which showed the main balance was between pressure gradient and advection.The sign and character of the hydmod forces near the contraction are qualitatively similarto the RAMS forces shown in figure 5.41 between -120 and -160 km for example. In theRAMS force balance, the zone of increasing wind has positive velocity tendency due topressure gradient, which is partially balanced by a negative advection velocity tendency,and vice versa in the zone of decreasing wind. This is similar to the force pattern in figure7.7b near, and downstream of the contraction. The magnitude of the hydmod forces arehowever considerably larger than the RAMS forces.terraingap wind......................................... • • •...........................................a)000CoE0000Ca>a)-47 000b)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 16750^40^30^20^10^0Distance down channel (km)50^40^30^20^10^0Distance down channel (km)Figure 7.6: Gap wind flow for rectangular channel with "most likely" input parameters.a) Height of gap wind; b) Gap wind speed.Sensitivity testsFigures 7.8 to 7.13 show the sensitivity of mean and maximum wind speed to h o (initialgap wind height), hf (gap wind height at end of channel), u o (initial wind speed), `,17 -(external pressure gradient), g' (effective gravity - by varying the potential temperatureof the upper layer over a 20° range), and C (drag coefficient)..04t0.0frictionadvectionpgf elevationpgf heightpgf external0.E0OOO-.02.-.04.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 168a)E0OLLO ^b)50^40^30^20^10^0Distance down channel (km)Figure 7.7: Cap wind flow for rectangular channel with "most likely" input parameters.a) Froude number; b) Force balance components.50 40 30 20 10 0Distance down channel (km)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 169200 400 600 800h0 (m)1000^1200^1400Figure 7.8: Sensitivity of mean and maximum gap wind speed to changes in h o (initialgap wind height) for a rectangular channel with one contraction.200 400 600 800ht (rn)1000^1200 1400Figure 7.9: Sensitivity of mean and maximum gap wind speed to changes in h f (gapwind height at end of channel) for a rectangular channel with one contraction.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1702 4 6 8PO (m/s)10 12 14Figure 7.10: Sensitivity of mean and maximum gap wind speed to changes in u 0 (initialwind speed) for a rectangular channel with one contraction.0.0 0.005 0.010dpdx (Pa/m)0.015 0.020Figure 7.11: Sensitivity of mean and maximum gap wind speed to changes in 2 (externalpressure gradient) for a rectangular channel with one contraction.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1710.2 OAg' (m s'-2)0.6Figure 7.12: Sensitivity of mean and maximum gap wind speed to changes in g' (effectivegravity) for a rectangular channel with one contraction.0.005 0.010 0.015 0.020C (-)Figure 7.13: Sensitivity of mean and maximum gap wind speed to changes in C (dragcoefficient) for a rectangular channel with one contraction.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 172The results show that increases in It o , 110 , and di lead to increased gap wind speed -this will be called positive sensitivity. Increases in h 1, and C lead to decreased gap windspeed - this will be called negative sensitivity. Increases in g', first increase and thendecrease the maximum wind speed (ie. there is an optimum g'), while the mean windspeed shows a slight, but steady decrease.The sensitivity of flow speed to It o (figure 7.8) and u0 (figure 7.10) shows similarpositive sensitivity and will be grouped together for discussion. The maximum flow speedhas the greatest sensitivity - the largest increase across the range - to these variables.Three distinct regions of flow can be noted from the maximum wind speed curves ineach of figures 7.8 and 7.10. The first zone, at low values of /t o and tio , has subcriticalflow throughout the channel. Typical flow characteristics from this regime are depictedin figures 7.14 and 7.15 which are for /t o of 300 m. The flow everywhere is subcritical,with maximum speed at the channel contraction. The force components show a balance,mainly between the external pressure gradient force and the height pressure gradientforce. Since the RAMS force balance analysis doesn't differentiate between the variouspressure gradient components of the force balance, this would correspond to a smallpressure gradient term - between -100 and -120, and -155 and -170 km in figure 5.41.Advection becomes important near the contraction and gap wind height increases alongthe channel.The second distinct flow regime in the sensitivity of wind to h o and u0 is whencritical flow begins. This is indicated in figures 7.8 and 7.10 by a very rapid increase inmaximum wind speed. Figures 7.6 and 7.7, which depict the flow for the "most likely"input parameters, show this mixed flow transition.The third sensitivity regime occurs with large h o and uo , where the flow speed in-creases at a rate similar to the subcritical regime. Here, the extent of supercritical flowChapter 7. Hydraulic channel flow: an analog to gap wind^ 173is increasing and the various flow features resemble figures 7.6 and 7.7 except the super-critical flow downstream of the contraction is of greater extent.a)terraingap wind.............................................................^...................................050 40 30 20 10 0Distance down channel (km)EC0>a)a) 0b) OOLC)O050 40 30 20 10 0Distance down channel (km)Figure 7.14: Gap wind flow for rectangular channel showing subcritical regime, withh o = 300 m. a) Height of gap wind; b) Gap wind speed.The flow speed sensitivity to dc-L=. (external pressure gradient, figure 7.11) is positiveand similar to that for h0 and u0 . Again, there are three distinct regimes, the low speedregime where the flow in everywhere subcritical, a middle regime of rapidly increasingmaximum flow where the flow is starting to become supercritical near the contraction,and a regime for large values of 'ff-, where the extent of supercritical flow is increasing.In the third regime, supercritical flow exists as an initial condition at the start of thechannel, transits to subcritical in a hydraulic jump upstream of the contraction, transitsfrictionadvectionpgf elevationpgf heightpgf externalChapter 7. Hydraulic channel flow: an analog to gap wind^174a).cCa)z2u_CNJ0b )50^40^30^20^10^0Distance down channel (km).04.02a)^0.0E-.028-.0450^40^30^20^10^0Distance down channel (km)Figure 7.15: Gap wind flow for rectangular channel showing subcritical regime, withho = 300 m. a) Froude number; b) Force balance components.to supercritical at the contraction, and then jumps back to subcritical further downstreamunder the controlling influence of the fixed gap wind height at the channel end. This canbe seen in figures 7.16 and 7.17 which are for d(-1-:- of 0.013 Pa m -1 . In the RAMS forcebalance, figure 5.41, friction is an important component in the zone of strong supercriticalflow (near location -145 km), however it is less than or equal to the advection term. Theplots for maximum-dc-E- of 0.02 (figures 7.18 and 7.19), show supercritical flow throughoutthe channel, except near the end where the flow jumps to subcritical due to the end ofchannel control. In the supercritical flow created by the large externally imposed pressuregradient, the primary force balance (figure 7.19b) is between external pressure gradientterrain^ gap windEC0TT:1>aa 0Chapter 7. Hydraulic channel flow: an analog to gap wind^ 175and friction. Advection and height pressure gradients are smaller, but become importantnear the contraction.a)50^40^30^20^10^0Distance down channel (km)b)50^40^30^20^10^0Distance down channel (km)Figure 7.16: Gap wind flow for rectangular channel showing predominantly supercriticalregime, with LE = 0.013 Pa m -1 . a) Height of gap wind; b) Gap wind speed.The sensitivity of gap wind to h f is opposite to that of /to . Increasing values of Ivmean that subcritical flow controlled by the the end point height is able to propagatefurther upstream, resulting in decreased flow speeds in the channel. Once again, there arethree flow regimes apparent in figure 7.9. The first, for low values of hf have relativelyhigh wind speeds. Here, the height of the gap wind at the channel end is too low to act asa control so that no influence is exerted upstream. The second flow regime with h f of 450to 1050 m, is where the end point is able to act as a control on the flow. This is similarb).04-.02.<1.)2OC02a)0.0 •0E0frictionadvectionpgf elevationpgf heightpgf external-.04.Chapter 7. Hydraulic channel flow: an analog to gap wind^176a)Ea)-o0U-50^40^30^20^10^0Distance down channel (km)50^40^30^20^10^0Distance down channel (km)Figure 7.17: Gap wind flow for rectangular channel showing predominantly supercriticalregime, with r .= 0.013 Pa m -1 . a) Froude number; b) Force balance components.to the simulation with the "most likely" input parameters shown in figures 7.6 and 7.7.The third regime, for large values of h f, is one in which the downstream control is able tocompletely "drown" the flow upstream, forcing slow, subcritical flow throughout. Thisis shown in figures 7.20 and 7.21 which are for h f of 1050 m.The sensitivity of the flow speed to increasing C (drag coefficient) is also negativewith increasing drag coefficient resulting in decreasing wind speed (figure 7.13) as wouldbe expected. However the sensitivity is not large compared to most of the other param-eters. Indeed the curve is quite flat for values of C larger than 0.003. This is becausethe frictional term in the force balance is typically of minor importance compared witha)EC0Caiv>b)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 177terraingap wind0OU,050 40 30 20 10 0Distance down channel (km)50 40 30 20 10 0Distance down channel (km)Figure 7.18: Gap wind flow for rectangular channel showing entirely supercritical regime,with ( 3 = 0.02 Pa^a) Height of gap wind; b) Gap wind speed.dxchanges in gap wind height, external pressure gradient, and advection. In the case ofpredominantly supercritical flow, the sensitivity would be much more negative (as it isfor small C values), because the force balance is primarily between friction and externalpressure gradient. Initially high flow speeds for low values of C (0.001), are due to prop-agation of supercritical flow through the contraction which jump to subcritical furtherdownstream in response to the upstream influence of h f. This is shown in figures 7.22 and7.23. Larger drag coefficients result in critical flow at the contraction, with subcriticalflow extending upstream and supercritical flow downstream.The sensitivity of gap wind flow to g' (effective gravity) shown in figure 7.12 is mixed..04t')^.028-.04........ • • •a)0.00E0-.02.frictionadvectionpgf elevationpgf heightpgf externalb)Chapter 7. Hydraulic channel flow: an analog to gap wind^178a)Ea)-o0lLO50^40^30^20^10^0Distance down channel (km)50^40^30^20^10^0Distance down channel (km)Figure 7.19: Gap wind flow for rectangular channel showing entirely supercritical regime,with`f-' 0.02 Pa m -1 . a) Fronde number; b) Force balance components.clx/The mean flow speed declines as g' increases while the maximum speed first increases andthen declines. The initial flow, for low values of g' is nearly everywhere supercritical. Thisflow state is shown in figures 7.24 and 7.25. Supercritical flow can exist for relativelysmall wind speeds with low g' because of the inverse relationship between g' and theFroude number. As for the case of supercritical flow with large dc-t', the force analysis(figure 7.25b) shows the main balance is between friction and external pressure gradient,and that changes in height are only important near the contraction. A difference betweenthe two situations (large 11,-/ ' , and small g') is the force component magnitudes are muchsmaller for small g', resembling RAMS force balance component magnitudes. Becauseterrain^ gap wind........................................^• • •..........................................a)EC0.4E5,.17)0Chapter 7. Hydraulic channel flow: an analog to gap wind^ 179b )50^40^30^20^10^0Distance down channel (km)1/T.0-(1)0C.)U)00.110050^40^30^20^10^0Distance down channel (km)Figure 7.20: Gap wind flow for rectangular channel showing influence of downstreamcontrol on flow, with hf = 1050 m. a) Height of gap wind; b) Gap wind speed.the force balance is between external pressure gradient and friction in these situations,the friction model of chapter 6 would be an appropriate simple model to apply. Thisis expected since under these conditions, the pressure gradient resulting from variationsin gap wind height which is fundamental to hydraulic flow, will be small compared toother forces. Values of g' in the middle of the probable range result in a mixed flowregime similar to the "most likely" flow shown in figures 7.6 and 7.7 with supercriticalflow downstream of the contraction and subcritical flow upstream. The effect of this is toincrease the peak wind, but decrease the mean wind - the flow becomes more variable.As g' is further increased the flow becomes subcritical everywhere, resulting in decreased.04E^.02 •a)0.0 •8-.04frictionadvectionpgf elevationpgf heightpgf external•Chapter 7. Hydraulic channel flow: an analog to gap wind^180a)C.)0b )50^40^30^20^10^0Distance down channel (km)50^40^30^20^10^0Distance down channel (km)Figure 7.21: Gap wind flow for rectangular channel showing influence of downstreamcontrol on flow, with h f = 1050 m. a) Froude number; b) Force balance components.peak wind speeds and somewhat decreased mean wind speeds. This flow regime is shownin figures 7.26 and 7.27. Simulations for small values of g' may not be valid due toviolation of basic assumptions in the extension of hydraulics to gap winds.50 40 30 20 10 0Chapter 7. Hydraulic channel flow: an analog to gap wind^ 181a)b)E0a) 00U,terrain^ gap wind......................................050 40 30 20 10 0Distance down channel (km)0Distance down channel (km)Figure 7.22: Gap wind flow for rectangular channel showing effect of small frictionaldrag, with C = 0.001. a) Height of gap wind; b) Gap wind speed.0U)0C \ IU)0U,Chapter 7. Hydraulic channel flow: an analog to gap wind^ 182a)b)50^40^30^20^10^0Distance down channel (km)Figure 7.23: Gap wind flow for rectangular channel showing effect of small frictionaldrag, with C = 0.001. a) Froude number; b) Force balance components.•cr^•if)Ea)00Ou_C)050 40 30 20 10 0Distance down channel (km).04N02frictionadvectionpgf elevationpgf heightpgf externalO• 0.00.E0• -.02 ,a)00-.0450 40 30 20 10 0Chapter 7. Hydraulic channel flow: an analog to gap wind^ 183a)b)Distance down channel (km)Figure 7.24: Gap wind flow for rectangular channel showing effect of small effectivegravity due to a difference in potential temperature between the layers of 1° C. a) Heightof gap wind; b) Gap wind speed.0a) 0 ................................terraingap wind• • •^_ ....................................050 40 30 20 10 0Distance down channel (km)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 184a)b)50^40^30^20^10^0Distance down channel (km)Figure 7.25: Gap wind flow for rectangular channel showing effect of small effectivegravity due to a difference in potential temperature between the layers of 1° C. a) Froudenumber; b) Force balance components.a)Ea)zOLL050 40 30 20 10 0Distance down channel (km)-.04.0.0frictionadvectionpgf elevationpgf heightpgf external.04Fi.0250 40 30 20 10 0Chapter 7. Hydraulic channel flow: an analog to gap wind^ 185a)b)0C N. I00terrain^ gap windE0Cta)a)00O8U)U)............................................... • •^..0 •50 40 30 20 10 0Distance down channel (km)aDistance down channel (km)Figure 7.26: Gap wind flow for rectangular channel showing effect of large effective gravitydue to a difference in potential temperature between the layers of 19° C. a) Height ofgap wind; b) Gap wind speed.0c)cs.1U)OU)0OO-.04..04 • frictionadvectionpgf elevationpgf heightpgf external.02a)0.00E-.02.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 186a)EOLLb)50^40^30^20^10^0Distance down channel (km)Figure 7.27: Gap wind flow for rectangular channel showing effect of large effectivegravity due to a difference in potential temperature between the layers of 19° C. a)Froude number; b) Force balance components.C.)050 40 30 20 10 0Distance down channel (km)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1877.3.2 Howe Sound — realistic and modified channelResults from rectangular channel simulations are useful to clearly show the effects ofvarying external parameters, and to better understand atmospheric application of hy-draulic theory. They will serve as a benchmark for comparison with the results fromchannels of more realistic, geometry. Such a channel has been constructed, as mentionedpreviously, by taking cross sections perpendicular to the channel orientation at 2500 mintervals from Squamish Airport (SQA) near the head, to Lookout Point (LOO) at themouth of Howe Sound. The cross section locations are shown in figure 7.28 and thearea data are summarized in tables B.1 and B.2 in appendix B which tabulate the crosssectional area below the given height in 100 m intervals from 0 to 2000 m, at each of the21 locations (0 km is SQA, 50 km is LOO).One problem with using actual terrain cross section data without modification stemsfrom limitations inherent in the hydraulic model. Hydmod is 1-dimensional. It allowsvariation in the flow only in the along-channel direction, and presumes that flow in thelower layer is constant in the vertical and cross-channel directions. Observations andRAMS simulation results (figure 5.16) indicate the flow is not constant in the cross-channel direction, especially where the channel widens. Rather, observations suggest thesignificant flow is constrained by topography to the main channel along the eastern sideof Howe Sound, with more stagnant flow elsewhere. Tests using the unmodified terraincross section data shown in tables B.1 and B.2, which will be presented subsequently,show simulated gap winds too slow and shallow where the channel widens. To circumventthis problem, a modified channel was created by connecting the main ridge lines of Anvil,Gambier, and Bowen Islands with a vertical "wall". The location of this unique numerical"geomorphic formation", as well as the position and orientation of cross sections areshown in figure 7.28. The cross sectional areas at each location and height for theChapter 7. Hydraulic channel flow: an analog to gap wind^ 188modified channel, are shown in tables B.3 and B.4.Hydmod will be compared with actual data and RAMS model output. To simplifycomparison with RAMS output, as in chapter 6, plots will be made with horizontalorientation and scale corresponding to that of the RAMS simulation. The numbers alongthe top of each plot correspond to the cross section number in figure 7.28. Hydmodoutput for the "most likely" values of input parameters for the (unmodified) realisticchannel are shown in figures 7.29 - 7.30. The "most likely" input parameters are slightlydifferent than for the rectangular channel simulations and are given in table 7.2. Themain difference is the "most likely" value for g' was reduced to correspond to a potentialtemperature difference of 5° C, h f was reduced to 600 m, and the drag coefficient, C, wasset to 0.02 over land and 0.005 over water. This was so the base configuration for themodified and realistic channels would more closely match observations. The potentialtemperature difference of 5° C, depending to some extent upon how it is measured, iscloser to what is found from the AIRsondeTM profiles than the 10° C difference used in therectangular channel tests which was chosen because it lay in the middle of the probablerange. Drag coefficient values are chosen following arguments outlined in chapter 6. Sucha large value of C over land was chosen because the aerodynamically rough coniferousforest is combined with high form drag due to rough terrain. The value of C over wateris also large because it must include the effects of aerodynamically rough sidewalls. Avalue for hf was difficult to estimate, as there were no data available on which to basethis. The RAMS h f is thought to be too large for reasons discussed in chapter 5 — afactor which contributed to poor RAMS results in the southern part of Howe Sound. Forthis reason an h f value of 600 m was chosen as smaller than those estimated from RAMSvertical cross section plots (800 - 1200 in) in figures 5.22 to 5.32. The probable range ofthese variables, used in sensitivity tests remains the same.Initially subcritical flow in figures 7.29 and 7.30 becomes supercritical in a hydraulicChapter 7. Hydraulic channel flow: an analog to gap wind^ 189Figure 7.28: Topography of Howe-Sound region, showing locations of cross sections andof artificial "wall" along western side used to reduce channel width.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 190Input Variable most likely value probable rangehoinitial height800 m 150 - 1500 mh fending height600 m 150 - 1500 inuoinitial speed5 m s -1 1.5 - 15 m s -1dpdxpressure gradient0.004 Pa m -1 0.0 - .02 Pa m -101lower pot. temp.267 K 267 K02upper pot. temp.272 K 268 - 287 KCdrag coefficient.02 land; .01 water .001 - .02Table 7.2: Values used in hydmod runs and sensitivity tests for modified channel.drop near the horizontal coordinate of -126.5 km between SQT and WAT. This locationcorresponds to the horizontal contraction at 12.5 km in the cross section data of tablesB.1 and B.2. The supercritical flow then reverts to subcritical in a hydraulic jump near-147 km as a result of subcritical flow upstream of the fixed gap wind depth at the channelterminus (mouth of Howe Sound). The simulated winds in the wide southern part of thechannel are less than usually observed since the flow expands to fill the channel.Simulation results for the "most likely" parameter values in the "modified channel"are given in figures 7.31 and 7.32. These results, as for the unmodified channel, show flowwhich is controlled by the contraction at -126.5 km (12.5 km in tables B.3 and B.4). Themodified channel, however also has a control point at -142.5 km (32.5 km in the table)which is the contraction between Anvil Island and BRU. This seems closer to observedgap wind patterns which show strong winds downstream of this second contraction.(See for example the down-channel wind time series for Finisterre Island - figure 5.7b.)EcCD 0OU)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 191During the hydmod simulations, between 8 and 16 potential control points were found,however only horizontal contractions at these two points were significant enough to actas controls. A comparison of the hydmod force balance for the "most likely" reducedchannel conditions (figure 7.32) with the RAMS force balance (figure 5.41) is qualitativelysimilar to the comparison of the rectangular channel forces with RAMS forces. Zones ofincreasing winds are marked by large tendencies due to pressure gradients (primarily fromhorizontal gradients in gap wind height in the hydmod case), which are mostly balancedby advection. Friction becomes an important force in the areas of fast supercritical flow.a)21^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)21^19^17^15^13^11^9^7^5^3^1b)0CVCV0CVU)OO-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.29: Gap wind flow for "realistic channel" using "most likely" input parameters.a) Height of gap wind; b) Gap wind speed.Hydmod simulations using the modified channel geometry will now be compared with.04.02a)c^0.00.E0-.02.a)O72-.04- friction^ advectionpgf elevationpgf heightpgf externalChapter 7. Hydraulic channel flow: an analog to gap wind^ 19221^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)^21^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.30: Gap wind flow for "realistic channel" using "most likely" input parameters.a) Froude number; b) Force balance components.observations and RAMS model output at the four times which were used in chapter 6 totest the simple analytic models. In order to do this it is necessary to choose appropriatevalues of Ito , hf , uo, g', and the drag coefficient C. C is estimated over land to be .02,and .005 over water (see chapter 6 and the preceeding paragraphs for a discussion of this).As discussed in chapter 6, there was difficulty estimating the external pressure gradientat specific times because of conflicting pressure data. As a consequence, results using twoestimates of external pressure gradient at each time are shown. Effective gravity, g' (dueto a potential temperature difference between the two air layers), is difficult to estimatebecause the air, while showing distinct layers, is nevertheless continuously stratified. Ita)b)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 19321^19^17^15^13^11^9^7^5^3^1a)EOa O-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)b)^21^19^17^15^13^11^9^7^5^3^1-o-ooCoNo •-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.31: Gap wind flow for "modified channel" using "most likely" input parameters.a) Height of gap wind; b) Gap wind speed.is set at values corresponding to a potential temperature difference of 3 or 4 °C which areestimated from AIRsondeTM profiles. h0 and u0 are estimated from AIRsondeTM profiles,leaving only h f unobserved and unestimated. There is no easy solution to this problem,so h f has been simply set to 600 m for reasons outlined previously. Higher values of h fwere found to degrade the flow representation near the channel terminus.Table 7.3 gives the input parameters used as input to hydmod for the four timessimulated. Figures 7.33 — 7.36 compare hydmod gap winds with observations and RAMSsimulation values. The comparison being made is between modelled volume averagedwind (hydmod) and observed 10 m wind at a point so that one would expect hydmod winds-170 -160 -150 -140 -130^-120 -110 -10021^19^17^15^13^11^9^7^5^3^1O- friction^ advectionpgf elevationpgf heightpgf externala)c^0.0E-.02.O-.04..04.02Chapter 7. Hydraulic channel flow: an analog to gap wind^ 194Distance along channel S - N (km)21^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.32: Gap wind flow for "modified channel" using "most likely" input parameters.a) Froude number; b) Force balance components.to be somewhat stronger than observed. Hydmod shows some success at replicating theobserved gap wind flow at these times. The surface wind observations for the most partlie between the high and low external pressure gradient gap wind curves. In particular,hydmod simulates both the lowest wind speeds near the start of the channel (which isexpected since this is near where the initial conditions are applied), and the highestwind speeds in supercritical flow near the end of the channel. It is also able to modelthe observed decrease in wind near the channel exit, which in hydmod is due to the"backwater" effect of fixed gap wind height at the exit. The hydmod simulation (comparedto observations) is qualitatively inferior to the RAMS simulation in the northern half ofa)b)302520-0 150 1050• - observed^ RAMShydmod (SQR-LOO)hydmod (SQT-LOO)-----^• ..............•^• - observed^ RAMShydmod (SQR-LOO)hydmod (SQT-LOO)-• .. ... .. .. .^.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 195the channel, but superior to RAMS in the southern half where the RAMS simulation haddifficulties.21^19^17^15^13^11^9^7^5^3^1-170^-160 -150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.33: Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 30, 23:00 PST.21^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.34: Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 05:00 PST.Sensitivity testsAs for the rectangular channel, sensitivity tests have been carried out on the modifiedrealistic, channel. The input data and probable range are summarized in table 7.2. Theresults for the modified channel, which are qualititatively the same as for the rectangular302520151050• - observed^ RAMShydmod (SQR-LOO)hydmod (SQT-LOO)A - observed^ RAMShydmod (SQR-LOO)hydmod (SQT-LOO)-000302520151050Chapter 7. Hydraulic channel flow: an analog to gap wind^ 19621^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.35: Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 11:00 PST.21^19^17^15^13^11^9^7^5^3^1-170^-160^-150^-140^-130^-120^-110^-100Distance along channel S - N (km)Figure 7.36: Comparison of hydmod output for two pressure gradient possibilities withobservations and RAMS output for January 31, 17:00 PST.and realistic channels, are shown in figures 7.37 to 7.42. The main difference betweenthe sensitivities in the modified and rectangular channel tests is in the magnitude ofthe maximum wind sensitivity (ie. the change in maximum wind over the parameterrange) which is greater for the rectangular channel tests. This is mostly due to thesmaller potential temperature difference (g') used in the modified channel sensitivitytests which, as noted previously, tends to reduce the variability of the flow.3025To- 20150^1050OOOa200^400^600^800^1000^1200^1400)10 (m)Chapter 7. Hydraulic channel flow: an analog to gap wind^ 197ParameterJan 30,23:00Jan 31,05:00Jan 31,11:00Jan 31,17:00initial height - h o (m) 1000 900 900 800ending height - hf (m) 600 600 600 600initial speed - uo (m s -1 ) 5 8 7 7pressure gradient - '2SQR-LOO (Pa m -1 )0.002 0.0025 0.0029 0.003pressure gradient - sii:,SQT-LOO (Pa m -1 )0.0086 0.0083 0.0083 0.0092lower pot. temp. - 0 1 (K) 267 267 267 267upper pot. temp. - 0 2 (K) 270 271 271 270drag coefficient - C .02 over land and .005 over waterTable 7.3: Values of parameters used in hydmod simulations. Times are PST.Figure 7.37: Sensitivity of mean and maximum gap wind speed to changes in h o (initialgap wind height) for modified channel.N...max wind speedmean wind speedChapter 7. Hydraulic channel flow: an analog to gap wind^ 198LO0200^400^600^800^1000^1200^1400hf (m)Figure 7.38: Sensitivity of mean and maximum gap wind speed to changes in /i f (gapwind height at end of channel) for modified channel.2^4^6^8^10^12^14u0 (m/s)Figure 7.39: Sensitivity of mean and maximum gap wind speed to changes in u0 (initialwind speed) for modified channel.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 1990.0^0.002^0.004^0.006^0.008^0.010dpdx (Palm)Figure 7.40: Sensitivity of mean and maximum gap wind speed to changes in 2 (externalpressure gradient) for modified channel.NNvONvOC OO0.2 0.4 0.6g' (m s^-2)Figure 7.41: Sensitivity of mean and maximum gap wind speed to changes in g' (effectivegravity) for modified channel.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 2000.005 0.010 0.015 0.020C HFigure 7.42: Sensitivity of mean and maximum gap wind speed to changes in C (dragcoefficient) for modified channel.Chapter 7. Hydraulic channel flow: an analog to gap wind^ 2017.4 Discussion and summaryOpen channel hydraulic flow has been proposed as a possible analog to gap wind. Thishas been prompted by perceived similarities: gap winds are the flow of cold, dense low-level air horizontally constrained by a channel, which resembles the flow of water in ariver, with the density difference across the inversion representing the water surface.There are, however a number of limitations intrinsic in the hydraulic analog and itsextension to gap wind, which may cause problems. Because hydmod is 1-dimensionalwith constant flow in the vertical and cross-channel directions, it is unable to correctlysimulate gap wind where the channel widens unless the actual flow widens as well. Insuch a situation, observations suggest a stagnant zone of air forms, and that gap windis constrained by smaller topographic features to the eastern channel of Howe Sound.In order to achieve realistic flow results in this part of Howe Sound, it was necessary toreduce the horizontal extent of gap winds by modifying the cross sections to include avertical "wall" along the topographic ridge lines of Anvil, Gambier, and Bowen Islands.Gap wind, while showing indications of two layer structure, is nevertheless contin-uously stratified, and so not completely represented by two dissimilar airmasses with astep density change between them. This results in practical problems in specifying anappropriate effective gravity (g'), as well as potential fundamental problems because thedynamics of the interface are not modelled. In particular, entrainment of air from above(or of air from slopes along the channel) is not included in hydmod. This limitation couldbe circumvented in future work by implementing the theory of Smith and Sun (1987)which allows layers of constant stratification.Another problem related to the practical application of hydmod is that not all theinput data required for initialization are directly available from routine data. The mostdifficult parameters to specify are the gap wind height at the channel start and end (ItoChapter 7. Hydraulic channel flow: an analog to gap wind^ 202and hi ). If this model were being used in a routine forecast setting, these would have tobe estimated from nearby radiosonde data, or from numerical weather prediction modeloutput.Despite these limitations, hydmod is able to simulate the main features of gap windand its variation along a channel with some accuracy. This implies the essence of gapwind is contained in the simple physics of hydraulic theory. The qualitative applicationof hydraulic theory is instructive to understand spatial gap wind patterns indicatingwhere to expect strong gap wind. In situations where the flow is light and everywheresubcritical, the strongest wind can be found at the location of a horizontal contraction.When the flow is very strong and supercritical everywhere, the speed will be a minimumat contractions. The most striking result is when the flow becomes critical at a controlpoint: the gap wind height decreases and wind speed increases in a zone of very fastsupercritical flow which forms downstream. The fast supercritical flow transits suddenlyto slow subcritical flow in a turbulent hydraulic jump. These zones of strong gap windcan be inferred both from observations of surface wind and RAMS vertical cross sectionoutput which depict descending isentropes in zones of accelerating wind, and ascendingisentropes in zones of decreasing wind.The hydraulic model force analysis indicated flow regimes when the simpler analyticmodels developed and discussed in chapter 6 would be applicable. For subcritical flow,away from contractions, the primary force balance is between the pressure gradient dueto gap wind height variations, and the external pressure gradient. For supercritical flow,away from contractions, the primary force balance is between friction and external pres-sure gradient, implying the "friction" model of chapter 6 is applicable in this situation.For flow near a contraction, the primary balance is between advection and pressure gra-dient due to height variations.Sensitivity tests indicated the importance of various initial and boundary conditionsChapter 7. Hydraulic channel flow: an analog to gap wind^ 203to gap wind speed. Maximum and mean flow speed was positively sensitive to initial gapwind height, initial wind speed, and externally imposed pressure gradient. Maximum andmean wind speeds were negatively sensitive to gap wind height at the channel terminus,and drag coefficient. The response of mean wind speed to increased effective gravity wasslightly negative. The response of maximum wind speed to increased effective gravity waspositive for small and moderately large values of g', reaching an optimum and becomingslightly negative at large values of g'. Thus the effect of increased effective gravity overmost of the likely range was to increase gap wind variability (increase the wind maximum,but decrease the mean).Hydmod was only tested for one case at four times. To be more certain of the model'sapplicability, a test involving several cases should be made in the future. This would notonly test the model, but allow values of some of the more poorly known parameters tobe empirically determined.Chapter 8Summary of conclusionsThis chapter summarizes and synthesizes findings of observation analysis, and variousmodelling approaches. The questions and objectives for the thesis given in chapter 1are restated and resolved as far as possible. The significance of this work, along withrecommendations and future work are mentioned.8.1 Questions answeredCharacteristics of gap winds — internal dynamicshorizontal outflow structure:• Where does the maximum wind speed occur?Since virtually all biological (including human) activity occurs at the surface, the hori-zontal distribution of surface wind has important implications, especially when the windis strong and potentially damaging. Therefore, this question has been of prime concernin all parts of the thesis, from analysis of data to RAMS and hydraulic modelling. Theobservational network, despite its sparseness was able to give an indication of zones ofmaximum wind speed. RAMS output had excellent horizontal resolution, but had accu-racy problems in the southern part of the domain. Hydraulic modelling gave the simplestrealistic representation of gap flow, and clearly indicated where zones of maximum windwould occur, based on the flow regime and topography.204Chapter 8. Summary of conclusions^ 205The observations suggest (figures 5.15 to 5.17) the axis of strongest gap wind is alongthe eastern main channel of Howe Sound. The precise wind maximum location alongthis axis, cannot be pin-pointed from observations due to station sparseness, however forthis case, the strongest winds were observed at Finisterre Island, Defence Island, andBrunswick Point (figures 5.7 and 5.6).RAMS output which shows the wind field in more detail, also indicates a narrowzone of strong flow, the axis of which however passes through the middle of Howe Soundinstead of along the eastern edge for reasons discussed in chapter 5. Within this axis,zones of strongest flow are found around the horizontal coordinate of -150 and -130 km infigures 5.22 to 5.32 which are near Brunswick Point and Watts Point respectively. Theselocations are also quite close to relative maximum horizontal channel contractions.Both observations and RAMS output are in accord with hydraulic modelling resultswhich predict that zones of strongest wind should be at locations of horizontal contrac-tions for subcritical flow, and downstream of these contractions for flow which becomessupercritical at them. Froude numbers determined from RAMS output seem to con-firm this pattern - in figures 5.35b, c, d, and 5.36a a zone of supercritical flow developsdownstream of the horizontal contraction near Watts Point, as well as downstream ofBrunswick Point.• How do changes in internal boundary conditions (topography, valley slope, rough-ness, and width) affect the flow?These questions can be best answered by hydraulic modelling and sensitivity tests. Theeffect of valley slope is like that of external pressure gradient - see equation 7.8 where itis apparent the two have an equivalent effect. Therefore the hydmod sensitivity test inwhich the external pressure gradient varied is also applicable to valley floor slope so thatincreasing slope will increase gap wind speeds. (The equivalent range in slope shown inChapter 8. Summary of conclusions^ 206figure 7.40 is 0 to 1.) In the case of fjords such as Howe Sound however, the only locationwhere the valley floor can have a downward slope is over land, where enhanced frictionalretardation tends to counteract the effect of slope. Hydmod sensitivity tests showed theeffect of increasing roughness (drag coefficient) is to decrease gap wind as expected. Theforce balance analysis of RAMS output has indicated that friction (diffusion) is the thirdmost important force, after pressure gradient and advection. A force analysis of hydmodoutput shows that friction is only a large term when the flow is fast and supercritical. Thisis confirmed by sensitivity tests which indicate only supercritical flow has strong negativesensitivity (figure 7.42). Valley width determines locations of horizontal constrictionswhich play a key role in determining the location of wind maxima. If one were to adjustthe width of valleys, the hydraUlic analog indicates the narrower the contraction, thegreater likelihood that it will act as a control resulting in supercritical flow downstream.Therefore one would expect, if all else were equal, a stronger gap wind response in valleyswhich have a greater degree of contraction.• What are the effects of obstacles such as islands, on outflow winds?The effects of islands are three-fold. First, they act to increase surface friction, becausethey are aerodynamically much rougher than the ocean which surrounds them. Second,hydraulically they can act as controls on the flow in the same way as horizontal channelcontractions. If flow is forced over an island, it can become critical at the peak ofthe island, and supercritical on the downwind side, resulting in decreased wind speedsupwind, and increased winds downwind. This can be seen in the RAMS Fronde numberplots in figures 5.35 - 5.37, downwind of Gambier Island. Finally, they can deflect airthrough channels, creating channel contractions and hydraulic control points. This thirdeffect was utilized in hydraulic modelling when the channel horizontal extent was reducedto obtain more accurate simulation results.Chapter 8. Summary of conclusions^ 207• How does flow vary temporally / diurnally? Are there wave-like (periodic in spaceor time) fluctuations?Airflow in valleys under light synoptic conditions frequently exhibits thermally drivenmountain — valley circulation: during the day there is light up-valley flow (anabatic),while at night there is light down-valley drainage flow (katabatic). While gap windsdo not occur under light synoptic conditions, it is possible these thermally driven localflows could modulate, or be superimposed on gap wind flow. Observations show (figures5.5 to 5.10) that strong gap winds began at most stations in the early evening — at thetime when, under light synoptic conditions, an anabatic wind would be ending, and akatabatic wind starting. The wind at the two southern-most stations, Finisterre Islandand Lookout Point (figures 5.7b and 5.8a) show an afternoon decrease in gap wind —when one would expect up-valley anabatic flow, under light synoptic conditions. Otherstations do not show a speed decrease. The decrease in gap wind speed near the end of thechannel, could also be due to increased boundary layer height during the daytime near thechannel terminus which, according to hydraulic model results, causes greatly decreasedgap wind speed near the end of channel. This follows from the negative sensitivity of gapflow to h f seen in figures 7.9 and 7.38.All stations however show diurnal variation in temperature. If the higher daytimetemperatures are completely mixed in the gap wind layer, which is reasonable giventhat this layer is mixed by mechanical turbulence and of neutral stability according toAIRsondeTM data, then this would result in a decrease in effective gravity (g') duringthe daytime, and an increase at night. According to the hydmod sensitivity tests, themaximum wind is usually positively sensitive to g' (the maximum wind decreases for verylarge values of g'), while the mean wind is slightly negatively sensitive. The result ofdiurnal temperature variations then, from a hydraulic perspective, would be an increaseChapter 8. Summary of conclusions^ 208in maximum gap winds just before dawn, and a decrease during the day, which is inagreement with qualitative mountain / valley flow considerations.Gap winds are the flow of stratified air over rough terrain. Therefore, it is reasonableto suppose that gravity waves could be generated. Wave-like fluctuations at time scalesless than a few hours, are not observable in the data. Output from RAMS were onlysaved at 15 minute intervals, so that fluctuations with time scales less that an hour or soare not resolvable at a point in RAMS output. However with horizontal resolution of 1.25kin, gravity wave features with wavelengths larger that 5 km or so should be observable inRAMS fields at a given time. Since airflow closely follows isentropes, it is expected thatgravity waves would be visible as wavy features in potential temperature cross sections(figures 5.22 to 5.32). While these cross sections do clearly show larger scale wave likefeatures related to hydraulic transitions from subcritical to supercritical flow, there is noclear indication of smaller scale gravity wave features, either near the surface, or alongthe density interface marking the top of gap winds. It is however possible that thesefeatures exist, but at scales too small to be resolved. A complete treatment of questionsconcerning internal gravity waves, which will not be done here, could follow the workof Scorer (1949), in which trapped internal gravity wave are explained as resulting fromvertical variations in the Brunt-Vaisala frequency.vertical outflow structure:• What is the depth of outflowing air, and how does it vary along a fjord?The gap wind depth at Squamish Town can be found from AIRsondeTM observationsat four times during the event. RAMS output, which agrees well with AIRsondeTMdata, gives temperature and wind structure at 1.25 km horizontal and approximately100 m vertical resolution over the entire domain. Hydmod output gives an analysis ofgap wind depth and layer averaged speed along the main channel axis. The gap windChapter 8. Summary of conclusions^ 209depth at Squamish was observed to be 800 to 1000 m (figures 5.11 to 5.14). RAMSvertical cross sections of potential temperature along the main channel (figures 5.22 to5.32) indicate that gap wind depth varies in a manner consistent with hydraulic theoryduring the course of the event. In particular, zones of decreasing gap wind height areassociated with subcritical flow approaching channel contractions, or possibly with atransition to strong supercritical flow. Zones of increasing height are associated withsubcritical channel expansions, and possibly with hydraulic jumps in transitions from fastsupercritical to slow subcritical flow. The depth from the hydmod "most likely" simulationfor the modified channel (figure 7.31) varies between 200 and 1000 m. Typical heightvariations from RAMS vertical cross section plots of wind and potential temperature(figures 5.22 to 5.32) are between approximately 200 and 1200 m.• Where is the vertical speed maximum? How does the height of the speed maximumvary along the fjord?Hydmod, which computes layer mean wind speed, cannot give any information aboutvertical variations in gap wind speed. AIRsondeTM observations from Squamish Town(figures 5.11 to 5.14) show peak winds usually near the top of the gap wind layer — at319, 955, 718, 887 in. The peak gap wind for January 30, 16:00 PST (figure 5.11) at319 m is the exception, being considerably below the top of the boundary layer. RAMSvertical cross sections (figures 5.22 to 5.32) also show an increase in gap wind speed awayfrom the surface and place the peak speed in the center of the boundary layer.• What is the vertical temperature structure? Does an inversion mark the top of theoutflowing air?Both AIRsondeTM observations and RAMS output show the lower gap wind layer isapproximately neutral, presumably due to mechanical turbulent mixing. This layer isChapter 8. Summary of conclusions^ 210surmounted by a stably stratified layer. The stably stratified layer usually includes aninversion or near isothermal layer which is confirmed by both AIRsondeTM observationsand RAMS output.• Is it possible to extrapolate results from the study of one fjord to others? Is itpossible to separate the phenomena from their internal boundary conditions?In order to completely answer this question, observations of gap wind depth and speedwould have to be made in other fjords, and then used to test the findings of this work. Ifthe dynamics of gap flow can be represented by a simple hydraulic analogy, then hydmodcould be applied to other fjords. The qualitative relationships between topography, gapwind height, and speed which follow from the hydraulic analogy, would also apply in otherchannels. However, the probable range of input parameters may differ. In particular, forfjords further north, one would expect potentially larger external pressure gradients andeffective gravity.Reaction of flow to external boundary conditionsThe major external parameters which, based on previous studies of related wind flows,were thought to control and influence outflow are: direction and magnitude of horizontalsurface pressure gradient; temperature contrast between the cold air inland and warmermaritime air on the coast; geostrophic wind velocity at mountain top level; depth of coldair in interior (height of inversion); vertical wind profile - presence of critical layers andregions of wind reversal.The assessment of these parameters and their importance for gap wind is made byusing hydmod to perform sensitivity tests.• Are these the important external parameters for gap winds?Chapter 8. Summary of conclusions^ 211Hydmod sensitivity tests have been made on all of the above parameters exceptgeostrophic wind velocity at mountain top level, which however could be thought ofas being related to the external pressure gradient; and the vertical wind profile whichcannot be represented in the hydraulic model. The gap wind flow was found to besensitive to each of the parameters (see the discussion in chapter 7).• What is the relative importance of each?It was found the flow was positively sensitive to external pressure gradient, and thedepth and speed of gap wind at the channel start. The difference in temperature betweenthe cold air inland and warm coastal air is related to effective gravity, and also to theexternal pressure gradient. Gap flow was found to become more variable with increasingtemperature contrast (effective gravity): the mean speed decreased while the maximumspeed increased, until an optimum value of effective gravity was reached after which themaximum speed also decreased.• Are there other important external parameters?Hydraulic modelling showed the importance of the boundary layer height at the chan-nel terminus (mouth of Howe Sound) in determining winds near the end of the channel.It was found that increased terminus boundary layer heights resulted in decreased windspeed. This is likened to the rising level of a lake "backing up" a river flowing into it.• Are there threshold values which these parameters must exceed for the flow to beginor to be maintained?The hydraulic analog indicates that for the flow to begin, there must be down-channelflow at the channel head (otherwise there would be a negative discharge) which meansthe external pressure gradient should be directed down-channel. For strong winds, theChapter 8. Summary of conclusions^ 212flow must become critical at some point in the channel. This will first occur when theright hand side of equation 7.8 is zero, which is near the point of maximum horizontalor vertical contraction. The height and speed of critical flow can be found by iterativelysolving equation 7.7, and will depend on the topography at the point of maximum con-traction, as well as on the discharge. Whether or not critical flow will be achieved atthe maximum contraction point will depend mainly on whether uniform height is belowor above critical height. For a given discharge this will depend on external pressuregradient, drag coefficient and topography at the control point. If the channel terminusboundary layer height is large enough, it could extend influence upstream to "drown out"the control point.• How do external forcing parameters affect flow characteristics?• Which parameters are most important?Hydraulic modelling indicates that increasing external pressure gradient and discharge(initial wind speed, and height), result in increased wind speeds. Increasing surface fric-tion and end channel boundary layer height, result in decreased gap wind strength.Increasing effective gravity (difference in potential temperature between the lower andupper layer), results in increased variability in the flow — higher wind speeds for su-percritical flow (until an optimum effective gravity is reached), but lower speeds forsubcritical flow. The flow is most sensitive to discharge, external pressure gradient, andend channel boundary layer height. Only fast, supercritical flow showed strong sensitivityto surface friction.8.2 SignificanceSeveral contributions have been made.Chapter 8. Summary of conclusions^ 213• This work provided the first reasonably detailed surface, and vertical sounding dataof gap winds in a British Columbia fjord.• The study used a 3-dimensional numerical model to simulate a real gap wind event.The modelling utilized real topography and input data and was able to provide aplausible simulation. The work highlighted the difficulty in applying a mesoscalemodel to phenomena which span many topographic and atmospheric scales, andpointed out the importance of resolving major topographic features. The modelwas very sensitive to the way in which topography was smoothed and represented,with the best simulations resulting when the topography was filtered so that alltopographic variations with wavelength less than four times the horizontal spacingwere removed. Despite some limitations in the RAMS simulation, the flow wasadequately represented over much of the domain. The high resolution of RAMSoutput in 3-dimensions, indicated a close resemblance between gap wind and openchannel hydraulic flow. This prompted the creation and application of a simplemodel based on river channel hydraulics to simulate gap winds.• A hydraulic model of gap wind was created in which classical hydraulic theory wasextended to include external pressure gradients. The hydraulic model contained theessential features of gap flow when compared to observations and RAMS output.By applying the ideas of hydraulics, qualitative information on the location of zonesof maximum wind speed under various flow conditions can be found for any fjordin gap wind conditions.• As there is starting to be a consensus in the literature that downslope winds arealso fundamentally similar to hydraulic flow (Durran, 1986, 1990; Smith 1985), thispoints out the dynamic similarity between what are traditionally termed "downs-lope winds", and the Squamish or gap wind described in this thesis. PreviousChapter 8. Summary of conclusions^ 214studies of gap winds in nearby locations (Overland and Walter (1981) for example)have not explicitly found hydraulic effects.8.3 Recommendations and future work• A simulation using a 3-dimensional mesoscale model, like RAMS, should be madeof a severe gap wind event to confirm the conclusions and inferences drawn fromsimulations of the present moderate event are applicable to stronger events as well.Such a simulation should include an expanded grid 3 and grid 4, so that topographicchannels are better resolved, to improve simulation accuracy in the southern partof the domain.• Hydmod should be tested and implemented as an analysis / forecast tool for me-teorologists forecasting winds in channels under gap wind conditions. It could beused with current data to analyze wind conditions at locations between observingstations. It could also be used with forecast data to provide a wind forecast in achannel. The computational requirements of the model are slight, so that it willrun quickly on any modern computer. The topographic data needed for the modelare easily obtained from a topographic map. The meteorological data required forthe model could be obtained from a combination of surface observations and nu-merical weather prediction model output. With hydmod in routine use, some of themore poorly known parameters could be "tuned" to improve simulation results bycomparing model output with observations, and the usefulness of the model as aforecast tool evaluated.• Hydmod could be extended to include two layers of constant stratification (ratherthan two neutral layers separated by a step change in temperature), after thetheoretical work of Smith and Sun (1987) for downslope winds. The new modelChapter 8. Summary of conclusions^ 215would then need to be tested and compared both with observations and the presentmodel.Appendix ARAMS descriptionIn writing this description, extensive use has been made of notes prepared by Morran(1988) which were based on Tremback et al. (1986). CSU RAMS (Colorado State Univer-sity Regional Atmospheric Modeling System) represents the merging of three numericalmodels. These were a non-hydrostatic cloud model (Tripoli and Cotton, 1982), and twohydrostatic mesoscale models (Mahrer and Pielke, 1977a; Tremback, Tripoli and Cotton,1985). RAMS has been written in a modular fashion with many options possible. Thecode is written in non-standard FORTRAN 77 which requires the use of a special prepro-cessor to convert it to standard fortran and enables the use of extended features. Someof the non-standard features that the preprocessor allows are:• use of more structured loops avoiding statement numbers• use of activation characters in the first column of a line to activate conditionalcompilation of that line• global inclusion of COMMON blocks and PARAMETER statements in chosen mod-ulesA.1 Model formulationRAMS is non-hydrostatic, elastic, uses the quasi-Boussinesq approximation (Dutton andFichtl, 1969), a terrain following vertical coordinate, and is integrated using a semi-implicit "time-split" numerical technique.216Appendix A. RAMS description^ 217Some of the options and features available in RAMS (bold face are those used inthis study) are: (from Morran (1988), Tremback et al. (1986))1. Horizontal coordinate:• Standard Cartesian.• Latitude / longitude.2. Vertical coordinate:• Standard Cartesian.• Sigma-z. The vertical coordinate is terrain following and transformed ac-cording to: (Gal-Chen and Somerville, 1975)(z — zs )z* = H( (H — zs))^ (A.1)where z* is the height of a particular grid point in the terrain following coordi-nate system; z3 is terrain elevation at that grid point; z is the untransformedvertical coordinate; and H is the height of the model top at which the z*coordinate surface becomes horizontal (ie. 18507.493 metres in this case).After Clark (1977), this vertical coordinate transform, leads to the followingtransformations of derivatives of some quantity A:where a is given byaAaOahu A(A.2)(A.3)=ax ia(x,y) = 1)(^)ae.;z,(x, y)^azOz*and the tensor b 1j is1 0 la -8—"Lax (^— 1 ) \1;3 = 0 1 1^z*a ay^H (A.4)\ 0 0 1aAppendix A. RAMS description^ 218which then results in the following transformed velocity components= uV* = Vu ab13 v ab23 w)1-a-(A.5)(A.6)(A.7)3. Basic equations:• Non-hydrostatic time-split compressible (Tripoli and Cotton, 1980) witha semi-implicit scheme for the small time step. The non-hydrostaticmodel was chosen because on grid 4, terrain steepness and small grid spac-ing violates assumptions implicit in the hydrostatic assumption. A non-hydrostatic model permits fast moving sound waves which normally meansthat the time step must be small so that the Courant-Friedrichs-Lewy (CFL)stability criterion is not violated. This means that waves or flow featuresmust travel no further than one grid distance per time step (otherwise themodel would be numerically unstable). For computational efficiency, the time-split semi-implicit scheme of Klemp and Wilhelmson (1978) is used. This in-volves stepping the "acoustic terms", (those which contain sound waves) at asmaller time-step than the more slowly varying terms of interest. The quasi-Boussinesq approximation is used to separate the the high frequency variableof density from the Navier-Stokes predictive equations. The quasi-Boussinesqapproximation differs from the fully Boussinesq approximation in that elas-ticity is permitted and the base state varies with height. The result of this isthat in the formulation of model equations, when the terms are decomposedinto base state plus perturbation quantities plus sub-grid scale perturbations,quantities which are ratios of perturbation to base state are ignored, exceptP100P z'Ts,7r = Cp (A.9)Appendix A. RAMS description^ 219when multiplied by gravity.The model momentum equation in tensor notation is (Tripoli and Cotton,1982):1^2aPoui^poeo aabtsir'at^a ax?3^ 4ADV(POUz) PoTURB(Ui)( Oo0'1.61r, — rT)6i3+Ei 33f uz65(A.8)where: quantities subscripted "0" are fixed reference state variables; primedquantities (') are model resolvable perturbations from the reference state; u,is velocity; x: is the transformed coordinate; p is density; 0 is potential tem-perature; r is the Exner function which replaces pressure and is defined as:where Cp is the specific heat capacity at constant pressure for dry air, P is totalatmospheric pressure; P100 is 100 KPa, and R is the gas constant for dry air;ADV is the advection operator; TURB is the turbulence operator describedbelow; 71, and r„ are the total and vapour mixing ratios; 6, 3 is the Kroneckerdelta function; and f is the Coriolis parameter. In equation A.8, term 1 is themomentum tendency (acceleration); term 2 the pressure gradient force; term3 the momentum advection; term 4 the sub-grid scale friction; term 5 thevertical acceleration due to buoyancy; and term 6 the Coriolis acceleration.The advection operator for a variable A is defined as:1ADv(poA)=-_-_ —(-c-)[-a-.—zi (a177kpou A) A a4 (Pou )]^(A.10)Appendix A. RAMS description^ 220which is the difference between a mass flux divergence term and a momentumdivergence term. The turbulence operator is:1 „^TURB(A)^( a ) aax .[alr'k (A"uj )]^(A.11)kwhere a double prime (") denotes perturbations at a scale smaller than thosewhich are resolved in the model (ie. sub-grid scale perturbations). In additionto the momentum equations, there are equations for Exner function tendency(Klemp and Wilhelmson, 1978):Or'^1 R 7ro a^02) = 0^(A.12)at^a Cy p000ax abisp00and a thermodynamic energy equation:apoeii ADv(poeio+ po TURB (Oil) + poS(Oit)at (A.13)where O i/ is the ice-liquid water potential temperature which is conserved overall phase changes (equivalent to potential temperature in this case becausephase changes weren't allowed), and S is a source or sink operator for O iiwhich would be due only to radiational diabatic heating. There is also a masscontinuity equation for water substance which will not be shown.Equations A.8,A.12, A.13, and the mass continuity equation for water are acomplete set of time dependent equations.• Hydrostatic incompressible or compressible (Tremback, Tripoli and Cotton,1985).4. Dimensionality: 1, 2 or 3 dimensions.5. Grid Structure:Appendix A. RAMS description^ 221• Arakawa-C grid stagger. This staggers variables on a grid so that velocitycomponents are defined at different locations than the rest of the variables,and results in increased finite difference accuracy, especially for the pressurefield. If T, representing the thermodynamic variables is located at the gridintersections, then U (east-west velocity) is located half a grid distance to theeast and west of T; V (north-south velocity) is located half a grid distance tothe north and south of T; and W (vertical velocity) is located half a grid pointabove and below T. This is illustrated in figure A.l.T ^ U ^ T ^ U ^ TV^V^VT ^ U ^ T ^ U ^ TV^V^VT ^ U ^ T ^ U ^ TFigure A.l: Arakawa type C grid stagger used in the model.T represents location of thermodynamic variables; U east-west velocity; V north-southvelocity; and W (not shown, but located half a grid distance above and below T)vertical velocity.• unlimited number of nested grids and levels of nesting (4 nested grids used).6. Finite differencing:Appendix A. RAMS description^ 222• time split - leapfrog on long time step (for slowly varying, non-acoustic terms on the right hand side of equations A.8 and A.12),forward-backward on small time-step (for acoustic terms on lefthand side of equations A.8 and A.12) (Tripoli and Cotton, 1980),2nd or4th order flux conservative advection.• forward-backward time split, 2nd or 6th order flux conservative (Tremback etal., 1987).7. Turbulence closure:• Smagorinsky-type eddy viscosity Smagorinsky (1963) with Ri depen-dence. The sub-grid scale dissipation is down gradient with eddy viscos-ity coefficients dependent upon length scale, deformation, and Brunt-Vaisalafrequency. The vertical scale length is buoyancy adjusted according to theRichardson number (Ri).• Level 2.5 type closure using eddy viscosity as a function of a prognostic tur-bulent kinetic energy.• O'Brien profile function in a convective boundary layer (Mahrer and Pielke,1977a); local exchange coefficient in a stable boundary layer (McNider, 1981).8. Condensation:• Grid points fully saturated or unsaturated.• No condensation. The case simulated was dry and cloudless. Water vapourwas therefore carried in the model only as a passive tracer.9. Cloud microphysics:Appendix A. RAMS description^ 223• Warm rain conversion and accretion of cloud water to raindrops, evaporationand sedimentation (Tripoli and Cotton, 1980).• In addition to the above: specified nucleation of ice crystals, conversion nu-cleation and accretion of graupel, growth of ice crystals, evaporation, meltingand sedimentation (Cotton et al., 1982).• In addition to the above: predicted nucleation and sink of crystal concentra-tion, conversion and growth of aggregates, melting, evaporation and sedimen-tation.• No precipitation processes. The case simulated was observed to be dryand cloudless, hence precipitation processes were not included in order to savecomputer time.10. Radiation:• Shortwave radiation model including molecular scattering, absorption of clearair (Yamamoto, 1962), ozone absorption and reflectance (Lacis and Hansen,1974), transmittance and absorptance of a cloud layer (Stephens, 1978), clear-cloudy mixed layer approach (Stephens, 1977).• Shortwave radiation model described by Mahrer and Pielke (1977a)which includes the effects of forward Rayleigh scattering (Atwaterand Brown, 1974), absorption by water vapour (McDonald, 1960), andterrain slope (Kondrat'yev, 1969).• Longwave radiation model including emissivity of a clear atmosphere (Rodgers,1967), emissivity of cloud layer (Stephens, 1978), and emissivity of a "clearand cloudy" mixed layer (Herman and Goody, 1976).Appendix A. RAMS description^ 224• Longwave radiation model described by Mahrer and Pielke (1977a) in-cluding emissivities of water vapour (Jacobs, Pandolfo and Atwater,1974) and carbon dioxide (Kondrat'yev, 1969) and the computation-ally efficient technique of Sasamori (1972).• No radiation.11. Lower Boundary:• Specified surface temperature and moisture function or specified surface fluxescoupled with constant flux layer condition based on similarity theory (Mantonand Cotton, 1977).• Surface layer temperature and moisture fluxes are diagnosed as a function ofthe ground surface energy balance (Mahrer and Pielke, 1977a). The energybalance includes longwave and shortwave radiative fluxes, latent and sensibleheat fluxes, and conduction from below the surface. To include the lattereffect, a multilevel prognostic soil temperature model is computed.• As above, but modified to be applied prognostically rather thandiagnostically and increase computational efficiency. (Tremback andKessler, 1985).12. Upper boundary conditions:• Rigid lid. This is the only boundary condition that can be used in thisversion of RAMS with variable initial conditions. The flow feature of interestis shallow relative to the vertical extent of the model so that problems withtop boundary conditions should be minimized.• Rayleigh friction layer.Appendix A. RAMS description^ 225• Prognostic surface pressure (hydrostatic only).• Material surface top. (hydrostatic only) (Mahrer and Pielke, 1977a)• Gravity wave radiation condition (Klemp and Durran, 1983).13. Lateral boundary conditions:• Klemp and Wilhelmson (1978) radiative boundary condition.• Orlanski (1976) radiative boundary condition.• Klemp and Lilly (1978) radiative boundary condition.• Any of the above coupled with the "mesoscale compensation region" describedby Tripoli and Cotton (1982) with fixed conditions at the boundary.• Sponge boundary condition of Perkey and Kreitzberg (1976) when large scaledata are available. This includes a viscous region and the introduction of largescale fields into the model computations near the lateral boundaries.• Lateral boundaries which are "nudged" toward specified larger scalefields, following Davies (1976). The fields at the boundaries are froma larger scale model run (CMC FEM).14. Initialization• Horizontally homogeneous.• Horizontally homogeneous but with variations to force cloud initiation.• Variable initialization with large scale data obtained from a largermodel (CMC FEM), possibly enhanced by vertical soundings. The largescale data is objectively analysed on isentropic surfaces and inter-polated to the model grid.Appendix BHydmod dataht (m) 100 200 300 400 500 600 700 800 900 1000x (km)0.0 .1375 .5375 1.075 1.713 2.450 3.300 4.175 5.063 6.013 7.0502.5 .2250 .4875 .8750 1.550 2.300 3.138 4.063 5.050 6.113 7.2885.0 .3250 .8875 1.550 2.425 3.488 4.675 5.900 7.175 8.525 9.9637.5 .2750 .7750 1.425 2.088 2.813 3.588 4.413 5.288 6.213 7.18810.0 .4125 .8625 1.350 , 1.875 2.463 3.188 4.038 4.963 5.925 6.91312.5 .2125 .4750 .7750 1.100 1.463 1.888 2.388 2.963 3.613 4.37515.0 .3500 .7375 1.163 1.638 2.138 2.675 3.250 3.875 4.550 5.27517.5 .3500 .7375 1.250 1.838 2.650 3.575 4.575 5.625 6.738 7.96320.0 .4125 .9375 1.563 2.238 2.975 3.763 4.600 5.525 6.575 7.66322.5 .2750 .6625 1.088 1.550 2.063 2.625 3.225 3.863 4.538 5.32525.0 .3500 .7625 1.250 1.838 2.563 3.325 4.138 4.988 5.863 6.78827.5 .4875 1.063 1.788 2.588 3.425 4.300 5.225 6.175 7.175 8.21320.0 .8500 1.850 2.950 4.100 5.350 6.738 8.150 9.600 11.09 12.6532.5 1.000 2.075 3.338 4.750 6.363 8.225 10.25 12.34 14.51 16.7535.0 1.175 2.638 4.163 5.763 7.525 9.488 11.51 13.59 15.71 17.9237.5 1.100 2.413 4.025 5.850 7.800 9.900 12.07 14.40 16.80 19.2540.0 1.100 2.700 4.563 6.538 8.625 10.80 13.00 15.24 17.51 19.8142.5 1.563 3.463 5.413 7.438 9.538 11.71 13.96 16.30 18.72 21.1945.0 1.900 4.075 6.463 8.863 11.27 13.70 16.14 18.61 21.10 23.6047.5 1.375 2.975 4.775 6.775 8.825 10.94 13.11 15.41 17.79 20.1750.0 1.000 2.800 4.838 7.038 9.338 11.71 14.14 16.56 18.99 21.41Table B.1: Cross sectional areas below the given height, along the "real" channel. Heightsare from 100 to 1000 m. Area is x10 6 m3 .226Appendix B. Hydmod data^ 227ht (m) 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000x (km)0.0 8.288 9.600 10.99 12.51 14.24 16.01 17.84 19.69 21.59 23.492.5 8.525 9.800 11.15 12.59 14.06 15.59 17.14 18.70 20.27 21.855.0 11.44 12.96 14.54 16.19 17.84 19.49 21.14 22.79 24.44 26.097.5 8.275 9.488 10.71 11.94 13.16 14.39 15.61 16.84 18.06 19.2910.0 7.938 9.038 10.41 11.82 13.29 14.76 16.25 17.75 19.25 20.7512.5 5.200 6.088 7.075 8.225 9.488 10.80 12.17 13.57 15.00 16.4215.0 6.050 6.850 7.713 8.688 9.763 10.84 11.91 12.99 14.06 15.1417.5 9.263 10.64 12.09 13.56 15.04 16.51 17.99 19.46 20.94 22.4120.0 8.813 9.988 11.16 12.34 13.51 14.69 15.86 17.04 18.21 19.3922.5 6.225 7.175 8.175 9.238 10.34 11.44 12.54 13.64 14.74 15.8425.0 7.775 8.813 9.950 11.20 12.55 13.90 15.25 16.60 17.95 19.3027.5 9.288 10.45 11.66 12.90 14.15 15.40 16.65 17.90 19.15 20.4020.0 14.27 15.96 17.67 19.40 21.15 22.90 24.65 26.40 28.15 29.9032.5 19.05 21.42 23.80 26.25 28.80 31.37 33.97 36.57 39.17 41.7735.0 20.16 22.41 24.72 27.11 29.56 32.04 34.54 37.04 39.54 42.0437.5 21.75 24.27 26.81 29.37 31.97 34.61 37.26 39.91 42.56 45.2140.0 22.19 24.62 27.09 29.56 32.05 34.55 37.05 39.55 42.05 44.5542.5 23.67 26.17 28.69 31.22 33.77 36.32 38.87 41.42 43.97 46.5245.0 26.12 28.67 31.22 33.77 36.32 38.87 41.42 43.97 46.52 49.0747.5 22.57 25.00 27.42 29.85 32.27 34.70 37.12 39.55 41.97 44.4050.0 23.84 26.26 28.69 31.11 33.54 35.96 38.39 40.81 43.24 45.66Table B.2: Cross sectional areas below the given height, along the "real" channel. Heightsare from 1100 to 2000 m. Area is x10 6 m 3 .Appendix B. Hydmod data^ 228ht (m) 100 200 300 400 500 600 700 800 900 1000x (km)0.0 .1375 .5375 1.075 1.713 2.450 3.300 4.175 5.063 6.013 7.0502.5 .2250 .4875 .8750 1.550 2.300 3.138 4.063 5.050 6.113 7.2885.0 .3250 .8875 1.550 2.425 3.488 4.675 5.900 7.175 8.525 9.9637.5 .2750 .7750 1.425 2.088 2.813 3.588 4.413 5.288 6.213 7.18810.0 .4125 .8625 1.350 1.875 2.463 3.188 4.038 4.963 5.925 6.91312.5 .2125 .4750 .7750 1.100 1.463 1.888 2.388 2.963 3.613 4.37515.0 .3500 .7375 1.163 1.638 2.138 2.675 3.250 3.875 4.550 5.27517.5 .3500 .7375 1.250 1.838 2.650 3.575 4.575 5.625 6.738 7.96320.0 .4125 .9375 1.563 2.238 2.975 3.763 4.600 5.525 6.575 7.66322.5 .2750 .6625 1.088 1.550 2.063 2.625 3.225 3.863 4.538 5.32525.0 .3500 .7625 1.250 1.838 2.563 3.325 4.138 4.988 5.863 6.78827.5 .4125 .9125 1.438 2.013 2.600 3.213 3.850 4.513 5.188 5.90020.0 .4625 .9625 1.488 2.038 2.600 3.175 3.775 4.400 5.050 5.73832.5 .2500 .5250 .8250 1.150 1.525 2.000 2.500 3.025 3.563 4.13835.0 .5750 1.175 1.800 2.450 3.113 3.788 4.488 5.213 5.963 6.72537.5 .7125 1.525 2.425 3.350 4.300 5.275 6.275 7.300 8.350 9.43840.0 .6000 1.275 2.038 2.863 3.763 4.713 5.688 6.688 7.700 8.73842.5 .8625 1.775 2.725 3.688 4.663 5.663 6.688 7.725 8.775 9.85045.0 .9250 1.875 2.838 3.813 4.800 5.800 6.825 7.875 8.950 10.0447.5 .5500 1.188 1.950 2.850 3.775 4.725 5.688 6.688 7.713 8.75050.0 .4250 1.125 1.950 2.900 3.938 5.013 6.138 7.263 8.388 9.513Table B.3: Cross sectional areas below the given height, along the modified channel.Heights are from 100 to 1000 m. Area is x10 6 m3 .Appendix B. Hydmod data^ 229ht (m) 1100 1200 1300 1400 1500 1600 1700 1800 1900 2000x (km)0.0 8.288 9.600 10.99 12.51 14.24 16.01 17.84 19.69 21.59 23.492.5 8.525 9.800 11.15 12.59 14.06 15.59 17.14 18.70 20.27 21.855.0 11.44 12.96 14.54 16.19 17.84 19.49 21.14 22.79 24.44 26.097.5 8.275 9.488 10.71 11.94 13.16 14.39 15.61 16.84 18.06 19.2910.0 7.938 9.038 10.41 11.82 13.29 14.76 16.25 17.75 19.25 20.7512.5 5.200 6.088 7.075 8.225 9.488 10.80 12.17 13.57 15.00 16.4215.0 6.050 6.850 7.713' 8.688 9.763 10.84 11.91 12.99 14.06 15.1417.5 9.263 10.64 12.09 13.56 15.04 16.51 17.99 19.46 20.94 22.4120.0 8.813 9.988 11.16 12.34 13.51 14.69 15.86 17.04 18.21 19.3922.5 6.225 7.175 8.175 9.238 10.34 11.44 12.54 13.64 14.74 15.8425.0 7.775 8.813 9.950 11.20 12.55 13.90 15.25 16.60 17.95 19.3027.5 6.625 7.375 8.125 8.875 9.625 10.38 11.12 11.87 12.62 13.3720.0 6.438 7.163 7.900 8.650 9.425 10.20 10.97 11.75 12.52 13.3032.5 4.738 5.363 6.013 6.688 7.463 8.263 9.088 9.913 10.74 11.5635.0 7.500 8.300 9.175 10.13 11.12 12.15 13.20 14.25 15.30 16.3537.5 10.59 11.76 12.95 14.17 15.42 16.71 18.01 19.31 20.61 21.9140.0 9.788 10.85 11.94 13.04 14.14 15.24 16.34 17.44 18.54 19.6442.5 10.96 12.09 13.22 14.39 15.56 16.74 17.91 19.09 20.26 21.4445.0 11.14 12.26 13.39 14.51 15.64 16.76 17.89 19.01 20.14 21.2647.5 9.800 10.87 11.95 13.02 14.10 15.17 16.25 17.32 18.40 19.4750.0 10.64 11.76 12.89 14.01 15.14 16.26 17.39 18.51 19.64 20.76Table B.4: Cross sectional areas below the given height, along the modified channel.Heights are from 1100 to 2000 m. Area is x10 6 m 3 .GlossaryAIRsondeTM instrument package which, when attached to a helium balloon, can giveatmospheric vertical sounding information (dry and wet bulb temperature, andpressure)CMC FEM Canadian Meteorological Centre Finite Element Model — a numericalmodel of the atmosphere used for weather forcastingRAMS Colorado State University Regional Atmospheric Modeling System — a stateof the art mesoscale numerical model developed by several researchers over severalyears at Colorado State University.AES Atmospheric Environment Service — Canadian Government Department respon-sible for the provision of weather services (among other things)MOE British Columbia Ministry of the EnvironmentMTH British Columbia Ministry of Transportation and HighwaysUBC University of British ColumbiaT TemperatureW WindTD Dew point temperatureP PressureASL Above sea levelRMSD Root mean square difference230UTC Coordinated Universal TimePST Pacific Standard TimeATK Point Atkinson lighthouse manned weather station (AES)ALT Alta Lake (Whistler) manned weather station (AES)PAM Pam Rocks automatic weather station (AES)SQA Squamish Airport manned weather station (AES)SQT Squamish Townsite automatic weather station (MOE)LAN Langdale automatic weather station (MOE)DEE Deeks Peak automatic weather station (MTH)HAR Mount Harvey automatic weather station (MTH)STR Mount Strachan automatic weather station (MTH)ALB Alberta Creek automatic weather station (MTH)DAI Daisy Lake automatic weather station (UBC)SQR Squamish River automatic weather station (UBC)WAT Watts Point automatic weather station (UBC)DEF Defence Island automatic weather station (UBC)BRU Brunswick Point automatic weather station (UBC)MEL Port Mellon automatic weather station (UBC)231FIN Finisterre Island automatic weather station (UBC)LOO Lookout Point automatic weather station (UBC)RAG Ragged Island automatic weather station (UBC)BibliographyArakawa, S., 1968: A proposed mechanism of fall winds and dashikaze, Met. 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