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The evaluation and modification of a prediction model for road surface temperatures McClean, Arthur A. 1993

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THE EVALUATION AND MODIFICATIONOF A PREDICTION MODEL FORROAD SURFACE TEMPERATURESbyARTHUR ALLEN McCLEANB.Sc., The University of British Columbia, 1986A THESIS SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFMASTER OF SCIENCEinTHE FACULTY OF GRADUATE STUDIESDepartment of GeographyWe accept this thesis as conformingto the required standardTHE UNIVERSITY OF BRITISH COLUMBIAMarch 1993© Arthur Allen McClean, 1993In presenting this thesis in partial fulfilment of the requirements for an advanceddegree at the University of British Columbia, I agree that the Library shall make itfreely available for reference and study. I further agree that permission for extensivecopying of this thesis for scholarly purposes may be granted by the head of mydepartment or by his or her representatives. It is understood that copying orpublication of this thesis for financial gain shall not be allowed without my writtenpermission.(Signature) Department of GeographyThe University of British ColumbiaVancouver, CanadaDate April 26, 1993DE-6 (2/88)ABSTRACTOne version of a Surface Temperature Prediction Model has beenevaluated and modified to precisely predict road temperatures androad conditions during winter nights under all weather conditionsat rural, suburban, and urban sites. The Partial DifferentialEquation approach gives encouraging results with average errorsbeing close to -0.5 °C and worse case errors of +/- 1.0 °C. TheWillmott 'D' statistic generally remains greater than 0.8 foreach site for all weather conditions. The model performs best ondata for calm and clear nights. Poorest performance occurs fornights with large sensible and/or latent heat convective fluxes.An evaluation of the meteorological characteristics of each site(open rural, east-west forest, and east-west urban canyon) isperformed. The urban canyon is consistently warmer than eitherof the other two sites. Air temperatures are not a dependableindicator of road surface temperatures because the relationshipvaries with weather conditions. Pavement near the center of theurban canyon tends to be slightly cooler than that near it's edgehowever no significant relationship is observed between thetemperature at the center of the lane and within the lane's tiretrack. No clear relationship is observed between traffic volumeand pavement temperature. The results are sufficientlyencouraging to suggest further work with the Partial DifferentialEquation Model is warranted.iiTABLE OF CONTENTSPageABSTRACT^ iiTABLE OF CONTENTS^ iiiLIST OF TABLES viLIST OF MAPS, PHOTOS, AND FIGURES^ viiLIST OF SYMBOLS^ xiACKNOWLEDGEMENTS xiiiPART I INTRODUCTIONCHAPTER 1^INTRODUCTION^ 11.1 Rationale for Research^ 11.2 Method of Testing and Modification^ 31.3 Determining Model Performance 4PART II RESEARCH DEVELOPMENTCHAPTER 2^SURFACE COOLING MODELS^ 62.1 Summary of Processes^ 62.2 General Model Development 92.3 Road Surface Temperature Research^ 142.4^Summary^ 19PART III DATA COLLECTION AND SITE ANALYSISCHAPTER 3^INSTRUMENT INSTALLATION^ 203.1 Data Requirements^ 203.2^The Sites^ 203.3^Instrument Installation^ 22iiiCHAPTER 4^OBSERVED ROAD CLIMATES^ 324.1^Site Specific Characteristics 324.2 Site-by-Site Analysis Using Time Averaged Data^424.3 Pavement Response to Weather Conditions^454.4^Inter-Site Relationships^ 48PART IV EVALUATION AND MODIFICATION OF THE MODELCHAPTER 5^REVIEW OF THE SURFACE TEMPERATURE PREDITIONMODEL^ 585.1 Theory 585.2 Modifications to the Model^ 64CHAPTER 6^MODEL SENSITIVITY^ 746.1 Sensitivity to View Factors^ 746.2 Sensitivity to Depth Temperature andWall Temperature^ 766.3^Sensitivity to Thermal Properties^ 796.4 Sensitivity to Initial Surface Temperature^796.5 Sensitivity to Air Temperature^ 806.6 Sensitivity to Wind Speed 806.7 Sensitivity to Cloud Type and Cloud Amount^80CHAPTER 7^MODEL EVALUATION AND RESULTS^ 857.1^Selection of Test Data^ 857.2 Cloudy and Windy Conditions 867.3^Calm and Clear Conditions^ 887.4^Stormy Conditions^ 887.5 Assessment of Model Performance^ 917.6 An Accounting of Model-Measured Deviations^997.7^The Influence of Traffic^ 1017.8^Summary of Force/Restore Performance^105ivPART V SUMMARYCHAPTER 8^CONCLUSIONS AND FURTHER WORK^ 1078.1 Summary of Conclusions^ 1078.2 Suggestions for Further Work^ 109REFERENCES^ 111LIST OF TABLESTable 3.1^Climate Normals For The Lower Fraser Valley1951 - 1980^ 22Table 3.2^Summary of Measurement Locations^ 25Table 3.3^Summary of Instruments^ 26Table 4.1^Evaluation of Time Averaged Site Data^38Table 4.2^Pavement Temperature Variation -Mean Bias Error^ 38Table 4.3^UBC Pavement Temperature Variation -Mean Bias Error 40Table 5.1^Atmospheric Longwave Cloud CorrectionConstants^ 66Table 7.1^Summary of Model Test Days^ 86viLIST OF MAPS, PHOTOS, AND FIGURESFigure 2.1^Various energy exchanges present at aroad surface^ 7Map 3.1^Study region showing locations of roadmeasurement sites 21Photo 3.1a^Site 1 location in urban canyon^ 23Photo 3.1b^Site 1 Close-up view. Slot cut can beseen near second lamp standard to theright of intersection^ 23Photo 3.2a^Site 2 location in vegetation canyon^24Photo 3.2b^Site 3 location in rural farmland 24Figure 3.1^Pavement thermistor installation plan^27Figure 3.2^Installation configuration diagram forVancouver (Site 1)^ 28Figure 3.3^Installation configuration diagram forU.B.C. (Site 2) 29Figure 3.4^Installation configuration diagram forDelta (Site 3)^ 30Figure 3.5^Site 1 Lamp standard installationconfiguration for urban site^ 31Figure 4.1a Infrared thermal image for Vancouverpavement and lower portion of northfacing wall^ 33Figure 4.1b Diagram of surfaces making upFigure 4.1a image^ 33Figure 4.2a Infrared thermal image for Vancouvermiddle of north facing wall^ 34Figure 4.2b Diagram of surfaces making upFigure 4.2a image^ 34Figure 4.3a Infrared thermal image for U.B.C.eastbound lanes 35Figure 4.3b Diagram of surfaces making upFigure 4.3a^ 35Figure 4.4a Infrared thermal image for Deltasouthbound lanes 36vi iFigure 4.4bFigure 4.5Figure 4.6Figure 4.7Figure 4.8Figure 4.9Figure 4.10Figure 4.11Figure 4.12Figure 4.13Figure 4.14Figure 4.15Figure 4.16Figure 4.17Figure 5.1Diagram of surfaces making upFigure 4.4a^ 36Subsurface - Surface temperature difference^41Daily temperature ranges for (a) urban site,(b) suburban site, and (c) rural site^43Daily average temperatures for (a) urban site(b) suburban site, and (c) rural site^44Time series of observed data for the urbansite under various weather conditions^46Time series of observed data for the ruralsite under various weather conditions^46Time series of observed data for the sub-urban site under various weather conditionsWestbound lanes (a-c) andEastbound lanes (d-f)^ 47Average nighttime inter-site road temperaturesfor (a) maximum and minimum at time ofminimum (b) ranges^ 49Average daily inter-site road temperatures for(a) daily maximum and minimum (b) ranges^51Average nighttime inter-site air temperaturesfor (a) maximum and minimum at time ofminimum (b) ranges^ 52Average daily inter-site air temperatures for(a) maximum and minimum (b) ranges^53Average inter-site wind speeds for(a) nighttime (b) daily^ 54Average daily road temperaturerelationship between (a) urban - suburban(b) urban - rural (c) suburban - rural^55Average daily air temperaturerelationship between (a) urban - suburban(b) urban - rural (c) suburban - rural^57Energy exchanges present on a road surface^59Figure 5.2^Surface Temperature Prediction Model(STPM) Flow Chart^ 65viiiFigure 5.3^Sky view factor geometry showing (a) actualview seen by the camera and radiatingground surface (b) view factorangle orientations^ 72Figure 5.4^Fisheye lens photographs for (a) Vancouver(b) U.B.C. and (c) Delta with computerinterpretation of each image (d-f)^73Figure 6.1^Model sensitivity to Height/Width ratios^75Figure 6.2^Model sensitivity to changes in depthtemperatures for (a) urban (b) and(c) rural^ 77Figure 6.3^Model sensitivity to changes inwall temperature^ 78Figure 6.4Figure 6.5Model sensitivity to changes in thermalproperties (a) conductivity(b) diffusivityModel sensitivity to changes in inputvariables (a) initial surface temperature(b) air temperature (c) wind speed and(d) cloud type8182Figure 6.6^Model sensitivity to cloud type for(a) cirrus (b) alto-cumulus(c) strato-cumulus and (d) fog^84Figure 7.1^Model performance at each site undercloudy, light wind, and intermittentrain conditions^ 87Figure 7.2^Model performance at each site undercalm and clear conditions^ 89Figure 7.3^Model performance at each site understormy conditions^ 90Figure 7.4^Model predictions compared to observedsurface temperatures at each site^92Figure 7.5^Daily mean bias errors for each site. MBEfor Vancouver notably improves whensensible and latent heat fluxesare excluded^ 93Figure 7.6^Daily Willmott statistics for each site(a) RMSDu (b) RMSDs (c) RMSD (d) D-stat^95Figure 7.7^Average hourly mean bias error for each site^97ixFigure 7.8^Average hourly Willmott statistics for eachsite (a) RMSDu (b) RMSDs(c) RMSD (d) D-statFigure 7.9^Model performance at each site under highhumidity conditions with fog observed atVancouver International AirportFigure 7.10 Time series of lane temperature differencesfor weekday and weekend days under calmand clear conditions at the urban siteFigure 7.11 Daily totals of number of vehicles usingroadway at (a) Vancouver and (b) Delta(data for U.B.C. are not available)Figure 7.12 Model performance results for Force/Restoreversion for all sites under (a-c) cloudyand windy and (d-f) clear and calmconditionsFigure 8.1 24 Hour forecast for Delta under (a) partlycloudy and windy (b) clear and calmconditionsLIST OF SYMBOLSQ= net radiation flux density at the surface ( W M-2Q= sensible heat flux density ( W m2 )QE= latent heat flux density ( W m 2 )QG= ground heat flux density ( W m 2 )QA= advective heat flux density ( W 111-2 )QF= anthropogenic heat flux density ( W 111-2 )Ki= short-wave radiation to the surface ( W M-2 )KT= short-wave radiation from the surface ( W 111-2 )LI= long-wave radiation to the surface ( W ra -2 )LT= long-wave radiation from the surface ( W Ta-2 )K= net short-wave radiation balance ( W in )L= net long-wave radiation balance ( W m2 )a = Stefan-Boltzman constant ( 5.67 x 10 -8 W rn-2K-4T = temperature ( °K )TA= air temperature ( °K )Tdew^ °Kdew point temperature ( K )T= minimum surface temperature ( °K )T11= minimum air temperature ( °K )Tsfc = surface temperature ( °K )T = initial temperature ( °K )0Tt= temperature at some time ( °K )T= temperature of surface i ( °K )TG= sub-surface temperature ( °K )1 = length of night ( hrs )k = thermal conductivity ( W m-1 K 1 )K = thermal diffusivity ( m2 s -1-1= thermal admittance ( J rn-2 S-1/2 K )xiKH eddy diffusivity ( m2 S-1 )p = density ( kg In-3 )7 = temperature lapse rate with height ( °K m 1 )1-B = soil temperature lapse rate ( °K m )Cp= specific heat of air at constant pressure ( J kg -1 K 1 )eA= vapour pressure ( mb )es= saturation vapour pressure ( mb )t = timec= emmissivity of surface i ( i=1,2, or 3 )0 = view factor0= wall view factorhis= sky view factor0 = angular frequency of the earth ( 7.292 x 10 -5 rad s-1 )A = wavelength ( m )H= heating coefficient ( W m2 K-1 )F = latent heat flux wind function ( mm day 1 mb 1 )EA= drying power of air ( mm day -1 )Es= drying/wetting function of the surface ( mm day 1 )a 1= azimuth angle to wall edge 1 ( rad )a2 azimuth angle to wall edge 2 ( rad )a3= elevation angle from horizon to top of wall ( rad )x = distance ( m )D = depth from surface ( m )Ci = amount of cloud of type i ( tenths )xi iACKNOWLEDGEMENTSDr. Tim R. Oke and Dr. Douw G. Steyn provided never endingsupport and encouragement throughout this research project.Their academic wisdom and insight has been vital to thecompletion of this research. Without their assistance andguidance none of this work could have been undertaken.Jamie Voogt and Rachel Spronken-Smith provided more than justencouragement. They were constant sources of information,advise, and new ideas that proved invaluable. Their help in thelab and in the field is greatly appreciated.Personal funding was provided through teaching and researchassistantship appointments. Research funding was provided underNSERC and AES grants.The research installations were completed with co-operation fromthe City of Vancouver Department of Engineering and The Provinceof British Columbia Ministry of Transportation and Highways.Without their approval and interest, the model could not havebeen validated using real-time data. The management and staff ofMainroad Contracting provided the labour and expertise inpreparing the road surface for the thermistor installations.My wife Carmel and my parents Arthur and Nan were always at myside to enjoy the successes and help me through many of thedifficulties encountered along the way. Their encouragement andsupport is so greatly appreciated.PART I INTRODUCTIONCHAPTER 1 INTRODUCTION1.1 Rationale for ResearchAs traffic volume increases on our major roadways, the demand formore effective road maintenance practices grows. Motor vehicleinsurance claims have increased dramatically over the pastseveral years, due in part to adverse winter road conditions.Maintenance authorities have come under increased pressure tomaintain safe road conditions during this critical time of yearwhile reducing the amount of environmentally harmful deicingcompounds used to treat those roads. In the early 1980'sBritain's Ministry of Transportation expressed interest indeveloping better procedures for treating winter road conditions.Their interest stemmed from concerns about the rising cost ofwinter maintenance, increased accidents due to poor roadconditions, and impacts on the environment from the use ofdeicing compounds. Ministry officials were aware of ongoingresearch where road surface temperatures and conditions wereforecast using standard meteorological parameters. Although thisresearch was in it's initial stages, preliminary results wereencouraging. In a joint research venture with the University ofBirmingham, a model was developed to provide winter maintenanceengineers with valuable information regarding the expectedconditions of their road network for an upcoming night. Althoughsuccessful, the Thornes' 1983 Model was based on a 1969 algorithmadapted to determine temperatures and conditions of road surfaces1from standard meteorological parameters. This model has acted asthe cornerstone in the development of modern road weathersystems.Comprised of several components, road weather systems arebecoming a valuable asset to the road maintenance engineer. Aroad condition sensor is installed at a strategic location withinthe road network providing data on road surface and sub-surfacetemperature, surface moisture, and the amount of deicingchemicals present on the road surface. This data is subsequentlyused by a local weather forecaster to generate input data for amodel used to develop predicted road surface temperatures for theupcoming night. The success of this system depends highly on allof it's components, specifically the forecast model itself.Much work has been performed developing the technology formonitoring road conditions, however until recently, little workhas been devoted to developing a more up-to-date model. Thepresent research is performed to evaluate the feasibility ofapplying a new model to predict the conditions to be expected ata road site between sunset and sunrise. The Surface TemperaturePrediction Model (STPM) used in this research was originallydeveloped to determine the magnitude of the urban heat island oncalm and cloudless nights. The original model considers onlythis ideal case and is not applicable to nights where winds andclouds influence the surface energy balance. There are twoversions of STPM; the Partial Differential Equation Model (PDE -JOHNSON), and the Force Restore Model (Force - OKE). This2research concentrates on the PDE version of STPM, however asummary of both versions follow in a comprehensive evaluation ofSTPM in Chapter 5 and test results using the F/R version arepresented in Chapter 7.1.2 Method of Testing and ModificationSeveral steps are undertaken to modify and test STPM beginningwith a review of previous work leading to our present dayunderstanding. These works are separated into two classes; thedevelopment of modern surface climate models and researchspecifically directed toward road surface temperature prediction.Three sites within the Lower Fraser Valley of British Columbiaare identified as prime locations to test the performance of themodel in a variety of physical settings. Each site isinstrumented to measure road temperature, sub-surface roadtemperature, air temperature, wind speed and wind direction.Hourly averages and hour-ending minute averages are measured foreach parameter at each site from December 16, 1991 to June 01,1992. Spatial and temporal variations in surface temperaturesare measured at each site in an attempt to determine theinfluence of traffic and how variations in the physical make-upof the observation site may influence surface temperatures. Theeffect of averaging times during data collection is investigatedusing data averaged over one minute and one hour periods.Comparisons are made between sites to determine the character ofthe inter-site variation.3The model is tested (night-time only) using a combination ofsite-specific data and weather observations from the AtmosphericEnvironment Service station at Vancouver International Airport.A sensitivity analysis is conducted on the model to determine theeffect of variations in model inputs on model performance.Sixteen days within the measurement period are selected to give afully representative cross-section of weather conditions for testpurposes. Model results are compared to road surfacetemperatures measured at the site with an evaluation beingperformed on the model's ability to predict measured cooling andheating rates and it's response to changing weather conditions.The performance of the model is determined through the use ofWillmott statistics (Willmott et al., 1985) and mean bias errors.Willmott statistics are generally accepted as being the standardmeasure of model performance. They are based on observed andmodeled means and standard deviations, the total root meansquared difference and it's systematic and unsystematiccomponents, and an index of agreement.1.3 Determining Model PerformanceSpecific goals and expectations should be outlined prior toconducting an evaluation of the model's performance. Only thencan meaningful conclusions be drawn on the model's ability tosimulate reality and it's potential for further use and/ordevelopment. Several characteristics are commonly used to judgethe effectiveness of road temperature prediction models. First,the model's ability to match measured surface temperatures4throughout the night is the most effective test. A deviationgreater than +/- 1.0 degrees Celsius from measured values raisesquestions about the model's performance. Second, accuratepredictions of the time of freezing and the duration the road isfrozen demonstrate the model's ability to simulate relevantfluxes at this critical temperature. Finally, how well the modelresponds to changing inputs determines it's ability to react tochanging weather conditions throughout the night.Although the model has potential applications other than for roadsurfaces, these three tests allow a clear and fair evaluation tobe performed. To be considered successful, the model must followmeasured temperatures to within +/- 1.0 degrees Celsius. Time offreezing and the duration of the road being frozen should bepredicted to within one hour. The model's response to changinginputs (e.g. low clouds) must occur within the designated inputtime step (ie. one hour).5PART II RESEARCH DEVELOPMENTCHAPTER 2 SURFACE COOLING MODELSFrom the initial work conducted nearly sixty years ago to modernday efforts, one can clearly see a pattern in research into thequestion of estimating surface temperatures. Surface energy andradiation balance approaches form the fundamental framework forestimating surface temperatures with most of the early workconsidering natural surfaces such as grass and bare soil. It wasusual to consider the simple case by setting complex variables toconstant values. More recently, efforts have been made toevaluate more complex processes in order to obtain a moreaccurate representation of the conditions experienced at avariety of different locations.A summary of processes is presented to account for the energy andradiation exchanges occurring at a road surface. A review ispresented summarizing some of the early work conducted on surfacecooling models and their development toward an application forroad surfaces. Finally, work conducted specifically on roadsurfaces is summarized.2.1 Summary of ProcessesThe temperature of a surface varies as a function of the energyexchange found at the surface as shown in Figure 2.1. A generalform of the surface energy balance equation can be written as(refer to the List of Symbols for symbol definitions);Q * = QH^QE^QG^QA^QF^(W m-2) ( 2.1)6Figure 2.1 Various energy exchanges present at a road surfaceEnergy exchange at a road surface is influenced by all of theseexchanges, the magnitude of each depending on local, site-specific conditions. The convective sensible heat flux isdetermined by the heat exchange between the surface and the airimmediately above. It is most efficient during episodes of largetemperature gradients between the surface and air with moderateto strong winds. The convective latent heat flux is influentialwhen there is a change of phase of water (condensation on thesurface and/or the freezing of existing surface water whichreleases heat, evaporation from the surface and/or the melting ofsurfdte ice which absorbs heat from the underlying road surface).Ground heat flux is a function of the temperature gradientbetween the surface and sub-surface layers and the thermal7properties of the materials. These properties characterize themedium's ability to transport and store heat. The advective heatflux impacts the surface only if there is wind and thesurrounding surfaces are at a different temperature.Anthropogenic heat flux results from the activity of humansimpacting both the surface directly and the air overlying thesurface. In the case of a road site, this includes heat inputsdue to the passage of vehicles over the road surface. Frictionaland radiational heating from vehicles lead to a warming or simplya reduction in the pavement cooling rate.The energy balance is driven by the external forcing of theradiation budget which is written;Q* = K* + L*^(2.2)Short-wave radiation is a function of sky condition (clouds andaerosols), solar angle, and presence of sky view obstructionsthat may block direct beam solar radiation from reaching thesurface or reflect additional short-wave to the road surface.Long-wave radiation is a function of sky condition (clouds andaerosols) and the presence of vertical structures near the roadsurface (eg. buildings, trees, hillsides). The radiation balanceis, like the energy balance, highly site-specific such thatdetailed knowledge of physical characteristics of the site isrequired to accurately determine magnitudes of the components.82.2 General Model DevelopmentThe first significant step in this process was work conducted byBrunt (1932) as he thoroughly investigated the role of watervapour in the atmosphere on the long-wave radiation balance atthe surface. Brunt developed a model that related theatmospheric long-wave radiation to vapour pressure recorded atthe surface. He investigated the radiation absorption andemission of both water vapour and liquid water in the atmosphereand found an increase in long wave emissions from the atmospherewith increased vapour pressure. He obtained a correlationbetween modelled and observed radiation values of 0.83, asignificant improvement over previous work. He made somelimiting assumptions in his calculations; long-wave emission fromthe surface is constant over the night, heat flux due to thecondensation of water vapour at the surface and the flux due toeddy conduction in the air are both set to zero (ie. no latent orsensible heat fluxes). These assumptions resulted in acontinuous temperature drop with time. The resulting surfacecooling equation is written as;T = To^2 L^t ) 1/21/2Or)(2 . 3 )His empirical approach, although quite simplistic, formed thebasis for further work by others.Groen (1946) expanded on Brunt's earlier work to derive a newformula using the Brunt equation as the limiting case. Groenassumed a flat surface and that the properties of the air mass9were uniform enough to permit the use of mean values (theseproperties did not change during the night).Ti = To -ff2t[^erfc^ft1/2exp - 12 (2.4) Groen's additions included the consideration that flux densitiesof eddy conductivity and condensation (sensible and latent heat)would be represented by non-zero constants and that radiationfrom the surface varied over time. Groen's results gave anexponential cooling curve that approached some asymptotictemperature limit as time approached infinity.Reuter (1951) continued the development of Brunt's work butunlike Groen, he believed some of the assumptions Brunt made werejustified under very restrictive conditions. His expansionincluded accounting for wind speed in the surface temperatureapproximation, but it did not consider advection, up or downslopemotion, or the effects of phase changes of water at the surface.2 L*Bk + (7-7d)Cp KBATo = Ti - To = - ^  (1)1/2,^,+ Opp UCH)1/2 (2.5)= (pck) 1/2His empirical constants gave good results for representativesites, however they would have to be re-evaluated for eachdifferent location.10Lettau (1951) and Lonnqvist (1962) began looking at the diurnalcycle of short-wave radiation based on the assumption that thiswas the driving force behind the surface energy balance. Theybelieved that all surface fluxes were based on the harmonicnature of solar radiation. Lonnqvist assumed there was noadvection or turbulence while looking at the first harmonic of asmall number of terms in a Fourier Series. Heating and coolingdue to condensation and evaporation respectively were notconsidered. The model appeared to operate well, however theweather from one day to the next had to be similar. The modelfailed when this was not the case. To adjust for this,fictitious data were created to simulate an identical "previous"day as each "real" day was considered separately. This work wasthe first to recognize and account for the cyclic behavior ofsurface temperatures.Since Brunt's work in 1932, the most significant step takentoward developing an operation model to forecast surfacetemperatures began with the work of Myrup (1969) who developed asimple energy balance model based on the "equilibrium temperatureconcept" which states;For a given set of boundary conditions (themeteorological and geographical input data) forced by theextraterrestrial radiation flux (a temporal-geographicgenerated function) there is one and only one surfacetemperature which will balance the flow of energy acrossthe surface.- Outcalt (1971)11Myrup's 1-dimensional model (i.e. no advection of heat ormoisture) relies on the conservation of energy approach. Netall-wave radiation (Q * ), comprised of net short-wave (K* ) and netlong-wave (L* ), is dissipated via three surface heat fluxes,namely sensible heat (QH), latent heat (QE), and subsurface heatstorage (Qs). The net short-wave is determined from radiativetransfer theory and a specific surface albedo. Net  long-wave andthe three surface fluxes are functions of temperature. Theenergy balance is then solved iteratively for the equilibriumsurface temperature.Myrup assumed horizontal homogeneity in all fluxes, a 20 cm depthof concrete for cities, an urban roughness length ofapproximately two meters per building story, an atmosphericdamping depth of 300 meters (above which conditions were assumedto be constant) and a constant evaporation flux in the city. Theintent of the model was to develop a simple climate simulator foruse by climatology students in the classroom but he discoveredanother application for the model by evaluating the magnitude ofthe urban heat island. The success of initial tests encouragedfurther, more detailed analysis of the model's potential. Thegreatest achievement gained from the model was to evaluate themagnitudes of the relevant processes. However it's operation wasnot favorable at the summer solstice and fall equinox where urbanheat island maximums were calculated to be largest in the day,opposite to the real world. Myrup believed the surprisingsuccess of the model called for further work.12Outcalt (1971) reviewed Myrup's work, making some adjustments inthe model to forecast needle ice formation. Outcalt outlinedsome restrictions for the model's operation, such as clear skies,reliable surface temperatures, detailed knowledge of thermalproperties of the soil, reliable net radiation and diurnal energybudget data, no freeze-thaw during the diurnal cycle, and minimumvariation in diurnal wind speed. His adjustments allowed themodel to function more efficiently giving better simulations ofnet radiation and surface temperature amplitudes. The model hada tendency to underestimate measured temperatures except duringheating where temperatures and maximum temperatures wereoverestimated. Outcalt (1972) continued his modifications toallow changes in elevation, station pressure, and precipitablewater to be considered. He also made changes to the atmosphericdamping depth bringing it much closer to the surface (25 meterscompared to Myrup's 300 meters) and considered all urban pavementsurfaces to be dry thus allowing the relative humidity to berepresented by the percentage of the total surface area occupiedby evaporating surfaces. The model requires sixteen boundaryconditions based on meteorological, temporal, and geographicaldata. After this work Outcalt discovered the model could beeffectively used in teaching as it allowed students toinvestigate the effect of changes in various inputs.Johnson et al. (1990) developed a model which uses a series ofpartial differential equations to estimate the heat gains andlosses between a number of surface layers exposed to the13atmosphere on one side and a sub-surface heat source (or sink) onthe other. The solution to these equations is based in part onthe assumption that heat transfer is greater perpendicular to thelayer than parallel. Associated research summarized by Oke etal. (1990) uses the force restore method and a series of ordinarydifferential equations to estimate these heat gains and losses.These two models act as the cornerstone for this research and arepresented in detail in Chapter 5.2.3 Road Surface Temperature ResearchThe first research directed to road surface temperatures wasconducted in 1969 by several British researchers. Although notrue models were developed, their work opened a new applicationin the development of surface temperature models. Hay (1969) wasthe first to see the application of this work for road weather.Using a small network of thermocouples imbedded in concrete hecompared minimum temperatures found on road surfaces with thosefound in the air nearby. He concluded that air-road minimumtemperature differences were not dependent on road wetness,traffic, magnitude of minimum temperatures, time of minimumtemperatures, or the time interval between air and road minimumvalues. Richie (1969) also studied differences in air andsurface minimum temperatures for various surfaces. He concludedthat road surface temperatures were generally higher than forgrass, slightly higher than bare soil temperatures, and are lesserratic spatially than grass minimum temperatures. Parrey (1969)related the air-road minimum temperature difference to the length14of night. A simple empirical equation was developed tocalculated this temperature difference based on the length ofnight, given byTA - TR = 0.28t - 2.9^ (2.6)t = Length of night in hoursalthough a correlation of only 0.59 was obtained.Parrey et al. (1970) evaluated three methods of estimating theminimum temperature of concrete surfaces. Using an empiricalapproach to correct for cloud and taking measurements on standardconcrete slabs (as stipulated by the United KingdomMeteorological Service) they found the following simpleregression equation provided satisfactory results;T^= 0.59 T + 0^- 4.6(Min)^(t=12)^.69^(Dew) ( 2.7)Thornes (1972) expanded Reuter's formula to account for therelease of latent heat below freezing and included a term toaccount for the variation in cloud amount. Thornes' attempted toapply this model to a concrete road surface to forecast ice orfrost formation. His work was encouraging with a nearly perfectfrost occurrence prediction.In 1979, Thornes began developing a surface climate model basedon the work of Myrup and Outcalt for direct application in acommercial venture. Thornes identified two important criteriafor successful application of this model. First, it was vital todevelop a simple, yet accurate, model to forecast road conditions15based on readily available meteorological parameters. The modelwould be applied to a site-specific location to develop anaccurate time-dependent temperature profile of the road surface.Secondly, he recognized the need to apply the results to a largerarea such as a complete road network within a given climaticregion. A technique, he called Thermal Mapping, was developed tointerpolate surface temperatures elsewhere in the road networkfrom the site-specific forecasts generated by the model.McClean (1990) presented a case study of thermal mapping for theCity of Vancouver, British Columbia by reviewing the process andresults of a thermal mapping survey conducted for the City ofVancouver in 1987. The technique involves the evaluation of roadsurface temperature data for characteristic temperature patternsbased on weather, geographic, and anthropogenic characteristics.The representative temperature pattern is transposed onto a colorcoded temperature map called a Thermal Map, one map for eachgeneral weather type as defined by the amount of cloud and wind.These maps are used by maintenance engineers to determine whichroads within their road network are most susceptible to freezing.Thornes (1989) evaluated the performance of the United KingdomIce Prediction System which used the Thornes Model and ThermalMapping and has tested the Meteorological Office Model. TheThornes Model requires three-hour average inputs for airtemperature, dew point temperature, precipitation amount, windspeed, cloud amount, and cloud type (high, medium, and low levelclouds). The model produces twenty minute forecast values for16road surface temperature and condition over a twenty-four hourperiod. Short-wave radiation is generally poorly modelledleading to very poor daytime surface temperature forecasts.There is no account for topographical influences, thus the site-specific forecast can only be generated for a roadway located inopen and flat terrain. Complex radiation geometry is notaccounted for resulting in the radiation balance being poorlymodelled at rural sites where the horizon is blocked by roadsidestructures.Rayer (1987) and Thompson (1989) have summarized the developmentof the United Kingdom Meteorology Office Surface Condition Model.It's operation is similar to the Thornes model in that the inputsand their formats are identical, however the results indicate adifference in the performance of the two models. The objectiveof the Met. Office Model has been not only to forecast minimumsurface temperatures in the winter, but also to forecast maximumsurface temperatures in the summer.Borgen and Gustafson (1989) evaluated the role of topography inroad surface temperatures. They conducted field tests alongsections of Swedish highways where road surface temperatures werecollected using an infrared thermometer mounted on a vehicle (asimilar process to that used for thermal mapping data collection)and compared their results to profiles of the surroundingtopography. They discovered roads passing through valleys werecolder than those outside valleys and the degree of coolingwithin the valley was related to the valley width and depth.17Although no model was produced, this work may lead to a betterunderstanding of the role of topography in the development ofroad temperature patterns.The effect of urban developments on air and surface temperatureshas been studied in depth by Oke (1973,1981), Oke and Maxwell(1975), and Nunez and Oke (1977). Oke studied the cooling ratesof surfaces in urban canyons using a scale model to simulatevarious canyon geometries. He also studied the urban-ruraltemperature differences and found an increase in surfacetemperatures with a decrease in sky view factors (the percentageof the hemispheric dome occupied by sky as seen from a point onthe surface). McClean (1986) studied the microscale effect ofsky view factors on urban air and surface temperatures inVancouver concluding that, although a role was played by sky viewfactors in the radiation balance of a surface, many other factorsmust be taken into consideration when modeling urbanenvironments.Sass (1992) summarizes the work performed by the DanishMeteorological Institute developing a road condition forecastmodel. The model is based on the solution of equationsrepresenting the surface energy balance and the subsurface heatflux. Model results presented by Sass (1992) show the modeltends to underpredict road surface temperatures, however theresults are most encouraging especially considering they run themodel to predict temperatures for a 24 hour period. He states18further testing is anticipated prior to the model being used inan operational form.2.4 SummaryWork has been performed to develop our understanding of variousaspects of the cooling and heating of surfaces. From the early1970's, significant research has been conducted on applying, anddeveloping further, this knowledge toward road surfaces. Variousmodels have been developed to utilize standard weather data topredict road surface temperatures. The present researchcontinues this trend by modifying and testing an existing modelto predict surface temperatures on roads using standard weatherobservation data.19PART III DATA COLLECTION AND SITE ANALYSISCHAPTER 3 INSTRUMENT INSTALLATION3.1 Data RequirementsOn-site data required for this study include road surfacetemperature, road sub-surface temperature, air temperature, windspeed, and wind direction. These data were recorded once everyhour for average hourly values and average minute values (for theminute at the end of each hour). Sky view and obstruction viewfactors were obtained using a 35mm camera with a fish-eye lens.Thermal characteristics of road materials (thermal conductivity,diffusivity, albedo, and emissivity) can be found in theliterature. Meteorological variables such as cloud type andamount, precipitation, atmospheric moisture, and barometricpressure were obtained from observations taken at VancouverInternational Airport by Environment Canada. These data arerecorded every hour and are readily available to users. It isassumed that observations from the airport are representative forthe region of study, although it is recognized that there may besome error introduced due to spatial variation of weatherparameters.3.2 The SitesThe Lower Fraser Valley of British Columbia contains the City ofVancouver, it's surrounding municipalities, and open rural areascontaining a variety of agricultural uses (see Map 3.1). Thevalley is bounded by the Strait of Georgia to the west, the NorthShore Mountain range to the north, and the Chuckanut, Lookout,and Skaggit Mountain Ranges in Washington State to the south.20North ShoreMountainsSkaggit RangeFerry TerminalSITE 1ChilliwakLuluIslandVancouver ^DeltaInternational^ ,414000,...„AirportStrait of SITE 3GeorgiaFerry TerminalBellingham LookoutRangeChuckanutRangeAbbotsfordTo SeattleSurreyTrans-Canada HighwayMap 3.1 Study region showing locations of road measurement sitesTABLE 3.1^CLIMATE NORMALS FOR THE LOWER FRASER VALLEYPERIOD^1951 - 1980STATION^FIRST FROST^LAST FROST^MEAN MIN^MEAN MAXJAN. T. JAN. T.Delta Oct 21 Apr 15 N/A N/AVan. U.B.C. Nov 16 Mar 16 N/A N/AVan. Harbour Nov 20 Feb 22 N/A N/AVan. Int'l Nov 03 Mar 31 1.6 4.0AirportThese ranges converge to the east forming a broad, v-shapedvalley and delta at the mouth of the Fraser River. The regioncontains a wide range of different road types to effectively testand validate climate models related to urban-rural settings.The region's climate is influenced by the Pacific Ocean to thewest, reducing the difference in maximum - minimum extremes intemperature and humidity. Table 3.1 summarizes the winterclimate of the region (Environment Canada, 1982).Three sites were identified for installation of instrumentationto collect relevant site data as discussed in Section 3.1. Thesesites, presented in Photos 3.1a, 3.1b, 3.2a, 3.2b and summarizedin Table 3.2, were selected to represent a range of roadconditions from a heavily used urban road passing through a deepurban canyon to a rural highway passing through farm land.3.3 Instrument InstallationThe configuration of instruments was site dependant in order toaddress each site individually. A summary of instrumentationused is presented in Table 3.3. A 15 x 50 mm slot was cut in theroad from the shoulder across the road using a twin blade22II^JAJAJAJ.,os,Photo 3.1a Site 1 location in urban canyonPhoto 3.1b Site 1 close-up view. Slot cut can be seen nearsecond lamp standard to the right of intersection23Photo 3.2a Site 2 location in vegetation canyonPhoto 3.2b Site 3 location in rural farmland24pavement diamond saw. At predetermined locations, additionalslot cuts were made parallel to the road (15 x 10 mm) where thethermistor head was placed and a 120 mm deep hole was drilledTABLE 3.2 - SUMMARY OF MEASUREMENT LOCATIONS^SITE^LOCATION^AUTHORITY^CHARACTERISTICSUrban^Georgia/^Vancouver^- high traffic volumes(1) Burrard - generally slowvehicle speed- low sky view factors- complex radiationgeometrySuburban^Pacific^Province of^- light-mod. traffic(2)^Spirit Regional British volumesPark^Columbia^- mod. sky viewfactors- dense forest on bothsides of road- significant temp.differences betweeneast- and westboundlanes due to shadingpatterns- mod. vehicle speedRural^Hwy 99/^Province of^- moderate traffic( 3 ) Hwy 17^British Columbia^volumes- high sky view factor- simple radiationgeometry- high vehicle speednear the end of the cross-road slot cut to house the sub-surfacetemperature thermistor. The thermistor cables were laid in thecross-road slot cut protected below and above by 15 mm diametercylindrical foam backer rod, as shown in Figure 3.1. The entireslot cut was back filled with a fast setting epoxy pavementresin. Site configuration diagrams are presented in Figures 3.2,3.3, and 3.4.25TABLE 3.3 SUMMARY OF INSTRUMENTSPARAMETER^ INSTRUMENTTemperature - Air^ CSI 101 Thermistor- Surface CSI 107B Thermistor- Sub-surface^CSI 107B ThermistorWind Speed^ CSI Met One 014A AnemometerWind Direction CSI Met One 024A Wind VaneData Collection and Processing^CSI CR21x Data LoggerData Storage - Delta & U.B.C.^Data Logger Memory- Vancouver^CSI SM196 Storage ModulePower Source^ D-Cell Alkaline BatteriesThe thermistor cables were carried underground through 50 mmdiameter PVC plumbing pipe to the data logger housing located ina protective box in the median at the sub-urban site and withinthe Municipality of Delta Public Works Yard at the rural site.At these two sites, a mast (5 m at the sub-urban, 10 m at therural) was erected to expose the air temperature thermistor,anemometer and wind vane. All instruments were connected to aCampbell Scientific CR21x data logger. At the Vancouver site,the data logger housing was strapped to a roadside lamp standardat a height of 4.8 m (see Figure 3.5). The thermistor cableswere carried up the lamp standard through 25 mm diameter aluminumpipe for protection. The air sensors were installed on analuminum cross-arm mounted to the lamp standard at a 10 m height.26Figure 3.1 Pavement thermistor installation planFigure 3.2 Installation configuration diagram for Vancouver(Site 1)28Figure 3.3 Installation configuration diagram for U.B.C.(Site 2)29Figure 3.5 Lamp standard instrument configuration for urban site31CHAPTER 4 OBSERVED ROAD CLIMATESEvaluating the variation of meteorological parameters and theroad surface's response to these variations is important to helpunderstand the context of this study. Only with thisunderstanding can a model be developed to perform adequately forurban, sub-urban, and rural locations. Additionally, theknowledge gained from this evaluation allows model results to bemore thoroughly evaluated.The analysis conducted on the observed data is comprised of fourparts. First, an analysis of the meteorological variability isperformed for each individual site using hourly averaged data.From this the variation in road surface temperature andcomparisons between road surface and air temperatures can be madeat each site. Second, data averaged over one hour is compared tothat averaged over one minute to determine the effect ofaveraging times during data collection. Thirdly, the response ofpavement temperatures resulting from a change in weatherconditions is studied. Finally, the inter-site variation insurface and air temperatures is evaluated to determine thedifferences among the three study sites. From this anunderstanding of the dependence on location and meteorology tothe characteristics of the local road climate can be developed.4.1 Site Specific CharacteristicsSelected infrared images of each site taken during September of1991 under clear and calm conditions are given with correspondingimage diagrams in Figures 4.1, 4.2, 4.3, and 4.4 These images32PeopleGlass Building WallConcrete SidewalkTruckTurning LaneSlow LaneFast LaneOppositeFast Lane ---Bus17.0^1^21.9 - 22. 5^1111. 0 - 17.6^1111^22.6 - 23.2^111117. 7 - 12. 3^11111^23. 3 - 23. 9 III18.4 - 19.0^111111^24.0 - 24.6^i - 119.1 - 19.7^111 24.7 - 25.3 i -19. 8 - 20. 4 MI 25.4 - 26.0 1-120.5 - 21.1^al 26.1 - 26.7 111121.2 - 21.8 In > 26. 7 C^111Figure 4.1a Infrared thermal image for Vancouver pavement andlower portion of north facing wallLamp PoleLamp PoleFigure 4.1b Diagram of surfaces making up Figure 4.1a image3318. 6 C:8. 6 - 19.019.1 - 19.619.7 - 20.120.2 - 20.620.7 - 21.121. 2 - 21. 621.7 - 22.122. - 22.622.7 - 23.123.2 - 23.623.7 - 24.1- 24. 61111 24.7 - 25.11111 25. 2 - 25.61111 > 2E5. 6 C•1111Metal FacingGlass WindowsCanopy SupportsLamp StandardFigure 4.2a Infrared thermal image for Vancouver middle of northfacing wallFigure 4.2b Diagram of surfaces making up Figure 4.2a image3412.7 - 13.013.1 - 13.13.5 - 12.813.9 - 14.214.3 - 14.6 i f14.7 - 15.015.1 - 15.415.4 C^111119.9 C9.9 - 10.2 C10.3 - 10.610.7 - 11.0- 11.411.5 - 11.811.9 - 12.212.3 - 12.6Figure 4.3a Infrared thermal image for U.B.C. eastbound lanes1 24.5 - 25.715.3 C15.4 - 16.E16.7^17.18.0 - 19.218.3 - 21.521.6 - 22.922.9 - 23.123.2 - 24.41111 25.8 -1111 31.01111 32.3 -III 33.532.233.51111is 27.1 - 28.31111 28.4 - 29.6^129.7 - 30.9L.-Traffic SignTraffic Sign)Northbound Slow LaneConcrete DividerMerge LaneFast LaneSlow LaneShoulderGrassFigure 4.4a Infrared thermal image for Delta southbound lanesFigure 4.4b Diagram of surfaces making up Figure 4.4a image36show the diverse thermal character of each site with pavementtemperatures being generally warmer than surrounding surfaces.It should be noted that a significant spatial variation exists inpavement temperatures with vehicle tire tracks being slightlycooler than the surrounding pavement. Urban canyon walls show awide range of surface temperatures ranging from near pavementtemperatures to several degrees cooler.It has been common practise to evaluate road weather modelperformance based on hour-ending (instantaneous) data collectedat a site. Hour averages were compared to just such minuteaverages collected at the end of the hour (see Table 4.1).Pavement surface temperatures and air temperatures show littlevariation between hour and minute averages with a correlationgenerally higher than 0.99. Wind speeds show a slightly greaterdifference, on the order of +/- 0.01 ms -1 , with correlationsimproving as the physical geometry of the site becomes lesscomplex. From these results it is concluded that averaging overeither one minute or one hour does not adversely impact thevalidity of the data used for evaluation or model input.The variation in temperature across the road surface at Vancouverand Delta is summarized in Table 4.2. This evaluation helps toestimate the effect of traffic on the temperature of thepavement, to assist in choosing the optimum location for a roadsensor installation, and to evaluate individual thermistorperformance. At Vancouver, the center of the eastbound fast laneis 0.2 degrees cooler than the eastbound slow lane and37TABLE 4.2 PAVEMENT TEMPERATURE VARIATION - MEAN BIAS ERRORVANCOUVER ( 4054 Observations )RT2 RT3 DEPTH^AIRRT1 -0.187 -0.352 -0.085^1.029RT2 -0.165 0.102^1.216RT3 0.267^1.381RT1RT2RT4RT5DELTA^( 4056 ObservationsRT2^RT3^RT4^RT5-0.203^---^-0.107^-0.161^0.096^0.042-0.054)DEPTH-0.0630.1400.0440.980AIR1.3131.1561.4201.474TABLE 4.1^EVALUATION OF TIME-AVERAGED SITE DATAPARAMETER^MEAN BIAS ERROR^CORRELATIONSITE NUMBER^1^2^3 1^2^3RT1 0.0026 0.0028 -0.0028 0.995 0.996 0.993RT2 0.0027 0.0039 -0.0026 0.993 0.996 0.992RT3 0.0055 -0.0720 ---- 0.993 0.913 ---RT4 ---- -0.0025 --- 0.993RT5 0.0021 -0.0042 0.997 0.992RT6 0.0022 ---- --- 0.997 ---RT7 ---- 0.0038 ---- --- 0.996 ---DEPTH1 -0.0007 -0.0012 0.0004 0.998 0.999 0.997DEPTH2 ---- -0.0000 ---- 0.993 0.999 ---AIR TEMP -0.0085 -0.0006 0.0168 0.742 0.994 0.992WIND SPEED -0.0126 -0.0101 0.0168 0.742 0.812 0.959temperatures along the tire track tend to be cooler than that ofthe lane's center by nearly 0.2 degrees. This horizontal surfacegradient is due to slightly higher exposure to the sky toward themiddle of the urban canyon, allowing for greater nocturnalradiation exchange with the sky. Road temperatures are slightlygreater than one degree warmer than local air temperature(measured at ten meters).38At the rural site in Delta, sky view factors across the roadwayhardly vary thus variations in surface temperature are moreclosely tied to traffic effects. Observations indicate almosttwo-thirds of all traffic travel in the slow lane (except duringperiods of high volumes such as the peak commuting period) resultin center lane temperatures being almost 0.1 degrees Celsiuswarmer in the slow lane compared to the fast lane. Additionally,the fast lane center is normally almost 0.1 degrees Celsiuswarmer than the surface within the tire track. Gradualcompression of the asphalt in the tire track may lead to agreater ability to transfer heat away from the surface giving aslightly cooler temperature. Traffic lanes are nearly 0.2degrees warmer than the shoulder indicating traffic may increasesurface temperatures by this amount averaged over a long period,but traffic flow variations may lead to greater difference duringpeak flows.The same analysis for the suburban site (U.B.C.) is performed forthree time frames due to the differential daytime solar heatingof the east- and westbound lanes (see Table 4.3). During thefirst period neither lane direction receives short-waveradiation, during the second period the eastbound lanes remainshaded while the westbound lanes are sunlit, and during the thirdboth receive direct sunshine for significant portions of the day.During the first period westbound lanes are only slightly warmerthan eastbound, whereas during period two this differenceincreases to over two degrees Celsius, due to the receipt of39TABLE 4.3 UBC PAVEMENT TEMPERATURE VARIATIONPERIOD 1^( 2015 ObservationsRT2^RT3^DEPTH1 RT5^RT6^RT7- MEAN BIAS ERROR)DEPTH2 AIRRT1 -0.10 -0.25 -1.28^0.08^0.13^0.06 -0.38 -0.23RT2 -0.15 -1.18^0.18^0.23^0.16 -0.28 -0.13RT3 -1.03^0.33^0.38^0.31 -0.14^0.02DEPTH1 1.36^1.42^1.34 0.89^1.05RT5 0.05 -0.02 -0.46 -0.31RT6 -0.07 -0.52 -0.36RT7 -0.44 -0.29DEPTH2 0.15PERIOD 2^( 600 Observations )RT2 RT3 DEPTH1 RT5^RT6^RT7 DEPTH2 AIRRT1RT2RT3DEPTH1RT5RT6RT7DEPTH20.41 0.530.12-1.29-1.70-1.822.572.152.043.862.492.081.963.77-0.082.432.021.903.72-0.14- 3RT2^RT3-0.25 -0.62-0.37( 1512 Observations )DEPTH1 RT5^RT6^RT7-4.61^1.50^0.96^0.74-4.36^1.75^1.21^0.98-3.99^2.12^1.58^1.36^6.11^5.57^5.34-0.54 -0.77-0.23DEPTH2 AIR0.68^4.550.93^4.801.30^5.175.29^9.17-0.82^3.05-0.28^3.59-0.06^3.823.87RT1 RT2 RT3 : WESTBOUND SFC^RT5 RT6 RT7 : EASTBOUND SFCDEPTH1^: WESTBOUND DEPTH DEPTH2^: EASTBOUND DEPTH(For specific locations of sensors, seeFigures 3.2, 3.3, and 3.4)solar radiation by the westbound lanes. This differentialheating is carried over to period three with westbound lanesbeing nearly one degree warmer than eastbound lanes. Withoutsolar heating pavement temperatures are very close to airtemperatures, but when sunshine heats the pavement, air40'Ctemperatures can be more than five degrees cooler than the road.This difference generally increases as the Sun's elevationincreases.From these results it is clear that at the suburban site asignificant deviation in the westbound sub-surface temperatureexists compared to that of the eastbound and the subsurfacetemperatures at the other two sites. Figure 4.5 displays thedifference between depth temperature and surface temperature overthe observation period. As time progresses it is expected thatsurface temperatures be slightly warmer than temperature at depthdue to the net downward heat flux associated with the march ofthe seasons. Both Vancouver and Delta show this trend after Day70, however U.B.C. shows quite the opposite, especially for the41westbound lanes. The sub-surface temperature is generally warmerthan at the surface throughout the early portion of the recordbut becomes notably warmer from Day 80 onwards. This suggestseither a significant heat source exists under the road at U.B.C.or the thermistor has failed. This site is know tohave a high water table which has caused some structural damageto the pavement in previous years. A culvert was installed tohelp alleviate this drainage problem several years ago and noflooding was observed during the measurement period (frequentlyflow from this culvert was minimal except during and afterperiods of heavy precipitation). It is therefore concluded thatthe thermistor cable has been pinched during installation therebyreducing it's resistance and elevating it's temperature reading.This may not be a constant offset if expansion and contraction ofthe road changes the amount to which the cable is being pinched.4.2 Site-by-Site Analysis Using Time Averaged DataThe temporal variation in the range of average daily surfacetemperatures is presented in Figure 4.6. Average daily pavementtemperature ranges tend to increase throughout the measurementperiod. At Delta this trend is fairly constant whereas at bothVancouver and U.B.C. a sharp change occurs in the trend (Day 70at U.B.C. and Day 90 at Vancouver). The time of this changematches the point when the elevation of the sun rises above thatof the local southern sky view obstruction. At U.B.C. thisoccurs near Day 70 whereas in Vancouver, with a much highersouthern obstruction, occurs nearly one month later.4240^( b )35-2) 3140w 26-aa 20-a0Cala^I^141111^t^i^Ul^ 11^ IU/ V VDAY WEEPti0aah1a1DAY MISERVANCOUVER DAILY TEMPERATURE RANGE^MC DAILY TEMPERATURE RANGEDELTA DAILY TEMPERATURE RANGE^30-U041 25-aa 20-waUI- 16-oa 10-DAY NUMFigure 4.6 Daily temperature ranges for (a) urban site,(b) suburban site, and (c) rural siteVANCOUVER AVERAGE DALY TEMPERATUREDAY RIVERUBC AVERAGE DAILY TEMPERATUREDAY MISERDELTA AVERAGE DAILY TEMPERATURE•^a^to a aj^141.■• X v  q1DAY MISERFigure 4.7 Daily average temperatures for (a) urban site(b) suburban site, and (c) rural siteAt Vancouver, direct short-wave radiation reaches the roadsurface only for short periods during the day, due to breaks inthe south canyon wall.Commonly, maintenance engineers use air temperature as a means todetermine pavement conditions, however the data suggest this maynot be a good practise. Daily average pavement and airtemperatures are plotted in Figure 4.7 showing the twotemperatures follow each other reasonably well early in theperiod (up to about Day 60) although differences of one degree ormore are common. This difference increases notably as solarheating elevates pavement temperatures more dramatically duringthe day toward the end of the measurement period. The deviationbetween air and pavement temperature is more clearly seen if datafrom a site for one day are plotted, as discussed in Section Pavement Response to Weather ConditionsA significant modulating force behind the spatial and temporalvariation in pavement temperatures is the character of theweather in the region. Spatial variability is enhanced duringperiods of calm and clear weather and is greatly reduced duringperiods of cloud and wind.Three days have been selected to exemplify this control. Daysrepresenting cloudy / windy, calm / clear, and stormy conditionsare shown in Figure 4.8 a-c for Site 1, Figure 4.9 a-c for Site3, and Figure 4.10 a-f for Site 2. Air temperatures tend to be45SITE 3 DAY 001 CLOUD, WIND, LT.RAIN14 ^12v10-.Waa 8-caWaEkJ 6-s-4-2 1 . i ' 4 ' 6 ' 6 'gill 'IN 12 ' 1'4 ' is ' la^20 ' 2.2 'SITE 1 DAY 001 CLOUD, WIND, LT. RAIN10^12 14^16^18 20^22TINE IN HMSSITE 3 DAY 008 CLEAR, CALMSITE I DAY 008 CLEAR, CALM10^12^14^16^18^20^22TIME 18 HOURS-2447654t 36^6-6 'i^4 10^12^14 16 18 20^22TIME IN HOURS......-^i...^N,^........^%, 1..--^'h,..^h.SITE 1 DAY 009 CLOUD, WIND, H. RAIN14^12-.100-usa7 8l-caWaW• 6I-46^i^4^i^6^10^12^14 . is ' fa ' ab ' ia 'TINE IN HMSSITE 3 DAY 009 CLOUD, WIND, H.RAINAIR815RT2814DEPTHRTI6 ' § 6^64 10^12^14^16^18^20^22TIME IN MIS1r)........ _ ......0-21086Figure 4.8 Time series of observeddata for the urban siteunder various weatherconditionsFigure 4.9 Time series of observeddata for the rural siteunder various weatherconditions46SITE 2W. DAY 001 CLOUD, WIND, LT.RAINs3 10aCa1.1a10 12^14^16 18 20^22TINE IN 1011$SITE 2E. DAY 001 CLOUD, WIND, LT.RAIN12(d)10t▪ 8-UaCz 6.aaul•.....................^..^..PTHRT7AMWifMR2-TINE IN MRS64i 2aCmoaa-46'^4^6^6^ 10^12^14^16 18^20^22TINE IN MRSSITE 2W. DAY 008 CLEAR, CALM SITE 2E. DAY 008 CLEAR, CALM10^12 14^18 18 20 22THE IN MIS(e)SITE 2W. DAY OM CLOUD, WIND, H.RAIN^SITE 2E. DAY 009 CLOUD, WIND, H.RAIN' ^6 ' 6 '^' 12^14^16^18^20^22TIM IN 9:11R3^12 ^10oconiMRRn eftr2ATI^a• 6-Ca4.4aU• 4-I-2-6^2^4^6•10^12^14TIME IN HOURS16^18 20 22Figure 4.10 Time series of observed data for the sub-urban siteunder various weather conditions.Westbound lanes (a-c) and Eastbound lanes (d-f)47warmer than pavement temperatures during cloudy / windyconditions for all three sites but are similar to pavementtemperatures during stormy conditions. The greatest variabilityexists during calm / clear conditions. In Delta, air andpavement temperatures are very close during the day but the airremains significantly warmer during the night. Surfacetemperatures are elevated above air temperatures throughout the24 hour period at Vancouver, the reverse of that found at U.B.C..Anthropogenic heating and sky view factor influences playimportant roles in creating these differences. Pavementtemperature ranges are greatest at the rural site, reachingalmost ten degrees Celsius. On the other hand, the urbanpavement has a range of only 4.5 degrees and is greatly elevatedrelative to the rural pavement. Although absolutely colder, therange at U.B.C. is similar to Vancouver.4.4 Inter-Site RelationshipsDifferences between maximum and minimum surface temperatures, airtemperatures, and wind speeds were evaluated between the threesites. Nighttime minimum and maximum temperatures are shown inFigure 4.11a and the differences between the two are given inFigure 4.11b showing a range between 2 and 9 degrees (at time ofminimum temperature). Since the difference is almost alwaysbetween the rural (coldest) and urban (warmest) pavements, it iseffectively the magnitude of the urban heat island defined interms of road surface temperatures. Maximum and minimumtemperatures for each day are given in Figure 4.12a and the daily48605040030aCaWa1 00 (b)-10^ununnnmmnnnH lllllll M llll MMMMMMM llll IMM lllllllllllllllll IMMMM llllll MMIIIMMMMMMMMM llllllll MMMHINTER-SITE NIGHTTIME ROAD TEMPERATURESBO500( a )MAX [numMINIMUMU0aaaLJ40302010-10347 357 2 12 22 32 42 62 62 72 82 92 102 112 122 132 142 152DAY NUMBERNIGHTTIME ROAD TEMPERATURE RANGE347 357 2 12 22 32 42 62 62 72 82 92 102 112 122 132 142 152DAY NUMBERFigure 4.11 Average nighttime inter-site road temperatures for(a) maximum and minimum at time of minimum (b) ranges49temperature range is presented in Figure 4.12b. Both the daytimemaximum temperature and the daily variation in daytime maximumtemperature gradually increase throughout the measurement period.During the winter period (Days 347 to 70) the diurnal temperaturerange lies between ten and fifteen degrees Celsius.Nighttime maximum and minimum air temperatures between sites areshown in Figure 4.13a and the range shown in Figure 4.13b. Thecorresponding daily values are given in Figures 4.14a and 4.14b.Air temperature ranges show a much smaller variation than thecorresponding surface values, commonly having a range close toeight degrees C as shown in Figure 4.14b. Daily wind speeddifferences between urban and rural sites (Figure 4.15) fluctuatedramatically between one and fourteen ms -1 in extreme cases.Average daily pavement and air temperatures were compareddirectly between sites. Figures 4.16(a-c) display therelationship between average daily road temperatures betweenurban and rural, urban - nd suburban, and suburban and rural sitesrespectively. Urban surfaces appear to be warmer at lowtemperatures and slightly cooler at high temperatures. This maybe a function of solar heating during the day playing a dominantrole at sites with higher exposures to shortwave radiation.Additionally during cloudy days or clear nights radiative heatingfrom roadside obstructions and anthropogenic heat sources tend todominate, elevating local surface temperatures compared tosurrounding areas.50MAXIMUM(a)^ MINIMUMP..... i•:.^; •1%. Il'it.^I ‘ III ^la,' I i: v• ...„, v^V} V-10n^ m^347 367 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152DAY NUMBER"Ua...Wa7I-aaOEWI-10(b)00%I)INTER-SITE DAILY ROAD TEMPERATURESINTER-SITE DAILY ROAD TEMPERATURE RANGE*1 0Innmmmllmunrmllll 'I llllllll I lllllll H1111111111 lllll MIIIIIIIIITUM lllll 11,1 llllll 11111111U llllll III llllll 'I llllllllll IIIII lllllll If lllll 11111111111 llllll 1347 357 2 12 22 32 42 62 62 72 82 92 102 112 122 132 142 152DAY NUMBERFigure 4.12 Average daily inter-site road temperatures for(a) daily maximum and minimum (b) ranges51(a) MAXIMUMMINIMUM30-6347 367 2 12 22 32 42 52 82 72 82 92 102 112 122 132 142 162DAY NUMBER30 (b)INTER-SITE NIGHTTIME AIR TEMPERATURESNIGHTTIME AIR TEMPERATURE RANGE-5  nnnnnunnnnnnnnannnunnunnnnnnannaunnnuununnnnunnnnnnnnnunnnnnnnnnaunnanunnunnnnnnrtnnnrt347 367 2 12 22 32 42 52 82 72 82 92 102 112 122 132 142 162DAY NUMBERFigure 4.13 Average nighttime inter-site air temperatures for(a) maximum and minimum at time of minimum (b) ranges52MAXIMUMMINIMUM-6347 367 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 162DAY NUMBER30 b)UaW 16-aW 1 -aINTER-SITE DAILY AIR TEMPERATURESDAILY AIR TEMPERATURE RANGE-6 347 367 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152DAY NUMBERFigure 4.14 Average daily inter-site air temperatures for(a) maximum and minimum (b) ranges53\e. M P.: t.: W "i: -^l^-....^•.-1 6MAXIMUMMINIMUM(a)12-8-i14-16 ^14-12-ivl(b) MAXIMUMMINIMUM,I)INTER-SITE NIGHTTIME WIND SPEEDS0^IIIIIMIIIIII1 11111 I lllll 11111111111 lllllllll ITU lllll IIIIIIIIII lllll U lllll ITITI lllllllll UITIMI lllll U lllllll 1111111111111111111H1111111UMMI1111111111111 llllll I347 357 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152DAY NUMBERINTER-SITE DAILY WIND SPEEDSP.0 nmmmmmm m mmmmmmm mmmmm mmummmm m mmlmmmmmm m mmmmm mmmnmmmmmnm m m m mmilummmmmmmmmmm347 357 2 12 22 32 42 52 62 72 82 92 102 112 122 132 142 152DAY NUMBERFigure 4.15 Average intersite wind speeds for(a) nighttime (b) daily5410^15MIA ROAD TEN:MATURE ('C)10^16ECM ROAD TOPERATUREAVERAGE DIURNAL ROAD TEMPERATURESb^1.0^1'6^a^a^a^asLOC ROAD itlPEiATlllEAVERAGE DIURNAL ROAD TEMPERATURESIllLri^ AVERAGE DIURNAL ROAD TEMPERATURESFigure 4.16 Average daily road temperature relationship between(a) urban - suburban (b) urban - rural(c) suburban - ruralAir temperature relationships between the three sites show a moreconsistent bias as displayed in Figures 4.17(a-c). Average dailyair temperatures are lowest at U.B.C. compared to the other twosites due in part to the vegetation canyon shielding the airwithin it's volume from solar heating and providing littleanthropogenic heat such as that found at the Vancouver site.Daily average air temperatures in the urban center are notablywarmer than the other two sites. Significant contributions fromanthropogenic heat sources and multiple reflection and re-emission of radiation tends to keep air temperatures elevated,especially during the night at the urban site.56u 20a1-16.aai- 10-aa 6-WO1'0^16WC AIR TEMPERATURE CT)250aaawiaaDO0^16DELTA AIR TEMPERATIVE OC)8wiaaaatafd10^16DELTA AIR TEMPERATURE OC)AVERAGE DIURNAL AIR TEMPERATURES AVERAGE DIURNAL AIR TEMPERATUREAVERAGE DIURNAL AIR TEMPERATUREFigure 4.17 Average daily air temperature relationship between(a) urban - suburban (b) urban - rural(c) suburban - ruralPART IV EVALUATION AND MODIFICATION OF THE MODELCHAPTER 5 REVIEW OF THE SURFACE TEMPERATURE PREDICTION MODEL5.1 TheoryMaterials cool and heat due to the energy exchanges at theirsurfaces and their ability to store and transfer heat. Bothversions of the Surface Temperature Prediction Model (STPM) takethis into account in their attempts to estimate nocturnaltemperatures. Figure 5.1 shows the energy sources present at aroad pavement surface by night and day. The rural surface can besimulated by considering a flat horizontal plane with only a fewminor vertical surfaces present whereas the urban surface systemincludes both horizontal and vertical surfaces thereby creatingmore complex interactions between energy sources and sinks.The Partial Differential Equation (PDE) version of the model usesa series of partial differential equations to estimate the heatgains and losses between a number of surface layers exposed tothe atmosphere on one side and some subsurface heat source orsink on the other (see Johnson et. al., 1990). The model assumesthat heat conduction perpendicular to the layer greatly exceedsconduction parallel to the surface. This allows a one-dimensional heat conduction equation to be used for each surfacein the form;OTI^a2Ti = Ktat^ax2 (5.1)58(a)^RURAL - NIGHTLskyL obj1(b)^RURALKdown- DAY_LskyL obiKu.^Lu•Lup1 Deep Heat SinkT Deep Heat Source(c)^URBAN - NIGHTLLwallkyLwal(d)^URBAN - DAYI,/KdownLskyLwallNLwallHeatSink<HeatSink<—HeatSource /---HeatSourceNil ----Lup Lup KupDeep Heat Source v Deep Heat SinkFigure 5.1 Energy exchanges present on a road surfaceThe radiative heat gain by a point on a surface exposed to othersurfaces can be expressed as;L* = Ci T [EE .1 O Ji j T^i4 - 4J. 1 (5.2)The model assumes no latent or sensible heat transfer, groundheat flux is in balance with the net long-wave radiation balanceat the surface, and there are no temporal changes in weatherconditions throughout the model run. Boundary conditions set forthe model are, for the interior of the layerTi (0,t) = TG (t)^ (5.3)for the interior of the building wallsaT i (o,t)k1 ^ - £1 T [ est T: i (t) - T i:(0,t)]axrs+ 2.09 [ TBi(t) - T i (0,t)and for the exterior of the layer(5.4)aT i (D i ,t)^Atk ^ — L^1=1,...,n^ (5.5)iaxwhere the net long-wave radiative flux density is given asNL*i =c[ jE1 c 0 ji c• T4 (D i ,t) +0Si Ly -TT4 (D i ,t)]i^=^j^l*jN N+Ci o- k=E1 j=E 1 0^(1-£ k ) 0 jk C j T4 (D j ,t)kik*1 j*k(5.6)To solve these equations, emissivity, thermal diffusivity andconductivity, and both the inner and outer temperatures for eachlayer must be specified. View factors for all other surfaces60(including sky view factor) for each surface must be given. Inthe case of the urban canyon, a height to width ratio may beused. Incoming long-wave radiation must also be given oralternatively, air temperature (TA) and vapour pressure (eA) maybe supplied to calculate incoming long-wave using one of(1500/T )-"( Idso, 1981): Lj = T^[ 0.70 + 5.95 x 10-5 eA e^A ] T4A(5.7 a)SKY or ( Idso -^ ,-4 „..2(-7.77X10Jackson, 1969): L =^1 - 0.261 eSKY^A I T4cA(5.7 b)Once a time step and a finish time have been specified, the modelis used to solve these equations using the Crank-Nicholsonmethod, iterating to a solution of temperature as a function oftime and depth in the layer. The model has commonly been run fortime periods between sunset and sunrise to avoid the daytimeshortwave radiation flux input. However, diffuse short-waveradiation near sunset and sunrise is allowed for within themodel.The Force Restore Model (F/R) is a simplified version of the PDEapproach whereby the partial differential equations have beenreplaced by a set of ordinary differential equations which modelheat flow within a single surface slab. The major assumptionsmade in this approach are that the forcing function is sinusoidalin character with frequency equal to the Earth's angularfrequency: 7.292 x 10 -5 rad s -1 and that the thickness of thelayer is approximated by the depth of penetration of the diurnal61dT (D ,t)(20) 1/2dt Li - 0 ( T(D I ,t) - T )^(5.8 b)Atemperature wave. Temperature as a function of time may bedetermined usingdT(D,t)^ - (20)1/2dt^A^Li - 0 ( Ti (DI ,t) - TG)^(5.8 a)where^ ui= (c A ) 1/2for horizontal and vertical surfaces respectfully. The initialcondition isTi(0,0) = f (0)^ (5.9)To solve these equations values for the thermal diffusivity andheat capacity of the layer (or the thermal admittance), initialsurface temperature, and an initial deep layer temperature mustbe specified. These equations may be solved using standardcomputer packages capable of solving ordinary differentialequations. Originally, IVPRK was used which solves initial valueproblems using the Runge-Kutta-Verner fifth-order and sixth-ordermethod. Another alternative is to use ODEINT and RKQC routinesfrom Press et al. (1986) which uses a fifth order Runge-Kuttamethod. The second method is used in the present version ofSTPM.The F/R version of STPM was tested for three real surfaces andone model canyon constructed from concrete blocks arranged invarious configurations to simulate a variety of urban canyonstructures. The tests were conducted using data sets that metthe 'ideal' weather condition scenario (i.e. calm winds and62cloudless skies). The model performed well for a tropicalsavannah case with modelled temperatures being within 1.3 degreesof those measured (within the stated measurement error if +/- 2degrees Celsius). Similar results were obtained versus datacollected at a cultivated bare soil site near Vancouver.Simulated temperatures were within 1.2 to 1.4 degrees of measuredvalues respectively for two different loam/silt-loam plots.Surface temperatures for the urban canyon case were not availableso model performance was inferred from air temperatures. Withthis limitation it was concluded that STPM (F/R) simulated theurban canyon case well with cooling trends matching thosecollected from other studies. Using data from a model canyonmade of cement blocks the model estimated temperatures for thecanyon floor well, however the measured temperatures for thewalls showed a more linear decline than the model predicted.Estimates of urban-rural differences (the magnitude of the urbanheat island) were obtained for various initial conditions andurban configurations. STPM (F/R) tended to have a poor fitduring the early evening period of urban heat island growth.However the lack of appropriate data sets restricted the abilityto fully evaluate the response of STPM (F/R).Oke et al. (1990) applied the Force Restore version of STPM toevaluate the relative importance of the commonly accepted causesof the urban heat island by studying the affect of urban canyongeometry, thermal properties, anthropogenic heating, and theeffect of cloud (upon the incoming long-wave term) on model63results. They concluded that radiation geometry plays asignificant role in the temperature regime of urban heat islands,and that differences in thermal properties alone can generate asignificant heat island. Variations in cloud conditions betweenurban and rural sites can eliminate a heat island altogether whenfog is present over rural locals but not over the urban area.They summarized that STPM (F/R) provided a reasonable estimate ofthe magnitude of the relevant processes contributing to thedevelopment of the urban heat island.5.2 Modifications to the ModelModifications to STPM were made to account for additionalprocesses present at a road site. Work concentrated on the PDEversion of STPM, although all changes made to STPM were made toboth the PDE and F/R versions. A flow chart depicting theoperation of the model is presented in Figure 5.2. Input fileswere altered to use hourly data for all relevant parameters.Oke et al. (1990) suggested the F/R version did not adequatelyhandle the early evening cooling in an urban canyon. This may bedue in part to the temporal variability of the inputs used to runSTPM. Hourly values would assist the model by making step-wiseadjustments in the model inputs throughout the model run period.Additionally, attempting to model the real 'active' rural andurban settings, where conditions do not remain constant duringthe night, requires changes in the model input files. A modelfor ideal conditions would certainly give better results, but isonly relevant to a limited set of conditions. Weather conditions64[IF--IF TPRIADL PRIADFEUDPRIADIF— PREALD—IF—PREALD— PREPLYFSYSINTSYS— PRPSYSFREPLYDPREPLYIFPREPLY—PRPLAD— IF—PREPLYPREPLY— IF— PRPLAD— PRPIAD— PREPLY— IF—PREPLY— IF—PINTOPREPLYPREPLYSTSYS^TI SYS^STENSS^[IF— VT^IF— SURFTPI RIVAL^L. NMI— LNVCT— SOLAR.- SUNPOS— CLRSXY— CLOUDNETCFP IF^CFFSYS BDSTS^OUTS^IF DSTS^ BDSYS IF^IF^1 I LIF^CNCOEFF —IF IF^SURFTP —.- IF^SLVSYS^IOUIPLTST -.- IF LINTP CNSLYZ —IFI- LINTP IF[IFLIMPLIE. IF —^ET DSOSSEIT— IIT-.LINTP L IINTP I— LINTP —TURDIF —IF — NO IST— IF I— LINTP — TURD — SXYLV— TURDLINT? — MOIST — WETLY— MOIST-- LVEIT— LIMITUPOS— S IP — IF-- NTU0RISTI3I— SXYLV --. CLRSXY L LINT? — SXYLV— IF — CLOUD — WETLYLINT? — ODEINTPREPLY— DOSEIT— UDSYSIF^IF^ IF— IF LINT?^FPLSYS^— IFOUTS^• L FIN2PLT^L IFIF IF^ h. PLOT3D^  /Ia.^L FPLSYS^IFPLTST^L F/12PLT^I- non^- IFIFLPSYS — FLOTDL FN2PITIFL FLPSYSL IN2PLT—IFPLOT3DIFLpurnFigure 5.2 Surface Temperature Prediction Model (STPM) Flow Chartchange over time and a full test of a surface temperature modelwould include an evaluation of it's response to such changes.As Oke et al. (1990) suggest, cloud can alter the sky long-waveradiation output by nearly 30 percent. The presence of clouds atthe beginning, and certainly at some time during the modellingperiod, can have drastic effects on surface temperatures inurban, but especially rural settings. Using a form suggested byOke (1987) the clear sky long-wave radiation is corrected for thepresence of clouds usingLI = LI [ (1 + a1C1) (1 + a2C2) (1 + a 3 C3 ) (1 + a4C4) (5.10)(1 + a5 C5 ) (1 + a6 C6 ) (1 + a7C7 )where the values of the constants are given in Table 5.1 (Oke1987, p374).TABLE 5.1 ATMOSPHERIC LONG-WAVE RADIATIONCLOUD CORRECTION CONSTANTSCIRRUS^al = 0.04CIRROSTRATUS^a2 = 0.08ALTOCUMULUS a3 = 0.17ALTOSTRATUS^a4 = 0.20STRATOCUMULUS a5 = 0.22STRATUS a6 = 0.24FOG^ a7 = 0.25Sensible heat exchange between pavement and overlying air hasgenerally been assumed to be very small during calm nightscompared to the long-wave radiation and ground heat fluxes.However in the presence of wind, the air's ability to transportheat away from, or to, the surface can not be overlooked althoughthe magnitude of the sensible heat term may still be relatively66small. Several methods exist to estimate the sensible heat fluxpresent at a site (see Stull, 1988). Aerodynamic similarityprofile methods require measurements at two levels and must obeyseveral assumptions; steady state conditions (no marked changesin the radiation or wind fields during observations), constantflux with height (no vertical divergence or convergence),similarity of all transfer coefficients, and a uniform,homogeneous surface. Initial tests using the collected data andthe aerodynamic approach, assuming the air in contact with thesurface was at the surface temperature, gave unrealisticallylarge fluxes especially in an unstable atmosphere.The turbulent sensible heat flux can be estimated using a simplebulk aerodynamic approach utilizing a heat transfer coefficient(a function of wind speed) and the surface to air temperaturegradient. Clark (1985) presents a well-established empiricalcorrelation between the surface heating coefficient and the near-ground level wind speed. The advantage of this method is thatonly surface temperature, air temperature, and wind speed arerequired, the latter two being measured at one level only.Considering the expected small size of the sensible heat term atnight, this approach was deemed reasonable for inclusion andtesting in STPM.The importance of latent heat exchanges can best be seen byconsidering the condensation of a 0.1mm thick layer of water onthe surface. The resulting release of 240.9 KJ would balance anenergy loss rate of 100 Wm -2 (typical early evening rate) for67just over forty minutes. Should this same layer freeze, anadditional 33.4 KJ would be released, balancing the same energyloss rate for just over five minutes. This is important whenconsidering the time and duration of freezing of a road surface.The exchange of latent heat at a pavement surface can be a verycomplex process. It is dependent on the presence or absence ofmoisture on the surface, the relationship between the surfacetemperature and the dew point temperature of the overlying air,the dew point depression, the occurrence of precipitation, thepavement's temperature in relation to freezing, and the role oftraffic in splashing free water away from the surface (therebyreducing the amount of water to be evaporated). Road pavement isimpermeable to vertical water transport making it different frommost natural surfaces such as soil. Much of the precipitationfalling on the pavement will run off to gutters, thereby limitingthe amount of free water remaining on the surface.Two routines were developed to estimate sensible and latent heatexchanges at the road surface. The sensible heat flux density asa function of wind speed and the temperature difference betweenthe pavement and the air is given byH = 5.8 ( 4.1 11 )QH = He ( TA - Tsfc )68The latent heat flux density is estimated using pavement, air,and dew point temperatures, and the moisture gradient between thepavement and the air by way of a bulk mass transfer equation (seeBrutsaert, 1984). The advantage of this method is thatmeasurements of specific humidity, wind speed, and temperatureare required at one level only which is useful when such profilemeasurements are often not available. The wind function isexpressed as(5.12)and the drying power of the air is given byEA = Fe ( U ) ( eA• — eA- )^ (5.13)The drying/wetting function of the surface is given byEs = Fe ( u ) ( es- eA )^ (5.14)with the actual latent heat transfer, to or from the surface,(considering the time step of the model) is given by^F (^) ( ;;Ak )QE^e S (5.15)The magnitude of the resulting latent heat flux is limited by theamount of water present on the surface for evaporation and thedrying ability of the overlying air mass. If neither of thesetwo factors limit evaporation then evaporation occurs at thepotential rate. The energy exchange due to freezing of water orthe melting of ice on the road surface is determined from themass of water present on the surface and the relationship betweenF = 0.26 [ 1.0 + ( 0.54 i3 )e8640069surface temperature and the freezing point. It is assumed thatthe maximum amount of moisture present on a road surface is0.1 mm, due to runoff and traffic splash. Freezing of this watergradually occurs over a one hour period to prevent the model fromadding a step change energy input. Sensible and latent heatfluxes are added to the incoming long-wave term as supplementalenergy sources.The inclusion of an estimate of the magnitude of the solar heatflux received at the surface during the day is vital if the modelis to be modified to perform for the entire diurnal cycle. A newroutine was developed to estimate solar heat flux at the surface,including the effect of local geometry and cloud. The model usesa method suggested by Davies and Hay (1980) to determine thecomponents of short-wave radiation. The routine determines theposition of the Sun in the sky and the resulting potential short-wave radiation receipt at the surface. This value is thencorrected for the presence of any cloud. Sky view geometry isused to determine if the direct solar beam is intercepted byobstacles on the horizon and one general reflection term isincluded in the estimate. Albedo is added so as to be able toestimate the net solar and all-wave radiation balance for thesite.In the original version of STPM, the rural case was considered topossess simple geometry with sky view factors near unity.Although the model accommodates a non-unity view factor, it doesnot incorporate the long-wave contributions from horizon70obstructions. A modification was made under the assumption thatthese obstructions were comprised of vegetation and theireffective surface temperature matched that of the local airtemperature. The contribution of this long-wave emission is verysmall in this study, but could potentially be quite large in amore geometrically complex rural site.The horizon obstruction geometry for each location is determinedusing a method similar to that suggested by Steyn and Lyons(1985). Sky view photographs are taken using a 35 mm camera witha standard fish-eye lens which allows the full hemisphere to beviewed. Angle measurements are taken from the image in polarco-ordinates as shown in Figure 5.3.71ttoFish-eye lens photographs for the three study sites, with thecomputer interpretation of their images, are presented in Figure5.4. Using these images the obstruction view factors can beobtained using0w =^( a2- a3 ) + cos (a) [ atan (cos (a3 ) tan (a 1 )) -atan ( cos (a3) tan (a2 )^/ 2110 = 1 - E 0For an urban canyon the model requires similar view factors fromboth walls of the canyon. These are obtained from the floor viewfactor photo relating known canyon width to estimated wallheights using standard geometrical relationships (e.g. Oke 1987).A new simulated view factor image is then created for the middleof each wall allowing view factors for the floor, opposite wall,and sky to be obtained.270(a)l'.... \ V \\ .'..Ae/ 82 7‘ \^/• \/ . . / \ \^1 / I ti,L.-_:' t.---_-\-o--77-÷..-- L--- — ===--k- ...  -Figure 5.3 Sky View Factor geometry showing (a) actual viewseen by the camera and radiating ground surface(b) view factor angle orientations72Figure 5.4 Fisheye lens photographs for (a) Vancouver (b) U.B.C.and (c) Delta with computer interpretation of eachimage (d-f)7 3CHAPTER 6 MODEL SENSITIVITYThe Surface Temperature Prediction Model (STPM) has been testedusing the data collected from three road sites in the LowerFraser Valley of British Columbia. Performance of the model inforecasting pavement temperatures depends significantly on theaccuracy of inputs supplied to the model. Using observed data tovalidate a model makes no statement of the model's response toerrors in input values, thus an analysis has been conductedprior to validation, to determine STPM's sensitivity tovariations in input values. Oke et al. (1990) performed anevaluation of the Force Restore version of STPM to determine thesensitivity of its output to each parameter. A similar analysiswas not undertaken on the PDE version. The sensitivity of thePDE version of STPM to variations in view factors (urban), depthtemperature (urban and rural), canyon wall temperature (urban),thermal properties (rural), initial surface temperature (rural),initial air temperature (urban and rural), wind speed (urban andrural), and cloud type and amount (urban and rural) are testedand compared to data observed on a calm and clear night(January 06 - 07, 1992).6.1 Sensitivity to View FactorsView factors contribute significantly to the development andmagnitude of the urban heat island and to the magnitude ofpavement temperature variations in rural road networks. Thisanalysis was performed using variations in height to width (H/W)ratios for an urban canyon (see Figures 6.1a-d).742-I^,7(b)8- - - - .:F:ii:!!Hil:::::--. ;ii iii - 1!=ii:":"=": ':..-.,..:::::::lizf.::-::21::::.:::::::::: ' :::::F.:3 '''''''' .•.' ' •,zi:::::::::::=::;:::=t::: '' = -- -...::::::::-:::::::..-..:----------- ----. ----- rz:.---- ---.:::---------::::::::::: ----- :::::----------^' Ihlulhhiao 17.0 lao 12.0 20.0 21.0 220 23.0 0.0 1.0TINE IN HOURS--------^--60 7.04.0 603 , f ----3020ao4.03 6302.6MEASo-16-4-3-2-H/W RATIO SENSITIVITY TEST - PDE2.01.5MEAS1 .00.118.0 17.0 190 19.0 20.0 21.0 220 230 0.0 1.0 20 aoITT IN HOURS40 ao a° 7.0H/W RATIO SENSITIVITY TEST - PDEFigure 6.1 Model sensitivity to Height/Width ratios75All other parameters remained unchanged while the H/W ratio wasvaried. As expected PDE demonstrated increased cooling with adecrease in H/W ratio. The model output became more linear asH/W increased but continued to cool throughout the night. PDEapproximated the linear trend in urban surface cooling well. Themodel became less sensitive to H/W changes as H/W became large.A height to width ratio of close to 1.0 resulted in the closestmatch to measured values. The model assumes an infinitely longcanyon with solid walls at relatively constant heights. For areal urban canyon, the assumption of a solid canyon wall ofconstant height is unrealistic (there are many spaces betweenbuildings, especially near intersections, and wall heights arerarely constant along the canyon's length). The sky view factorfor the Vancouver site determined from a fish-eye lens photographfor the center of the street, is 0.41. This corresponds to a H/Wratio of approximately 1.1, in good agreement with the model.Individual canyon segments have significantly higher H/W ratiosthan 1.0, but the canyon taken as a whole, with it's variationsin wall heights and building spacing effectively reduces the H/Wratio.6.2 Sensitivity to Deep Sub-surface Temperature and WallTemperatureKeeping all other values at 'base' values, the depth temperaturewas varied for both urban and rural sites. Figures 6.2a-c showthe PDE model is not very sensitive to changes in the 120 mm deep76( c ) RURAL SITEa do 6.00 3.0 4.0atcad '1 t.d '1 a.d 'led '26d '21.d^CLO 1.0TIME IN HMS0.01.13 1.0181.0U0azW •1aW2- 2-DEEPTEMPERATURESENSITIVITYTEST-PDE6-URBAN SITE WALL TEMP=15.0(a )0DEEP TEMPERATURE SENSITIVITY TEST - PDEo-(b)^ RURAL SITE6.3--3-.4--6-0a0^aa0 00 7'.0 Sad .44^Od '254 d 0.0 1.0 20 3.0 4.0 et, 6.0 7.0TIME IN ROMScad^'ad '16d '2dd 'lid '2id^ao 1.0 24 3.0 4.0TIME IN HOURSDEEP TEMPERATURE SENSITMTY TEST - PDEFigure 6.2 Model sensitivity to changes in depth temperatures for(a) urban (b) and (c) rural,,,,,^,^,,,,,,,,20 ao 6.0 .7:04.0(a)^URBAN SITE DEEP TEMP = 3.06-4-3-2-0^-120.0MEAS15.010.00.0160 17.0 18.0 19.0 230 21.0 220 230 0.0 1.0TIME IN HOURSFigure 6.3 Model sensitivity to changes in wall temperature78LI0aratemperature. A change of four degrees in deep temperature,results in a one degree change in surface temperature at the endof a 16 hour night at the urban site, and a 2.5 degree change indeep temperature gives less than one degree change in surfacetemperature over the same period at the rural site. Increasingthe deep temperature results in a decrease in cooling rate atboth sites.The model is less sensitive to changes in wall temperature asshown in Figure 6.3. A change of five degrees in walltemperature results in slightly less than a one degree change inpavement temperature at the end of 16 hours. Increased walltemperature produces increased modelled surface temperatures.This is to be expected due to the increased long-wave radiationemission of the walls to the canyon floor.WALLTEMPERATURESENSITIVITYTEST-PDE6.3 Sensitivity to Thermal PropertiesThermal properties of pavement materials are readily available inthe literature. A range of values for both thermal conductivityand thermal diffusivity were used from Oke (1987). Thermalconductivity for the pavement was varied for the rural sitekeeping all other parameters at base values. Increasing thethermal conductivity resulted in higher predicted surfacetemperatures, and a more linear cooling trend (Figure 6.5a).Decreasing the conductivity drastically increased the earlyevening cooling rate in both cases. Increasing the thermaldiffusivity provided an increase in predicted pavementtemperatures (Figure 6.5b). The model becomes more linear withincreasing thermal diffusivity.6.4 Sensitivity to Initial Surface TemperatureInitial surface temperatures were varied between 0.0 and 8.0degrees and compared to measured temperatures as shown in Figure6.6a. After this initial deviation, predicted temperatures beganto converge to a common value in both cases, although a smallvariation of approximately 0.5 degrees remained at the end of 16hours. The accuracy of initial surface temperatures is criticalshould freezing occur early in the night. The model errssignificantly during this time in it's prediction of bothabsolute temperature and the time at which the pavement surfacedrops below freezing.796.5 Sensitivity to Air TemperatureAir temperatures were modified by allowing them to deviate by -3,-1, +1, and +3 degrees from actual measured values keeping thetemporal trend in air temperatures the same (Figures 6.6b and6.7b). Both models responded similarly with a negative deviationin air temperature resulting in a higher predicted cooling rate,and a positive deviation giving a lower predicted cooling rate.A consistent deviation of two degrees in air temperature resultedin a surface temperature difference of just over 0.5 degrees forPDE and just under one degree for F/R by the end of the night.6.6 Sensitivity to Wind SpeedWind speed was varied from 0.0 to 8.0 ms -1 with the windremaining constant throughout the night. Increasing the windspeed resulted in an increase in predicted surface temperature.It is recognized that this is highly dependent on therelationship between air temperature and surface temperaturethroughout the night (an air temperature colder than the roadwould result in a lower predicted surface temperature withincreased wind speed). The magnitude of the differences variesthroughout the night due to the size of the difference betweenair and predicted surface temperature.6.7 Sensitivity to Cloud Type and Cloud AmountKeeping all other inputs unchanged from base values, cloud typewas varied to include clear skies, Cirrus (Ci=0.8), Alto-cumulus(Ac=0.8), Strato-cumulus (Sc=0.8), and Fog (F=0.8) with the cloudtype and amount remaining uniform throughout the night.80CONDUCTIVITY SENSITIVITY TEST - PDE160 17.0 1a° 19.0 20.0 21.0 220 2a0 ao 1.0 2.0 ao 40 6.0 8.0 7.0TINE IN HOURSDIFFUSIVITY SENSITIVITY TEST - PDE(b)^THERMAL CONDUCTIVITY = 1.51 Wm KU -4-0-o -6-a -I-• 13-O'^_a• -1 O-E _I- A2-.............^..... _:::::: .....^. .-14--18-aoMEAS4. 1 71111111 111111111 1 ..........160 17.0 18.0 180 20.0 21.0 22.0 230 ao 1.0TINE IN HOURS1111^ 11120 ao 40 ao 80 7.0Figure 6.4 Model sensitivity to changes in thermal properties(a) conductivity (b) diffusivity811 .^143^' d ' 8d '14d '264 '21 dSURFACE TEMPERATURE SENSMVITY - PDE2-aCaaW -2-04-8184 'lid 'Ad '14.dd 26 d^d '224 '284 ao 1.0 2.0 3.0 4.0TIME IN HOURSo a0 iaWIND SPEED SENSMVITY - PDE(C)4-0^•^,,, .m!t!r?1Ft,!! !.n: := !:t!r:E:',''4-aaA-.+0.0^1.0^2.0^3.0^4.0 ill^6.0TIME IN HOURSe.os.o4.02.00.04-2-0^aaacaW .2-w4-2-0a7aaW -2-w+-e-AIR TEMPERATURE SENSITIVITY - PDE CLOUD SENSMVITY - PDE 3.01.0ICUS-1.0CI( b ) (d)-3.081a.d^'id .d  '16.d '28d^d^'2id 0.0 1.0 2.0^3.0^4.0^0 6.0^110 eilkd if.d 'id.d '14d '28.d '21 d '221 '24.d 0.0 1.0 2.0 3.0 4.0 60 6.0 /ATIME IN HOURSTIME IN HOURSFigure 6.5 Model sensitivity to changes in input variables(a) initial surface temperature (b) air temperature(c) wind speed and (d) cloud typeFigure 6.6d shows that lowering the cloud layer (keeping thecloud amount unchanged) results in an increase in predictedsurface temperature. Changing cloud type in this way resulted ina deviation in predicted surface temperature of about twodegrees.Cloud amount was varied for Ci, Ac, Sc, and F while keeping allother variables at base values. From Figure 6.7a-d it is clearthat PDE predicts higher surface temperatures with increasedcloud amount and responds more dramatically to increasing lowercloud compared to higher cloud. Final predicted temperaturesdeviate by no more than 0.5 degrees when the amount of Cirruscloud cover is changed from 0.2 to 0.8, whereas nearly twodegrees deviation results when Fog is varied by the samefraction.83t 1Ca-3-0.0 1.0 2.0 a0 4.0^0 6.0TIME IN HOURSsad f d ' id ' id 'aid '21d '2id '24d( a ) CIRRUS (C) STRATO-CUMULUS3.QWC•"N. 6 4.4 f d ' id 'lid^'21 d '24d '24.d 0.0 1.0 20 3.0 4.0 e, 80 7.0TIME IN 10.112S0.6SM0.21.^ 80ALTO-CUMULUS(b)3-s leso^lid thd 21 d 240 2i.d 0.0 1.0 2.0 3.0 4.0Ir^ 5,3.41-Ed^16.1 ,id ai(d) FOGCLOUD SENSMVITY - PDE^CLOUD SENSITIVITY - PDECLOUD SENSITIVITY - PDETIME IN HOURSCLOUD SENSITIVITY - PDETIME IN HOURS0.80.5MKS0.20.80.5MKS0.2Figure 6.6 Model sensitivity to cloud type for (a) cirrus(b) alto-cumulus (c) strato-cumulus and (d) fogCHAPTER 7 MODEL EVALUATION AND RESULTS7.1 Selection of Test DataThe Surface Temperature Prediction Model was tested usingcollected data from sixteen days within the observation period.These days present a variety of weather conditions in which tofully test the performance of STPM (see Table 7.1). Values ofsurface thermal properties were selected to obtain a best fitwhen cloud, wind, and precipitation were absent from within arange of literature values. In the case of the U.B.C. suburbanforest site the vegetation wall temperatures were set to airtemperature at the start of the modelling run with interiorforest temperatures set two degrees higher. The walls of theurban canyon were considered to be a mix of glass and concretewith some steel thus thermal properties were selected torepresent this mixture. Building interior temperatures were setat 20 degrees C and wall surface temperatures were set at 15degrees C giving a temperature difference of five degrees for thevertical layer. Dew point temperatures measured at VancouverInternational Airport were assumed to be uniform at all threestudy sites. If the site's air temperature was lower than thisdew point temperature, then the dew point temperature was set atthe site's air temperature. STPM was tested using data fornocturnal conditions only (1600 to 0700, a total of 16 hours).The results from three of the model days representing cloudy andwindy (January 01-02), calm and clear (January 06-07), and stormyconditions (January 09-10) are presented. An assessment of model85performance is performed using mean bias error and Willmottstatistics for all sixteen test days. An accounting of thedeviations between modelled and measured values is given alongwith a summary of the role of traffic on road surfacetemperatures.TABLE 7.1 SUMMARY OF MODEL TEST DAYSDAY NUMBER^ WEATHER CONDITIONS^347-348 SCATTERED HEAVY CLOUD, LIGHT WIND348-349^SCATTERED HIGH CLOUD, LIGHT WIND349-350 SCATTERED HIGH CLOUD, LIGHT WIND350-351 SCATTERED CLOUD, STRONG WIND361-362^HEAVY CLOUD, MODERATE WIND, LIGHT RAIN362-363 LOW CLOUD, LIGHT WIND, LIGHT RAIN001-002^HEAVY CLOUD, STONG WIND, HEAVY RAIN004-005 SCATTERED CLOUD, MODERATE WIND, LIGHT RAIN005-006 SCATTERED HIGH CLOUD, STONG WIND006-007^ CLEAR AND CALM007-008 SCATTERED HIGH CLOUD, LIGHT WIND008-009^HEAVY CLOUD, LIGHT WIND, LIGHT RAIN009-010 HEAVY LOW CLOUD, MODERATE WIND, HEAVY RAIN016-017^SCATTERED CLOUD WITH FOG, MODERATE WIND017-018 FOGGY AND CALM018-019 HIGH CLOUD, FOG, CALM7.2 Cloudy and Windy ConditionsThe conditions observed on the night of January 01 - 02 consistedof moderate winds (fluctuations of about 2 m/s) and significantcloud cover (dominantly Altocumulus with some Stratocumuluspresent). Light to moderate precipitation was measured at theairport during this night. Figure 7.1 displays the model'stendency to under-predict surface temperatures at both the ruraland vegetated canyon sites. The sharp drop in surfacetemperatures after 0400 is not modelled well at either site as862 Ad^'16.0 odd 24.0aid iV N.I ao ^1.0 Do ao 4.0TINE SITE 1 VANCOUVER DAY 001 - 002 PDE SITE 2 U.B.C. DAY 001 - 002 PDE° Id 'Ad Ad 'idd aid-4 d tai INd ao 1.0 do DO 4.0 e0 80 70TiSITE 3 DELTA DAY 001 - 002 PDE21111^.1e.d^.26.d '21.d 'did 'aid ao 1.0 do Do 4.0 do do 10TIME IN HOURSFigure 7.1 Model performance at each site under cloudy, lightwind, and intermittent rain conditions(solid: measured dotted: modelled)the model predicts too shallow a cooling rate. At the urbancanyon, the model overestimates temperatures by no more than 0.7degrees through the middle of the night, and it matches theshallow cooling rate after 0400 reasonably well.7.3 Calm and Clear ConditionsThe calm and clear conditions of January 6 - 7 (Figure 7.2)provide a good test for all sites. Winds remained light(generally under 1.5 ms -1) and skies were predominantly clear(some cirrus). PDE models the cooling of the rural site almostperfectly with errors less than +/- 0.2 degrees Celsius. Awarming trend after 0600 is not followed by the model. Thevegetated canyon at U.B.C. shows similar results although somesmall variations in temperature are not modelled by PDE. Awarming trend is predicted after 5:30 A.M. at all three sites butis only modelled well at the forested site near U.B.C. Still, anerror of less than +0.5 degrees results. The urban canyon isalso modeled well with a slight deviation toward the end of therun, when PDE estimates greater cooling than is measured.7.4 Stormy conditionsWeather conditions on the night of January 09 - 10 comprisedstrong winds (between 2.0 and 5.0 ms -1), heavy cloud cover(dominantly Stratocumulus and Stratus), and periods of heavyrain. PDE (Figure 7.3) performed well, underestimating the ruraland urban sites by no more than 0.7 degrees Celsius. Thetemperature trends for the two sites were also modelled well.Predicted surface temperatures for the U.B.C. vegetated canyon88CALM AND CLEAR(a)Vaca14-3-2-0^If^73^(b) CALM AND CLEAR0^ -6-CALM AND CLEAR4-3-2-0^-3--4-SITE 1 VANCOUVER DAY 006 - 007 PDE2 1A.4^d '16.d ' 6 6 26.d -'2i .d^'26.4 ' do"^rio" do" 44" do"^ ' 1.0TIME IN HOUPSSITE 2 U.B.C. DAY 006 - 007 PDE1 i.d '1^'16.d '264 '2i d^'25.0 0.0 1.0 20 30 4.0 do 6.0 1.0TIME IN HOOPSSITE 3 DELTA DAY 006 - 007 PDETIME IN NOU113Figure 7.2 Model performance at each site under calm and clearconditions (solid: measured dotted: modelled)61Ad ' d '^'16.d '264 '21 d^"23 " ' " " " ' " ''''' do' '^'0^0 0.0^1.0 2.0 3.0^4.012^11-10-(b) LOW CLOUD, STRONG WIND, H.RAIN9-Vaa• 7-a 6-=4-3-SITE 1 VANCOUVER DAY 009 - 010 PDE13^1211-10-!!:a■?. 1• 6'Caa▪ 7-6-5-4- (a) LOW CLOUD, STRONG WIND, H.RAIN3113^'Rd T2i.d^dos-'^''^ea '' ''TIM IN NOMSITE 2 U.B.C. DAY 009 - 010 PDE2 ito 'lid '16.d 'lid '26.d '2i.d '26.dn;1 IN1.d ao 1.o 2.0 3.0 4.0 s'a ao 7.0IOo^ SITE 3 DELTA DAY 009 - 010 PDE^12 ^(C)^LOW CLOUD, STRONG WIND, H.RAIN24d 'Ad Ad 'iad '26.d '21.d '2i.d 'nitidIN 0.0 1.0 2.0 3.0 4.0 ga ea ><o 10.59Figure 7.3 Model performance at each site under stormyconditions (solid: measured dotted: modelled)were slightly higher than measured, but by no more than 0.8degrees Celsius. Measured surface temperatures remainedapproximately constant through the night, and this was generallymatched by modelled values.7.5 Assessment of Model PerformanceA comparison between predicted and measured pavement surfacetemperatures is presented in Figure 7.4 for all sixteen testdays. The scatter tends to be slightly greater at lowertemperatures. The model tends to under-predict at the rural andurban sites, and over-predict at the forest site at lowtemperatures and slightly under-predict at all sites at hightemperatures.Figure 7.5 presents the daily mean bias error for the PDE versionof STPM. The model tends to underestimate surface temperaturesin both the rural and urban sites with average errors for the 16day test period being -0.5 and -0.3 degrees Celsius for Delta andVancouver, respectively. The vegetated canyon at U.B.C. presentsthe highest variation in errors as the model under-predictssurface temperatures by about 0.4 degrees Celsius during thefirst portion of the test record, and over-predicts temperaturesby 0.5 degrees during the latter portion. PDE tends to greatlyunderestimate temperatures in the urban canyon but performanceimproves when sensible and latent heat (turbulence) is excludedfrom the model. A further comment on this behaviour is given inSection 7.5.9112^10-i &Laa 6-z64.EV 2-0tdt- G.u8W 4-aa-4-64^.4^-i^b^i^4^i^b^iotEASUIED TEMPERATURE ('C)12wa e-CWaC1• 2.-0La1- a-u8W -2-a+°4^.4^-'2^b^i^4^h^h^1'0^12MEASURED IMMATURE OC)SITE 1 VANCOUVER ALL DAYS PDE^14^12-^Lilo-0Wa t4.1-Ca a-waCW1- 4-OLiF 2-u8wa 0.a-2-^4^ 2^b^i^4^h^b^1'0^1.2^14MEASURED TEMPERATURE (0C)SITE 2 U.B.C. ALL DAYS - PDESITE 3 DELTA ALL DAYS - PDEFigure 7.4 Model predictions compared to observed surfacetemperatures at each site( a)^NOT INCLUDING SENSIBLE OR LATENT HEAT1..1•1.347 348 349 360 381 382 1 4 6 8 7 8 9 16 17 18DAY NUMBER 348 349 360^382 1 4 6 8 7 8 9 16 17 18DAY RISERaCaa347 348 349 360 361 382 1 4 5 6 7 8 9 18 17 18DAY NUMBEREi$347 348 rue reee-reei rent- 1 r 4 -r r e r 7 r r e r le r 17 r 1DAY NUMBERno.azCaaa-1(d)SITE 1 VANCOUVER MEAN BIAS ERROR PDE^ SITE 1 VANCOUVER MEAN BIAS ERROR PDESITE 2 UBC MEAN BIAS ERROR PDE^SITE 3 DELTA MEAN BIAS ERROR PDEFigure 7.5 Daily Mean Bias Errors for each site. MBE forVancouver notably improves when sensible andlatent heat fluxes are excludedWillmott statistics are presented for daily values in Figure 7.6.Unsystematic (random) root mean square differences (RMSD) arehighest for the urban canyon reaching as high as 2.0 degreesCelsius. Both the rural and suburban sites have errors rangingbetween 0.1 and 1.2 degrees Celsius. For all days combined, theurban canyon error is approximately three times that found ateither rural or suburban sites. Systematic RMSD is similar forall sites, ranging from 0.1 to 0.5 degrees Celsius and the totaldaily RMSD follows a similar pattern to that found for theunsystematic case. Willmott's 'D' statistic, a measure of howclosely the modelled values follow observations, is lowest forthe urban canyon and highest for the rural site. This indicatesthe model performs well with 'D' greater than 0.9 for the entirerecord. Some exceptions occur on a daily basis, especially forthe night of January 8 - 9, 1992. This night is characterized bylow, heavy cloud, strong, variable winds, and precipitation.The forest site at U.B.C. presents the greatest difficulty indetermining site-specific input variables. It is susceptible tosporadic occurrences of both radiation and advection fog whichmay not be observed at the airport. If fog is present but notmodelled it will contribute to the underestimates during thefirst seven days of the test record. The overestimates on thelast four days are due to an attempt to model local fog eventsfrom observed weather data. Variable fog was observed at theairport on these days, but it may have been restricted to lowlying areas. The higher elevation of the U.B.C. site may have94347 348 349 340 341 342 3^4^4^4^6^b 16 i7 18 ?6?DAY WW1—.0 DELTA^U6.0. ^ VAMC4NER I26-2z 2-a1.aoOzo cs-O0^2C-UZaE1.6..aoOfA 1-z0▪ 0.6•0aZ 2-WaE• to-aOU 1-z0▪ 0.Er0a° 347 348 349 340 341 3132i^light^661617113Tb?DAY WinDAILY SYSTEMATIC RMSD^ DAILY WILLMOTT 'D . STATISTIC09-o te-1.=(8 07-tab as.1-04.2 113.....1aa.01-0^317 3118 349 g0 341 342^4 4 h^6^b 16 17 18 ?6?DAY MISERDELTA^U.B.C. ^ VANCOUVER DELTA ^ VANXWERDAILY UNSYSTEMATIC RMSD DAILY TOTAL RMSD347 348 349 340 341 362 I^4^h^h^4^6 1'6 i7 ie tb?DAY AMEROEITA --uma ^wmmuisiFigure 7.6 Daily Willmott statistics for each site(a) RMSDu (b) RMSDs (c) RMSD (d) D—Statprevented fog formation. Since dew point temperatures were notcollected at any of the three sites, it is a potential source oferror in the input values.The average hourly variation in the PDE model's deviation wasalso investigated to determine average deviations throughout thenight (Figure 7.7). The 16-night average deviation betweenmodelled and measured values is fairly constant at the ruralsite; just under -0.4 degrees Celsius. No significantrelationship exists between model error and time through thenight. Deviations at U.B.C. were slightly positive throughoutthe night with errors increasing slightly toward dawn suggestingthat cooling rates for the vegetation canyon are underestimated.The deviations for the urban canyon increase throughout the nightto a maximum of -0.7 degrees at dawn. Hence, when averaged overall weather types, PDE overestimates the cooling rate for theurban canyon, but errors remain less than or equal to 0.7degrees.Average hourly Willmott RMSD statistics increase for all sitesimmediately after the model is initialized at sunset as shown inFigure 7.8. By approximately 1800 hours the error becomes fairlyconstant at all sites with the urban canyon consistently havinghigher errors. The 'D' statistic is exceptionally high for allsites, again with the urban canyon having the worst value.However, 'D' values remain above 0.9 showing the model performswell on an hour-by-hour basis.96Figure 7.7 Average hourly Mean Bias Error for each site1.6^W 1.4-zza1.2-L.8 1te-0.4-a 0.2-AVERAGE HOURLY UNSYSTEMATIC RMSD1 .•1 .0 1'^ .^• 28.d 0.0^1.0^2.0^3.0^4.0 6.0^6.0 70TIME IN MIAS1 ■■• DELTA^- U.B.C. ^ VANCOUVERAVERAGE HOURLY SYSTEMATIC RMSD01 •4 '1+4 'itd '151.4 '28.d '2i.d^o.o^1.0^2.0^3.0^4.0 6.0^6.0^-71.0TIME IN HOLRS09.m^U.B.C. ^ VANCOUVER IAVERAGE HOURLY TOTAL RMSD1.6-LIza 1.2-Su- 1-c0.8-OIA0.8-Z0.4-r00 d 'if.d '111.d 'lid '26.d '21.0^'25.d ' do '1A" io"so" 'o 'so' ^ 'i IN MIPSDELTA^U.B.C. ^ VANCOUVERAVERAGE HOURLY WILLMOTT D' STATISTIC10.8uu88-w 07-H 08-100.6-r 0.4-r0Z0. 3.g 0.2-oid.d 'it.d^Ad '26.d '21.d2id o.o 1.0 2.0 3.0 4.0 6.0 6.0 7.0TIME IN HOURSDELTA^U.B.C. ^ VANCOUVER IFigure 7.8 Average hourly Willmott Statistics for each site(a) RMSDu (b) RMSDs (c) RMSD (d) D-Stat7.6 An Accounting of Model-Measured DeviationsThe inclusion of sensible heat exchange in the urban canyon isdetrimental to the performance of the PDE version of STPM, butbeneficial at the other two sites. This might be explained ifthe role of traffic in the mixing of the air volume within thecanyon is considered. On several occasions the anemometer atU.B.C. was observed to be motionless but there was significantair motion felt close to the surface during periods of hightraffic volumes. Observations of passing vehicles on wet roadsallowed a visual approximation of the height to which thevehicle's turbulent wake reached by observing the mist sprayed upbehind the vehicle. Although no direct measurements were made,observations suggest the turbulent spray reaches to about 1.5times the vehicle height above the road surface, and is dependenton vehicle speed and local wind speeds. Schock (1989) suggeststhat the turbulent effect of traffic reaches up to 4.5 metersabove the pavement surface. Local winds and turbulence fromother vehicles tend to horizontally stretch the turbulent plumealong or across the roadway.Air temperature measurements at the urban site were taken 10meters above the surface, well above the vehicle turbulent layersuggested by Schock. A de-coupling of the general canyon air,and near-pavement air temperatures, may occur due to the passageof traffic and the structural boundaries formed by the canyonwalls. Should this be the case there may be periods when adownward heat flux exists at the surface, but an upward heat flux99exists higher in the canyon volume. Canyon air temperatures areobserved to be generally cooler than surface temperatures,resulting in a consistent sensible heat loss from the surface inthe model, thereby giving lower surface temperatures.To fully test this hypothesis, the canyon should be instrumentedwith a vertical array of thermistors to determine the verticaltemperature profile for the air volume. Decoupling may existonly because the walls of the canyon restrict the cross-road flowof air. This is not the case at either of the other two sites.At U.B.C. the wide vegetated canyon and low to moderate trafficvolumes allow the canyon air to be flushed, preventing adecoupled layer from developing. Only with very calm winds andhigh traffic flow will this traffic-induced turbulent layer existover the road surface. Even light winds at a rural site areenough to diffuse/advect any turbulent layer away from the roadsurface. Clearly, work should be performed to investigate thispoint further.The role of moisture on the road surface can be significant, assummarized earlier. The weakness of STPM in determining acondensation event is due in large part to the use of airport dewpoint temperature. Although moisture is generally conservedthroughout a region under similar weather conditions, site-specific variations can occur. These moisture variations may beenough to initiate localized condensation or evaporation events.STPM appears to estimate the magnitude of the latent heatexchange well, but it's timing is less successful.100Uncertainties in atmospheric moisture content also leads todifficulty in estimating the presence of fog at a site. STPMassumes that when air and dew point temperatures converge, someamount of fog is present, especially if airport observationsinclude fog. Figure 7.9 displays the PDE model runs for allthree sites for the night of January 18 - 19, 1992. Humidity wasgenerally high in the region and fog was observed throughout bothdays at the airport. Up to 0400h cooling at all sites isrelatively weak, and fog was observed at the airport. After0400h Delta and U.B.C. demonstrate increased cooling rates. Themodel follows the rural site well (it attempts to model acondensation event at 2300), however it overestimatestemperatures at U.B.C. and underestimates those at Vancouver. Agood fit for both can be obtained if the amount of fog isadjusted, however the observations do not support such action.7.7 The Influence of TrafficFigure 7.10 shows the deviation in surface temperature betweenthe fast lane and the slow lane averaged over weekdays andweekends at Vancouver. A significant increase in temperaturedifference between the fast lane tire track (RT1) and the middleof the slow lane (RT3) occurs at about 0700 on weekdays but notuntil 1100 on weekends. The timing of this effect on weekdaysmatches closely with the weekday peak traffic flow (between 0700and 0800h). Although traffic data is not available for weekends,the morning delay is consistent with later timing in peaktraffic.101(b) FOG - HIGH HUMIDITY. ••••• •••.^........0^2--3.44d '174 'Ad Ao"264 '21d '26d 0 0.0 1.0 2.0 30 4.0THE IN IS-VS0 60 7.0Mi4-3.2-SITE 1 VANCOUVER DAY 018 - 019 PDE1111.d '4.0"16.d '16.d '26.d '21.d^ao to 2.o ao 4.0 ' do' . a.o 7.0TIME IN NOMSITE 2 U.B.C. DAY 018 - 019 PDESITE 3 DELTA DAY 018 - 019 PDE7^ (c) FOG - HIGH HUMIDITYa-Mi4-2-0^2-4-e.d^'16.1:1 '264 '21 d^ao to 2.o ao 4.0 doTIME IN NUSFigure 7.9 Model performance at each site under high humidityconditions with fog observed at Vancouver InternationalAirport (solid: measured dotted: modelled)^aaLANE TEMPERATURE DIFFERENCE0.40 1^ 3^ 6 6^8^10 11^112 13 14 16 16 1'7 18 19 20^22 23TIME IN HOURSFigure 7.10 Time series of lane temperature differences forweekday and weekend days under calm and clearconditions at the urban siteDifferences between modelled and measured road surfacetemperatures were analyzed to determine if there is arelationship between model 'error' and traffic flow patterns.None was obtained. Figure 7.11 presents traffic flow volumes forVancouver and Delta. No relation existed between traffic volumesand the daily temporal variation in Mean Bias Error for eitherthe PDE or the F/R versions of STPM. STPM's tendency tounderestimate temperatures may, in part, be due to a trafficeffect at each site that is not incorporated directly within themodel. Traffic influences may be modelled indirectly throughinitial surface temperatures input to the model and to the airtemperature input at each iteration.103Figure 7.11 Daily totals of number of vehicles using roadwayat (a) Vancouver and (b) Delta (data for U.B.C. arenot available)1047.8 Summary of Force/Restore PerformanceFor comparative purposes, the Force/Restore (F/R) version of STPMwas tested and the results are presented for cloudy and windy(January 1 - 2, 1992) and clear and calm (January 6 - 7, 1992)conditions in Figure 7.12. The F/R version responds well tochanging inputs for all three sites, but predictions tend to bewarmer than observed at the urban site. Deviations from observedtemperatures are no worse than for PDE at either suburban orrural sites. During calm and cloudless nights, F/R performs muchpoorer than does PDE. Predicted temperatures tend to be lowerthan observed during the early portion of the night and higherthan observed during the latter portion of the night. This ismost clearly seen in the results for the rural site where thedeviations between modelled and measured temperatures aresignificant.Clearly, the performance of the Force Restore version of STPM isnot sufficiently encouraging enough to warrant further work,especially when compared to results obtained from the PartialDifferential Equation version. F/R's inability to model thelinear cooling trend in the urban setting, overestimate coolingin the early evening, and underestimate cooling later during thenight at all sites under calm and cloudless nights show it is notmodelling the relevant energy exchanges properly.1052140 1TA ISA leo so.* 21.0 22.0 23.0 0.0 . 11 LOTIME IN Mins3.0 40 6.0 40 tO1a-10.................................. .................SITE 2 U.B.C. DAY 001 - 002 FIRi"aaISA 1TA ISA 10.0.................................... ............ •4a8-aacLSITE 2 U.B.C. DAY 006 - 007 F/R000 21A 22.0 23.0 OA 1.0 AOTUE IN HOURSTA40 AA3.0 OA2 1-IL 17.0 ISO 14.0 20.0 21.0 22.0 22.0 0.0 1A 2A 3.0 40 SA 0.0 7ATINE IN ICURSISO 17A 150 10.0 NA 210 220 23A 0.0 IA 20 2A 40 60 SA 7.0TINE IN (000ISA 20A 210 22.0 23.0 00 1.0TIM IN HOURSSITE 3 DELTA DAY 006 - 007 F/R160 17.0 16.0SITE 3 DELTA DAY oat - 002 FIR2 T rrrr,T. 1-1-1 TT^0.0 -r-r-r-■160 17.0 100 19.0 200 210 220 23.0^1.0 2.0 3.0 40 6.0 6.0 TO7111( IN IPASSITE 1 VANCOUVER DAY 001 - 002 F/R SITE 1 VANCOUVER DAY ooa - 007 F/RFigure 7.12 Model performance results for Force/Restore versionfor all sites under (a-c) cloudy and windy and(d-f) clear and calm conditions(solid: measured dotted: modelled)106PART V SUMMARYCHAPTER 8 CONCLUSIONS AND FURTHER WORK8.1 Summary of ConclusionsThe thermal character of roadways at both a regional and a site-specific scale has been evaluated using data collected from threeroad sites ranging from rural to urban canyon road environmentsin southwestern British Columbia. The Partial DifferentialEquation version of a Surface Temperature Prediction Model hasbeen modified and evaluated to account for varying weatherconditions and the character of a road site.Air and surface temperatures in the urban canyon are consistentlywarmer than in either the rural or vegetated canyon sites. Theurban heat island is more pronounced during nights with calmwinds and clear skies and is notably reduced during cloudy andwindy conditions. Air temperatures are found to be a poorestimate of surface temperatures at all three sites, because therelation between air and surface temperature is highly weatherdependent. There was no consistent spatial distribution ofsurface temperatures at each site. Tire tracks were notconsistently warmer than the middle of the lane and there was nosignificant relationship between the average temperature of theslow lane and that of the fast lane. Surface temperatures towardthe middle of an urban or forest canyon tend to be slightlycooler due to increased radiation exchange with the colder nightsky. The east-west vegetated canyon is found to be slightlycooler than the rural site due in part to in-canyon solar shadingduring the day.107Traffic appears to have an effect on the surface temperature ofthe roadway, especially in the urban canyon, however no conciserelationship could be determined. The divergence of lanetemperatures from the average cross-road temperature is clearlyevident during peak commuter periods during the week, but it isdelayed by several hours on weekend days. Air temperature andwind speed measurements were observed at a level beyond thetraffic turbulent layer thus making a relationship betweensurface temperature and traffic-induced sensible heat fluxdifficult to determine.The PDE version of STPM performs well at all three sites. Theclosest fit with observations occurs on clear and calm nightswith little turbulent sensible or latent heat fluxes. Maximumdeviations from measured values are less than one degree Celsiuswith the mean error being close to -0.4 °C and Willmott 'D' valuesremain above 0.9 indicating strong model performance. Thegreatest difficulty encountered is to properly model site-specific sensible and latent heat fluxes using the simpleparameterizations introduced here. Frequent intermittent fogevents in the vegetated canyon are also difficult to model andsignificant errors between predicted and measured surfacetemperatures result.Regional weather data obtained from Vancouver InternationalAirport provide reasonable input data for the model, however itis not fully representative for periods with low cloud,intermittent precipitation, or high humidity. Use of regional108humidity measurements is satisfactory except when roads are wetor the humidity is fairly high. Adjustments to the dew pointtemperatures at the rural and vegetated canyon sites arenecessary to obtain realistic simulations during these highhumidity episodes.Sensitivity tests of STPM's response show it's response tovarying the input parameters. The model is somewhat forgivingwith respect to errors in initial conditions, but is moresensitive to errors in inputs such as cloud, humidity,precipitation, wind speed, and air temperature.8.2 Suggestions for Further WorkAt present STPM has only been fully tested for road conditionsbetween sunset and sunrise. A simple routine to calculate solarfluxes is incorporated in STPM so it is possible to provideestimates of the fluxes forced by the daytime solar input.Figure 8.1 shows results from a test for two separate full daysusing the PDE version of STPM for the rural site. The modeltracks measured values exceptionally well for January 6, 1992which is characterized by calm winds and clear skies.Performance on other days with strong wind and cloudy skies ispoorer as shown for January 4, 1992. Improvement requires thatSTPM be modified to fully incorporate turbulent heat transferduring daytime hours. A full turbulent model would also assistin the estimation of these fluxes during the night as well.Solar access to canyons could also be better estimated than atpresent, including multiple reflection.109• •0 OO 10 11 ta 13 U 1• 11 1? 1• 15 SO al asTHE IN IMESaaae I e $^• • 10 11 1•TIM IN NIXESDELTA DAY 004 PARTLY CLOUDY AND WINDY^ DELTA DAY 006 CLEAR / CALM CONDITIONSFigure 8.1 24 Hour forecast for Delta under (a) partly cloudy andwindy (b) clear and calm conditionsThe role of traffic has not been fully evaluated. Observationssuggest traffic has a distinct impact on the thermalcharacteristics of the road surface, however no significantrelationship has been derived to relate road surface temperatureto traffic counts. A more comprehensive evaluation of thisfeature is recommended using a more detailed instrumentationscheme (vertical profiles of air temperature, humidity, and windspeed from the surface up through the 'traffic boundary layer')and concurrent traffic counts.The site specific nature of fog events, precipitation, and roadwetness requires further instrumentation. 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