A First Principles Pavement Thermal Model for Topographically Complex Terrain

Transcription

1 Sxth Internatonal Symposum on Snow Removal and Ice Control Technology A Frst Prncples Pavement Thermal Model for Topographcally Complex Terran E.E. Adams*, P. Gauer**, L. McKttrck* and A.C. Curran*** Abstract In the wnter envronment, pavement temperature has a sgnfcant nfluence on hghway mantenance and safety ssues concerned wth snow and ce management. Temperature nfluences the effcacy of freezng pont depressant chemcals and plowng operatons as well as smply ascertanng whether avalable water wll freeze or melt. A forecastng model chan that allows predcton of pavement temperature n topographcally vared terran has been developed and s beng tested on US hghway I-90, whch crosses Bozeman Pass, Montana. The chan s ntated wth the meteorologcal forecast ETA model calculated on 20 km spacng. Ths s refned to a 1 km spacng usng ARPS, a meso-scale meteorologcal forecastng model. These results are then nterpolated to essentally provde a 30 m resoluton weather forecast. Fnally, RadThermRT s mplemented to calculate pavement temperature at ths 30 m resoluton. The 30 m resoluton was chosen snce t concdes wth dgtal elevaton maps (DEM) avalable from the US Geologcal Survey. The DEM s are ncorporated nto RadThermRT, where terran maps used for the thermal calculatons are constructed. The RadthermRT grd s n effect draped over the DEM to provde a three dmensonal thermal topography whereby each 30 m element or facet s gven thermal characterstcs approprate to the partcular materal type. For example, the thermal conductvty of rock, grassland, snow or pavement s approprately assgned to a facet. Utlzng the spatally calculated meteorologcal nputs, the energy balance of the terran surface s calculated for each facet and the surface temperature s forecast for each tme nterval. The aspect and orentaton of the terran surface takes nto account the nfluence of radaton exchange between facets as well as the shadowng of drect solar and the sky vew factor. Temporally anmated surface temperature maps are produced. The model mplemented on Bozeman Pass s run n a 24 hour forecast mode, updated every 12 hours and avalable on the web for access by the Montana Department of Transportaton mantenance secton for assstance n decson-makng. The pass s a mx of canyon and somewhat open terran and well suted for applcaton of ths type of modelng effort. Snce the temperature of each facet s calculated, durnal varatons due to shadowng are n clear evdence, based on the thermal sgnature of rdges vs. valleys and materal propertes such as pavement contrasted wth snow. In order to smplfy the nformaton for more effcent utlty by hghway mantenance decson makers, a subset of the full terran thermal map s provded whch dsplays only the hghway temperature as a trcolor map. Red ndcates the freeze transton temperature taken as 2 C to 2 C. Blue desgnates a temperature below ths range and green warmer. Comparson of the pavement temperature calculated and measured at the RWIS staton near the top of the pass are qute good when the meteorologcal forecasts are accurate.

2 Introducton Weather forecastng, measurement, and communcaton technologes are presently n development, whch have potental to greatly mprove roadway safety for the commutng publc. As these technologes mature, government enttes responsble for transportaton nfrastructure mprovements must respond and work to mplement systems that delver antcpated results. It s typcal for the commutng publc to develop ncreased expectatons of transportaton nfrastructure and nformaton systems. Wth ncreased publc expectatons comes an ncrease n demands from provders of these servces. Ice formaton on roads s an obvous safety ssue on roadways n cold clmates. In an ongong effort to address the problem, Departments of Transportaton and Meteorologcal Servces have establshed a network of automated meteorologcal statons on ther ground transportaton nfrastructure systems. These networked statons delver valuable real tme nformaton to a central locaton where decsons regardng an approprate course of acton to ensure hghway safety may be made. The usefulness of these statons s lmted by ther dstrbuted geographcal postons: Any decsons made based on delvered data must nclude nterpolaton or guessng wth regard to the condtons on road surfaces located between the fxed postons statons. A case n pont s pavement cng where temperature and water sources determne the extent of cng. Thermal effects of sunlght, shadowng and radant heat exchange wth the surroundng landscape n topographcally complex terran, such as mountanous and forested areas, wll cause sgnfcant dfferences n pavement temperature even on sectons of road that are n close proxmty to one another. However, t s vrtually mpossble to confgure the entre hghway system wth sensors, so nterpolaton between stes s a necessty. It should also be noted that measurements are useful n provdng a means to react to the current stuaton, but a forecast of the pavement condtons wll provde an added tool to the hghway operatons manager to be proactve. To enhance the accuracy of ths nterpolaton a thermal model s presented, whch has as ts geness a mltary applcaton for the dentfcaton of the nfrared sgnature of vehcles. An adaptaton of ths modelng to topographcally complex terran was advanced for a snowcover by Adams and McDowell n As a demonstraton of the applcablty of the concept, a relatvely smple topography was presented. However, wth the advent of readly avalable dgtal elevaton maps and ncreasngly accurate meso-scale meteorologcal models t s now practcal to combne these elements n an operatonal settng. RadTherm s a commercally avalable software product developed for structures from these same prncples. A verson of ths program specfcally developed for topographcally complex terran, wth a specfc emphass on hghway applcatons, n a collaboraton between Montana State Unversty and ThermoAnalytcs Inc. has been developed. The program, RadThermRT (Radaton Thermal model for Road Temperature), s currently beng tested to forecast pavement temperatures on a secton of I-90 through Bozeman Pass, Montana usng meso-scale meteorologcal forecast data as nput.

3 RadthermRT Terran and Topography The frst step n developng models for a partcular locale s to descrbe the area n a format useful for the thermal calculatons. Surroundng landscape features ncludng aspect, elevaton, and surface materal propertes (such as vegetaton and exposed sol, rock, or snow) all nfluence the pavement temperatures. The nfluence on pavement temperature due to the energy exchange s determned by the thermal propertes of the surroundng terran materals such as albedo, emssvty, conductvty and specfc heat. From the outset, t was determned that for the most wdespread utlty the model must be readly transportable to new locatons. Snce dgtal elevaton maps (DEMs) and land cover maps (LCMs) are now readly avalable for many regons and the thermal modelng presented here s based on applcaton of well establshed frst prncples, as outlned below, ths approach acheves the goal of beng hghly portable for modelng addtonal areas. Accurate terran models are generated from Geographc Informaton Systems (GIS) to utlze the DEM and LCM nformaton. Preprocessng programs are used to categorze GIS land cover types, defnng approprate materal parameters for each element or facet that defnes the landscape. A RadthermRT grd s n effect draped over the DEM to provde a three dmensonal thermal topography whereby each element or facet s gven thermal characterstcs approprate to the partcular materal type. These thermal parameters (e.g. thermal conductvty, albedo, etc.) are appled so that temperatures may be calculated based on envronmental condtons. Topography s currently nput at 30 m resoluton snce US Geologcal Survey DEMs are readly avalable at ths scale. From ths are determned the geometrc nfluences ncludng such thngs as slope and elevaton, terran self-shadow and obscuratons, surface-to-surface reflectons and emssons and drectonal solar load on a sloped surface. Each facet has a vew factor defned, whch s n essence what t would see lookng out, gven ts orentaton wth respect to the sky and the other facets representng the landscape. These vew factors are used to ncorporate shadowng, sun angle, and facet orentaton for surface-to-surface radaton. Dscuss vew factors and rays n RadThermRT Frst Prncples Utlzed n RadThermRT Computatonally, one dmensonal, fnte dfference heat conducton equatons are solved n the drecton of the surface normal, determnng the temperature profle through the thckness of each facet. Boundary condtons, used to solve the equatons, assume a durnal depth temperature for the lower bound and a flux condton for the energy exchange at the upper surface. The upper energy exchange ncludes radaton, convecton, and phase change. Surface orentaton s used to account for durnal solar varatons, ncludng shadowng and reflecton and longwave adaton calculatons nclude facet to facet as well as facet to sky exchange. The surface temperature of the pavement as well as the surroundng terran s calculated n RadThermRT by accountng for the energy balance at every facet. Atmospherc nput s accounted for at the upper surface n terms of energy fluxes. Q represents ths flux to each facet,

4 Q = Q + Q + Q + Q, (1) lw where the contrbutng components are Q lw, long wave radaton ( μm - nfrared), Q sw - short wave radaton (0.2 3 μm solar), Q lh, - latent heat due to phase change and Q sh - convectve or sensble heat flux. sw In order to account for radaton exchange between facets and wth the sky, enclosure theory s employed to quantfy each facet s radaton vew factor, F j. Ths conceptually assumes a hemsphere centered over the facet, wth the vew factor F j, beng the fracton of the hemsphere that the projecton of facet j (or the sky) ntercepts as vewed by facet. In RadThermRT a ray-tracng algorthm s employed to calculate the vew factor. The net long wave radaton flux for each facet s Qlw lh sh n = ε F ( Q σ θ ) + ε σ F ( θ θ ). (2) s l Whch, thus, accounts for the exchange wth the sky through the frst term on the rght hand sde and the exchange wth all of the other facets through the second term. F s represents the facet to sky vew factor, ε s emssvty, Q l the ncdent long wave sky radaton, σ s the Stephan-Boltzman constant, n the number of other facets. Somewhat smlarly, the solar contrbuton, Q sw, for the th facet s Q sw j= 1 j= 1 A n p = α ( I n + Fs I d ) + ( Bj (1 α ) Qsw ) (3) j A α s the absorptvty (for non-transmssve terrans α = 1 albedo) I n s the drect solar radaton, I d s the dffuse solar, A s the facet area, BBj s the shape factor from the to j facet. Multple reflectons are accounted for wth the reflected solar consdered dffuse. Newton s Law for coolng s used for the sensble heat flux, Q sh h c ( a j j = θ θ ) (4) where hc s the average convectve heat transfer coeffcent over the facet, θ a s the ar temperature Qlh = L h C C ) (5) m m ( a L m s the latent heat of phase change, hm s the convectve mass transfer coeffcent, C a and C are the mass concentratons of water vapor. The nfluence of lqud precptaton s handled by assumng no more than a XX mm thckness wll accumulate and that ths wll eventually be removed through phase change. The nfluence of the phase change s the pavement temperature s taken nto account through ths equaton, however, there s presently not yet a practcal and accurate means to automatcally update changng road surface condtons (e.g. snowfall). Ths s not due to techncal lmtatons, for example of addng snow accumulaton based on snowfall rates, but rather the nablty to handle the anthropomorphc nfluences, such as traffc and mantenance operatons, n a forecast mode. RadThermRT n ts current operatonal form s, by default, used to forecast road surface temperatures. The assumpton for snowfall s that the road s dry and not snow

5 covered wth regard to the temperature calculatons. Wet and snow covered road condtons can be specfed for a partcular run, but these condtons are not updated as actual road surface condtons change durng the course of that run and are not provded to the mantenance personnel n the operatonal test case. The Energy Equaton for a dfferental volume wthn the opaque terran provdes the tme, t, rate of change of temperature, θ, as proportonal to the dvergence of the heat flux, q, θ q = ρ c p. (2) t ρ s the materal mass densty and c p s the specfc heat of the materal. The heat flux, q, through the terran and pavement s prmarly due to heat conducton and thus accordng to Fourer s law s represented as, wher k s the thermal conductvty. So that where the thermal dffusvty, α = ρ c p k q = k θ, (2) 2 θ θ = α, (3) t, s determned by the specfc materal propertes. Modelng Chan To utlze the terran/pavement thermal model n an operatonal mode, a model chan has been developed. Ths chan begns wth a synoptc-scale weather forecast that provdes condtons to a meso-scale model, whch n turn provdes the meteorologcal nput requred for the pavement temperature calculaton at the scale of the DEM, usng RadThermRT. Ths computatonal chan functons as follows(more specfc detals are provded n McKttrck et. al (ths volume). Forecast weather data are taken from exstng meteorologcal models (for forecasts n the Unted States, contnental or synoptc scale forecasts are frst run by the Natonal Center for Envronmental Predcton (NCEP)), whch are posted on a publc ftp server. These results are then downloaded and used as nput nto a mesoscale modelng program, the Advanced Regonal Predcton System (ARPS), whch s desgned to more accurately account for topographc and turbulent flow factors. ARPS models are then used to provde forecast data wth resolutons on the order of 1 km. These values are subsequently nterpolated to the scale of the DEM (e.g. 30 m), essentally provdng ndvdual forecasts for each facet. To accurately model current (now-cast) condtons, t s possble to use a meso-scale modelng tool such as the ARPS Data Assmlaton System (ADAS). As the name ndcates, ADAS can assmlate measured meteorologcal data throughout the entre modelng perod and can be used to drve the responses near those measured ponts, by forcng or weghtng a statstcal mnmzaton between the error between the model and the measured data. Data from ether of these types of meso-scale programs can then be used as nput nto RadTherm/RT. RadTherm/RT nputs are ar temperature, solar

6 radaton, long-wave (sky-temperature) radaton, wnd speed, wnd drecton, humdty, and precptaton rate, as a functon of tme. Results The frst prncples thermal model s then employed to calculate the temperatures assocated wth each cell. Calculated results of the surface temperatures are color lnked for dsplay as a tme sequence map. An example snapshot of the output s shown n Fgure 1 for two perspectves (at the same tme) on a computer smulaton of surface temperatures along the Rocky Canyon secton of Bozeman Pass (appox. 12 hghway km). Notce the nfluence of the topography on the mage. Fgure 1. One frame of a tme seres anmaton of calculated color assocated surface temperatures for I-90 through a porton of Bozeman Pass, Montana. Ths example ncludes about 12 km of hghway.

7 Fgures to nclude Week long plots Fg 1 accuracy Full temperature terran map Fgure 2 Temperature tr color Fgure 3 dscuss smlar for wnd In addton to the spatally vared weather forecast, meteorologcal nformaton may be ncorporated nto the model usng a sngle set of condtons from a weather staton n the case of a now-cast or a regonal forecast. If meteorologcal nput data are accurate, forecasts of terran surface temperatures are accurate. However, accuracy degrades f the land cover types change sgnfcantly durng the modeled perod, such as wth changes n snow surface albedo or coverage. Conclusons The model chan presented offers a References Bographcal Sketch Edward E. Adams receved hs Ph.D. n Mechancal Engneerng from Montana State Unversty. He spent four years at Mchgan Technologcal Unversty's Keweenaw Research Center and served as an adjunct Assstant Professor n the Mechancal Engneerng-Engneerng Mechancs Department. In 1992, he returned to Montana State Unversty and s currently an Assocate Professor n the Cvl Engneerng Department. Dr. Adams' research focus s on snow and ce related phenomena. Specfc areas wthn the topc nclude, snow metamorphsm, avalanches, thermal processes nvolved n cng and chemcal ant-cng for hghways and descrbng the physcal habtat whch affords the condtons for sustanng mcrobal lfe wthn Antarctc ce. *Cvl Engneerng Department, Montana State Unversty, Bozeman, MT USA ** Norwegan Geotechncal Insttute, Oslo, Norway

8 *** ThermoAnalytcs, Inc, Calumet, MI USA