Introduction

GMD

Geoscientific Model Development

GMD

Geosci. Model Dev.

1991-9603

Copernicus Publications

Göttingen, Germany

10.5194/gmd-9-547-2016

Accounting for anthropic energy flux of traffic in winter urban road surface temperature simulations with the TEB model

Khalifa

abderrahmen.khalifa@gmail.com Marchetti

Bouilloud

Martin

https://orcid.org/0000-0002-1491-9590

Bues

Chancibaut

1IFSTTAR, Centre de Nantes, route de Bouaye, CS4, 44344 Bouguenais CEDEX, France 2Cerema – DTer Est – LR Nancy, 71 rue de la grande haie, 54510 Tomblaine, France 3Météo France, Direction de la Production, 42 avenue G. Coriolis, 31057 Toulouse CEDEX, France 4CNRM-GAME (Météo-France, CNRS), Météo France, 42 avenue G. Coriolis, 31057 Toulouse CEDEX, France 5Université de Lorraine, UMR 7359-GeoRessources CNRS/UL/CREGU, ENSG, 54518 Vandoeuvre-lès-Nancy CEDEX, France

A. Khalifa (abderrahmen.khalifa@gmail.com)

9February2016

9 2 547565 23April2015 22June2015 26December2015 5January2016

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Snowfall forecasts help winter maintenance of road networks, ensure better coordination between services, cost control, and a reduction in environmental impacts caused by an inappropriate use of de-icers. In order to determine the possible accumulation of snow on pavements, forecasting the road surface temperature (RST) is mandatory. Weather outstations are used along these networks to identify changes in pavement status, and to make forecasts by analyzing the data they provide. Physical numerical models provide such forecasts, and require an accurate description of the infrastructure along with meteorological parameters. The objective of this study was to build a reliable urban RST forecast with a detailed integration of traffic in the Town Energy Balance (TEB) numerical model for winter maintenance. The study first consisted in generating a physical and consistent description of traffic in the model with two approaches to evaluate traffic incidence on RST. Experiments were then conducted to measure the effect of traffic on RST increase with respect to non-circulated areas. These field data were then used for comparison with the forecast provided by this traffic-implemented TEB version.

Introduction

During the winter period, precipitations may accumulate on road surfaces, with special danger in the case of snow and black ice, since they reduce road grip and therefore impact the road users' safety. One of the roles of maintenance services during winter is to ensure network practicability, and in France the winter season for road services runs from 15 October one year to 15 March of the following year. Their work is grouped under the term “winter maintenance” designed to provide optimal conditions of safety and of mobility. For years, winter operations services have been aware of the environmental risks such as the extensive use of de-icers on road networks. Through training and standard productions, they have begun to make infrastructure managers aware of the need to control the amounts spread. Many studies are dedicated to forecasting of the road surface temperature (RST) . A forecast of the snowfall and RST helps coordination of winter maintenance services, optimizing their costs, and reduces the environmental impacts caused by an inappropriate use of de-icers. Considerable effort has been devoted to meteorological forecasting of these adverse weather conditions, particularly for road freezing conditions . To forecast RST, winter maintenance operators rely on numerical models. Improvement of these models consisted in producing a forecast for a full network by incorporating the influence of both meteorological and geographical parameters. However, traffic has so far been a challenging parameter to include in RST forecasts . In the present study, we will be interested in taking into account the impact of traffic in modeling the RST. A short literature review of the thermal effect of the traffic will be presented to identify and to quantify these impacts. A model dedicated to an urban configuration was chosen. The heat fluxes associated with traffic were investigated in detail for their introduction into this model. The modification in the energy balance caused by the presence of vehicles was then evaluated. Compared with initial traffic implementation in the model, two different approaches were considered. The first consisted in improving the evaluation of the heat flux released by traffic. The second was based on an explicit representation of traffic within the model. Forecasts and field results will be compared and discussed.

State of the art and objective of the study

Accumulation of snow or ice on roads generates hazardous traffic conditions. Several models exist and are based on forecasts of the road surface status. The heat flux associated with passing vehicles was partially taken into account by some models (IceBreak, ; IceMister, ; the energy balance model from the UK Meteorological Office with a modified radiation scheme, ) and neglected by others (DMI-Hirlam-R, ; the energy balance model from the UK Meteorological Office, ; ISBA-Route/CROCUS, ). included traffic through a modification of the exchange coefficient between the road surface and the atmosphere layer above it, and a correction of the net infrared radiation the road received according to traffic density. selected three traffic effects: increase in RST through a correction factor, a change in net infrared balance due to passing vehicles with a multiplication coefficient applied to the emitted radiation, and an increase in turbulent exchange by adding 2 m s-1 to the wind speed. considered that traffic increased turbulent exchanges, and therefore imposed a minimal wind speed of 5.14 m s-1 in daytime, and 2.57 m s-1 at night and during the holiday seasons. In such cases, only specific physical processes associated with traffic are considered as relevant, while other ones are neglected. None provided or analyzed the relative importance in terms of the energy fluxes of these processes related to the presence of vehicles.

Schematic illustration of the impact of traffic on road surface temperature (adapted from ).

Recently several studies have been undertaken to evaluate the thermal effects of traffic on the RST. A vehicle is a source of multiple forms of heat (Fig. ). Indeed, we can distinguish between direct and indirect consequences due to passing vehicles on the road. Direct impacts are created by the heat flux generated by the engine and the exhaust system, the radiative flux emitted by the bottom of the vehicle and the tire frictional heat flux. Vehicles also indirectly influence the road surface energy balance by modification of the radiative balance. They can block longwave radiation exchange whilst also preventing shortwave radiation from reaching the road surface during the day. Traffic motion will also cause additional mixing of air above the road surface, promoting increased turbulent flow. The bibliographic study has led to the identification of the different processes associated with traffic, and their contribution to an increase of 2 to 3 °C of RST. However, no literature data provide any quantitative evaluation of these different impacts. used physical equations and thermodynamic laws to evaluate the thermal input of some of the processes associated with traffic (exhaust system, engine, friction, etc.). Their approach did not state to what extent each process contributed, nor was it validated by any experimental study. showed that the general cumulative effect of these impacts on the diurnal temperature cycle is to promote warmer RST on heavily trafficked roads. As an example, in a study in the Stockholm area (Sweden), showed RST differences by up to 2 °C due to the differences in traffic conditions between urban and rural areas, especially during peak hours. reported that recorded RST was usually several degrees greater on roads where traffic is the heaviest. The impact of vehicles can be quantified on multi-laned roads, where the increased volume of slow vehicles on nearside lanes can raise the RST by up to 2 °C . This result was confirmed by . They also indicated that making an accurate evaluation of the traffic heat input on RST is relatively difficult, firstly because of the plurality of the impact processes, and secondly because of the change in heat input according to these parameters (traffic density, vehicles speed, road topographic profile and atmospheric stability, etc.). showed that the temperature in the vehicle-passage area was approximately 3 °C above that in the non-vehicle-passage area during a sunny winter day. Furthermore, reported that the RST under vehicles waiting at traffic signals was 3 to 4 °C higher than that nearby. Some experiments with a thermal mapping vehicle indicated that traffic has a significant effect on RST , especially in traffic light areas and/or on roads with high traffic density.

All the references quoted above are related to the winter season and show that traffic has a significant effect on the RST, especially near traffic signals and/or on roads with a high density of traffic. Our study aimed at describing this traffic effect during the winter season on the pavement energy balance. This involved integrating a theoretical traffic description into the TEB numerical model dedicated to an urban configuration, and then quantifying how much the traffic energy input affects the RST both on the basis of field experimental measurements (weather, traffic) and numerical experiments.

The Town Energy Balance model and the introduction of the fluxes associated with the traffic The Town Energy Balance model

The Town Energy Balance (TEB) model aims to parametrize the interactions between the town and the urban atmospheric canopy, and is valid for a grid mesh larger than a few hundred meters. It is based on the canyon hypothesis . Previous work was performed to use the TEB in a specific winter context , with a simple description of the traffic effect on the street atmosphere: the corresponding heat flux is added as a source term in the urban canyon. In the study presented here, an analysis is conducted of the possible ways of taking into account traffic impact in modeling the RST in the winter season on the basis of Prusa and Fujimoto's approaches . That of involved incorporating a global energy source representative of the traffic heat input. The approach by is based on an explicit representation of the different physical processes related to traffic.

Different physical processes involved in the calculation of road surface energy balance in the initial TEB model configuration.

The physical processes involved in modeling the road surface energy balance by the TEB model are summarized in Fig. . In this configuration, the road surface energy balance is expressed by the following equation: (ρc)road∂RST∂tΔZs=Rn+Sa+L+G. ΔZs is the thickness of the first layer of the road surface, (ρc)road is the volumetric heat capacity of the road surface layer (J m-3 K-1), t is the time (s), G is the conductive heat flux across the bottom of the road surface layer (road surface heat flux, W m-2), Rn is the net radiation flux (W m-2), Sa is the sensible heat flux associated with natural wind (W m-2) and L is the latent heat flux associated with phase transition of water (liquid–vapor, and liquid–solid) (W m-2). We chose a very low thickness value (ΔZs equal to 0.001 m) so that its temperature reflects the RST. This gives a quick response of the road surface temperature to heat flux changes without thermal inertia.

Figure also shows the radiative interaction coefficients LWx_to_y between the various components x and y (sun, road, walls, garden, snow) of the urban canyon. The urban canyon interacts with the road surface, and the interactions are represented by the coefficients (LWx_to_y), as specified by . LWRoad_to_Sun is the interaction radiative coefficient between road and sun, LWRoad_to_Road is that between road and road, LWSnow_to_Road between the snow layer and the road, LWWalls_to_Road between walls and road and LWGarden_to_Road between garden and road. σ is the Stefan–Boltzmann constant (5.67 × 10-8 W m-2 K-4), εroad, εwall, εsnow and εgarden are, respectively, the emissivity of the road (0.95), walls (0.90), snow layer (1) and garden (0.98). SVFroad and SVFwalls are, respectively, the sky view factors of the road and walls. These sky view factors are calculated by the TEB model on the basis of building height and on the road width of the urban canyon.

Among the interaction coefficients mentioned above, the one between snow and road occurs only in the presence of snow on the road. However, at this stage, the road surface was considered cleared of snow. Therefore this coefficient will not be taken into account in the following calculation. The interaction coefficients involved in the calculation of net radiation at the road surface are described by the following equation. Rn=Rnl+RnsRnl=Rld+RluRns=Rsd+Rsu Rnl (W m-2) and Rns (W m-2) are, respectively, the net of longwave and shortwave radiation received by the road surface. Rld (W m-2) is the downward longwave radiation, Rlu (W m-2) is the longwave upward radiation, Rsd (W m-2) is the downward shortwave radiation and Rsu (W m-2) is the upward shortwave radiation.

Figure also shows the aerodynamic resistance of the road Rroad, used in the calculation of the turbulent sensible and latent heat fluxes Sa (W m-2) and L (W m-2), respectively, defined in the TEB model by the following equations.

Sa=ρaircpRroadRST-Tlowcan=ρairACroadRST-TlowcanL=ρairLvRroad-wattQsat_road-Qcanyon=ρairACroad-wattQsat_road-Qcanyon cp is the specific heat capacity (J kg-1 K-1), ρair is the air density (kg m-3), RST the road surface temperature (K), and Tlowcan is the temperature of the lower limit layer of the urban canyon (K), and thus corresponds to the air temperature at a high of 2 m. Lv is the latent heat of liquid water evaporation (J kg-1), Qsat_road is the specific humidity in the road surface (g kg-1), Qcanyon is the specific air humidity (g kg-1), Rroad is the aerodynamic resistance of a dry road, Rroad_wat is the aerodynamic resistance of a wet road, and ACroad, ACroad_wat are the aerodynamic conductance for dry and wet roads, respectively.

The conduction heat flow (G) between the first two road surface layers is calculated through the following equation using RST (first layer) and RST2, the temperature of the second layer; λ1 (W m-1 K-1) is the thermal conductivity of the first road layer, RST its temperature (K), RST2 the temperature of the second road layer (K), d1 the thickness of the first road layer (0.001 m, as mentioned above) and d2 that of the second road layer (0.01 m).

In this configuration of TEB, the traffic heat flux is involved in the calculation of the sensible QH_TOP (W m-2) and latent turbulent heat flux QE_TOP (W m-2) of the urban canyon. They are, respectively, represented by the following equations: QH_TOP=QH-ROAD+2hwQH-WALL+1froadQH-TRAFFIC,QE_TOP=QE-ROAD+1froadQE-TRAFFIC. QH_TOP and QE_TOP represent the fluxes at a high 2 m above the urban canyon. h is the representative height building of the urban canyon in the TEB model (m); w is its width (m). 1/froad represents the fraction of the road relative to the width of the urban canyon. QH_TRAFFIC and QE_TRAFFIC represent the sensible and latent heat generated by traffic (W m-2), respectively. The values that were assigned to these two parameters are QE_traffic =0 W m-2 and QH_traffic=20 W m-2, based on analysis of traffic inputs . These fluxes follow a simple diurnal cycle (zero at nighttime and equal to the prescribed values at daytime). The urban canyon interacts with the road surface, and the interactions are represented by the coefficients (LWx_to_y) quoted previously.

The bibliographic quoted above in the state of the art section indicates that traffic has a significant effect on RST. Our interest is then to integrate traffic parameters in modeling the road surface energy balance and to evaluate the effects of these energy inputs of traffic on the RST. To do so, two approaches were then considered.

Improving the evaluation of the heat flux released by the traffic (first approach)

The first approach is based on a study conducted by . The influence of the traffic is represented by the traffic sensible and latent heat fluxes (QH_traffic and QE_traffic in Fig. ). In this study, a constant flow was considered and was added to the turbulent heat flux of the urban canyon. This configuration was not adapted to a specific RST forecast. The traffic energy input is not only involved in calculating the total heat flux generated by the urban canyon, but it also affects the road energy balance. Furthermore, this heat input is not constant and depends on the traffic characteristics (volume, vehicle velocity and the daily distribution density).

The improvement provided by this first approach is to consider the traffic heat input variability with respect to urban traffic characteristics (volume, vehicle velocity and density). The greater the traffic, the lower the speed, and the larger its energy input. Therefore, the heat flux generated by the traffic would no longer be considered as a constant throughout the whole period of the simulation. In addition, this approach allows us to test the TEB model sensitivity to the variation of the traffic heat inputs.

Dimensions of the vehicle impact zone.

Item Symbol Value Road width

Wroad

10 m Vehicle length

Lveh

4.5 m Vehicle width

Wveh

1.5 m Length of the impact area of the engine

0.25 Lveh Width of the impact area of the engine

0.8 m Length of the impact area of the tires

Lveh

Width of the impact area of the tires

0.12 Wveh Radius of the impact area of the exhaust system

Rex

0.40 Wveh

The energy provided by traffic has been studied by several authors . The global heat flux generated by a vehicle, named Qv, can be expressed as a function of the net heat combustion (NHC), the fuel density ϱfuel and its average consumption FE as follows: Qv=NHCρfuelFE. According to Guibet , the NHC (J kg-1) is equal to 42 700 for gasoline and 42 600 for diesel. The fuel density ϱfuel (kg L-1) is equal to 0.775 for gasoline and 0.845 for diesel. The average fuel consumption FE (km L-1) depends on the type of fuel and on the type of traffic. In the study made by Colombert , FE is on the order of 8.5 km L-1 (this includes among other things over-consumption due to air conditioning: 3.1 L 100 km-1 for gasoline cars in the urban cycle and 3.2 L 100 km-1 for diesel ones). According to the values from the literature , an average Qv value of 3903 J per vehicle travel distance was selected, which corresponds to an energy per second for a given average vehicle speed. Based on the formula defined by , the instantaneous flux of heat generated by traffic can be evaluated by the following equation: Qtraffic(t)=1Simpact1VvehDveh(t)Qv. DVeh is the traffic density (vehicles s-1), Vveh is the vehicle velocity (m s-1), and Simpact is the traffic area impact. In this configuration, Simpact will be considered as being equal to the width of the street canyon (Simpct=Wcanyon). Qv is the global heat flux from a vehicle (J s-1). Based on Eq. (10) and considering traffic data in a given street in Nancy (France), where the study was conducted, the traffic heat contribution Qtraffic to the energy balance varies with time. It increases with the traffic volume and is low during off-peak hours when traffic density is low. This is illustrated in Fig. . To introduce the energy provided by the traffic in the TEB model, we should distinguish between the sensible and latent heats. Based on the estimation from , Qtraffic was then partitioned into sensible and latent heats, respectively represented by the following equations: QH-traffic(t)=0.92Qtraffic(t),QE-traffic(t)=0.08Qtraffic(t).

Explicit representation of traffic into the model (second approach)

This approach is based on a detailed study of the various processes of traffic impacts, and a parameterization of their physical equations was performed. The tire friction heat St in an extended temperature range, the shield effect on radiative flux received by the road surface from the environment and the radiative flux from the vehicle (Rv, FIR_veh_inf, FIR_veh_sup), the turbulent flux generated by passing vehicles, the sensible and latent heats released by the engine and exhaust system (Sm, Eex) and the aerodynamic drag associated with the vehicle's movement were selected. These impacts have been examined in many research papers by many authors. Some effects were studied by and , and mentioned previously. A detailed description of physical processes associated with traffic is provided by , which included friction from tires, forced convection on the road surface and the surrounding atmosphere, a modification of the radiation budget on the road owing to the presence of vehicles, and the emission of longwave radiation by their lower parts. gave an extended description of RST changes due to tire friction, with a heat transfer coefficient as a function of the vehicle speed, and tire temperature experimentally identified as dependent on air temperature and vehicle speed, along with the heat from the lower parts of vehicles, and the heat and moisture heats from the exhaust systems. The turbulent sensible heat was also investigated with a heat transfer coefficient dependent on vehicle speed. The radiative fluxes emitted by the upper and lower parts of vehicles were also specifically considered by and , and were based on the Stefan–Boltzmann law. A presentation of modified equations to take into account these processes in the TEB model was made and fully described in a previous paper , and illustrated in Fig. a. The heat fluxes generated by the traffic vary considerably depending on the traffic conditions (traffic congestion, fluid circulation, urban context or highway, etc.) and traffic parameters (velocity, density, volume). Furthermore, shielding due to vehicles on the road and the impact zone of their associated physical processes is partial. have identified an impact factor for each traffic physical process to evaluate its contribution, as indicated in Fig. b and Tables and .

Hourly variations of thermal traffic contributions, and variations of the shield effect coefficient (rue Charles III, Nancy, France) for the first experiment.

TEB configuration with traffic integration (a), its impact zones of the different processes (b) and the limits of the traffic impact zone (c).

In the following paragraphs, we have attempted to summarize the different approaches found in the literature and that have been analyzed in order to identify and to evaluate the different thermal traffic processes. Once the physical phenomena have been identified, a choice was made on the equations used to describe them and their adaptation for their integration into the TEB model.

Weighting of traffic area impact zones .

Item Impact area (m2) Contribution (%) Engine 2.025 0.25 Exhaust system 1.765 0.21 Tires 1.800 0.22 Body 2.510 0.32

According to , the tire frictional heat flux St (W m-2) due to tire friction can be evaluated with Newton's law of cooling as follows: St≅αtpTt-RST.

This equation is valid for an extended temperature range . αtp is the heat transfer coefficient between the tire and the road surface (W m-2 K-1), Tt is the tire temperature (K) and RST the road surface temperature (K) as mentioned above. showed that the tire temperature depends on the ambient air temperature and the vehicle velocity. For a velocity lower than 70 km h-1, the tire temperature is expressed by the following equation: Tt≅0.9Tair-273.16+0.33Vveh+273.16.

Tair is the ambient air temperature (K) and Vveh is the vehicle velocity (km h-1). The heat transfer coefficient αtp between the tire and the road surface (W m-2 K-1) is determined by and is defined by the following relationship: αtp≅5.9+3.7Vveh.

Vehicle-induced turbulence may also be an important factor in modifying the energy exchange between the air and the road surface in urban areas, especially under conditions of low wind speeds that are typical for the urban canyon. The turbulence generated by passing vehicles promotes forced convection between the road surface and the surrounding atmosphere. This physical process has been studied by several authors . have defined an approach to assess the vehicle sensible heat flux Sva (W m-2) due to vehicle-induced turbulence, removing energy from the pavement for a transfer to the urban canyon. Their approach consisted in defining a heat transfer coefficient αs (W m-2 K-1) between the road surface and the surrounding atmosphere, depending on the vehicle's velocity.

Sva≅αsTair-RST

αs is estimated from the natural wind velocity Vw (m s-1) using the following equation: αs≅10.4Vw0.7+2.2.

The radiative heat flux Rv (W m-2) emitted downward from the bottom of a vehicle has been studied by several authors . These studies reported that radiant heat from the bottom of a vehicle significantly affects the heat balance on a road surface, and may be evaluated by the Stefan–Boltzmann law: Rv≅ϵvehσTveh4.

ϵveh is the vehicle emissivity, σ the Stefan–Boltzmann constant, and Tveh is the vehicle temperature. In order to make calculation easier, the heterogeneity of materials constituting the vehicle bottom surface was ignored and an average value was therefore chosen (ϵveh=0.95). In this study, the vehicle will be represented by two temperatures. One is representative of the lower part, Tveh_inf (K), and another the upper part, Tveh_sup (K). Tveh_inf can be evaluated within the context of the study by . Tveh_inf≅0.2Tair+44+0.2Tair+25.9+0.2Tair+20.3

It is assumed that the upper part of the circulating vehicle body is in thermal equilibrium with air. Then, Tveh_sup is assumed to be equal to the ambient air temperature (K).

Tveh_sup≅Tair

The infrared radiative flux emitted by the lower (FIR_veh_inf) and upper (FIR_veh_sup) parts of the vehicle is thus evaluated in the following way:

FIR_veh_inf≅ϵvehσ0.2Tair+444+0.2Tair+25.94+0.2Tair+20.34,FIR_veh_sup≅ϵvehσTair4.

Fuel consumed by the vehicle is transformed into different types of energy necessary to operate the vehicle. Most is transformed into kinetic energy for the vehicle to run and electrical energy for the battery and all the electric components of the vehicle. The other portion of energy produced by vehicle is transformed into heat flux generated by the engine and the exhaust system. Based on physical approaches and thermodynamic laws, assessed the heat flow generated by the engine Sm (W m-2) and exhaust system Eex (W m-2), explained by the following equations: Eex≅mexCexTex-Tair,Sm≅αcombmH2Omexλfg.

The parameters of these equations depend on the traffic conditions. Eex (W m-2) and Sm (W m-2), respectively, are the exhaust and engine sensible heats, Tex is the exhaust system exit temperature (K) with a selected value of 350 K, mex is the combustion products mass flow rate considered as constant and equal to 0.0323 kg s-1, and Cex is the specific heat of the combustion products (1.16 kJ kg-1 K-1). mH2O is the water vapor mass fraction in the exhaust system considered as constant and whose chosen value is 0.089, αcomb is the fraction of water vapor that condenses, and λfg is the latent heat of condensation of water vapor (equal to 2.50 MJ kg-1). Maximum effects are achieved with αcomb=1. All values indicated above were given in the article by .

Traffic also impacts the energy balance by an intermittent interruption of the radiative flux towards the surface of the road. This phenomenon is called vehicle shield and depends on the traffic parameters. Vehicle shield firstly prevents the incident solar radiation from reaching the surface of the road. It consequently leads to a loss of energy on the surface energy balance, and secondly it blocks the radiation emitted by the road surface. This physical traffic process can be evaluated by a shield effect coefficient Cshield (dimensionless number). The vehicle shield effect on the road has been investigated by and can be defined by the following expression:

Cshield≅TvehttimeDtraffic.

ttime is the modeling time step (s), Dtraffic represents the traffic density (dimensionless number) and Tveh is the shielding time caused by the passage of one vehicle (s), equal to the ratio between the length and the vehicle velocity.

Traffic influences the heat transfer between the road surface and the surrounding atmosphere by increasing the aerodynamic resistance of air. This process has been studied by several authors and different approaches were used to evaluate it . Here we will use that of illustrated by the following equations:

ACroad*≅ACroad+CshieldACtraffic,ACroad_watt*≅ACroad_watt+CshieldACtraffic.

ACroad* and ACroad_watt*, respectively, are the aerodynamic conductance of a dry and a wet circulated road. They are computed with those of a non-circulated road, ACroad and ACroad_watt, and the aerodynamic conductance specific to traffic ACtraffic=10-3 experimentally determined by and validated with the NORTRIP model.

The incidence of traffic in shortwave radiation will be calculated as follows:

Rns*≅Rsd*+Rsu*,Rsd*≅1-CshieldRsd+Cshieldaveh_supRsd,Rsu*≅1-CshieldRsu+Cshieldaveh_infRsu.

aveh_sup is the albedo of the upper part of vehicle, it depends on the color of its paint and an average value was chosen as equal to 0.75 (dimensionless); aveh_inf is one of the lower parts of vehicles. The heterogeneity of the lower parts of vehicle bodies is neglected and an average value of 0.057 was selected (average between that of steel (0.075) and aluminum (0.039)).

The energy absorbed by vehicles constituting the traffic is incorporated into the road as a first approximation. This hypothesis is consistent with winter conditions when shortwave and longwave radiation flux are small enough, and with a traffic density profile similar to the ones used in this work. This assumption presents some limits for very heavy traffic or bolted situations (Cshield≃1) and for forecasts over large periods because of the risk of the accumulation of this vehicle-absorbed energy into the pavement. The application to another urban site will be possible on available traffic data, or considering a generic traffic density profile representative of the site. In the case of an entire city, considering the canyon hypothesis, an average traffic density could be selected, and the chosen parameterization applied, though a partition of the local climate zone will be necessary.

The other parameters chosen for the description are the road width Wroad, the vehicle length Lveh, and width Wveh, those of the impact area of the engine, respectively, Lm and Wm, those of the impact area of the tires, respectively, Lp and Wp, and the radius of the impact area of the exhaust system Rex. Based on traffic data from rue Charles III (Nancy, France), the magnitude of the corresponding shield effect coefficient Cshield on the radiative flux of the road surface is shown in Fig. .

This second approach of integrating traffic into the TEB model is based in the resolution of town surface energy balances. For the area not impacted by passing vehicles, the energy balance corresponded to the initial TEB configuration. However, in the area impacted by the traffic, the physical processes of traffic were substituted for the road surface parameters. Then, a weighted average of RST was calculated with the surface temperatures from the resolution of the energy balances. The ponderation is based on Ztraffic, a constant between 0 and 1. It represents the percentage of the road impacted by the vehicle passage (Fig. c).

To integrate traffic simply and relevantly into the TEB model, some assumptions were made. First, the heat flux generated by the engine Sm, the exhaust system Eex and the flow of forced convection Sva generated by passing vehicles are added to the urban canyon QH_TOP and QE_TOP. Then, the heat friction flux St is added to the road surface energy balance. This energy contribution is taken into account in the most appropriate location of the urban canyon, along with its interaction with the flux of other components (road, walls). Concerning the radiative flux, the infrared radiation flux emitted by the vehicle is added to the infrared radiative flux received by the road surface. The infrared flux emitted by the bottom of the vehicle FIR_veh_inf is added to the longwave radiation flux received by the road surface Rld, and the infrared flux emitted by the upper part of the vehicle FIR_veh_sup is added to the long wavelength flux of the atmosphere Rlu. The shield effect caused by passing vehicles will decrease the radiative flux of the road surface. Based on these assumptions, the road surface energy balance is written in the following form:

(ρc)road∂RST∂tΔZs=1-ZtrafficRn+Sa+L+G+Ztraffic(Rn*+Sa*+L*+G-CshieldSva+0.22CshieldSt).

The (*) symbol denotes surface parameters impacted by traffic. The constant 0.22 represents the impact factor defined by for the tire frictional processes (Table ). The net radiation impact on traffic Rn* is expressed by the following equations: Rn*=Rnl*+Rns,Rnl*=Rld*+Rlu*,

Rld*≅1-CshieldRld+CshieldRIR_veh_inf,Rlu*≅1-CshieldRlu+CshieldRIR_veh_sup.

The sensible Sa* (W m-2) and latent L* (W m-2) heats in the presence of traffic on the road are, respectively, written as Sa*=ρairACroad*RST-Tlowcan,L*=ρairACroad-watt*Qsat_road-Qcanyon.

According to the first hypothesis of integration of traffic impacts, the heat flows through the engine and the exhaust system are added to the turbulent heat flux of the urban canyon, which influences the road surface energy balance. This is reflected by means of the following equations:

QH_TOP=QH-ROAD+2hwQH-WALL+Cshield1froadQH-TRAFFIC,QH_TRAFFIC=0.25Sm+0.21Sex+Sva.

The constants 0.25 and 0.21 represent the impact factor defined by for the engine and the exhaust system, respectively (Table ). An exhaustive list of abbreviations is provided in Appendix A, giving the all terms used in equations for both this article and that of .

Experimental measurements of traffic effect on urban RST

To identify the most appropriate approach to implementing traffic in the TEB, some experiments were conducted. They consisted in RST measurements on pavement zones subjected and not subjected to traffic. The experimental zone was located in rue Charles III (Nancy, France), having a canyon configuration consistent with TEB, with a width around 12 m (Fig. ). This street is straight, orientated slightly north of west–east, and consisting of one non-circulated lane, nearly 3 m wide, and two circulated lanes to give a total width of nearly 9 m, and with a one-directional vehicle flow going east.

Configuration of the street in Nancy (France) for the validation of the two different approaches to traffic implementation in TEB.

Description of the experiments, meteorological and traffic data

RST and atmospheric measurements were obtained using a vehicle parked in the selected street with an on-board data acquisition system (Fig. a). The instruments were primarily devices dedicated to meteorological parameters (Tair, relative humidity, wind direction and speed). They were installed on the roof of the vehicle, and data collected every 2 s. A radiometer and an infrared camera were dedicated to RST without and with traffic, respectively. The radiometer was installed in a compartment at controlled temperature, attached to the front bumper of the car, also with measurements every 2 s. The infrared camera was installed in a compartment on the vehicle roof. Thermal images of the pavement submitted to traffic were taken every 60 s. An illustration of instruments is given in Fig. b. Traffic data for the selected street were obtained from the appropriate department in Nancy.

Two experiments were then conducted. They consisted in continuously monitoring all the parameters described above over a period of up to 48 h in the same locations and on two distinct dates, and with a variety of weather situations corresponding to an approaching winter.

Weather and urban data inputs for TEB

Meteorological data used as forcing input for the TEB surface model come from the Nancy weather station located 2800 m away from the measurement site. Measurements available and used from this station are air temperature at 2 m height (∘C), air relative humidity at a height of 2 m (%) (the specific humidity used for forcing was calculated from this relative humidity), wind speed at a height of 10 m (m s-1), direct and diffuse solar radiation (W m-2), rain and snow precipitation (mm) and air pressure (Pa). In the absence of coupling with an atmospheric model, TEB can be forced with meteorological parameters at 2.5 m. It was therefore consistent to take meteorological measurements available at 2 m as forcing data. Direct and diffuse radiation was calculated by the TEB model on the basis of global radiation data, assuming 80 % as direct and the 20 % remaining as diffuse. These data cover both measurements campaigns with an hourly time step. The first campaign started on 20 November 2014 at 04:00 (local time) and lasted 48 h, and the second campaign was initiated on 17 December 2014 at 11:00 and lasted 30 h.

Illustration of a car parked in the street with the radiometer on the front bumper (a), and details of instruments installed on the vehicle roof.

Examples of parameterization of the coatings constituting the built urban area in TEB.

Item Value Unit Percentage of built area 70 (%) Building height 15 (m) Ratio of the width of the canyon and urban building height 1.15 – Characteristics of the various components of the urban canyon Roof Road Walls Emissivity 0.90 0.94 0.90 Albedo 0.22 0.08 0.20 Number of layers 4 5 4 Layer thickness (m) 1 0.020 0.001 0.010 2 0.150 0.010 0.040 3 0.120 0.100 0.015 4 0.300 0.250 0.060 5 – 0.600 – Layer heat capacity (W K-1 m-2) 1 1 769 000 2 000 000 1 890 000 2 1 500 000 2 000 000 1 890 000 3 290 000 2 000 000 804 000 4 1 520 000 2 000 000 564 000 5 1 400 000 Layer thermal conductivity (W m-1 K-1) 1 0.90 2.00 1.77 2 0.93 2.00 1.77 3 0.50 2.00 0.75 4 0.19 2.00 0.18 5 – 0.40 –

Besides these meteorological parameters, the TEB scheme requires a parameterization of the coatings constituting the built urban area, such as the percentage of built area, the height of buildings, the road width, the number of component layers of each covered urban surface (roof, walls and road), their thickness, and their thermal characteristic (thermal conductivity and heat capacity). The selected elements were the ones initially present in the TEB urban data input and considered as consistent with the building configuration of the experimental site. Some of these are provided in Table , and the selected building density was 70 %.

Results and discussion Experimental results on RST

The first step in our experimental study is to assess the magnitude of the traffic impact on the road surface temperature. Figure indicates the RST of an area without traffic and the one subjected to traffic. It is noted that outside peak hours between the 20:00 and 06:00 RST curves merge for the two zones. This reflects the reduced traffic flux input. However, during the day, we found that the RST of the area subjected to traffic is greater by 1 to 3 ∘C with respect to the non-circulated one. The higher the traffic (especially during peak hours), the larger the gap between the two RSTs. The preliminary result of this experimental study confirms those reported in the literature . Firstly the RST differences do not only exist between an urban configuration and a rural one. The RST is also greater in a zone subjected to traffic with respect to another one that is traffic-free. This was observed in a full urban configuration. There is a clear relationship between hourly variation of thermal traffic contribution (Fig. ) and hourly RST variation too.

Assessment of the magnitude of traffic impacts on the RST, and illustration of a weighted average temperature of the road surface for the first experiment.

The TEB model simulates an average RST. It does not distinguish between an area impacted by passing vehicles and another one without traffic. In order to compare the results provided by the TEB model with field data, we calculated a weighted average RST. In the following text, the measured road surface temperature RSTmeasured corresponds to this weighted average RST according to the following relationship:

RSTmeasured=1σϵroad13σϵroadTWithout_traffic4+23σϵroadTWith_traffic44.

The constants 1/3 and 2/3 correspond to the portion of the road without traffic and the one subjected to traffic, respectively. These values are consistent with the numerical description of the second approach, 1-Ztraffic and Ztraffic, respectively. Therefore, in the text that follows, the results of the TEB model on RST will be compared to RSTmeasured. Its variations with time for the first experiment are illustrated in Fig. .

Assessment of air canyon simulation with TEB in its initial configuration

The next step in our study, and in the first one in the evaluation of the TEB parametrization, was to check the ability of TEB to simulate the air canyon temperature in a street without traffic. As indicated in the literature, some experiments have been conducted over circulated and non-circulated zones . TEB has already been validated to simulate the air canyon temperature for a street without traffic, or with heat flux from traffic neglected . The comparison between field measurements in Nancy and simulation results of Tair with the TEB model in its initial configuration (IC) is illustrated in Fig. a. At nighttime, there is no traffic in rue Charles III, and TEB provided results in good agreement with field data.

Comparisons between Tair from TEB in its initial configuration (Tair_TEB_IC), Tair from TEB via the first approach (Tair_TEB_A1) and field data (Tair_measured) (a), between RST from TEB in its initial configuration (RST_TEB_IC), RST from TEB via the first approach (RST_TEB_A1) and field data (RST_measured) (b), evaluation of the incidence of the traffic energy flux value on RST from TEB in its initial configuration (c), and disruption induced on Tair forecast from TEB in its initial configuration with larger values of QH_traffic (d) for the first experiment.

Comparison between RST from TEB in its initial configuration and field data

As indicated above, in the initial configuration of the TEB model, traffic heat flux was already introduced. It was considered as a constant flux that is added to the heat flux of the urban canyon according to a simple diurnal cycle. Figure a provides a comparison between the RST simulated by the TEB model via the initial configuration of traffic (RST_TEB_IC) and RSTmeasured. There is an offset of 3 to 4 °C, RST_measured being greater than the RST_TEB_IC. This initial configuration does not properly take into account this traffic heat flux. This offset can be explained either by an incorrect traffic heat values input, or by inadequate integration of traffic into the TEB model. Additional calculations were then made to evaluate to what extent the value of the heat flux generated by the traffic could be adjusted to obtain the best RST forecast. Values up to 200 W m-2 were considered and results plotted in Fig. c. They show that none of the values was enough to obtain the experimental results. Increasing Qtraffic up to 200 W m-2 was not enough to reach a coincidence between RSTmeasured and RST_TEB_IC curves, the offset remaining nearly 2 °C. Furthermore, the traffic peaks are not as visible as in field measurements, nor is the relationship with Qtraffic (Fig. ). The RST increase is not as great as expected due to Qtraffic increase during peak hours. Moreover, such QH_traffic values not only do not improve the modeling of the RST, but they also disrupt the Tair modeling, as illustrated in Fig. 8d. While taking into account the heat flux generated by the traffic according to the initial configuration value of QH_traffic=20 W m-2 gave Tair results consistent with the measurements, the allocation of larger values (QH_traffic=50, 100, 150, and 200 W m-2) induce disruption in the corresponding Tair. The results of Fig. c and d also justify the purpose for which the traffic was integrated into the TEB model. In fact, the heat flux generated by the traffic was included under this initial configuration for modeling the overall heat flow in the urban canyon, to assess the specific impact of anthropogenic heat flux on urban comfort. This initial configuration of traffic in the TEB model may be valid according to the objective for which it was taken into account, but it does not meet the objective of our study about the evaluation of traffic thermal impacts on the RST modeling. This method should be modified to better take into account traffic heat inputs, especially in winter conditions. This initial parameterization of traffic into the TEB model was not meant for RST forecast but more for global heat flux balance of a urban canyon .

Traffic integration results with the first approach

The constants of the traffic heat input set out in the initial configuration of traffic in TEB were not adapted with respect to flux generated by the traffic and indicated in the literature for the RST forecast . The first approach (A1) consists in introducing a more accurate heat flux generated by vehicles, expressed in W m-2 of road, with its daily cycle presented in Fig. , and then in testing the sensitivity of the road energy balance variation in this. Figure a illustrates the variations with time of RSTmeasured, RST_TEB_IC and the RST simulated according to the (A1) approach (RST_TEB_A1) in the case of the first experiment. Similar results were obtained with the second experiment.

The integration of traffic into the TEB model according to the (A1) approach did not affect the Tair forecast with respect to the initial configuration (Fig. a), and has led to a slight improvement in the RST forecast (Fig. b). However, this improvement did not manage to reach the values as observed in field data. The modification of this first approach mainly involved having a daily variation of traffic heat into the canyon that was nearly 40 W m-2 greater (Fig. ) at a given time of day. This change in energy, without significantly modifying its daily cycle, slightly increased the RST. It might also reveal some missing energy from the traffic.

The study of the thermal mapping of traffic impacts carried out by indicated that the maximum effect of traffic is generated by the tire friction and the sensible heat flux exchanged between the vehicle and the road surface. It also indicates that the maximum traffic effect occurs in the immediate vicinity of the vehicle, approximately 0.5 m from the ground. In the TEB model, the urban canyon heat flux interacts at the first level of TEB located at a height of 2 m from the ground. This integration of traffic as a source of heat in the urban canyon is therefore not suitable. This description of the first approach may also be valid in the case of a global appreciation of anthropogenic flux.

Traffic integration results with the second approach Analysis of results

Traffic integration results using this second approach (A2) are illustrated in Fig. . This compares the variation with time of RST for a traffic integration in the TEB as in the initial configuration and according to the (A2) approach for both experiments. RST results with the (A2) approach (RST_TEB_A2) are closer to the field data than the initial configuration. The difference between field and calculated RST is nearly 0.5 ∘C on average. RST variations reflect those of Qtraffic (Fig. ), and their amplitudes (3 ∘C Fig. a; 6 ∘C Fig. b) are consistent with field measurements. The RST_TEB_A2 profile indicates that this approach took the heat inputs generated by traffic more properly into account. We also found that heat input peaks of the traffic during rush hours were obtained with better agreement with respect to field measurements.

Comparison between RST from TEB in its initial configuration (RST_TEB_IC), RST from TEB via the first approach (RST_TEB_A1), RST from TEB via the second approach (RST_TEB_A2) and field data (RST_measured) for the first (a) and for the second (b) experiments.

Analysis of the RST_TEB_A2 shows that the RST forecast is improved by 2 to 3 ∘C with respect to RST_TEB_IC. This improvement primarily reflects the impacts of traffic on the RST and also that the configuration with which the traffic was introduced into the TEB model seems more appropriate for the case of the winter season. Although the experiments were conducted above freezing, RST is still underestimated and might lead to false alerts with respect to ice occurrence. This could be critical in the early commuting hours of the day, and some work is still needed to improve the mitigation of road hazards due to iced roads.

Another validation of the (A2) approach involved comparing the air temperature measured on the vehicle in the street with the forecast one obtained with TEB. Air temperature measurements are obtained at a height (1.8 m) and under conditions (generation of a continuous laminar air flow on the probe) compliant with those at which TEB provides its results (2 m). Results are presented in Fig. , and indicated good agreement between the forecast and the measurement in both experimental cases.

Model sensitivity

As indicated before, the TEB model provides an average RST and does not distinguish between an area subjected to traffic and another one that is not.

The parameter Ztraffic was integrated into the model to take into account the portion of the road affected by traffic. The sensitivity test of the TEB model to this parameter, Ztraffic, was conducted. Ztraffic=1 corresponds to the measurements made by the infrared camera (RST_With_traffic). Figure indicates that the results given by the TEB model (RST_TEB_A2 (Ztraffic=1)) are close to RST_With_traffic. This confirms that the physical description of the traffic impacts process is suitable for the traffic integration in the TEB model for the winter season.

Comparison between air temperature from TEB in its initial configuration (Tair_TEB_IC), air temperature from TEB via the first approach (Tair_TEB_A1), air temperature from TEB via the second approach (Tair_TEB_A2) and air temperature from field data (Tair_measured) for the first (a) and for the second (b) experiments.

In urban areas, besides meteorological parameters, the RST is also influenced by the buildings' configuration (percentage of buildings, building heights, widths of roads, type of materials used, etc.). Specific configurations where buildings are present everywhere in an urban environment, or totally absent, though not applicable in all urban environments, were tested to evaluate the sensitivity of the TEB model to this parameter. The results are shown in Fig. . It is found that without building the RST decreases by 0.5 °C, especially at night. This can be explained by the nature of the building materials that store heat during the day and restore it at the night along with the absence of a radiative well created by buildings. In the absence of buildings, the heat transfer phenomenon is absent.

Conclusions

An experimental study was conducted to quantify the anthropic energy flux of traffic impact on RST in the winter season. It indicated an RST increase by 1 to 3 °C with respect to the absence of traffic. Additional work was undertaken to evaluate to what extent an accurate description of traffic might improve the TEB numerical model when dedicated to RST simulations. Two approaches to traffic integration in this model were detailed and tested.

Comparison between RST measured by the IR camera in an area impacted by traffic and RST from TEB via the second approach with Ztraffic=1 for the first experiment.

The integration of traffic into the TEB model according to the first approach (A1) and based on a variable heat flux into the canyon with time did not improve RST forecasting, with a gap between simulations and measurements of 3 to 4 °C. This approach can be used to evaluate the global anthropogenic heat flux in the urban canyon, and is not meant for RST urban simulation. The results of the second approach (A2), consisting in an accurate description of energy contributions of traffic, were consistent with the experimental study as well as with the literature review. They indicated that the traffic increased RST by 1 to 3 °C, and this increase depends on traffic conditions (vehicle velocity, traffic density and traffic impact area). Some TEB model sensitivity tests showed that the traffic impact area affects the RST forecast. If this area is large, the thermal traffic flows are great, which results in an increase in the RST. The presence or absence of buildings also influenced modeling of RST. Validation was also successfully obtained with the air temperature. These results were obtained in some winter situations not considered as critical. RST is still slightly underestimated in this second approach, and could therefore trigger false alerts of ice occurrence on pavement. To obtain a better forecast for RST with the TEB model, it is necessary to properly define the configuration of the urban environment. It should be noted that the integration of traffic in the TEB model according to this second approach significantly improved the RST forecast in the winter season. However, there is still a difference of 0.5 to 1 °C between the measurements and the TEB-simulated RST. This can be explained either by the error that can be assigned to the measurement devices, or because the physical description we used for the process of traffic impacts still needs improvement, or by the existence of certain road parameters that have not yet been introduced into the RST forecast with this model.

Comparison between RST from TEB via the second approach (RST_TEB_A2), RST from TEB via the second approach without buildings (RST_TEB_A2_WB) and field data (RST_measured) for the first experiment.

An assumption was made about the energy absorbed by passing vehicles, which was included in the pavement as a first approximation. Such a hypothesis will limit the modeling to non-heavy traffic streets (Cshield<0.5, as is the case in Nancy) and to winter situations with low shortwave radiation flux. The implementation of traffic in the TEB model will certainly be improved by considering a full energy balance description of the vehicles (shortwave and longwave radiation). If some parts of this energy (infrared flux emitted by the lower part of the vehicles) will still be added to the pavement, other ones (shortwave downward radiation flux absorbed by their upper parts) will certainly be included in the sensible heat flux of the canyon.

Within the same context of this study, further work will be undertaken to analyze the sensitivity of the TEB model to these different physical processes of traffic, and on the basis of additional field data currently available. The objective is to assess the contribution of each traffic process in improving the RST modeling according to the traffic parameters and the variation of atmospheric stability. These thermal traffic impacts should also be coupled with the road surface water balance of the TEB model to identify and further quantify the influence of the presence of water in its various forms (liquid and solid (ice and snow)) on the RST modeling. Furthermore, the energy absorbed by vehicles has so far been added to the road surface, which was consistent with winter situations and the traffic profiles used. So as to extend the approach to other seasons, a detailed description of energy absorbed by passing vehicles will have to be considered.

List of abbreviations

Abbreviations Synonym Unit aveh_sup Albedo of the upper part of a vehicle – aveh_inf Albedo of the lower part of a vehicle – ACroad Aerodynamic conductance on a dry road – ACroad-wat Aerodynamic conductance on a wet road – ACroad* Aerodynamic conductance impacted by traffic on a dry road – ACroad-wat* Aerodynamic conductance impacted by traffic on a wet road – Cex Specific heat of combustion products J kg-1 K-1 Cshield Shield coefficient – Cturb Coefficient of turbulence caused by traffic – cp Specific heat capacity J kg-1 K-1 d1, d2 Thickness of the first and the second layer of the road m Dveh Traffic density vehicles s-1 Eex Sensible heat flux from the exhaust system W m-2 FE Average fuel consumption km L-1 FIRveh-inf Downward infrared radiation flux emitted by the lower part of vehicle W m-2 FIRveh-sup Upward infrared radiation flux emitted by the upper part of vehicle W m-2 G Conductive soil heat flux W m-2 h Representative height of urban canyon in the TEB model m L Latent heat flux W m-2 L* Latent heat flux impacted by traffic W m-2 Lv Latent energy of liquid water evaporation J kg-1 Lveh Vehicle length m LWRoad_to_Road Interaction radiative coefficient between road and road W m-2 K-4 LWRoad_to_Sun Interaction radiative coefficient between road and sun W m-2 K-4 LWSnow_to_road Interaction radiative coefficient between snow and road W m-2 K-4 LWWalls_to_road Interaction radiative coefficient between walls and road W m-2 K-4 LWGarden_to_road Interaction radiative coefficient between garden and road W m-2 K-4 mex Combustion product mass flow rate kg s-1 mH2O Water vapor mass fraction in the exhaust system – NHC Net heat combustion J kg-1 Qcanyon Specific air humidity g kg-1 QE_traffic Latent heat flux of traffic W m-2 QE_top Latent heat flux of urban canyon W m-2 QH_traffic Sensible heat flux of traffic W m-2 QH_top Sensible heat flux of urban canyon W m-2 Qtraffic Total heat flux generated by traffic W m-2 Qsat_road Specific humidity of the road surface g kg-1 Qv Global flux from a vehicle J s-1 Rn Net radiation flux W m-2 Rnl Net longwave radiation at the road surface W m-2 Rnl* Net longwave radiation at the road surface impacted by traffic W m-2 Rns Net shortwave radiation at the road surface W m-2 Rld Downward longwave radiation at the road surface W m-2 Rld* Downward longwave radiation at the road surface impacted by traffic W m-2 Rlu Longwave upward radiation W m-2 Rlu* Longwave upward radiation impacted by traffic W m-2 Rroad Aerodynamic resistance of dry road – Rroad-wat Aerodynamic resistance of a wet road – Rsd Downward shortwave radiation W m-2 Rsu Upward shortwave radiation W m-2 RST Road surface temperature K

Abbreviations Synonym Unit RST2 Temperature of the second layer of road K RSTWith-traffic RST measured by the IR camera (zone subjected to traffic) K RSTWithout-traffic RST measured by the IR radiometer (zone not subjected to traffic) K RSTmeasured Weighted average of the RST K RSTTEB-IC RST simulated according the initial configuration of TEB K RSTTEB-A1 RST simulated according the first traffic integration approach in TEB K RSTTEB-A2 RST simulated according the second traffic integration approach in TEB K Rv Radiative heat flux emitted by vehicle W m-2 Sa Sensible heat flux W m-2 Sa* Sensible heat flux impacted by traffic W m-2 Simpact Traffic area impact m Sm Sensible heat flux from the engine W m-2 St Frictional heat flux W m-2 Sva Vehicle sensible heat due to vehicle-induced wind W m-2 SVFroad Sky view factor of the road – SVFwalls Sky view factor of the walls – TEB Town Energy Balance – Tair Ambient air temperature at 2 m height K Tshield Time during which the road surface is covered by the vehicle s Tlowcan Temperature of the lower limit layer of urban canyon, assimilated to Tair K ttime Time step s Tt Tire temperature K Tv Shielding time due to only one vehicle s Tveh Vehicle temperature K Tveh-inf Representative temperature of the lower part of vehicle K Tveh-sup Representative temperature of the upper part of vehicle K Vveh Vehicle velocity m s-1 Vw Natural wind velocity m s-1 Wcanyon Width of the street canyon m Wimpact Width of the traffic impact area m Wveh Width of the vehicle m Wroad Width of the road m Y Limit of the turbulence zone beyond the vehicle width m Y* Normalized distance relative to the width of the vehicle Ztraffic Impact area of traffic % Greek letters αcomb Fraction of water vapor that condenses – αs Heat transfer coefficient between atmosphere and road surface W m-2 K-1 αtp Heat transfer coefficient between the tire and the road surface W m-2 K-1 ϵgarden Emissivity of the garden – ϵroad Emissivity of the road – ϵsnow Emissivity of the snow layer – ϵveh Vehicle emissivity – ϵwalls Emissivity of the walls – λ1 Thermal conductivity of the first road layer W m-1 K-1 λfg Latent heat of condensation of water vapor J kg-1 ρair Air density kg m-3 ρfuel Fuel density kg L-1 (ρc)road Volumetric heat capacity J m-3 K-1 σ Stefan–Boltzmann constant W m-2 K-4 ΔZs Thickness of the first layer of the road surface m 1/froad Fraction of the road relative to the width of urban canyon –

Acknowledgements

The authors would like to take this opportunity to thank IFSTTAR and Météo France for their financial support, and Mathieu Moutton and Stéphane Ludwig for performing all the measurements. Edited by: T. Poulet

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