In this article, TEB is improved with new parameterisations. The model will now take into account the heat released from engine inefficiencies, the impact of the vehicle body on the radiation budget and on the turbulent heat exchange, and the heat produced by the surface-tyre interactions, as shown in Fig. . The direct impacts of traffic on the water, ice, and snow cover are not modelled. They do not fall in the scope of this study. As TEB is an horizontally averaged model, the model must integrate horizontally averaged traffic impacts. So, for example, at one model grid point, despite the significant heterogeneity of the road traffic, the wind induced by the entire vehicle fleet returns a single horizontal average value. Traffic intensity is included in the model through average values of traffic counts and converted to vehicles per second. Therefore, traffic counts change at each atmospheric forcing time (each hour in this study).

Two energy budgets are parameterised: the internal energy budget and the vehicle body energy balance. The latter calculates the radiation impacts on the vehicle and, conversely, the impacts of the vehicle body on TEB energy balance. The former calculates the energy generated from the fuel combustion and transformed into mechanical energy or into heat. From the mechanical energy, a share is transferred to the road through the surface-tyre interaction. From the energy transformed into heat, a first share is released as sensible and latent heat into the air and a second share warms the bottom vehicle body as shown in Fig. . Each share is estimated through the dynamics of a vehicle, modelled by a simple Newtonian mechanics equilibrium equation inspired by .

The internal energy budget and the vehicle body energy balance are coupled in a simple way: (1) The temperature of the bottom vehicle body surface is prescribed as in . It increases the infrared radiation emitted by the surface. (2) The additional energy needed to increases the infrared radiation emission from the bottom of the vehicle body is extracted from the internal energy balance of a vehicle. Finally, the turbulent heat exchange coefficient between the road surface and the air is modified by the traffic-induced wind. A simple analytical formula is developed to calculate the wind induced by traffic inspired by the study of .

If the goal is to the parameterised the impact of electric vehicles, it is possible through modifying the internal energy balance parameterisation. Because of their much larger energy efficiencies , it is possible to consider no energy loss from their internal energy balance. In practice, this means multiplying the heat released into the air and the infrared radiation from the warm surface of the bottom vehicle body by the proportion of non-electric vehicles.

The urban energy balance without traffic impacts is written as : 1Q*+Qf=Qh+Qe+ΔQs+Qm+ΔQa In the urban area, Q* and Qf are the net radiative heat flux and the anthropic heat flux (without traffic), respectively. On the right-hand side of the equation, there are two turbulent fluxes Qh and Qe sensible and latent heat fluxes, respectively, and ΔQs the heat flux by conduction through the urban surfaces. Qm is the power exchanged by the melting and freezing of the water and finally ΔQa the horizontal advection, which is neglected in this study. All terms of the equation are expressed in watts per square metre.

Each traffic impact then modifies the energy balance within the canopy. First, three new source terms are added into this equation with the sensible QHengine and latent heat flux QEengine from the heat lost by the vehicle engine and the tyre-road friction heat flux Qr. Secondly, the turbulent fluxes Qh, Qe of the urban area are modified by the wind induced by the traffic Utraff. Indeed, traffic modifies the fluxes from the soil-atmosphere interaction. Finally, the solar and infrared net heat fluxes are modified by the vehicle body as depicted in Fig.  and the resulting energy from the vehicle balance is released as sensible heat in the air. The other terms are not formally modified, but react according to the new energy exchanges driven by the new and modified terms. The updated urban energy balance, function of the different traffic impacts gives: 2Q*(traff)+Qf+Qf_traff=Qh(Utraff)+Qe(Utraff)+ΔQs+Qm+ΔQa+QHengine+QEengine+Qr+Qveh with Qf_traff, the total source of energy coming from the vehicles distributed in the different right-hand terms of the equation.

The impact of traffic on local climate must be estimated considering the large heterogeneities of vehicle type, size, internal parts, engines, and driver behaviour. On one hand, traffic is a collection of vehicles with various characteristics: size, shape, internal parts, and engine type. From the distribution of all existing characteristics of the vehicles, a finite set of variables and parameters is defined. The inherent physical characteristics of a vehicle can be defined by its weight m (kg), length l (m), height h (m), cross-section A (m²), energy power efficiency η, and drag coefficient Cd. They are assumed to be the characteristics of a vehicle that influence the most the traffic impacts on local climate. On the other hand, at each location, traffic is a collection of driving behaviours, which can range from economical (with slow accelerations) to more aggressive. This variability in behaviour is modelled by the speed v and the acceleration a of a vehicle.

The vehicle characteristics are assumed to be independent from the driver behaviour. This assumption is reasonable, as most vehicles can reach the maximum speed allowed in all countries. However, energy power efficiency cannot be assumed to be independent from the driver behaviour: engine efficiency ηe depends directly on speed, acceleration, gear choice and engine type. Thus, the following assumptions are made: (1) The distribution of vehicle body characteristics is specified through its average values (m‾, l‾, h‾, A‾, C‾d) as shown in Fig. . They are independent from the other variables and represent a vehicle that has the average characteristics of the overall automobile fleet. (2) An average vehicular speed v‾ is measured at a specific location, but the distribution of the speed and acceleration of the vehicle fleet at this location is unknown. So, the relationships between v‾ and the distribution the of speed and acceleration are inferred from other data sources. They are then inserted into the traffic impact equations as explained in the next paragraph and in Sect.  to take into account the impact of the collection of driver behaviour. (3) Because instantaneous engine efficiency depends on each vehicle speed, and the vehicle fleet has a distribution of speed, an average engine efficiency η‾e(v‾) of the total automobile fleet depending on the average speed v‾ is computed. It is estimated from other input data sources, as shown in Fig. .

The collection of driver behaviour and its impact on traffic impact is estimated using the Worldwide Harmonised Light vehicles Test Cycles (WLTC). These cycles have been designed to provide a common and reliable measure of the energy consumption of all vehicles sold in the European Union. Since 2019, for every vehicle sold, car manufacturers have the legal obligation to provide detailed vehicle energy consumptions measured with the WLTC. For passenger cars, researchers designed four subcycles, s={1,2,3,4}, of low-speed, medium-speed, high-speed, extra-high speed representative of different road types. In this study, these cycles are considered to be associated with urban areas, suburban areas, rural areas, and highways, respectively. Each WLTP cycle has been built from a speed and acceleration data sample of the world's driving habits .

Each vehicle is modelled as a flat 2-side surface, each with a different surface temperature. The upper vehicle body temperature is modelled equal to the air temperature Tcan (K) of the lower air layer of TEB. The bottom vehicle body temperature warmed by the vehicle engine is modelled as in  equal to Tcan+22.5 K. In addition, vehicles are modelled as a new component at ground level which shade the road, contributes to infrared emissions and radiation inter-reflections within the canyon calculated as in . Immersed in the urban canyon of TEB, the traffic takes part in the radiative exchange with the other TEB components: road, walls, windows, ground-based vegetation, and tree canopy. The footprint of traffic impact on energy exchanges is assumed to be strictly equal to the total area occupied by the vehicle fleet. Thus, each vehicle impact on the TEB energy exchanges is aggregated with the traffic occupation fraction ftraff, which represents the entire vehicle fleet.

The vehicle body energy budget composed of the shortwave and longwave radiation is solved. In addition, each vehicle is modelled without explicit thermal capacity: it means that the extra energy from the radiative budget absorbed by the vehicle body is transferred directly as sensible heat directly into the urban canyon air bottom layer. It is written as follows: 4Sveh*+LWveh*=Qveh where Sveh* (W m⁻²) is the shortwave radiation absorbed by a vehicle, LWveh* (W m⁻²) the longwave radiation absorbed by a vehicle and Qveh (W m⁻²) the residual energy drive by the radiative balance excess that is transferred as sensible heat directly into the urban canyon air bottom layer.

The solar radiation received by a vehicle is modelled as the sum of three terms: the direct Sr⇓ and diffuse solar radiation Sr↓ received at the ground level and the infinite solar reflection within the urban canyon. A share of the solar radiation received by a vehicle is then reflected by the vehicle albedo αveh. In addition, the reflection within the urban canyon are modified by the new aggregated surface albedo α‾g written: 5α‾g=(1-fsn)(1-ftraff)αrd+ftraffαveh+fsnαsn With fsn the fraction of the snow occupation on the road, αsn the albedo of snow, αrd the albedo of the snow-free road surface and ftraff the traffic occupation fractions defined Eq. ().

The longwave exchanges are computed following a linear approximation of the Stefan–Boltzmann law as in . As for the solar radiation, TEB solves the energy budget from the infrared radiation for each component. The vehicle longwave exchange are calculated with the walls, the windows, the sky, the road and summed over to give the total longwave radiation absorbed by a vehicle. Each component in TEB is also impacted by the vehicle at ground level: for each component in TEB, the additional exchange with vehicle body is added to the longwave exchanges.

Each vehicle is an autonomous system with its own internal behaviour and physical response. It affects the physical variables of the street while passing with heat relased in the atmosphere and with heat transferred to the road surface from tyre friction. The heat relased in the atmosphere is lost from the combustion of fuel in an internal combustion engine (ICE) due to mechanical inefficiencies ηm from all the mechanical frictions and rotating parts of the vehicle and the thermodynamic inefficiencies of its engine ηe(n,M). The product of both ηm and ηe(n,M) gives the total instantaneous vehicle efficiency coefficient η. The thermodynamical inefficiencies of its engine depending on the engine rotation n (rpm) and torque M (N m⁻¹) are a key variable for representing the energy lost by vehicles and for tracking changes in energy performance over the years . The maximum engine efficiency ηemax can be reached with a specific engine rotation speed and torque, but most of the time the engine efficiency of the vehicle is lower. A vehicle power-efficiency can either be directly measured (; ) or modeled to construct engine thermal maps (; ; ). Simple but precise enough physics-based tools can then be used to model the entire vehicle's response to a ride for internal combustion engines (; ; ) or electric engines (; ). In this study, ηm is considered constant and equal to 0.90 as in , since its variations for every driving condition are small compared to the variations of ηe(n,M) and an indirect estimate of ηe is developed η‾e(v‾) that accounts for the driver behaviour as explained in Sect.  and detailed in Appendix .

The vehicle dynamics and internal energy balance are modelled through a system of 4 simple equations. The vehicle trajectory is assumed to be a rectilinear motion on a road assumed to be flat. Following the simple tools developed to model the response of a vehicle, the traction force imposed by the engine on the wheels Ftrac in newton is calculated from an equilibrium equation applied to the vehicle following the kinematics of point masses. As the other terms of the motion equation can be estimated, this allows to deduce the force, and corresponding power Ptrac. A fraction of the oil consumed by the internal combustion engine of vehicles that deliver the power Pfuel in watts is transformed into mechanical power with traction power Ptrac in watt through the total instantaneous vehicle efficiency coefficient η. The power lost due to the vehicle mechanical and thermodynamical inefficiencies is then dissipated as heat Pheatloss in watts. This system is written: 6mdvdt=Ftrac-(Fr+Faero)Ptrac=vFtracPtrac=ηPfuelPheatloss=Pfuel-Ptrac with v (m s⁻¹) the vehicle speed, Fr in newton, the rolling friction force, and Faero in newton the aerodynamical drag force. Faero is expressed as usual for vehicle kinematics corresponding to high Reynolds number, and the rolling friction force Fr is expressed following  and  as an empirical formula valid for a 4-wheel passenger car: 7Fr=mg(8×10-4(5.1+5.5×105+90mgpt+1100+0.0388mgptv2))8Faero=12ρCdAv2 With pt (Pa) the tyre pressure, m (kg) the vehicle mass, g (m s⁻²) the gravity constant, ρ (kg m⁻³) the air density, Cd the drag coefficient and A (m²) the frontal area of a vehicle.

Then three strategies are used to parameterise the heat transferred to the road surface from tyre friction, and the heat released in the atmosphere. First, in the model, it is assumed that the rolling resistance is fully converted as heat flux to the road surface. Indeed, the constraining forces acting against the vehicle force produced (Ftrac) also contribute to the heat transferred to the environment. The rolling resistance acts as a mechanical constraint on the tyres and the road, part of which is dissipated as heat. Since the tyre temperature, the heat transfer coefficient, the amount of energy transferred to the tyre and the road, and the amount of energy directly converted into heat are unknown, the rolling resistance power Pr=Frv is fully converted as heat flux to the road surface.

Then, a part of the power dissipated as heat Pheatloss, calculated with Eq. (), is used to warm the bottom vehicle body at temperature Tveh as explained in Sect. . It increases the infrared radiation emitted to the road surface LWveh→rd↓ (W m⁻²) because of the warmer bottom vehicle body surface. So, starting from the bottom of the vehicle body in thermal equilibrium with the environment at Tcan (K), the power Plw (W m⁻²) to reach the infrared radiation emitted at temperature Tveh (K) is: 9Plw=LWveh→rd↓(Tveh)-LWveh→rd↓(Tcan) This power is then taken from the total heat produced by the vehicle Pheatloss.

Finally, to take into account the effects of the vehicle system in the TEB model, these effects are then aggregated for the entire traffic with a traffic flow Φ (vehicles s⁻¹) and an average traffic speed v‾ (m s⁻¹). In addition, the large heterogeneity of vehicle characteristics and behaviour is taken into account in these previous equations with the methodology explained in Sect.  and described in Appendix  through regression equation estimates (v‾2(v‾), p‾(v‾), η‾e(v‾), a‾) of v‾ and vehicle fleet average characteristics (m‾, l‾, w‾, A‾, C‾d).

So, the heat transferred to the road surface from tyre friction is modeled through the rolling resistance power averaged over the vehicle surface Sveh (m⁻²) for the entire vehicle fleet Qr in watt per metre squared written: 10Qr=ftraffFr(v‾)v‾Sveh

In addition, the power dissipated as heat Pheatloss over each vehicle surfaces Sveh (m⁻²) is released in the atmosphere. This power is calculated over the entire vehicle fleet averaged in watt per metre squared Ql and written in TEB as: 11Ql=ftraffPheatloss(v‾)Sveh-ftraffPlw Ql is then transformed as a source of sensible and latent heat flux using the formulation of : 12QHengine=0.92Ql13QEengine=0.08Ql These sensible and latent heat fluxes are released in the aggregated heat flux over the entire model tile. This energy is transferred directly to the atmosphere. Thus, the energy released by the traffic can have an effect on the town physical variables only when the model TEB is coupled with an atmospheric model.

The collection of vehicles driving on a street immersed in an urban canyon has direct effects on the physical variables of the environment. The physical body of a vehicle is an obstacle that induces drag, increases fluid velocities, and turbulence. Turbulence plays a key role in the boundary layer. It leads to heat and moisture exchange between the air layer and the different surfaces. In this study, only the influence of traffic on the road surface and the lower air layer is considered. Thus, the turbulent exchange coefficient between the road surface and the first air layer is modified by the traffic impact in the model.

Each vehicle is considered to be an independent system. The air motion triggered by a moving vehicle can be described using three regions: along the sides of the vehicle, in its near-wake, and in its far-wake. In the first area, the fluid flow is assumed to be laminar to prevent extensive calculations. From the Navier-Stokes equation, the fluid is assumed to be incompressible, without pressure forces, and to have reached a steady state. Under a vehicle, the fluid is considered to move between two infinite parallel plates with the upper one moving tangentially relative to the other. This flow is modelled as a simple linear Couette flow Ul (m s⁻¹) as shown in Fig. .

A simple power law U∼x-3/4 is used to calculate the average wind induced by vehicles in the wake of a vehicle from . They developed an analytical formula to calculate the longitudinal velocity field deficit U (m s⁻¹) in the wake of a vehicle. They linearised the Navier–Stokes momentum equation using a perturbation analysis. This equation depends on several parameters estimated on wind tunnel experiments. The longitudinal velocity field deficit U is determined in the absence of crosswinds, stable conditions, and low natural wind velocities and is valid after a downwind distance equal to approximately ten vehicle heights h . The reader should refer to  for a complete demonstration. The longitudinal velocity in the wake also depends on the other coordinates. It has been used in various studies to calculate the dispersion of pollutants in the wake of a vehicle (; ) and improved . The vertical and horizontal velocity components can also be calculated according to .

Two assumptions are made to keep the wind-induced formula simple and with consistent mathematical properties: (1) It is assumed that the formula U(x) is also valid in the near-wake of the vehicle (i.e x<10 h). However, a lower bound is determined (i.e x>leff) for continuity reason with the Couette flow Ul. Thus, the Couette flow is extended up to leff in the near-wake of a vehicle, then U(x) is used further in the wake of the vehicle when U(x)<Ul. (2) Then, an average wind speed induced by the entire traffic is found Utraff(v‾) (m s⁻¹) by calculating the integral along the x axis. Each wind induced by a vehicle is considered to have no overlap from the wind induced by each vehicle. So, the average wind speed is calculated along the vehicle and in the wake until the front of the next vehicle Utraff(v‾) as shown in Fig. . The complete demonstration is given in Appendix .

This analytical formula Utraff(v‾) has several refinements over the empirical equation from  and used by . The formula Utraff(v‾) depends explicitly on the vehicle height, length, speed, and traffic intensity, whereas the empirical formula from  depend on the vehicle speed only.

In TEB, the sensible and latent heat between the road surface and the air layer are calculated at ground level, and both use the wind speed at level z. So, the wind speed Utraff(v‾) is vertically interpolated to the level z using the Monin–Obukhov log-wind profile under neutral conditions adjustments as: 14Utraff(v‾,z)=Utraff(v‾)ln⁡(zz0)ln⁡(ztraffz0) With zo (m) the road roughness length, ztraff the height of the traffic-induced wind. In this study, ztraff is set at mid-height of the vehicle. Contrary to , the increased turbulent exchange caused by traffic is not a new component but a direct modification of the turbulent exchange coefficients embedded in TEB. The sum of the wind components at level z gives: 15Ueff=Ucan2+(u*+w*)2+Utraff(v‾,z)2 With (u*+w*)2 (m s⁻¹) the total turbulent wind component with w* (m s⁻¹) caused by the local canyon convection and Ucan (m s⁻¹) the natural wind at the lower level. It is used to adjust the aerodynamic resistance of the sensible and latent heat exchange with the road surface Rrd calculated as in .

A significant commuting pattern is observed at the Nupuri and Palojärvi road weather stations during the simulation period, with an average of 1200 and 1100 vehicles per hour, respectively, during morning peak hours towards Helsinki and 1000 and 800 vehicles per hour, respectively, in the opposite direction during the afternoon. The time series shown in Fig.  gives insights about the traffic-induced impacts throughout the simulation. It is composed of a subset period of 5 working days until the 23 December 2017 characterised by a clear commuting pattern, and of a subset period of 3 nonworking days up to the 26 December 2017 characterised by a similar traffic intensity in both directions.

There is a clear increase in road surface temperature (RST) simulated by TEB-CAR in both directions compared to the TEB simulation. TEB exhibits a significant cold RST bias with respect to the observations, which is corrected by the new processes integrated into the model. Even during the night, when traffic is sparse, the RST is higher due to the strong heating effects throughout the day. This effect can be highly relevant given that dangerous conditions for drivers occur more frequently in the morning with a lower RST reaching freezing temperatures. In addition, the TEB-CAR simulations accurately follow the observed RST in both directions in Fig.  in terms of trend and maximum or minimum.

One should confirm that the bias reduction is not coincidental with other potential biases such as sensor bias. So, the temperature difference caused by the commuting pattern between the two lanes is used to verify the accuracy of the traffic-induced effects modelled in TEB-CAR. In Fig. , the TEB-CAR RST differences (ΔRSTdir) match the observed ΔRSTdir amplitude. The strongest ΔRSTdir during peak traffic, especially in the morning, are well reproduced by TEB-CAR. The traffic intensity differences are lower in the afternoon than in the morning, leading to a lower observed ΔRSTdir. These amplitudes are well reproduced by TEB-CAR.

The RST differences between the two directions are analysed more precisely in Fig. . During weekends, traffic intensity differences are smaller as shown in Fig. . Lower traffic intensity differences between the two roads directions (ΔTraff) in the weekends should lead to lower observed ΔRSTdir in the weekends panels of Fig. . However, this pattern is less evident for the observed ΔRSTdir than for the simulated ΔRSTdir. During working days, the traffic intensity differences are much bigger as the ΔRSTdir for both observed and simulated values. The ΔTraff distribution is positively skewed at both locations during working days with values mostly between 0 and -250 vehicles per hour. Natural factors and road energy inertia have a direct impact on the RST with scattered simulated values around the regression line. The RST heteroscedasticity for the higher ΔTraff suggests that the natural factor and the traffic-induced effects are more intertwined for higher traffic intensities.

Consistency is found between the simulated and observed traffic-induced effects with almost equivalent slopes between the observed and simulated ΔRSTdir from the robust linear regressions (RLM) , designed to be robust to outliers. Also, regression equations for both at Nupuri and Palojärvi location have the same slope depending on whether it is calculated on observations or simulations. So, there is a consistent behaviour of the traffic impact on TEB subject to different traffic patterns and atmospheric conditions. The TEB-CAR simulations accurately represent the traffic differences impact up to 750 vehicles per hour. At Nupuri location, the observed and simulated ΔRSTdir distributions are shifted, the intercept of the regression equation for observed ΔRSTdir is negative, and the observed ΔRSTdir have a negative intercept. These features suggest that there is elements that produce this cold bias at Nupuri location that are not taken into account into TEB-CAR. It can also suggests that there is a sensor bias at this location since this effect is not found at Palojärvi location.

Using the RST differences between two road directions subject to the same atmospheric conditions is relevant to extract the traffic impact on the road from natural factors. It also allow to evaluate modelling tools that include traffic impact parameterisation. In addition, the traffic impact parameterisation in TEB-CAR correctly reproduces the traffic impact at the Nupuri and Palojärvi locations with a similar regression equation slope between observed and simulated RST differences.

The cumulative effect of the new set of traffic parameterisations in TEB (named TEB-CAR) results in marked impacts on the temperature of the road. Each traffic parameterisation may have opposite or cumulative effects on the physical variables. In addition, each impact may change depending on atmospheric conditions, seasonality, and traffic intensity. Thus, in this section, the individual effect of each traffic impact in the model is studied using the Nupuri experiment throughout the entire simulation period. A total of eight more simulations at Nupuri are analysed here. Each simulation has a traffic impact removed from the model and is launched in both road directions.

To evaluate the relative contribution of each process on the physical variables, one must compare each simulation launched with a process removed, with the TEB-CAR simulation. Each process has a different marginal impact on the RST and the lower air temperature simulated at 0.5 m Tcan (K) as shown by Figs.  and . The figures show that the RST simulated without the wind-induced parameterisation is warmer than the one with the entire set of traffic impact (TEB-CAR simulation). Thus, it has a cooling effect on the RST because of the stronger heat exchange between the air temperature and the RST. The same trend is observed on the simulated RST with the radiative process removed. However, the cooling effect of the ablated wind-induced simulation is much stronger than for the ablated radiative simulation, in both seasons. This strong impact from the wind-induced parameterisation can be explained by the analysis of the processes Fig. : the wind induced by the vehicles accounts for 75 % on average of the total wind simulated by the model in the daytime. At night, this proportion falls between 15 % and 45 % on average due to much lower traffic and leads to a lower cooling effect. In spring, the cooling effect of the wind-induced impact is greater than in winter with up to around 2.5 K on average during peak traffic (13:00 UTC), as shown in Fig. . In addition, the Fig.  shows that the standard deviation of the road surface temperature differences with the reference simulation ΔRSTmod is the lowest with the wind-induced parameterisation removed. In fact, the cooling effect of the wind-induced process is more pronounced when the temperature difference between the road surface and the air is the highest. This effect is highly dependent on meteorological conditions and then explains most of the traffic impact variability.

The radiative and the wind-induced processes have an opposite effect on the air temperature simulated at the lowest level Tcan. As shown in Fig. , wind-induced leads to a slight warming effect whereas radiative impact leads to a slight cooling effect in both seasons. On average, these effects are greater in the daytime. Since the RST is almost always warmer than the air temperature, more energy is transferred when the differences in soil-air temperatures are higher, especially in the daytime. In addition, the radiative impact leads to a slight cooling effect on Tcan like for the RST.

Furthermore, the RST simulated with the rolling friction is cooler than the RST simulated by TEB-CAR. Thus, this parameterisation has a warming effect on the RST. The warming effect of the heat lost by vehicles is low, even during peak traffic (4:00 UTC and 13:00 UTC) throughout the period, as shown in Fig. . Indeed, the analysis of the processes in Fig.  shows the power produced by rolling friction and transferred to the road surface is approximately 30 W m⁻² on average during peak traffic for both road directions. This leads to a strong impact on the RST as shown by the significant shifts in descriptive statistics from the TEB-CAR simulation on the boxplot diagrams in Fig. . The source of energy from the rolling friction leads to an increased air temperature simulated at the lowest level Tcan as shown in Fig. . This behaviour is consistent throughout the day and throughout both seasons.

To summarize, the processes added in TEB-CAR each have a different marginal impact on the RST: rolling friction has a strong marginal heating effect, increased turbulence a strong marginal cooling effect and radiative effect a small marginal cooling effect. In addition, depending on the meteorological conditions, the impact of traffic can change significantly due to the temperature dependency of the wind-induced parameterisation. The cumulative effect of the new set of traffic parameterisations in TEB (named TEB-CAR) results in marked differences compared to the model without the traffic parameterisation. In both seasons, the overall impact on the RST is driven by the competition between the wind-induced impact and rolling friction. Competition between these factors eventually leads to an overall warming effect on the RST in winter and a cooling effect in spring in both direction as shown on Figs.  and . The simulated TEB-CAR RST is 0.5 K warmer during the winter period and is 0.9 K cooler in spring than the RST of TEB. For air temperature Tcan, in both directions, TEB-CAR compared to TEB simulations lead to equal air temperature in winter and and 0.14 K higher on average in spring.

Even if there is no direct impact of the heat released by the fuel combustion on the road surface temperature, it is interesting to look at the values. The total heat loss by the vehicle inefficiencies modelled in this study is comparable to the heat loss modelled in other studies. calculate 18.3 W m⁻² released in the atmosphere for 1400 vehicles per hour from the inventory approach in Toulouse city. In Fig. , the heat released by traffic is calculated considering the same traffic intensity (1400 vehicles per hour) spread over the same area 100 m × 100 m. Depending on the average speed of road traffic in cities, this study simulates an average heat released from 16 W m⁻² for 4 m s⁻¹ to 6.3 W m⁻² for 15 m s⁻¹.