Introduction

Urbanization has been taking place at an unprecedented pace around the world in the past decades. In conjunction with the agglomerations of population and economic activities, urban traffic has increased rapidly to meet the needs for mobility and accessibility to different parts of the urban areas. Cities only cover about 1% of the Earth’s surface, but they disproportionally consume about 78% of the world’s energy and produce more than 60% of all CO2 emissions1. The most apparent expression of the impact of urbanization on the environment is the Urban Heat Island (UHI) effect2, which refers to the phenomenon where the urban areas have a temperature considerably higher than the surrounding rural areas3. High temperatures in urban areas exacerbate thermal discomfort of city dwellers and increase human health risks (e.g., respiratory illnesses, cardiovascular mortality)4. The UHI effect greatly boosts energy consumption in cooling, accelerates air pollution in the form of urban smog, surface dioxide and greenhouse gas emissions, and contributes to global warming1,5. UHI effect has been recognized as one of the key indicators of environmental change and global climate change6.

The urban thermal environment is determined by the surface and atmosphere energy balance in urban areas7,8. The urbanization process modifies the land surface from natural rural landscape to artificial urban built-up fabric and substantially alters the energy balance and local climate. The proliferation of artificial urban construction materials (e.g. asphalt, concrete, tar and gravel pavements) with low albedo and high heat storage capacity absorbs and accumulates much more of solar radiation8. Anthropogenic heat discharge in urban areas9,10 represents the other major heat component contributing to the formation of UHI. Urban population and industries consume large quantity of fossil fuels for heating and cooling buildings, lighting streets and buildings, manufacturing goods and services, and transporting people and goods. There are two types of anthropogenic heat sources: stationary source from buildings, industries, and public infrastructure, and mobile source from automobiles. Previous studies suggested that the anthropogenic heat has smaller effect than the land surface modification in albedo and vegetation cover and is negligible in commercial and residential areas. Anthropogenic heat discharge in a large city can create a heat island of up to 2–3 °C both during the day and at night9,11.

Some studies have explored the effect of urban transport and road traffic on the UHI12,13,14. However, most of these studies were qualitative examinations of possible thermal effects of urban traffic in relation to urban road network and traffic density distribution. Little research has been reported on quantitative evaluation of the impacts of urban traffic on the urban thermal environment and heat intensity. The daily operations of urban automobiles (cars, trucks, buses, motorcycles, etc.) generate a large amount of artificial exhaust heat that immediately increases the temperature and emits waste greenhouse gases, which pollute the air and induce a screening effect for the long-term warming15. According to US Environmental Protection Agency (EPA), transportation accounts for 28.9% of the total greenhouse emissions, followed by electricity production (27.5%), industry (22.2%), commercial and residential (11.6%), agriculture (9%), and land use (11%)16. Nevertheless, the urban traffic effect is difficult to be quantified, since the mobile anthropogenic heat from automobiles is mixed with stationary anthropogenic heat sources from buildings, infrastructure and industries8.

In this study, we attempt a quantitative assessment on the effect of the anthropogenic heat generated by automobiles on the urban thermal environment, based on the time series Moderate-resolution Imaging Spectroradiometer (MODIS) satellite observations on land surface temperature during a special event, 2008 Olympic Games, with traffic restriction in the Beijing metropolitan area. As the capital of China, Beijing has experienced rapid economic growth and urban expansion since the national economic reform and open-door policy in 197817. The municipality of Beijing (Fig. 1) has an area of 16,411 km2, and more than 13 million permanent residents and 5 million seasonal workers in 201018. As the major transportation hub of the national highway network, Beijing had 3.3 million registered vehicles in 200815,19. Recorded warming in Beijing since the early 1960s is almost twice as large as the global mean temperature warming trend20.

Traffic congestion and air pollution were the two major challenges for the execution of the 2008 Olympic Games in Beijing21. To ensure good air quality and to alleviate the traffic congestion problem, Beijing municipal government implemented a large-scale short-term traffic restriction policy, namely, the odd-and-even number rule, during the Olympic Games from July 20 to September 20, 2008. During this two-month period, vehicles with even and odd license plate numbers were alternately allowed on road22,23. Only the vehicles with even plate numbers can be allowed on the road on one day, and the vehicles with odd plate numbers on the following day. Thus, the odd-and-even number traffic restriction effectively reduced the daily traffic volume by about half during the Olympic Games, compared with the normal traffic volume before and after the Olympic Games. This traffic restriction provided an extraordinary opportunity to observe and examine the impact of traffic volume variation on the urban thermal environment.

Results

We derived urban heat extent and intensity measurements for the Beijing metropolitan area in three summer months (from July 1 to September 30) in 2007 and 2008, by employing daily MODIS satellite thermal observations. The valid urban heat extent and intensity measurements derived from the MODIS data during the Olympic Games between July 20 and September 20 in 2008 are used to form the case group (also known as experimental group) for our statistical analysis, in which the odd-and-even number traffic restriction policy was enforced. The derived urban heat extent and intensity measurements in summer months (July 1–September 30) of 2007 and during the periods from July 1 to 19 (pre-Olympic) and from September 21 to 30 (post-Olympic) in 2008 are used to form the control group, when no traffic restriction policy was imposed (Table 1). The subdivision of thermal observations and measurements into the case and control groups and the use of traffic restriction dummy variable allow us to successfully isolate and quantify the impact of traffic volume on shaping and regulating the urban thermal environment. Our analysis results show that the half traffic volume reduction led to a shrinkage of the urban heat field (with a surface temperature higher than 35 °C) by about 820 km2 and also resulted in a marked decrease in the mean surface temperature by 1.5–2.4 °C in Beijing. Our results indicate that the traffic impact on the urban thermal environment may be significantly larger than what the previous studies suggested9,11,24.

Traffic impact on urban heat extent

We derived the daily surface temperature for the Beijing metropolitan area based on the MODIS satellite thermal images, and then measured the spatial extent of the urban heat field that has a surface temperature higher than a threshold value. The daily spatial extent measurements of the urban heat field $$({{{\mathrm {SE}}}}_{t})$$ are then regressed with the net radiation variable and traffic restriction dummy variable to construct a linear regression model for assessing the traffic impact on urban heat extent.

Figure 2a, b show the time series of the urban heat field over the Beijing metropolitan area, respectively, in the morning and afternoon. The morning time series was derived from Terra MODIS thermal observations, while the afternoon time series from Aqua MODIS observations. Following Meehl et al. 25, we used the 81st percentile of the frequency distribution of observed maximum temperatures as the threshold ($${T}_{{{\mathrm {thrd}}}}$$), to define the high-temperature urban heat field, which results in the selection of 35 °C as the threshold value. To evaluate the sensitivity of the threshold, one smaller value (34 °C) and one larger value (36 °C) are also used as additional thresholds for extracting the high-temperature urban heat fields. In Fig. 2a, b, the pixels with a surface temperature below 34 °C are coded in blue color. The pixels with a surface temperature of 34, 35, and 36 °C are, respectively, coded in dark green, light green, and yellow color. The pixels with a surface temperature higher than 36 °C are coded in orange, red and dark red color. The image pixels with a surface temperature larger than the threshold value are combined to calculate the spatial extent of high-temperature urban heat field for each day. As shown in Fig. 2, the spatial extent of urban heat field change from day to day. The spatial extent of high-temperature urban heat field is the largest on July 3 and 12, 2008, and the smallest on September 25 and 20, 2007.

The spatial extents of high-temperature urban heat field determined by three temperature threshold values of 34, 35, and 36 °C are regressed with the net radiation variable and traffic restriction dummy variable, resulting in three regression equations for the morning observations and three regression equations for the afternoon observations as shown in Table 2. All independent variables are statistically significant in explaining the spatial dynamics of the high-temperature urban heat field. In the morning, the net radiation and traffic restriction explain 57%, 55%, and 54% of the total variation of high-temperature heat field extent defined by surface temperature thresholds of 34, 35, and 36 °C, respectively. The regression modeling results show that the implementation of the traffic restriction policy decreased the spatial extent of high-temperature heat field in the morning by 945.7, 748.8, and 551.8 km2 for the thresholds of 34, 35, and 36 °C, respectively. Similarly, in the afternoon, both the independent variables are statistically significant, and they are combined to explain about 60% of the spatial extent dynamics of high-temperature urban heat field, as indicated by the value of $${R}^{2}$$ (Table 2). The traffic restriction during the Olympic Games reduced the spatial extent of high-temperature urban heat field in the afternoon by 863.7, 905.7, and 908.2 km2 for thresholds of 34, 35, and 36 °C, respectively. In comparison, the impact of traffic volume reduction on the urban heat extent is stronger in the afternoon than in the morning. The average areal shrinkage of the heat spatial extent due to the traffic restriction is about 820 km2.

Traffic impact on urban heat intensity

We use the mean surface temperature to represent the urban heat intensity. Based on the surface temperature measurements derived from MODIS satellite thermal observations, we calculated the daily mean surface temperature for each of six circular zones in the Beijing metropolitan area. The mean surface temperature for each zone as the response/dependent variable is regressed on the net radiation variable and traffic restriction dummy variable to construct statistical models, which are used for assessing the impact of the traffic restriction and associated traffic volume reduction on the urban heat intensity.

By using Terra MODIS satellite observations, we constructed six statistical models to express the relationship of the urban heat intensity of each zone in the morning with the net radiation and the traffic restriction policy (Table 3). Similarly, six statistical models were also constructed for assessing urban heat intensity in the afternoon by using Aqua MODIS satellite observations (Table 3). As shown in Table 3, the impacts of net radiation and traffic restriction on urban heat intensity are statistically significant. As indicated by the value of $${R}^{2}$$, those independent variables are combined to explain over 50% of the variations of the heat intensity in the morning for all urban zones except for Zone 6. Large agriculture and vegetated lands are distributed in Zone 6, which has a relatively low impervious surface coverage (Fig. 1). This zone appears less sensitive to the traffic volume variation in the morning. The reduction in the mean surface temperature associated with the traffic restriction during the 2008 Olympic games was 1.69, 1.65, 1.63, 1.59, and 1.56 °C from Zone 1 to Zone 5 (Table 3). The regression modeling results for the afternoon observations show that the impacts of the traffic restriction on the heat intensity for all concentric urban zones are statistically significant. The reduction in mean surface temperature induced by the traffic restriction during the Olympic Games is 2.44, 2.37, 2.27, 1.83, 1.71, and 1.50 °C from Zone 1 to Zone 6 in the afternoon (Table 3). It appears that the reduction level in the heat intensity by the traffic restriction gradually decreases outward from the urban center to the urban fringe zones in both morning and afternoon. In comparison, the heat intensity reduction effect of the traffic restriction in the afternoon is considerably stronger than in the morning.

Urban heat spatial extent and intensity at nighttime

We also derived the time series urban surface temperature maps at nighttime by employing Terra MODIS overpasses at 10:30 p.m. and Aqua MODIS overpasses at 1:30 a.m. local time. Figure 3 shows the nighttime surface temperature evolution in the Beijing metropolitan area before, during and after the Olympic Games, which derived from Aqua MODIS satellite thermal observations at local time of 1:30 a.m. Note that the surface temperature color scheme for nighttime in Fig. 3 is different from the daytime in Fig. 2. Apparently, urban surface temperatures at nighttime are significantly lower than at daytime. The thermal spatial structure remains a concentric pattern and the surface temperature decreases from the urban center to the rural periphery.

By using the threshold value of 23 °C, we defined the nighttime heat spatial extent. The statistical analysis results for nighttime heat spatial extent at 10:30 p.m. (based on Terra MODIS observation) and 1:30 a.m. (based on Aqua MODIS observations) are shown in Table 4. As indicated by the values of $${R}^{2}$$, the models only explain <20% of nighttime (10:30 p.m. or 1:30 a.m.) heat spatial extent variation. The impact of net radiation variable (Rn) is statistically significant, as indicated by its p-value ≤ 0.05. But, the p-value of the traffic restriction variable (RSRt) is away higher than 0.05, which indicates the failure to reject the null hypothesis and no statistical relationship between traffic restriction policy and nighttime heat spatial extent.

By using Terra and Aqua MODIS nighttime overpasses, we derived the mean nighttime surface temperatures for different urban zones. The statistical models for nighttime urban heat intensity at 10:30 p.m. (based on Terra MODIS observation) and 1:30 a.m. (based on Aqua MODIS observations) are shown in Table 5. As indicated by the values of $${R}^{2}$$, statistical models only explain less than 45% of nighttime (10: 30 p.m. or 1:30 a.m.) heat intensity variations for all urban zones. Again, the impact of net radiation variable (Rn) on the urban heat intensity is statistically significant, as indicated by its p-value ≤ 0.05. However, the impact of the traffic restriction variable (RSRt) on nighttime heat spatial extent is not statistically significant, as indicated by its very large p-values.

Discussion

Although anthropogenic heat discharge has been identified as an important factor contributing to the formation of UHI effect18,28, little has been known about the impacts of different anthropogenic sources on the urban thermal environment9,24. Since the mobile anthropogenic heat from automobiles is mixed with stationary anthropogenic heat from buildings, infrastructure and industries8, it has long been difficult to separate and quantify the impact of mobile anthropogenic source from stationary anthropogenic. Some studies have qualitatively examined the influences of urban road network and traffic density on the urban thermal environment12,13,29, but the magnitude of the urban traffic heat effect has not been quantified in previous studies.

By taking advantage of satellite thermal observations and drastic urban traffic volume variation during the 2008 Olympic Games, we were able to statistically assess the effect of the anthropogenic heat emission generated by automobiles of urban transportation system on the urban thermal environment. Our study period consists of two adjacent summer seasons in 2007 and 2008, and the odd-and-even number traffic restriction policy was imposed from July 20 to September 20, 2008 to support the Olympic Games activities, which dramatically reduced the urban traffic volume. In our research design, we have constrained our satellite observations of the case group (July 20–September 20, 2008) and control group (July 1–September 30, 2007; July 1–19, September 21–30, 2009) to a relatively short time period of the same season to minimize possible variations in land cover and stationary anthropogenic source. By using Landsat-7 multispectral images in summers of 2007 and 2008, we verified the land cover changes are minimal, and the slight albedo variation between 2007 and 2008 summers has been incorporated in the calculation of the explanatory variable of net radiation. The stationary anthropogenic heat source from buildings and factories was relatively stable and very similar in the case period and control period, which was reflected by similar annual electricity consumption between 2007 and 200830 and similar monthly electricity production in July, August, and September of 2007 and 2008 in Beijing31. Based on the urban surface energy balance equation, we determined that the daily land surface temperature variation in our study period was primarily influenced by the variations of the solar radiation intensity, surface albedo and traffic volume (mobile anthropogenic heat), which provides the physical basis for our multiple regression models. The variations of solar radiation intensity and surface albedo are reflected by the net radiation explanatory variable, which virtually accounts for the effect of the climate/weather differences in 2007 and 2008. By innovatively introducing a dummy variable for the traffic restriction policy in the regression models, we are able to statistically quantify the impacts of urban traffic volume variation induced by the traffic restriction policy on the spatial extent and intensity of urban heat field.

Our analysis results show that the traffic restriction and associate traffic volume variation is statistically significant in influencing the heat intensity for all urban zones. The traffic restriction during the Olympic Games effectively reduced the mean land surface temperature by 1.5–2.4 °C, depending on the urban zone. During the Olympic Games, besides the odd-and-even number rule, 70% of the vehicles owned by the governments, state enterprises and public institutions were suspended for the use, the high-emission vehicles with a yellow label were banned from the roads, trucks were not allowed inside the 6th Ring Road during the daytime. Essential service vehicles (police cars, fire trucks, ambulances, postal vehicles, taxies), and public transit vehicles (buses, trolleys, and subway) were exempt to the traffic restriction22. The traffic restriction during the 2008 Olympic Games in Beijing actually cut down nearly 1.95 million vehicles on road15,19, which was 54% of vehicles registered in Beijing19,22. Assuming the linear relationship, the average heat effect of 1 million vehicles would be 1–1.64 °C. Given the total vehicle number of 3.3 million in Beijing in 200815,19, the total heat effect of urban traffic would be 3.3–5.4 °C.

Like many other cities in the world, Beijing’s traffic flow exhibits a double-peak pattern32. Its morning traffic peak occurs during 7:00–8:30 a.m. and the evening traffic peak occurs during 5:00–6:30 p.m.26,33. The Terra MODIS satellite overpasses Beijing at 10:30 a.m., about 2 h after the morning traffic rush hour. The Aqua MODIS satellite overpasses Beijing at 1:30 pm, about four hours earlier than the afternoon traffic rush hour. Therefore, the actual magnitude of the traffic heat effect in rush hours could be even larger than our estimate based on Terra and Aqua MODIS satellite observations.

Previous studies suggest that the whole anthropogenic heat from buildings and vehicles may contribute 2–3 °C temperature increase both during the day and at night9,11 and that the anthropogenic heat has a smaller impact than albedo and vegetation cover, thus negligible in commercial and residential areas9,24. In comparison, the heat effect of the mobile anthropogenic source alone estimated from our study based on actual meteorological and thermal remote sensing data is remarkably larger than the combined effect of both stationary and mobile anthropogenic sources reported in the previous studies. Therefore, the actual contribution of the anthropogenic heat sources, particularly the urban traffic, to the urban thermal environment may be considerably larger than previously thought. We acknowledge that such a comparison with previous studies is crude and preliminary, and more rigorous investigation in this aspect is needed in future study.

Our analysis results also reveal that the heat effect of the urban traffic is not homogeneous in space and time. The spatial and temporal heterogeneity of the traffic heat effect is probably caused by the spatial variation in population density and urban functions, and temporal patterns of human activities. The Beijing metropolitan area has a concentric spatial structure. Zone 1 includes Dongcheng and Xicheng districts, which are the central business district and old downtown26, Zone 2 and Zone 3 include Haidian, Chaoyang, Fengtai, and Shijingshan districts, where commercial, high tech industries, educational institutions are concentrated. Zone 4 and Zone 5 are new urban development districts with some modern manufacturing, and Zone 6 contains agricultural and ecological conservation lands. We found out that the mitigation effect of the traffic volume reduction on the urban heat intensity decreases outward from the urban center to the urban fringe both in the morning and afternoon. The heat mitigation effect of the traffic restriction during the Olympic Games appears more apparent and stronger in the afternoon than in the morning for all urban zones. This differential effect of traffic volume variation in space and time tends to change the spatial structure of the urban thermal environment.

Our analysis indicates that the influence of urban traffic on the spatial extent of the high-temperature urban field is statistically significant. In the Beijing metropolitan area, the traffic restriction and associated traffic volume reduction of 1.95 million vehicles15,22 during the Olympic Games effectively reduced the spatial extent of the high-temperature urban heat field. With the threshold of 35 °C to define the spatial extent of high-temperature heat field, our statistical modeling results show that the traffic restriction and associated traffic volume reduction effectively reduced the urban heat extent by 748.8 km2 in the morning and by 905.7 km2 in the afternoon, which accounts for 12.4–15.0% of our case study area-the Beijing metropolitan area. On the assumption of the linear relationship, the traffic decrease by 1 million vehicles may lead to the shrinkage of high-temperature urban field by 394 km2 in the morning and 477 km2 in the afternoon on average. To examine the sensitivity of our analysis results to the selection of temperature threshold, we also tested a lower threshold value (34 °C) and a higher threshold value (36 °C) to define the spatial extent of high-temperature urban heat field, and both threshold values resulted in similar and consistent estimate results. This indicates that our findings are reliable and robust, insensitive to the selection of the threshold value.

The traffic restriction based upon the last digits of the license number during a certain period, also known as road space rationing or alternate-day travel scheme, has been practiced in many cities during major international events for cleaning the air and relieving traffic congestion, such as São Paulo (1997), México City for what (1989), Metro Manila (1995), Paris (2016)34, Beijing for the Olympic Games (2008) and for the Asia-Pacific Economic Cooperation (APEC) forum (2014). During the 2008 Olympic Games in Beijing, the traffic restriction was imposed and enforced for 62 days34. Such a long period of traffic restriction allows us to select a sufficient number of cloud-free MODIS thermal images in the case group to support a reliable and robust statistical analysis of the traffic volume effect on the urban heat dynamics. It should be noted that the primary objectives of the traffic restriction during the 2008 Olympic Games are to mitigate traffic congestion and to reduce ambient air pollution26,35. Our study suggests that the traffic restriction has additional benefit in the effective reduction of urban heat intensity and extent.

Most previous UHI studies emphasized the roles of the increasing urban construction materials and impervious surface, the decreasing vegetation cover and moisture content, and the canyon-like morphology of urban streets in the formation of UHI effect2,36. The impact of anthropogenic sources was considerably underestimated or ignored. Consequently, the recommended adaption options and heat mitigation strategies in urban planning and design mainly include high-albedo green and cool roofs and pavements24,37,38, landscaping with street trees, lawns and ponds10, urban parks, and urban ventilation corridors39 to offset the future greenhouse warming. Our study suggests that the heat effect of the anthropogenic sources, particularly the urban traffic, plays an important role in shaping urban thermal environment. The vehicles burn a large quantity of fossil fuels in urban areas to emit artificial exhaust heat and waste greenhouse gases to the urban environment40, hence causing air pollution and enhancing the urban heat effect (IPCC, 2007). The quantity of waste heat and greenhouse gases from urban traffic not only depends on the number of vehicles, but also on the vehicle model, running speed, and fuel type12. The future urban adaptation measures for heat mitigation should also include the control and management of urban traffic and vehicle fossil fuel use. The measurements to ameliorate the urban heat and pollution problems of urban traffic may include the control of vehicle number and density, improvements in running speed, reduction of heat storage volume, increase in vehicle engine efficiency, and improvement of fuel quality.

Our statistical analysis results indicate that the net radiation (solar radiation and albedo) and traffic volume statistically account for about 50–60% of the total observed daily variations of the urban heat intensity and the spatial extent of high-temperature urban heat field in our study period. There are 40–50% variations unexplained, which may come from other factors or measurement errors. For instance, about 40 factories were shut down in Beijing and Tianjin during the Olympic Games to improve air quality41. Although those closed factories were far away from the Beijing metropolitan area (>100 km to urban center), they may have the indirect urban heat effect through the screening effect of their reduced greenhouse gases. Further research efforts should be made to identify additional possible factors and variables that influence urban heat dynamics in the future.

It should be emphasized that although traffic restriction policy during the Olympic Games substantially reduced high-temperature urban heat field and decreased the mean surface temperature for all urban zones, its impacts on the nighttime urban heat spatial extent and intensity are minimal and statistically insignificant. It should be noted that the influences of the net radiation are statistically significant for both daytime and nighttime urban thermal environment, even though its influence is stronger at daytime than at nighttime. This indicates that the differential heating effect of solar radiation may last from the daytime to nighttime to a certain extent. Also, it must be recognized that the traffic flow volume reduction associated with the traffic restriction policy during the Olympic Games mainly occurred at daytime between 7:00 a.m. and 9:00 p.m., and the traffic volume at nighttime from 9:00 p.m. to 7:00 a.m. during the Olympic Games was almost the same as in pre-Olympic and post-Olympic periods19,26,27. Particularly at Aqua MODIS satellite nighttime overpass time of 1:30 a.m., the urban traffic volume kept a similar small value, no matter whether the traffic restriction policy was enforced or not. Since the traffic restriction policy did not induce the associated traffic volume changes at nighttime, therefore its impact on the nighttime urban thermal environment is negligible, as suggested by our statistical analysis results.

Methods

Satellite observations and in situ datasets

In this research, we employed daily Terra and Aqua MODIS satellite thermal images to derive the surface temperature at a spatial resolution of 1000 m for the Beijing metropolitan area, during the Olympic Games with traffic restrictions against the pre- and post-Olympic observations without the traffic restriction. Landsat-7 ETM + multispectral image data are used to estimate the albedo and assess possible land cover changes. In situ data from a local meteoritical station are used to represent the solar radiation and weather condition. We used NASA MODIS LST Version 6 (v6) products from both Terra and Aqua satellites. Terra MODIS satellite overpasses Beijing at 10:30 a.m. local time, and its daily thermal images form the time series for the morning. Aqua MODIS satellite overpasses at 1:30 p.m. local time in the afternoon, and its daily thermal images form the other time series for the afternoon. These two separate time series allow us to investigate the urban thermal environment temporal variation of urban heat environment between the morning and afternoon within a day.

We screened all MODIS images acquired from July 1 to September 30 in 2007 and 2008, and selected 77 images for this research (Table 1). Those images with more than 10% cloud coverage were excluded. Since the wind chill effect substantially influen ces sensible heat and ground heat through convection42,43, those images acquired on high-wind days (>5 m/s) were also ruled out to ensure model accuracy. Among 36 cloud-free Terra MODIS images, 16 of them were acquired during the Olympic Games with traffic restriction, which constitute the traffic restriction case group in the morning. The remaining 20 cloud-free Terra MODIS images, including 3 images acquired in 2008 and 17 images acquired in 2007 without traffic restriction, constitute the control group in the morning. Similarly, we used 13 cloud-free Aqua MODIS images acquired with the traffic restriction to form the case group in the afternoon, and the remaining 28 cloud-free MODIS images acquired without the traffic restriction to form the control group in the afternoon. It should be noted that the control groups include the summer images from both 2007 and 2008 to address the possible bias between different years.

Two cloud-free Landsat-7 ETM+ multispectral images acquired on September 9 in 2007 and September 11 in 2008 are used to estimate the overall surface albedo in the summers of 2007 and 2008. The surface albedo is the wavelength-integrated reflectivity of surface materials. Typically, urban albedos are in the range of 0.1–0.216. Figure 1b, c show the derived albedo maps in 2007 and 2008. The average albedo for Beijing metropolitan area slightly decreased from 0.145 in 2007 to 0.136 in 2008. The albedo difference has been incorporated to estimate the net radiation variation.

A meteorological station of China Land Data Assimilation System (CLDAS), located at latitude of 39.48°N and longitude of 116.28°E in Beijing (Fig. 1a), recorded the wind speed, total incoming solar radiation, net radiation, and instant radiation (in the unit of Mega Joules per square meter). Solar radiation observations at this station are used to represent and model the temporal variation of net radiation in the statistical models, while the daily wind speed is used to screen and select MODIS thermal images.

Statistical models

Based on the near-surface energy balance model that considers net radiation, anthropogenic heat, the sensible, latent, ground heat fluxes and surface albedo factors11,44, we developed two sets of statistical models to quantify the effect of traffic restriction and associated traffic volume on the spatial extent and intensity of the urban heat effect. The response variable of the first set of statistical models is the urban heat extent ($${\mathrm {S{E}}}_{t}$$) represented by the total urban area with a surface temperature higher than a specified threshold value, while the response variable of the second set of statistical models is the urban heat intensity $$({\mathrm {{{HI}}}}_{t})$$ represented by the mean surface temperature of an urban zone. Both sets of statistical models have the same explanatory (predictor) variables: net radiation variable ($${R}_{\mathrm {{n}}}$$) and traffic restriction variable ($${\mathrm {{{RSR}}}}_{t}$$). The net radiation variable ($${R}_{\mathrm {{n}}}$$) represents the natural heat source due to variations of incoming solar radiation and the surface albedo, while traffic restriction variable ($${\mathrm {{{RSR}}}}_{t}$$) indicates the variation of mobile anthropogenic heat discharge due to the traffic restriction.

The land surface temperature varies in response to the surface energy balance and is highly correlated with the near-surface air temperature45. Surface moisture, thermal admittance and surface emissivity, the radiative input at the surface from the sun and atmosphere, and the interaction between the near-surface atmosphere and the surface all influence the land surface temperature46,47. The surface energy balance terms in urban areas are different from the rural areas. In addition to solar radiation input (natural source), the anthropogenic heat discharge (human source) also plays an important role in the urban energy budget. The general form of the surface energy balance in urban areas can be expressed by the following equation9:

$${R}_{\mathrm {{n}}}+{Q}_{\mathrm {{f}}}=H+\,\lambda E+G$$
(1)

where $${R}_{\mathrm {{n}}}$$ is net radiation and $${Q}_{\mathrm {{f}}}$$ is the total anthropogenic heat discharge. On the right side of equation, $$H$$, $$\lambda E$$, and $$G$$ are the sensible, latent, and ground heat fluxes, respectively. The sensible energy H heats the lower layers of air through the conductive heat flux from the Earth’s surface to the atmosphere. The ground heat G is the storage of energy in land to warm the near-surface soil layers. The latent heat λE is absorbed by the evapotranspiration process, namely the transpiration of vegetation and the evaporation of land surface moisture.

The net radiation $$({R}_{\mathrm {{n}}})$$ is the sum of the absorbed incoming short-wave solar and long-wave radiations emitted from the atmosphere. It can be expressed by Eq. (2) below:

$${R}_{\mathrm {{n}}}=\left(1-\mu \right)* I+L$$
(2)

where L is the net long-wave radiation from the atmosphere and the land surface, $$I$$ is incoming short-wave solar radiation, μ is the surface albedo indicating the ability of the surface material to reflect the incident solar energy back to space.

The combination of Eqs. (1) and (2) results in a modified urban energy balance equation:

$$H+G=\left(1-\mu \right)* I+{Q}_{\mathrm {{f}}}+L-\lambda E$$
(3)

The two terms on the left side of Eq. (3), the sensible heat (H) and ground heat (G) control the land surface temperature and near-surface air temperature, which reflect the state of the urban thermal environment. Terms on the right side of Eq. (3) are the factors (variables) influencing the surface and near-surface air temperature. Actually, Eq. (3) explains the roles of key urban land surface properties (the surface albedo, vegetation transpiration, land surface moisture evaporation) and anthropogenic (man-made) heating in forming and shaping the urban thermal environment9. In an urbanized area, the decreased vegetation coverage and land moisture source for the evapotranspiration process result in the much lower latent heat flux (λE) to dissipate the absorbed solar heat (Rn) and anthropogenic heat (Qf). Artificial urban surface materials (e.g. asphalt, concrete, tar and gravel pavements) have a low albedo ($$\mu$$), and hence absorb and accumulate much more of solar radiations (Rn)8. Due to the large concentration of population and economic activities in the urban area, the anthropogenic heat discharge Qf from residential buildings, factories and transportation make a substantial input source to the urban energy balance, in addition to the natural solar source.

We use the urban surface energy balance in Eq. (3) as the physical basis to determine the response (dependent) variables and explanatory (independent) variables of our statistical models. The high-temperature urban heat field extent and urban heat intensity (mean surface temperature) reflect the combined effect of the sensible heat (H) and ground heat (G), and they are used as the response variables for urban thermal environment. Surface albedo $$\mu$$, and the radiation Rn are treated as two explanatory variables. Although the vegetation coverage has largely reduced in the Beijing metropolitan area in the past decades, there was no much change in vegetation coverage and impervious surface during our study period 2007–2008. Therefore, the latent heat latent heat flux (λE) is treated as constant for our study period. The stationary anthropogenic heat source (heat discharge from the residential buildings, factories) had a minimal change during 2007–2008 and hence is treated as a constant. The mobile anthropogenic heat from automobiles had a strong variation due to the traffic restriction during the Olympic Games. Therefore, the traffic volume associated with the traffic restriction is treated as an explanatory variable for representing the variation of anthropogenic head discharge (Qf). Based on the above physical interpretation of the urban surface energy balance equation, the response variables of the high-temperature urban heat field extent and urban heat intensity are modeled as a function of the surface albedo, radiation, and traffic volume in our study time period from June 1, 2007 to September 30, 2008.

The first multiple regression model represents the high-temperature urban heat spatial extent ($${\mathrm {{{SE}}}}_{t}$$), as the linear function of net radiation and the traffic variables as below:

$${\mathrm {S{E}}}_{t}={a}_{0}+{a}_{1}{R}_{\mathrm {{n}}}+{a}_{2}{\mathrm {{{RSR}}}}_{t}+\,{e}_{t}$$
(4)

where $${\mathrm {{{SE}}}}_{t}$$ is the high-temperature urban heat extent defined with a temperature threshold at time $$t$$. $${\mathrm {{RS}{R}}}_{t}$$ is the traffic variable at time $$t$$. $${a}_{0}$$, $${a}_{1}$$ and $${a}_{2}$$ are regression coefficients to be estimated, $${e}_{t}$$ is an error term. The coefficient $${a}_{1}$$ represents the impact of net radiation on the spatial extent of high-temperature urban heat field, while the coefficient $${a}_{2}$$ of the dummy variable $${\mathrm {{{RSR}}}}_{t}$$ represents the impact of the traffic volume variation on the high-temperature heat extent induced by the RSR traffic restriction.

The second multiple regression model represents the urban heat intensity $$({\mathrm {{{HI}}}}_{t})$$ as the linear function of net radiation and the traffic variables:

$${\mathrm {{{HI}}}}_{t}={b}_{0}+{b}_{1}{R}_{\mathrm {{n}}}+{b}_{2}{\mathrm {{{RSR}}}}_{t}+\,{e}_{t}$$
(5)

where $${\mathrm {{{HI}}}}_{t}$$ is the urban heat intensity expressed by the mean surface temperature at time $$t$$, $${b}_{0}$$, $${b}_{1}$$ and $${b}_{2}$$ are coefficients to be estimated, $${e}_{t}$$ is an error term at time $$t$$. The coefficient $${b}_{1}$$ represents the impact of net radiation on the heat intensity, while the coefficient $${b}_{2}$$ represents the impact of the traffic volume variation on the heat intensity. The second multiple regression model was constructed for each of six concentric urban zones in the Beijing metropolitan area.

It should be noted that a qualitative dummy variable ($${\mathrm {{{RSR}}}}_{t}$$) was used in the above multiple regression models to indicate the traffic volume variation. The dummy explanatory variable, also known as an indicator variable48, allows us to represent the traffic restriction in a standard quantitative regression model, without imposing unrealistic measurement assumptions on the categorical variable. The traffic restriction dummy variable ($${\mathrm {{{RSR}}}}_{t}$$) is set to 1, when the traffic restriction was imposed during the Olympic Games, namely for the MODIS images in the case group acquired during the Olympic Games. The traffic restriction dummy variable ($${\mathrm {{{RSR}}}}_{{t}}$$) is set to 0, when the traffic restriction was not imposed before or after the Olympic Games, namely for the MODIS images in the control group acquired before or after Olympic Games. The regression analysis with the dummy variable is able to inform if the impact of the traffic restriction is statistically significant and what is the magnitude of the impact of the traffic restriction on the spatial extent and the intensity of urban heat field. Since the odd-and-even number traffic restriction policy approximately cut off the regular traffic volume by half, the impact magnitudes of the traffic restriction determined through the regression analysis with the dummy variable virtually indicate the magnitude of the impacts of cutting off about half of the regular traffic volume on the extent and intensity of urban heat filed.

In the modeling, the daily net radiation ($${R}_{\mathrm {{n}}}$$) was calculated using Eq. (2), based on the observations from the meteorological station on incoming short-wave solar radiation (I), the net long-wave radiation (L), and the surface albedo (μ). A narrowband to broadband conversion algorithm is used to estimate the surface albedo (μ) with the input of Top of Atmosphere (TOA) reflectance of Landsat-7 ETM+ non-thermal bands (1, 3, 4, 5, and 7)49. Daily surface temperature from Terra and Aqua MODIS thermal image data was used to extract the urban heat extent ($${\mathrm {S{E}}}_{\mathrm {{t}}}$$) and intensity ($${\mathrm {{{HI}}}}_{\mathrm {{t}}}$$).