Present and projected future mean radiant temperature for three European cities

Present-day and projected future changes in mean radiant temperature, T mrt in one northern, one mid-, and one southern European city (represented by Gothenburg, Frankfurt, and Porto), are presented, and the concept of hot spots is adopted. Air temperature, T a, increased in all cities by 2100, but changes in solar radiation due to changes in cloudiness counterbalanced or exacerbated the effects on T mrt. The number of days with high T mrt in Gothenburg was relatively unchanged at the end of the century (+1 day), whereas it more than doubled in Frankfurt and tripled in Porto. The use of street trees to reduce daytime radiant heat load was analyzed using hot spots to identify where trees could be most beneficial. Hot spots, although varying in intensity and frequency, were generally confined to near sunlit southeast-southwest facing walls, in northeast corner of courtyards, and in open spaces in all three cities. By adding trees in these spaces, the radiant heat load can be reduced, especially in spaces with no or few trees. A set of design principles for reducing the radiant heat load is outlined based on these findings and existing literature.


Introduction
Exposure to heat may cause severe illnesses and deaths during intense heat events, especially in large urban areas due to the altered urban climate conditions (e.g., Dousset et al. 2011;Gabriel and Endlicher 2011). Elderly, infants and persons with pre-existing cardiovascular, respiratory, or psychiatric diseases and people living in social insulation are especially at risk (e.g., Kovats and Hajat 2008). In addition to health status and demographic and socio-economic factors, regional adaptation to heat effects heat stress risks. For example, heat-related mortality rises from lower apparent temperature (i.e., a measure of relative discomfort due to combined heat and high humidity) in north-continental European cities than in Mediterranean cities (Baccini et al. 2008), as people in north-continental cities have not adapted to heat as they have to cold. Although adverse health effects are most severe during intensive heat events, a large part of the population may suffer from heat stress symptoms also during normal summers (Näyhä et al. 2014). During the last decades, air temperature, T a , has risen and episodes of extreme heat have become more frequent in Europe, and the frequency as well as its effect on human health are projected to progressively increase as a result of climate change (e.g., Fischer and Schär 2010;Kovats et al. 2014); yet, research and policies to manage heat and increase adaptation to heat are in their infancy (Maller and Strengers 2011).
During periods with warm daytime and cool nighttime thermal conditions, such as in normal summers or in the beginning of a heat wave, heat-related deaths among the eldest (ages 80+) are primarily attributable to daytime heat stress (e.g., Rocklöv et al. 2011;Thorsson et al. 2014). This might be explained by the fact that those elderly people who are sensitive to heat stress (e.g., Kovats and Koppe 2005;Åström et al. 2011) may die from heat stroke or exhaustion after a single warm day . During periods with both warm daytime and nighttime thermal conditions, which often occur during long periods of consecutive hot days, heat-related deaths are primary attributed to the warm nighttime conditions among elderly and other age groups (e.g., Fouillet et al. 2006). During these events, the relative warm nighttime thermal conditions prevent people from recuperating at night from the heat stress experienced during the day .
In order to mitigate negative effects of intense heat events, it is necessary to identify and predict weather conditions which generate severe heat stress as well as spaces/geometries prone to heat with high accuracy. Furthermore, good knowledge about the efficiency of different strategies to reduce heat stress is important in order to take appropriate actions. During intense heat events, characterized by high T a , high solar radiation, and low wind speed, radiant heating constitutes the largest part of the heat load (heat stress) on humans (e.g., Mayer and Höppe 1987;Mayer et al. 2008), explaining 89% of the variance in thermal perception (Lee et al. 2013). The radiant heat load can be calculated with the mean radiant temperature, T mrt . T mrt is defined as the Buniform temperature of an imaginary enclosure in which the radiant heat transfer from the human body equals the radiant heat transfer in the actual non-uniform enclosure ( ASHRAE 2001). In other words, it describes the radiative exchange between a person and the environment. T mrt is directly influenced by the surface geometry (buildings, vegetation, and topography) and surface materials (albedo, emissivity, etc.), which also makes it useful to identify heat-prone urban geometries and to estimate the efficiency of different strategies to reduce the radiant heat load .
Compared to T a , which is characterized by rather small daytime spatial variations, T mrt shows large spatial variations during the day (e.g., Emmanuel and Fernando 2007;Mayer et al. 2008;Thorsson et al. 2011), primarily determined by the shadow pattern generated by buildings and vegetation. During clear and warm summer days, the highest T mrt are found near sunlit walls at noon, as a result of high direct and reflected short-wave radiation combined with long-wave radiation emitted from the neighboring surfaces exposed to the sun. On these days and in these locations, T mrt may be substantially higher than T a . At night, however, when short-wave radiation is absent, T mrt is more or less equal to T a .
There are a number of different strategies that can be applied to reduce radiant heating and thus mitigate outdoor heat stress, such as altering the building geometry (street direction, spacing and width, and building height), altering the surface or building materials, and increasing urban greenery. However, most of the strategies to reduce radiant heating during the day have an adverse effect on the radiant component during the night and vice versa (Andersson-Sköld et al. 2015). For example, increasing the building density reduces the radiant component during the day by increasing shadowing and thus reducing the solar radiation at street level and the convective heat transfer from sunlit building and ground surfaces, while it keeps the radiant component relatively high during the night by reducing the escape of long-wave radiation and thus the cooling of air and surfaces (e.g., Holmer et al. 2007;Mayer et al. 2008;Lindberg et al. 2013). The use of Bcool^building materials (i.e., high albedo surfaces with low thermal admittance) has only a minor impact on outdoor heat stress (Erell et al. 2014).
One of the few solutions that mitigate both daytime and nighttime outdoor heat stress is vegetation. During the day vegetation-and especially trees-efficiently reduce the radiant component (Ali-Toudert and Mayer 2007a;Lindberg and Grimmond 2011;Konarska et al. 2014) by blocking the solar radiation at ground level (e.g., Heisler 1986;Konarska et al. 2014) and reducing the surface temperature of neighboring shaded surfaces (e.g., Shashua-Bar et al. 2009). Vegetation also cools its nearby surroundings through transpiration (e.g., Rahman et al. 2011;Shashua-Bar et al. 2011;Konarska et al. 2016). However, the location of greenery, as well as species choice, shape, and amount of vegetation, must be considered in order to optimize the benefits derived from urban greenery and prevent potential side effects.
In this paper, present and projected changes in T mrt and the locations of hot spots are analyzed for representative examples of built-up areas for three European cities. Furthermore, the use of street trees to reduce radiant heat load during intense heat events (days with high T a , clear skies, and low wind speed) is analyzed, and the concept of hot spots is used to identify where trees are most beneficial. Based on the findings along with existing literature, a set of design principles to reduce radiant heat load at local level is outlined.

Study area
The cities of Gothenburg, Sweden; Frankfurt, Germany; and Porto, Portugal-representing one northern, one mid-, and one southern European city-were selected for this case study. Gothenburg, located on the Swedish west coast (57°42′ N, 11°59′ E), has a marine west coast climate, with relatively cool summers for its latitude (average T a of 16.3°C during June to August, 1960August, -1990 and because of the moderating influence of the warm Gulf Stream relatively mild winters (average T a of −0.4°C in December to February). Frankfurt, located in the south-western part of Germany (51°07′ N, 8°4 1′ E), has a temperate-oceanic climate with average summer and winter T a of 18.6 and 2.2°C, respectively. Due to its more inland location, it is slightly drier than Gothenburg. Porto is located on the Portuguese west coast (41°08′ N, 08°40′ W). The city has a Mediterranean climate with dry and warm summers (19.3°C) and rainy and mild winters (9.5°C).
Typical downtown built-up areas characterized by a relatively high building density and little vegetation in each city were selected for case studies ( Fig. 1 and Table 1). The building geometries vary across the three cities, from more low-to mid-rise building geometries with wide streets and few street trees in the Gothenburg (allowing solar radiation to reach streets and into the buildings), via a more mid-rise building geometry with some street trees in Frankfurt (creating shade and preventing heat stress in summer) to the low-to mid-rise building geometries with narrow and winding streets (creating shade and preventing heat stress in summer) with limited room for street trees in the more historical neighborhoods in Porto.

Meteorological data
Hourly meteorological data, including records of T a , solar radiation (global and diffuse components), and relative humidity, were obtained for each city ( Table 2). The observation period used for Gothenburg is 1998-2005, because solar radiation records were interrupted in 2005.

Climate scenarios
Hourly climate scenario time series were created by combining hourly meteorological observations with daily climate model outputs using the method of Rayner et al. (2014). With this method, change factors are first calculated from differences in ranked daily climate model outputs for a future period and a present day, using model time series extracted for a single grid point at the location of each city. Changes consistent with these daily factors are then applied to historical hourly meteorological observations to create hourly future scenarios. A summary of the Rayner et al. (2014) method, based on the description from Lau et al. (2015), is included below.
Climate scenarios were created for each of the three cities for two future periods-mid-century (2040-2069) and end of century . The scenarios used here are based on the fifthgeneration atmospheric general circulation model (ECHAM5)/ MPI-OM global climate model (GCM) (Roeckner et al. 2003) forced with the Special Report on Emissions Scenarios (SRES) A1B greenhouse-gas emission scenario, downscaled to 25-km resolution with the Rossby Centre Regional Atmospheric Model (RCA3; Kjellström et al. 2005). The SRES A1 scenario family describes rapid, global economic development and is thought to be the type of scenario Bbest represented^in academic literature when the SRES scenarios were compiled (Nakicenovic and Swart 2000). The A1B scenario, in which the A1 storyline develops using a balance of fossil and non-fossil energy sources, corresponds to a Bmid-range^reference scenario (that is, a scenario without deliberate greenhouse-gas mitigation actions), in the context of more recent scenario modeling (Moss et al. 2010). Outputs from regional climate models are widely used for climate-change impact assessments because they simulate finerscale climatic patterns more realistically than GCMs (e.g.,, Perkins et al. 2014).
Following the algorithm of Rayner et al. (2014), hourly T a scenarios were created by interpolating the change factors for daily maximum and minimum T a . That is, for each day in the historical record, a change factor for daily maximum T a was determined from the ranked changes in the regional climate model (RCM) maximum T a outputs. Change factors for minimum T a for each day were similarly determined. These series of change factors were then combined, and change factors for every hourly T a value in the historical record derived using linear interpolation.
For direct and diffuse radiation, change factors for daily global radiation were first calculated for each day in the  historical record based on differences in ranked daily shortwave downwelling radiation in the RCM simulations. The short-wave radiation change factor for a given day was applied to all hourly global radiation values for that day. Then, to calculate change factors for the hourly diffuse radiation values, the diffuse radiation was estimated from the global radiation using the method of Reindl et al. (1990), for both the observed and future hourly global radiation. The ratio of these estimates is the change factor that is applied to the observed historical diffuse radiation. Finally, the direct radiation component for the future scenario was determined from the future global and diffuse radiation components. This method ensures that the three radiation components of the scenario time series remain mutually consistent. Estimation of T mrt in Solar and LongWave Environmental Irradiance Geometry (SOLWEIG) model (see below) is most sensitive to short-wave radiation and long-wave radiation calculated via T a , whereas it is almost unaffected by air humidity (Onomura et al. 2015). Thus, the climate scenarios use the unmodified observed hourly relative humidity.

Spatial and temporal modeling of mean radiant temperature
Present and future spatial variations of T mrt within the selected case study areas were calculated using the SOLWEIG model (version 2013a; Lindberg et al. 2008;Lindberg and Grimmond 2011). The model requires hourly weather observations (i.e., T a , air humidity, global and diffuse solar radiation) together with spatial data in form of a digital surface model (DSM) and a geographical location (i.e., latitude, longitude, and altitude). T mrt is calculated for a standing or walking person where the angular factors (proportion of radiation received by the human body in each direction) are set to 0.22 for radiation fluxes from the four cardinal points (east, west, north, and south) and 0.06 for radiation fluxes from above and below. Standard values of absorption coefficients for shortwave and long-wave radiation are set to 0.7 and 0.97, respectively (Höppe 1992). Values for albedo and emissivity for buildings and vegetation are set to 0.20 and 0.95, respectively, according to Oke (1987). The transmissivity of short-wave and long-wave radiation through vegetation is set to 5 and 0%, respectively, according to Lindberg and Grimmond (2011). To estimate daytime incoming long-wave radiation (L↓), the approach developed by Crawford and Duchon (1999) is used including fractional cloud cover and T a . Since nighttime sky conditions (i.e., cloudiness) are unknown, we estimate nocturnal L↓ using a simple approach based on Offerle et al. (2003), where the closest daytime value of the sky conditions is used. Thus, nights when a change of weather occurs could affect the estimation of L↓. However, L↓ is in general the smallest of the long-wave fluxes and will therefore have a minor effect on T mrt during night. Evaluation of the SOLWEIG model has shown good agreement between modeled and measured radiation fluxes, with the model explaining 94% of the variations in T mrt , with an overall RMSE of 4.8 K (Lindberg et al. 2008). For a detailed description and evaluation of the SOLWEIG model, see Lindberg et al. (2008) and Lindberg and Grimmond (2011).
In order to study regional differences in T mrt with respect to future climate change, T mrt for a non-specific (generic) sunlit urban location was calculated using SOLWEIG1D (Lindberg 2012). Unlike the SOLWEIG model described above, where sky view factor (SVF) and shadow patterns are determined for each pixel in a DSM, SOLWEIG1D has a single, fixed, userspecified SVF and the location is assumed to be sunlit during the daytime hours. The latter would not be the case in a realworld situation, where surrounding objects would block the sun at specific times of the day and year when SVF <1. Otherwise, the same settings are used as presented. For these calculations, SVF was set to 0.60.

Classification of severe heat events and hot spots
Here, T mrt ≥60°C is used to represent severe heat events. The level corresponds to a physiological equivalent temperature, PET >40°C (Eq. 2 in Lee et al. 2013), i.e., hot thermal conditions (Holst and Mayer 2010). It should be noted that the same thermal conditions might be perceived differently and have different health impacts in the three cities due acclimatization and adaptation to heat (Baccini et al. 2008). However, in order to be able to make cross-European comparison, the same threshold value of T mrt for severe heat was used in all three cities. Furthermore, it should be noted that health impact, such as heat-related mortality, might occur at lower levels of T mrt ). SOLWEIG1D was used to identify severe heat events, and then, the full version of the model was used to identify the location of hot spots (BUrban geometries prone to heat^section). The method used to identify hot spots, introduced by Lindberg et al. (2016), is to select the highest (90th percentile) values of T mrt when T mrt at the generic site is ≥60°C and average these to create Bhot spot^maps. All other pixels are set to zero. The occasions when pixels are set to zeroes are included in order to compare the pixels throughout the time period investigated. At the end of a SOLWEIG run, an average of all the maps is calculated. The values in hot spot maps are not actual values of T mrt and should be interpreted as an ordinal scale (i.e., hot, hotter, hottest).

Regional climate change
Here, the observed and projected future changes in T a , solar radiation, and T mrt across the annual cycle, but focusing on the summer season, are presented and discussed for the three cities.
Air temperature Figure 2 shows the observed monthly-averaged daily maximum and minimum T a , and projected future changes, across the annual cycle for the three cities. In line with previous studies (e.g., Christensen et al. 2007;Fischer and Schär 2010;Kjellström et al. 2013), the downscaled scenarios show progressively increasing T a (both minimum and maximum) in all three cities by 2100. The magnitude, however, differs between the cities and seasons. In Gothenburg and Frankfurt, daily maximum T a increases less in summer (June-July-August (JJA)) (+2 and +2.1°C, respectively) than in winter (DJF) (+2.6 and +3.3°C, respectively), whereas in Porto, the largest increase takes place in summer (+3.3°C in summer and +1.6°C in winter; Fig. 2, middle row).
In Gothenburg, daily minimum T a (i.e., late night or early morning) increases more than daily maximum T a by the end of the century (Fig. 2, middle and bottom rows). In Frankfurt, the increases in maximum and minimum T a are more or less similar. In Porto, increases in average summer daily maximum T a are higher than for minimum T a , whereas they are similar in the winter.
The changes in monthly-averaged daily maximum T a by 2070-2098 hide potentially important changes in daily maximum T a distributions (not shown). In Frankfurt, the increase in T a of warm (98th percentile) summer days is +4.2°C, substantially larger than the median increases in maximum T a (+2.1°C). In Porto, the median increase in maximum T a (+3.6°C) is larger than the increase for cold (2nd percentile) summer days (+2.5°C). In Gothenburg, the increase in maximum T a is about the same for cold and warm summer days (1.8 and 2.0°C for the 2nd and 98th percentiles). The results imply that the cities with already high summer maximum T a will experience the largest increases on warm days. Fig. 2 top row Observed annual cycle of daily maximum and minimum air temperature, T a , for the three cities. middle row Projected future changes in monthly-averaged daily maximum T a across the annual cycle over the two time periods (2040-2069 and 2070-2098). bottom row Changes in monthlyaveraged daily minimum T a Solar radiation Figure 3 shows the observed monthly-averaged daily global solar radiation and projected future changes across the annual cycle for the three cities. Solar radiation, which is a function of latitude and time of year, increases further south (in northern hemisphere) and reaches its maximum in summer. Compared to the patterns of change in T a , patterns of change in solar radiation in the downscaled scenarios are much more mixed across the three cities (Fig. 3, bottom row). Daily-averaged global solar radiation in Gothenburg decreases by around 13 Wm −2 in summer (JJA) by 2100 due to increase in cloudiness. A smaller decrease occurs in Frankfurt (−3 Wm −2 ). Again, these average changes hide potentially important changes in distributions, with 98th percentile hourly global solar radiation in summer decreasing by 29 Wm −2 in Gothenburg but increasing by 3 Wm −2 in Frankfurt. In Porto, solar radiation increases in summer by the end of this century as cloudiness decreases.

Mean radiant temperature
Monthly average daily maximum and minimum T mrt and projected future changes across the annual cycle for the three cities are shown in Fig. 4. Although changes in T mrt are dominated by changes in long-wave radiation via an increase in T a in the future climate scenarios (Lau et al. 2015), changes in solar radiation may counterbalance or add to the effect on increased T a . For example, in Gothenburg, the projected decrease in solar radiation in summer (Fig. 3, bottom row) will counterbalance the effect of increased T a (Fig. 2, middle row), keeping the average summer maximum T mrt relatively unchanged at ∼45°C. Average summer daily minimum T mrt increases in all three cities (Fig. 4, bottom row), with a larger increase in summer in Porto, compared to Frankfurt and Gothenburg.
Days with T mrt ≥60°C occur in all three cities in the present climate (Table 3), although to a much lesser extent in Gothenburg than in Frankfurt and Porto. The frequency of such days increases in the downscaled scenario (Table 3), essentially doubling by 2100 in Frankfurt and tripling in Porto, whereas it is relatively unchanged in Gothenburg (+1 day). The average number of days per year in consecutive sequences (two or more days) of T mrt >60°C also increases. The large increase in the average number of days per year with T mrt ≥60°C in Frankfurt relative to Gothenburg can be explained by three factors. As mentioned above, summer daily maximum T a increases more on hot days in Frankfurt than on average summer days, which is not the case for Gothenburg. Secondly, typical summer maximum hourly global solar radiation in Gothenburg is lower in the future scenario, unlike in Frankfurt. Thirdly, many summer days in Frankfurt have daily maximum T mrt very close to 60°C in the present climate (Fig. 5), so even small increases in T mrt can cause relatively large increases in the number of days with T mrt ≥60°C. The highest daily T mrt also increases towards the south by the end of the century (Fig. 5).
This implies that radiant heat load will be exacerbated in cities where heat stress is already common, with expected severe impact on overall health and well-being as a result (assuming that the relation between T mrt and mortality does not change; Thorsson et al. 2014). Furthermore, using T mrt (which includes the effect of both solar radiation and T a ) as a predictor of heat stress implies that climate change has a larger impact in Porto than would be expected by using T a alone, whereas in Gothenburg, it implies a lower impact. As a result, the spatial pattern of severe heat stress assessed using T a alone as a predictor (e.g., Fischer and Schär 2010) is modified (e.g., exhibits a larger north-south gradient in latitude) when accounting for the effects of changes in solar radiation. It should be noted that the land use, distance to city center, and altitude of the meteorological stations differ between the cities ( Table 2). As T a exhibits a strong gradient between different land uses (e.g., urban-rural) at night, the associated health risks might be underestimated in Porto as the station used is located 15 km outside the city center (i.e., not representing the amplifying effects of the urban heat island).
Another limitation is that this study is based on the outputs from one regional climate model simulation from the ENSEMBLES project (ECHAM5/RCA3). A qualitative analysis of the ENSEMBLE simulations for the three cities shows that the changes in high-percentile summer global solar radiation for ECHAM5/RCA3 were near the middle of the range of the simulations, whereas the simulated changes in high-percentile summer maximum T a were at the lower end of the range for Gothenburg and towards the upper end of the range for Porto. Further work would be required to investigate how T mrt in the study sites changes for different climate models and under different greenhouse gas emission scenarios.

Urban geometries prone to heat
Here, the location of hot spots and the frequency of high T mrt (i.e., T mrt ≥60°C) at street level are presented and discussed for the three cities and time periods. The hot spot maps presented here were calculated without vegetation.

Location of hot spots
Despite differences in regional climate and climate change, in all three cities and time periods, the hot spots are generally confined to 5-10 m in front of sunlit southeast-southwest facing walls, in the northeast corner of the courtyards, and in open spaces, such as squares and wide streets with relatively high sky view factors (Fig. 6). This is a result of high direct and reflected short-wave radiation fluxes combined with longwave radiation emitted from Sun-exposed surfaces (e.g., Mayer et al. 2008;Lindberg et al. 2013). Although the general pattern is the same in all three cities and time periods, minor shifts in the location and extension of hot spots occur as a Fig. 4 top row Calculated annual cycle of daily maximum and minimum mean radiant temperature, T mrt , for the three cities. second top row Projected future changes in monthlyaveraged daily maximum, T mrt , across the annual cycle over the two time periods (2040-2069 and 2070-2098). third top row Changes in monthly-averaged daily minimum T mrt than the open site, as a result of reflection of long-and shortwave radiation from the surrounding walls (e.g., Thorsson et al. 2011). For the mid-and end-of-century simulations, some redistribution of the hottest spaces takes place, mainly in Gothenburg but also in Frankfurt. For example, in Gothenburg, spaces in front of west and south facing walls remain as hot spots, although they are no longer the most intense ones. Instead, the most intense hot spots are found in the large open squares. This can be explained by increased cloudiness, which results in reduced surface wall temperature and more intense incoming long-wave radiation from the sky as well as redistribution of short-wave radiation fluxes . Furthermore, spaces in front of east to northeasterly façades show up as being among the hottest spaces by the end of the century, presumably because increased cloudiness during afternoons prevents the west facing façades from heating up to the same extent. In Frankfurt, in particular, the spaces in front of west facing façades and in the northeastern parts of courtyards will no longer be among the most intense hot spots. In Porto, the spatial pattern of hot spots remains relatively stable.
Frequency of the occurrence of high T mrt Figure 7 shows the frequency of the occurrence of T mrt ≥60°C for each pixel in the three study areas over the three time periods. Hours with T mrt ≥60°C occur in large open spaces in all three cities. In Frankfurt and Porto, high T mrt also occurs in a majority of the intervening spaces between buildings (courtyards and streets of both directions, i.e., east-west and north-south oriented) as a result of the higher solar elevation. Only pixels in front of north facing walls (<5 m in Frankfurt and <3 m in Porto) are exempt. This concurs with previous findings that although a compact building structure reduces T mrt , additional measures must be taken to reduce the radiant heat load at lower latitudes (e.g., Ali-Toudert and Mayer 2007b).
It has been shown that in northern and mid-European cities, the orientation of street canyons should be considered in builtup areas with a height-to-width ratio of ≤1 (Lau et al. 2015). In southern European cities, the corresponding value is ≤2. At lower latitudes, high T mrt occurs less frequently in north-south oriented street canyons than in east-west oriented canyons because solar access is limited to a few hours during the Fig. 7 Spatial pattern of the number of hours per year when mean radiant temperature, T mrt ≥60°C, in the three case study areas (without vegetation) over the observation period (left). Projected future changes in number of hours by middle and late twenty-first century are shown to the right middle of the day (e.g., Erell and Williamson 2007). Northeast-southwest oriented streets are least favorable in terms of daytime radiant heat load; in that, they experience high T mrt because they are less shaded than other streets during the warmest part of the day (Mayer et al. 2008).
In the downscaled scenario, the number of hours of T mrt ≥60°C at street level increases by the middle and end of the century (Table 4), though to a lesser degree in streets and courtyards than in open spaces (Fig. 7). This is in line with previous studies showing that a dense building structure mitigates the impact of a changing climate on outdoor urban T mrt (e.g., Thorsson et al. 2011). In Gothenburg and Frankfurt, the average number of hours with T mrt ≥60°C per year is projected to double, whereas in Porto, it is projected to more than triple by 2100 (Table 4). The fraction of street-level space affected by high T mrt within the selected study areas will increase in all cities (Fig. 6), from 71 to 75% in Gothenburg, from 92 to 95% in Frankfurt, and from 96 to 98% in Porto by the end of the century. This implies that high T mrt will become more frequent and the areas affected will expand in all three cities in the future, with open spaces being most affected. Although a dense building geometry increases shade and reduces daytime heat stress, it cools more slowly at sunset (e.g., Oke 1987;Holmer et al. 2007) and can thus cause thermal discomfort at night. This implies that the spaces that are warmest during the day are not the same spaces that are warmest during the night. According to Lau et al. (2015), a dense building structure does not cause substantial changes in average and minimum T mrt in winter.
It should be noted that T mrt ≥60°C can occur at street level even though T mrt does not reach this level at our generic urban site, which implies that the number of hours per year with T mrt ≥60°C at street level can be larger than shown in Fig. 7 and Table 4.

Effect of street trees on mitigating radiant heat load
Here, the concept of hot spots is used to identify where trees are most beneficial. The extent to which the street trees in the study area mitigate radiant heat load is also investigated. Depending on the location and size of the trees, average T mrt can be reduced by up to 30°C and the number of hours with T mrt >60°C at street level can be reduced by up to 40 hours per year, with the largest reduction under and north/northeast of trees located in open, sunlit spaces (not shown). It should be noted that trees in Sun-exposed locations can increase heat stress underneath the tree canopy . This is because vegetation canopies block the relatively colder sky, resulting in increased incoming long-wave radiation originating from vegetation rather than from sky.
It has been shown that trees in open areas-those not shaded by buildings or other trees-reduce T mrt more than trees in dense and/or highly wooded sites (e.g., Ali-Toudert and Mayer 2007a;Lindberg et al. 2016). Furthermore, a few large trees provide more shade than many closely spaced small trees . While the cooling effect of trees is most needed in heat-prone areas, these areas are also stressful environments for trees, which may reduce tree vitality and shorten life span (e.g., Saebø et al. 2005).
It is important to recognize that creating too much excessive shade-either from trees or buildings-can have unwanted effects. This is especially important in high-latitude cities, which in winter benefit from direct sunshine. Compared to evergreen trees, defoliated deciduous trees allow 40 to 80% solar radiation to penetrate in winter when solar access is desired (e.g., Heisler 1986;Konarska et al. 2014). From this perspective, deciduous trees are more beneficial than evergreen trees in high-latitude cities. Another unwanted effect of street trees is that they can reduce ventilation (e.g., Shashua-Bar et al. 2009).
A set of general design principles for reducing radiant heat load, based on the findings presented and discussed above, is outlined in Appendix A.

Conclusions
Present and projected future changes in T mrt in one northern, one mid-, and one southern European city (represented by Gothenburg, Frankfurt, and Porto) were analyzed. In Gothenburg, the number of days with high T mrt is projected to be more or less the same at the end of the century as at present, whereas it will more than double in Frankfurt and triple in Porto. The result implies that the radiant heat load will be exacerbated in the cities where heat stress is already common, while remaining relatively unchanged where heat stress is today a limited problem. The location of hot spots within typical real-world, built-up areas in each city and the role of street trees in reducing the radiant heat load during heat stress days was also analyzed. The concept of hot spots was adopted to identify where trees are most beneficial. Although varying in intensity, frequency, and spatial extension, hot spots are mainly confined to in front of sunlit, southeast-southwest facing walls; the northeast corner of courtyards; and open spaces such as squares and wide streets with relative high sky view factors. Hot spots also occur in front of east facing walls in Frankfurt, in narrow street canyons of both directions in Porto, and at the southwest corners of buildings at street intersections in Frankfurt and Porto. This remained true also in the future.
Studies today still use T a , sometimes adjusted for humidity, when analyzing the impact of climate and climate change on health. However, changes in both T a (which influences longwave radiation) and solar radiation should be considered when analyzing the impact of climate and climate change on people's health. This is because changes in solar radiation (due to changes in cloudiness) could either counterbalance or aggravate the effect of increased T a . Using T mrt or humanbiometeorological indices such as PET could give more accurate estimates of the impacts of climate and climate changes on human health than using T a alone. In some cases, like the one presented here, the spatial pattern of severe heat stress assessed using T a alone as a predictor might be modified when accounting for the effects of changes in solar radiation.
Since problems with heat stress are expected to increase as a result of climate change, especially in middle and southern Europe, measures to mitigate heat stress must be taken. By increasing the amount of urban greenery, especially by adding trees in sparsely vegetated spaces prone to heat, the incidence of high T mrt and thus the magnitude and frequency of heat stress can be reduced. By considering the location of trees as well as the species, shape, and amount of trees, benefits derived from street trees can be enhanced and potential side effects can be prevented.
Acknowledgements This work was supported by the Swedish research counsel FORMAS (250-2010-122) and the Portuguese research council Fundação da Ciência e Tecnologia.

Design principles for reducing the radiant heat load in European cities
A set of general design principles for reducing radiant heat load is outlined below. These principles are intended to support urban development and renewal work at local planning levels in regions where a need to minimize outdoor heat stress has been identified. Although the principles are applicable across Europe, local conditions and regional climate peculiarities need to be considered.
Incorporating such design principles into locality's master or green plans would clearly need to be undertaken with consideration to other issues, such as effects of nighttime and indoor thermal comfort, energy requirements, ventilation of urban street canyons, and urban maintenance. Although we cannot analyze all the complexities, the principles outlined below describe both how the radiant heat load can be reduced and how some important unwanted side effects can be minimized.
The design principles reducing radiant heat load are Increase (and preserve) the amount of urban greenery In order to maximize the cooling effect from greenery Trees are to be preferred over lower vegetation, such as bushes and grass as trees provide more shade. Large trees are in turn preferred over small trees. Trees should be located in heat-prone areas, i.e., in front of sunlit southeast-southwest facing walls, in northeastern corner of courtyards, and in open spaces with high sky view factors, such as large squares and wide streets as trees in sunlit spaces provides more shade and transpire more. In mid-and low-latitude cities, hot spots also occur in front of east facing walls, in narrow street canyon of both directions, and in the southeast corner of buildings at the street intersections.
Add trees to open spaces with no or limited trees, as this provides greater heat load reduction than infilling existing tree stands in dense urban spaces. Choose species that thrive in relatively warm and dry environments as urban areas are characterized by relatively high air temperature and limited access of water.
In order to reduce side effects from greenery Use urban vegetation to create a mosaic of shaded and sunlit within short distances to enhance and prolong the use of outdoor space. Consider deciduous trees over evergreen trees, especially in high-latitude cities, as they give shade in summer but allow solar radiation to penetrate in winter (when solar access is desired). Consider vegetation species, location, and shape with a view to minimizing unwanted side effects such as unwanted shade and reduced ventilation.

Increase the building density
By increasing the building density (i.e., compactness) of urban areas, the spatial extension of hot spots as well as the frequency of high mean radiant temperature can be reduced. In narrow streets, with no room for trees, other types of shading devices should be considered.
In order to maximize the cooling effect during daytime but allow nighttime cooling, trees can be planted within streets and courtyards. This is especially applicable for low-latitude cities, as much of the street is sunlit during the day due to the high solar elevation.

Consider street orientations with respect to building density
At height-to-width ratio of ≤1, the orientation of street canyons has a significant impact on street-level heat load in north and mid-European cities. In south European cities, the corresponding value is ≤2. At low latitudes, dense north-south canyons tend to decrease solar access during day and thus the radiant heat load. Northeast-southwest oriented streets have higher heat loads because they provide less shading during the warmest part of the day. At higher height-to-width ratios, street orientation have less effect, but northeast-southwest oriented streets still experience less heat load.
The unwanted effect of creating too much building shadow can be reduced by considering the height and orientation of buildings. This is especially relevant in high-latitude cities, which benefit from direct sunshine in winter.

Use cool building material
The use of cool building material (i.e., light, reflective surfaces with high albedo, and low thermal admittance) has a minor effect on the radiant heat load at street level. However, light-colored building materials reduce the heat load on buildings and thus the indoor temperature and energy used for cooling and so may be preferred.