Geographic Information System-Based Model of Outdoor Thermal Comfort: Case Study for Zurich

The importance of walking, the most basic form of transportation, is growing. Climate change and the associated warmer temperatures could reduce comfortable walking distances drastically. There is a clear need to better understand how outdoor thermal comfort (OTC) and walking interact. In this work, thermoregulation of the human body is modeled with the two-node model to determine the influence of the microclimate on pedestrians’ OTC. First, the impact of the current microclimate in Zurich on the route choice of pedestrians is analyzed. No significant correlation is found between simulated OTC of walking a particular route and route choices for all trips, but results for longer trips indicate a possible influence of OTC. It is pointed out that the same assessment could be done for other regions, and the results could contribute to more accurate pedestrian modeling. Second, a tool is developed that can estimate OTC-corrected walking distances from any location. The tool is applied to the current climate and future climate scenarios. The results show that, in the future, OTC of pedestrians in Zurich will be severely decreased. Further, the tool can detect where there is potential for and, through its accessibility approach, quantify improvements to the built environment citywide. Future work should focus on enhancing physiological input parameters to the model. This work provides a novel use of the two-node model for walking subjects in a citywide assessment.

With the revival and reurbanization of inner cities around the globe, walking, the most basic form of transportation, has become a topic of growing interest over the last decade. For certain use cases, walking can be considered superior to other modes, as it does not come with negative externalities of emissions, landscape aesthetics, and space consumption (1). It further includes positive externalities on the individual level, such as physical and mental health (2), and can provide recreational value. For urban and transport planners, it is essential to know how to assess whether cities are walkable and where improvements should be targeted. Following Sim (3), walkability can be defined as being ''about accommodating walking, making it easy, efficient, and enjoyable.'' The topic of walkability has been extensively addressed by the literature (4)(5)(6)(7)(8)(9). For instance, walkability is enhanced by land-use diversity and density, nearby green areas, and less traffic. Reflecting on the existing research, one aspect which is often neglected when measuring walkability is the OTC of the pedestrian. Walkability comprises the influence of quality; in contrast, the term ''accessibility'' stands for the quantitative number of opportunities (10). Low OTC can restrict both walkability and accessibility. Evaluating OTC becomes of growing importance in the face of the global climate crisis. Public health is threatened by more frequently occurring, longer lasting, and fiercer heatwaves, especially in urban areas where the urban heat island effect (UHI) occurs (11,12). UHI describes the phenomenon of difference in air temperature between urban and rural areas caused by greater absorption of solar radiation from multiple reflections in the built environment, as well as greater uptake and delayed release of heat by buildings and paved surfaces, among others (13). Older people, with their reduced capacity for thermoregulation, and people with cardiovascular diseases are especially at risk (11,14). The official Swiss Climate Change Scenarios (15) indicate potential temperature increases in the summer months of 6°C for 2060 under the RCP8.5 scenario. Many studies have modeled OTC for a steady state of walking activities and environmental conditions (e.g., Mahmoud [16]). The results are typically maps that indicate which places are comfortable and which are not (17). However, none of the existing research has connected OTC, measured with dynamic environmental states that are mapped to the spatio-temporal dimension of a given pedestrian trajectory, to the concept of walkability or accessibility.
This paper focuses on the dynamics of OTC for pedestrians in the city of Zurich, Switzerland. It aims to answer the following questions: 1. How does OTC affect pedestrians' route choice on warm days in Zurich? 2. How does OTC restrict pedestrians' accessibility in Zurich today and in the future?
To do so, in a first step, we set up a data processing pipeline allowing us to estimate OTC by employing the implementation of the two-node model from Melnikov et al. (18). The relevant microclimate data for the city of Zurich is then calculated. We then conduct a descriptive analysis using real-world GPS pedestrian tracks to investigate how OTC affects the route choice in an urban environment. Finally, we present an OTC-corrected accessibility planning tool that uses an OTC-corrected routing engine to predict how far pedestrians can walk comfortably facing current and predicted temperature conditions. The remaining paper is structured as follows. The next section, ''Related Work,'' provides the theoretical foundation of the human thermoregulatory system, OTC assessment, and findings on pedestrian route choice. We then present the methodology. The results of the descriptive route choice analysis and the OTC-corrected accessibility planning are presented in successive sections. The final section discusses the results and concludes the paper.

Human Thermoregulation and the Two-Node Model
In this work, we model the human thermoregulatory system (HTS) with the implementation by Melnikov et al. (18) of Gagge's two-node model (TNM) (19). In the TNM, the human body is divided into two concentric shells: the interior core with uniform core temperature T cr and the outer skin shell with uniform skin temperature T sk . Heat transfer is realized between these two layers and between the outer shell and the environment. The human body aims to maintain a steady T cr and T sk and can initiate different thermoregulatory control functions to do so. If and by how much T cr and T sk deviate from target values is determined by the human heat balance. The body tries to reach a stable state where the heat storage rate St is calculated according to Equation 1 (20): Both the produced H p and lost heat H l are influenced by the individual's characteristics, such as weight, height, and clothing, and especially by the surrounding microclimate. Heat is produced as a result of metabolic activity M, which is not used for mechanical work WR, and through shivering S h in cold temperatures (20). The heat production is then: Heat loss is achieved by convection C (from the skin to the air) and radiative heat exchange R with surfaces in the environment, through evaporation of sweat E, and through respiration Re (warming and moisturizing inhaled air) (20). The heat loss rate is thus calculated as:

Skin Wettedness
The existing literature reveals that, in cold environments, thermal discomfort has a high correlation with skin surface temperature. In hot environments or while exercising, it is more related to sweating (21,22). Sweat is produced to keep the HTS in balance by evaporation. The share of skin surface needed to evaporate the produced sweat is called skin wettedness wt (22). It is a dimensionless variable with a minimum value of 0.06, because of moisture diffusion happening through the skin, and a maximum of 1 when sweat covers the entire skin surface (22). Nishi and Gagge (22) found that metabolism from exercise determines the thermal comfort limit, resulting in a wt threshold wt thr , defined as: with M in watts per square meter (W/m 2 ). Fukazawa and Havenith (21) confirmed this relation with a study for garment design on differences in comfort perception while walking at 4.5 km/h. The results of Lee et al. (23) with eight male Japanese subjects walking at between 6 and 8 km/h, and the work of Vargas et al. (24) with 16 young adults from the U.S.A., also found that the discomfort level follows the relation proposed by Nishi and Gagge. In general, when studies assess walking subjects, the M -dependent threshold from Nishi and Gagge (22) is used or referred to.

Pedestrian OTC Assessment
OTC can be defined as ''the condition of mind that expresses satisfaction with the outdoor thermal environment'' (25). There are several metrics to assess OTC, which are based on the TNM. The most widely used is that of physiologically equivalent temperature (PET) (26). An important feature of this index is that it provides a ''feels-like'' temperature, allowing the effect of the microclimate to be compared with the thermophysiological state of a person. Further, it considers a steady physiological state, which is reasonable for indoor conditions but barely the case for outdoor environments because of the significant variation of microclimate conditions and the diverse activities people perform outdoors. This is why thermal history, dynamic exposure, and the activity of a person are critically important to assess instantaneous and dynamic thermophysiological states. Existing studies using PET differ significantly in their results on comfortable temperature ranges because they lack these aspects (27). Some scientists have extended the TNM to overcome these fundamental limitations. Lai et al. (27) ''developed a human heat transfer model that considers outdoor radiative heat exchange and transient heat transfer in clothing.'' Their overall results were satisfactory, but during hot conditions the error in prediction of skin temperature was as much as 6°C. An extension of Gagge's TNM that is validated for a wide range of warm thermal environments is provided by Melnikov et al. (18). With their modified model for skin blood flow, they accurately predicted skin temperature in unsteady conditions for measured data on 15 subjects.

Pedestrian Route Choice
Pedestrian route choice has been studied by scholars from different sectors like public health (2), real estate (28), pedestrian interaction modeling (29), and pedestrian infrastructure design (30). From a perspective of urban and transport planning, this paper aims to understand how the micro-built environment affects walking route choice, since this is the prerequisite for improvement. Existing studies are based on stated preference (SP) and revealed preference (RP) data, where the latter is considered to provide a better representation of real-world behavior (6). Numerous studies show that trip length is the primary determinant for choosing a particular route (4, 6, 31). Broach and Dill (5) used 1,167 GPS tracks realized by 283 adults (average trip length = 875 m) and compared several route attributes with those of possible alternatives. They found that higher traffic (+14%), lack of crossing infrastructure (+73% for major roads), and primarily steep uphill gradients (+99%) increase perceived walking time. Neighborhood having commercial land use reduced the perceived walking time by 28%. Guo (4) observed subway egress trips and found that steepness and parks have a large effect on utility, while sidewalk width, intersection density, and neighborhood businesses only have a minor influence. Erath et al. (8) estimated elasticities for walking time based on SP and RP data. Among other variables, they found that active window frontages and relevant greenery reduced perceived walking time by 17.5% and 23%, respectively. A recent study from Salazar Miranda et al. (9) using GPS tracks found that pedestrians systematically deviate from their shortest path. They do so to walk on streets that are close to parks, with more business establishments, and with urban furniture. If humans cannot cope with the stress caused by the microclimate and their physiological responses, they must adapt their behavior (32). Several studies confirm that pedestrians incorporate behavioral adjustments to maintain their HTS in balance. Lee (33) found that it was not air temperature T air but global radiation GR from sunlight-which determines mean radiant temperature T mrt -that was the reason for pedestrians changing the side of the street in a study on four locations in New York City. A recent study from Singapore (32) examined the effect of shade on path choice. They found that pedestrians' assumed walking time in the sun was 16% longer than on a shaded path.

Estimation of the Microclimate Conditions
According to various studies, T mrt (average temperature of the surfaces that surround a person, with which the person exchanges thermal radiation) is the driving parameter of human OTC (34-36) as T mrt determines the level of radiative heat exchange and varies significantly. Other variables (e.g., T air , relative humidity RH) are steadier in urban environments; thus, there is less chance of them affecting the dynamics of HTS (20). T mrt is calculated with the Solar Long Wave Environmental Irradiance Geometry (SOLWEIG) model (37). The SOLWEIG model is part of the Urban Multi-Scale Environmental Predictor (UMEP), a tool that combines models essential for climate simulations (37). With its three-dimensional approach and high level of detail, it can simulate complex urban situations. Several studies have confirmed the ability of the SOLWEIG tool to predict T mrt in different places and often better than its competitor software, RayMan Pro or ENVI-met (34,37). SOLWEIG requires inputs such as digital elevation models, land cover information, sky view factor (fraction of sky which can be seen from a given place), meteorological data, and the albedo, emissivity, and absorption factors of different materials, all of which are accessible through open data or can be calculated with UMEP's preprocessors. From all these, the meteorological data represent the essential input for SOLWEIG, and their derivation requires extensive data processing and computation. For T air and RH, the study area is segmented into a 100 3 100 m grid resulting in 5,714 patches, that is, microclimate zones. For each microclimate zone, T air and RH are averaged from the three closest out of 28 weather stations, weighted by their inverse Euclidean distance. T air is corrected for altitude differences with a vertical temperature gradient of 0.62°C per 100 m (38) because of the hilly topology of Zurich. The global radiation GR is only measured through one sensor for Zurich and therefore it is set constant for all microclimate zones. For the final T mrt calculation, all input data apart from the microclimate zones are aggregated to 2.5 3 2.5 m to keep computation manageable. An example of the result is shown in Figure 1.

Model for Metabolic and Mechanical Work Rate
Metabolic M and mechanical work WR rates are essential variables in the human heat balance. They influence the level of heat gains. While there are simulations that consider level walking (18,27,40), the gradient of the walking surface, which dramatically affects M and WR, was not previously integrated in simulations of pedestrian heat stress. To estimate M for level walking, we adapt the metabolic cost of level walking C w from Ardigo`et al. (41): where a = e 4:911i , b = e 3:416i , c = 45:72i 2 + 18:9i, with i being the gradient in percent and v the speed in meters per second (m/s). Since Ardigo`et al.'s formula only accounts for the walking part of metabolic cost, the metabolic cost of resting M base of 1:00108 ½W Á kg À1 (42) has to be added to C w , resulting in: where v is walking speed in m/s, needed to convert from J Á kg À1 Á m À1 to W Á kg À1 .The mechanical work WR for walking can be divided into two parts: 1. external work WR ext ''necessary to sustain the displacement of the center of mass of the body (COM) relative to the surroundings,'' and 2. internal work WR int ''done to move the limbs relative to the COM'' and ''work done by the trailing limb against the leading limb during double support'' (43). We developed a new model to estimate speed-and gradientdependent WR based on two studies. Values for WR ext are taken from Dewolf et al. (43) and WR int is provided by the study of Minetti et al. (44). Their data points are fitted separately with polynomial regressions, given the parabolic nature of the data. Both M and WR for walking speeds considered in this research are shown in Figure 2.
Given the lack of research on M and WR for different walking-speed/gradient combinations, the derived models can be seen as the best approximation possible and viable for the purposes of this paper.

Descriptive Pedestrian Route Choice Analysis
OSMnx is used to create a routable network from the pedestrian network provided by the City of Zurich. The pedestrian network utilized is composed of 54,608 edges and 17,582 nodes. With elevation data sourced from the Google API (39), the gradient of each edge is calculated. The network is enriched with several (built environment) attributes which have been identified as relevant from the literature. The attributes are sourced from OpenStreetMap (OSM) and the City of Zurich. They include 4,639 business establishments (containing shops and food and beverage facilities), 7,867 urban furniture elements (including benches, trash bins, drinking water fountains, and public toilets), 73,042 trees (registered in the public cadaster), and neighboring parks and urban forests (see Figure 3). Business establishments are assigned to the corresponding edges of the pedestrian network if they are within a range of 20 m. This means that for two-lane streets the establishments on the other side of the street are also considered, which makes sense because of the ease of crossing such streets. The other features are assigned in a 10 m range because it is assumed that they only contribute to the attractiveness if they are close to the pedestrian. Furthermore, the network is enriched with the average weekday traffic (AAWT, in the following, ''traffic''), provided by the Federal Department of the Environment, Transport, Energy and Communications (45) with around 60% network coverage. The traffic data contains the street's centerline and is assigned to the edges using a 20 m range. This considers a maximum of three lanes per direction which occurs at intersections, for example (streets with higher hierarchy have one centerline per direction, so 20 m is adequate). Finally, the share of conveniently walkable gradients, that is, defined as 25% to 1% because of the ratio between M and WR rate, is encoded based on the network topology. The trajectory data used for this work comes from the MOBIS-COVID project, an app-based GPS-tracking travel diary study (46). The built environment and OTCrelated attributes of these trajectories are compared with the same attributes of the shortest path of the respective origin-destination pair. The study area does not contain the whole city of Zurich (see Figure 3) but only the parts that contain the majority (94%) of the trajectories because of computational constraints. The 70 warmest days in 2020 are selected for the analysis. These days fall into the time after the ''soft lockdown'' in Switzerland, when no differences to pre-pandemic travel patterns for walking can be observed (47). For the 70 days, the microclimate is calculated between 8:00 a.m. and 8:00 p.m. in 90 min steps because of the computational capacity of the T mrt calculation, resulting in nine points of time in a day and a total of 630 microclimates for each microclimate zone. Trips shorter than 200 m are removed because they are too short to obtain a satisfactory result on OTC in Zurich's climate. Moreover, paths where the start and endpoint are less than 200 m apart are sorted out because they are likely to be roundtrips, so the shortest path comparison would yield misleading results. The remaining trips are matched to the pedestrian network, using a hidden Markov model-based map matching framework from Meert and Verbeke (48). The microclimate zones (100 3 100 m) and the T mrt cells (2.5 3 2.5 m) are then assigned to the trips based on time and location. In many cases, trajectories lie in more than one microclimate zone or T mrt cell. In this case, the trajectory is cut, and each part of the segment is assigned to its corresponding microclimate zone and T mrt cell. To avoid further increasing computation times, the wind data are mapped on each trajectory segment's centroid. The final sample of trajectories contains 2,660 trips, realized by 333 different individuals, of which 59% are female, with an average age of 43 years. To initialize the thermoregulatory model, average weight and height for gender/age pairs of the participants are determined from the Swiss Health   Survey 2017 (49). The clothing level I CL is estimated through the linear function I CL = 1:625 À 0:0375T air , obtained from Melnikov et al. (40).

OTC-Corrected Accessibility Planning
The developed tool enables users to calculate the OTCcorrected maximum walking area from every given point in the city. The pedestrian network of the city of Zurich is also used here, but the maximum edge length is set to 30 m to obtain more accurate results. To calculate the isochrones from each point of interest, the shortest paths are calculated to all other nodes in the network, reachable in a defined walking time. The walking speed is assumed to be gradient-dependent, defined by Tobler's (50) hiking function. The assignment of the microclimate to the network and the clothing are done in the same way as in the descriptive pedestrian route choice analysis. Additionally, it is assumed that T mrt is equal to T air if the edge is inside a building. The weight of the assessed individual is assumed to be 72.3 kg and height 1.71 m, which represents the average Swiss citizen (49). The metabolic dependent wt threshold is calculated with 4. The trajectory's segments have an average length of just 2.8 m. M depends on speed and gradient, and they are different for every segment of the trajectory. wt thr would therefore fluctuate a lot, and it would be unrealistic to assume that someone stops walking when wt thr is reached for a fraction of the whole trip. For this reason, it was decided to calculate the threshold based on the weighted mean of the edges from the last ' 80 s. The paths are then cut when the threshold wt thr is exceeded. The tool's code will be made available to interested colleagues on request.
The tool's usefulness is demonstrated by evaluating two of the municipality's community centers for different climate scenarios. One community center (CC) is that of Ba¨ckeranlage, a dense urban district with relatively narrow street canyons. The other is Oerlikon, selected because new developments on former industrial production sites representing contemporary common building practice are within a 20 min walking radius of the CC. The area enclosing all comfortably reachable edges and the number of persons living in this area within 20 min walking time of the CC are assessed.
The tool draws on estimating the thermoregulatory model and derivation of microclimate zones from the previous route choice analysis. Median and hottest scenarios are based on the already computed microclimate for the 70 warmest days in 2020. As mentioned earlier, the average daily maximum temperatures are expected to increase drastically in the future. Therefore, the RCP4.5 and RCP8.5 for 2060 are additionally evaluated from the official Swiss Climate Change Scenarios National Centre for Climate Services (15). The mean daily maximum temperature increase in August from these scenarios (3.5°C for RCP4.5 and 5.6°C for RCP8.5) is added to the hottest temperature measured in 2020. The represented quantitative and qualitative evaluation focuses on the time of day with the highest solar radiation and thus highest T mrt , that is, 12:30 p.m. The specific scenarios are as follows: Scenario Median: the median (50% higher, 50% lower), T air at 12:

Discussion of Results on Descriptive Pedestrian Route Choice Analysis
Thermal Comfort Table 1 shows the comparison between the statistics of the chosen and shortest path. Mean T air and T mrt are almost identical. The average mean and maximum levels of wt experienced during trips are higher for chosen paths. The share of chosen paths with a higher mean and maximum wt was also higher, which is not surprising. For the 70 warmest days that this paper is considering, the body must compensate for excess heat during almost the entire path, leading to steadily increasing core and skin temperature. Increased heat loss in the form of evaporation therefore becomes necessary, causing wt to increase steadily during the trip (see metrics for an example path in Figure 4). The chosen paths are an average of 89 s/123 m longer, meaning that the body continues sweating during this surplus time with higher T cr and T sk , resulting in the higher mean and maximum wt value for chosen paths. The results in a subset with trips where the chosen path is less than 10% longer than the shortest path confirm the hypothesis that higher wt is the result of longer trips. In these cases, the mean and median for both wt variables are almost identical, and no more significant differences can be revealed. It has to be mentioned here that for the analyzed trips the ranges of maximum wt are on a level that does not cause strong thermal discomfort. The wt thr of 0.38 ( M = 190 W/m 2 , v = 1.4 m/s) is exceeded for only three trips. The short mean walking time (chosen paths: 9 min, shortest paths: 8 min) together with the temperatures present for the MOBIS-COVID data (mean T air is 25°C), leads to the conclusion that anticipation of level of thermal comfort is not considered by the participants in the process of route choice. This might be because of the relatively comfortable thermal conditions overall and smaller possible differences in thermal experience in such a short period. However, the results in Table 2 indicate that, for longer trips, thermal comfort might play an increasing role in the participant's route choice. Mean and maximum wt of chosen paths compared with shortest paths become more similar the longer trips are. For trips longer than 1,500 m, the values of mean and maximum wt for both paths sets are almost equal, despite the more than 3 min longer walking time for chosen paths, where wt continues to increase steadily because of permanent excess heat (Figure 4. Another indicator for a conscious OTC-seeking route choice behavior is the lower T mrt for chosen paths compared with shortest paths, which becomes higher with increasing trip lengths (by 0.17°C for trips . 696 m, by 0.35°C for trips . 1,100 m, and by 0.68°C for trips . 1,500 m). This would be in line with the findings of Melnikov et al. (32) and Lee (33) that pedestrians prefer to walk in the shade

Built Environment and General Observations
In general, participants of the MOBIS-COVID study preferred longer paths for their trips, in both distance and travel time. They chose the shortest path for only 22.5% of their trips. For the trips where the chosen path was different from the shortest path, 64.3% of the chosen route's length differed from the shortest route, meaning chosen paths are substantially different. In the overall results (see Table 1),all attributes of the built environment except business establishments have higher (or, for traffic, lower) mean values for chosen paths when compared with shortest paths, which mostly confirms the studies (5,6,8,9) that found that people anticipate these attributes in their route choices. For presence of urban furniture (WMN) and trees (WMN&KS2S), the distribution of the mean is significantly different. Nevertheless, the last three columns of Table 1 show that chosen paths have a greater share of higher values only for the percentage of flat gradients, or lower values for traffic. This reveals that there are some trips where chosen paths have significantly better statistics on the built environment. Otherwise the difference in the mean would not be possible.
It was found that the built environment gains importance for longer trips, as was also found by Guo and Loo (6) and Miranda et al. (9). In Table 2 it can be seen that the difference between the values of the attributes for chosen and shortest path becomes more pronounced for longer trips. For example, the traffic for chosen paths considering the overall results is approximately 100 vehicles per hour fewer than for the shortest paths. At the same time, there are around 300 fewer vehicles per hour for the subset of trips where the shortest path is longer than 696 m. The same pattern can be observed for the other attributes, except for business establishments which are consistently higher for shortest paths, contrary to the findings of previous studies. Also here the share of chosen paths that have greater, equal, or lower values than  their corresponding shortest paths are compared (not depicted in Table 2). The share of chosen paths that have higher (for traffic lower) values is greater for traffic, the percentage of flat gradients, the number of trees, and urban furniture, when considering longer trips. For the percentage of trips along a park, the share of chosen paths with higher values is slightly lower. The mean number of trees, percentage of the trip along parks, percentage of flat gradients, and traffic volume are higher than the overall results for longer trips. This can be explained by the probability of passing by green areas and busier roads on longer trips being higher, and the likelihood of steeper gradients also being higher for longer trips. The 40% increase in share of route along parks can be assumed to be a conscious decision, confirming the finding of Erath et al. (8). The numbers of urban furniture and business establishments could be lower because there are fewer businesses and less urban furniture along green areas.
The analysis of the MOBIS-COVID data showed that, currently, OTC has a limited influence on route choice in Zurich. This is partly because an insufficient number of trips were done under temperatures that noticeably negatively affected OTC, and the length of the trips was short. This is confirmed by the results on the OTC-corrected accessibility, where it was found that the current climate has a weak influence on the OTC-corrected walking distance for trips up to 20 min. Nevertheless, longer trips showed that OTC could potentially play a role in the route choice, but the low sample size (96) impedes secure conclusions. The methodology designed to assess OTC for the travel diary trips is novel, supporting that such estimation can be done with existing models and data, even on a citywide level. For the built environment attributes, it was shown that these become more important for longer trips. Table 3 shows the statistics for the different scenarios for the two community centers. For the median scenario, the area and population for both CCs are not affected at all (see Figure 5 for a spatial representation). CC Ba¨ckeranlage is almost unaffected by the hottest scenario. In contrast, CC Oerlikon shows 3.5% reduction for the area resulting in 3.8% less population inside this area. Also, for the more moderate RCP4.5 scenario, reductions for Oerlikon are more pronounced: the area is reduced by about 15%, and population inside the area decreases by 13.4%. The losses are all located at the fringes of the walkable radius, which is intuitive because wt steadily increases in hot conditions (see Figure 4). The decrease in the area (-10.6%) and population inside this area (25.2%) for CC Ba¨ckeranlage for the same scenario is smaller. In the RCP8.5 scenario for CC Oerlikon, the decrease of area (242.7%) and population inside the area (-36.1%) is more pronounced. For the new urban developments, no striking differences compared with the rest of the urban fabric can be observed. Compared with CC Ba¨ckeranlage, the comfortable walking paths are reduced spatially more uniformly. For CC Ba¨ckeranlage, the area is reduced by over 50%, and the population inside the area decreases by almost 40%. This can be explained by the already mentioned UHI given the high building density and extensive impervious surfaces (51). This is further confirmed with higher T air at CC Ba¨ckeranlage (37.2°C compared with 36.5°C at CC Oerlikon). The difference between scenario RCP4.5 and RCP8.5 for both CCs is notable because, in the RCP8.5 scenario, heat loss through convection is minimized because T air is warmer than T sk for many time steps (see Figure 6 for an example trajectory). In Figure 6 we can observe that for some time steps heat even convects from the air to the human body. Increased sweat production tries to compensate for this, resulting in a faster exceeding of wt thr limit. For both scenarios, radiation is negative (meaning that heat is not lost but gained by the body) because T mrt is always higher than the body's skin temperature. Very high T mrt values from lack of shade at big intersections before and on bridges lead to many paths ending at these places in the RCP8.5 scenario. Worth mentioning is the path that was not cut in any scenario inside the Sihlfeld cemetery (west of the isochrone). This is because of the high density of vegetation which provides a high proportion of shade, and lower air temperatures. Our analysis demonstrates that OTC is not harmed under the current climate conditions, but will be reduced enough in the context of future climate change that comfortable walking areas will be diminished. The incorporation of shading in bridge design could significantly increase the range of thermally comfortable walks. The low RH in Zurich (around 40% for the hottest scenario), despite the high temperatures in the hottest scenario, helps efficient dissipation of heat through evaporation, explaining the small negative impact of the current climate on OTC. We simulated a hypothetical scenario of 75% RH (typical for tropical cities like Singapore, where average walking distances are half the length of those in Switzerland [52,53]). The results reveal the significant impact of RH on comfortable walking (see Figures 3 and  7). The reachable area is reduced by 80% and the population inside this area by 70%. This represents more significant decreases than the 2060 RCP8.5 scenario and can be explained by the reduced possibility of losing heat through evaporation for climates with high RH (20).

Limitations
Despite the demonstrated contributions, some limitations of this study have to be mentioned. The biggest one is that, for the modeling, it is assumed that pedestrians walk precisely on the centerlines of the coded pedestrian network. In reality, pedestrians almost always have a margin of where they walk on the sidewalk. This can drastically affect the pedestrian's OTC. The same issue also affects behavior on public squares, where not all possible crossing possibilities are represented in the network. Furthermore, the threshold wt thr used in this work depends on M. It is the measure mostly used in research, but its explanation is insufficient.

Conclusion
This research applied a human thermoregulation model to comprehensive real-world data. First, we assessed OTC for the trips from a travel diary study and found that the pedestrian path choices in the current climate of Zurich do not suggest that pedestrians integrate anticipated heat stress in their path planning. There are indications that they do for longer trips, but the sample size is too small to draw robust conclusions. Nevertheless, the developed methodology can be used for other study cases where climate might significantly influence route choice. Most important, it was shown that this is possible with existing, mainly publicly available data. Extending this work by modeling the route choice using discrete choice models would provide additional valuable findings. These insights could be implemented in software to model pedestrians more accurately in hot temperatures. Furthermore, the results could be used to incorporate OTC in navigation software such as Google Maps. Further, we developed a tool to assess OTC-corrected accessibility based on an OTC-corrected routing engine. We evaluated its usefulness for two case study locations in Zurich. It could be shown that the current climate does not affect accessibility because of relatively low RH. A sensitivity analysis showed that high RH reduces OTC severely in hot temperatures. The results for the climate forecast for 2060 showed remarkable reductions in OTCcorrected accessibility. In general, the developed tool can be employed in the analysis stage of projects that aim to secure the OTC of urban dwellers by indicating the need for improvements spatially. A great advantage compared with the existing methods of OTC assessment (17) is the accessibility approach which permits the impact of interventions to be quantified with regard to gain in comfortable walking areas or inhabitants for a given location. By modifying the parameters of the thermoregulation model, OTC could also be assessed for particular groups of people and the public infrastructure related to them.
The presented work is of interest not only for practitioners and researchers in regions with harsher climates but also, given the future increase of global temperatures, especially for places where there is still time to react and implement adaptation measures to ensure attractiveness of the most fundamental transport mode: walking.