UvA-DARE The impact of pace of life on pedestrian heat stress: A computational modelling approach

Elevated walking speed is an indicator of increased pace of life in cities, caused by environmental pressures inherent to urban environments, which lead to short- and long-term consequences for health and well-being. In this paper we investigate the effect of walking speed on heat stress. We define the heat-stress-optimal walking speed and estimate its values for a wide range of air temperatures with the use of computational modelling of metabolic heat production and thermal regulation. The heat-stress-optimal walking speed shows three distinct phases in relation to air temperature, determined by different modes of interaction between the environment and physiology. Simulation results suggest that different temperature regimes require walking speed adaptation to preserve heat balance. Empirical data collected for Singapore reveals elevated average walking speed, which is not responsive to slight changes in microclimate (4–5 °C). The proposed computational model predicts the amount of additional heat produced by an individual due to the high pace of life. We conclude that there are direct implications of the high pace of life in cities on the immediate heat stress of people, and we show how a lower walking speed significantly reduces self-overheating and improves thermal comfort.


Introduction
The ongoing process of global urbanization (UN, 2019) is the manifestation of cities as a pinnacle of social, economic and political organization. The complex interaction of millions of people in the city results in economies of scale for more efficient wealth and innovation creation, use of infrastructure and provision of social services such as education and health care (Bettencourt et al., 2007). Urbanization, however, also results in more people being exposed to urban environment stressors such as noise, pollution and crowdedness. As a result, human behavior, being a function of the environment (Sansone et al., 2003), changes to adapt to the urban pressures and pace of life (Wohlwill, 1974). The study of Bornstein & Bornstein (Bornstein and Bornstein, 1976) demonstrated that the logarithm of walking speed is linearly dependent on the logarithm of population size of 15 considered cities. This finding is now commonly considered as one of the urban scaling laws (Bettencourt et al., 2007). Later studies of the pace of life by Levine (Levine and Norenzayan, 1999) confirmed high variation of average walking speed around the globe. Bornstein & Bornstein suggest that this phenomenon could be the evidence of avoidance and withdrawal behavior: "increased walking speeds serve to minimize environmental stimulation". A recent study (Franěk et al., 2018) has shown that urban noise causes significantly higher walking speeds in the same urban environment. Other personal (Pinna and Murrau, 2018) and environmental (Franěk, 2013;Finnis and Walton, 2008;Willis et al., 2004) parameters were found to also affect the walking speed. In this study we focus on the urban heat -a stressor of a growing concern due to the phenomena of climate change and urban heat island, which pose high risk to human health and well-being (Martinez et al., 2019;Schinasi et al., 2018). We consider immediate physiological implications of walking speed variation -its effect on metabolic rate and thus internal heat production. In hot urban environments, the increased walking speed would imply that people are producing extra heat amplifying their heat stress. Similar effects have been shown in other research, for example, in the study of the effect of urban pollution on walking speed (Bigazzi, 2017). In that paper lower-than-usual walking https://doi.org/10.1016/j.envres.2020.109397 Received 8 January 2020; Received in revised form 12 March 2020; Accepted 14 March 2020 speeds were suggested for walkers to minimize the uptake of pollutants in the body. Previous studies (e.g. (Rotton et al., 1990), in Florida, US) have found a significant difference in walking speeds in between cool air-conditioned and warm outdoor environments, as well as in outdoor environments between cool and hot seasons. Remarkably, the difference in the thermal environment was reflected in the participants' evaluation of sensation, but did not result in a difference in psychological arousal. The authors suggest that: "pedestrian tempo is ideally suited for identifying conditions under which individuals show little or no awareness of their actions". They also state that it is still necessary to determine why these differences in tempo are observed. In this paper we study whether thermoregulatory processes of the human body, and behavioral adaptation to the thermal environment (Melnikov et al., 2017), can be the determinants of these walking speed variations. Here we investigate walking speed and climate interaction by means of computational modelling. We combine our model of thermal regulation (Melnikov et al., 2018) with the model of energy cost of walking (Ralston, 1958) to simulate a wide range of scenarios. We describe the complex interaction of walking speed, internal heat production and its dissipation to the environment. The simulations enable us to approach the phenomenon from two perspectives: to estimate the heat-stressoptimal walking speed for given climatic conditions; and to evaluate heat stress implications of the pace-of-life in cities. We first demonstrate the dependency of heat-stress-optimal walking speed on thermal conditions and walking distance. We then present the results of our empirical study of walking speeds in Singapore and test them against the model predictions. Using the described models, we calculate the additional heat stress incurred by Singaporeans due to their urban lifestyle. We further discuss the empirical findings such as the effect of usage of smartphone or walking in a group on walking speed. We conclude the discussion with the analysis of simulation of self-overheating due to pace-of-life in 31 cities reported in Levine's study. The paper is organized as follows: we describe the models in Section 2; we describe and analyze the computational study in Section 3; in Section 3.2 we describe the procedure and results of the walking speed experiment performed in Singapore. We discuss the results and implications of the computational and empirical studies in Section 4 and provide the conclusions in Section 5.

Methods
In this section we describe the models used to perform the simulations and analysis of optimal walking speeds in terms of heat balance: a model of heat production due to walking and a model of thermal regulation of the human body.

Model of human body thermal regulation
Our model of human body thermal regulation is based on the Gagge's two-node model (Gagge et al., 1972), with optimized parameters of core-skin blood flow we performed earlier (Melnikov et al., 2018). This model with modified parameters reproduced accurately the dynamics of skin temperature and sweating in warm and hot microclimates. Fig. 1 demonstrates how walking speed affects the components of the model.
Below we briefly describe key parameters affected by the phenomenon in the current study: walking in outdoor environments. A complete model can be found in (Melnikov et al., 2018).
The ratio of effective radiative area rad describes the fraction of body surface directly exposed to the environment and thus exchanging radiative energy with it. This parameter depends on the posture of a person (Kurazumi et al., 2008), with values varying from 0.61 while sitting to 0.79 while standing with hands up. In our study, the value of = 0.72 rad for a standing person is used. Speed of walking directly affects the relative air velocity. In our simulations we assume a zero wind speed = v m s 0 / w , allowing the relative air velocity v a to be equal to walking speed ( = v V a ). Relative air velocity determines the efficiency of convective and evaporative heat removal from the body. These dependencies are expressed in terms of convection and evaporation coefficients for respective heat flows. From several existing formulations of the convection coefficient (Ishigaki et al., 1993;Ichihara et al., 1997;de Dear et al., 1997), we chose the one based on experimental data (Ichihara et al., 1997): The convection coefficient influences evaporation coefficient as follows: where = L 2.2 is the Lewis relation and I cl is the level of clothing insulation described below.
Clothing plays an important role in regulation of heat exchange between the body and the environment. In our simulation scenarios we use the level of clothing I cl appropriate for the climate, but not lower than clo 0.3 , which corresponds to a T-shirt, shorts and sandals (McCullough et al., 1985). Fig. 2 demonstrates the appropriate level of clothing as a piecewise linear function of outdoor air temperature, which is adopted from an empirical study of Mediterranean climate in Rome (Salata et al., 2018).
Internal heat production is a vital process of human body. The levels of heat production are often taken from reference tables for different types of activity (e.g. sitting, standing, walking). It is appropriate for approximate evaluation of thermal comfort, but not sufficiently accurate for the purpose of our study. An accurate model of internal heat production is described in the following section.

Model of internal heat production
The themoregulatory model considers metabolic rate M being  V.R. Melnikov, et al. Environmental Research 186 (2020) 109397 transferred into mechanical work W and heat, which is stored in the core of the body. For activities like sitting or standing the positive work is considered to be zero. However, a considerable amount of energy is spent on moving limbs and the core of the body while walking. It is important to mention that the ratio of positive work to metabolic rate is not constant for different walking speeds, thus models for both M V ( ) and W V ( ) are required to infer the amount of energy transferred into heating while walking. We derive the model of metabolic rate M V ( ) as polynomial fit of data reported for young adults of average age of 24 years, n = 6 (DeJaeger et al., 2001). In that study, the metabolic energy production was estimated from oxygen consumption and carbon dioxide production measured with a portable telemetric system. The corresponding data and quadratic fit are shown in Fig. 3.
We then define the metabolic rate M V ( ) with the following expression: We use the data reported in (Schepens et al., 2004) to infer the rate of positive work performed during walking. The calculations were done for young adults (n = 6) and include positive work of moving the centre of body mass and mechanical work of moving limbs relative to the body measured with a force platform and cinematography. The data and resulting fit is shown in Fig. 3. The model for W is defined as follows: By definition of energy transferred into heat we derive expression for H as follows:

Optimal walking speed
From the energy and mechanical work expressions (3)-(5), two values for optimal speed can be derived: First, the speed at which total energy expenditure per distance M V V ( )/ is minimized (Ralston, 1958) and second, the speed maximising efficiency of mechanical work (Cavagna and Kaneko, 1977). Fig. 4 is the metabolic rate while standing. This efficiency η reflects the ratio of positive work to energy expenditure associated with walking activity. The resulting value of optimal walking speed = V m s 1.40 / * is higher than V E * , but is still within the range of reported values (Franěk, 2013;Finnis and Walton, 2008;Willis et al., 2004). However, the reference energy expenditure M stand , on which efficiency depends, is chosen arbitrarily, therefore in our future analysis we will use a different value, given by the energy-expenditure-optimal walking speed = V m s

Heat stress optimal walking speed
We introduce heat storage rate S t ( ) as the left-hand side of a heat balance equation (eq. (7)) which is equal to sum of all the energy fluxes coming to and from the human body: metabolic rate M, mechanical work W, shivering Sh, respiratory heating and humidification of inhaled air Re, convection C, evaporation E and radiation R. The reader is referred to (Melnikov et al., 2018) for a detailed description of these fluxes. At a given point in time the body may experience a particular heat storage rate, which leads to a positive heat gain. Our definition of heat storage (joules) considers the total heat gain over a fixed time period, so the integral of heat storage rate (watts) over some fixed time.
The role of thermoregulatory system of the human body is to attain heat balance, i.e. reach the state of = S 0.
Here the energy fluxes are not normalized to the body surface area, unlike presented in (Melnikov et al., 2018), to avoid confusion with the weight-normalized models of metabolic rate, mechanical work and heat production. Instead we calculate these components for a person with height of 1.8 m, weight of 75 kg, and body surface area of 1.95 m 2 .
We adopt the classical definition of stress as proposed by Selye (1976): "Stress is the nonspecific response of the body to any demand". We define heat stress as thermoregulatory response of the human body to a specific stimulus: this happens when the body experiences a nonzero heat storage for some period of time (a non-zero integral). This definition implies that heat stress is proportional to heat storage, has polarity and magnitude. Thus, our definition differs from the standard definition of heat stress used in occupational health and safety literature, which considers heat stress as amount of heat storage that leads to disorders and disabilities in functioning of human body. V.R. Melnikov, et al. Environmental Research 186 (2020) 109397 We then define heat-stress-optimal speed V HS * as the one at which the absolute value of heat storage S d V , over distance d is minimized, as this corresponds to the minimal thermal stress of a person. Thus: . 5 demonstrates the contributions of different terms into the total heat storage over a stretch of 1 km in typical conditions of shaded outdoor area of Singapore for two walking speeds. As can be seen, previously found = V m s 1.21 / E * promises a higher heat gain than = V m s 1.0 / in this microclimate. In fact we later show that this walking speed corresponds to our definition of heat-stress-optimal walking speed V HS * in this microclimate.

Climate and thermally comfortable optimal speed
In this subsection we investigate the behavior of V HS * as a function of microclimate. We start with three scenarios of walking along a stretch of 1 km in cool, neutral and warm thermal environments at , where T MRT is mean radiant temperature. Here arbitrary microclimate conditions = T T air MRT are used and can be regarded as a clouded or evening-time condition, when the temperature of surrounding surfaces is equal to air temperature. We will investigate the impact of sun radiation and mean radiant temperature T MRT in the subsequent set of simulations. For each of the three microclimates, an appropriate level of clothing was assigned (see Section 2.1). Relative humidity (RH) was assumed 60%. Here and in the following simulations, we assume that people start walking with a thermoregulatory system in a steady state of . We also observe an intuitive increase in V HS * as the environment is changed from neutral to cool, this can be explained by a higher metabolic rate needed to compensate for higher rate of energy dissipation in the cold environment. A similar tendency is observed when switching to a warmer environment typical for Singapore. Here zero storage rate is not achievable: any walking speed will result in a heat gain. Walking speed minimizing this gain is = V m s 0.98 / HS * , which is higher than the value found for the neutral environment. This value of V HS * can be explained by the need to move slightly faster in the warm environment to enhance convection and reduce the time of exposure to heat.
We continue our investigation of thermally comfortable optimal speeds with varying another important parameter of outdoor environments: radiation. This parameter is usually expressed in terms of mean radiant temperature (MRT) T MRT . Fig. 7 demonstrates the results for three simulated scenarios corresponding to different levels of radiation: dense clouds (no sun), light clouds, and sunny day. The thermally comfortable walking speed V HS * grows with increasing sun radiation T MRT , reaching the value of m s 1.19 / for the scenario of exposure to a direct solar radiation. This is explained by the fact that as T MRT increases there is an additional source of heating, which is not mitigated, but instead is worsened by lowering the walking speed. This is why the prevailing strategy for minimizing the heat stress becomes minimization of time of exposure by walking faster. to the colder or hotter temperatures, the walking speed adaptation is required to preserve the heat balance or minimize heat gain or heat loss. This agrees with the previous observations reported in (Rotton et al., 1990). There the authors registered the minimum walking speed of 1.24 m/s at  V.R. Melnikov, et al. Environmental Research 186 (2020) 109397 produce additional energy to compensate for the heat loss in the environments cooler than C 20 . The form of this segment can be explained by the form of heat production curve H V ( ) shown in Fig. 3: it is a quadratic function of walking speed. This implies that at higher walking speeds a smaller increase of walking speed is required to attain heat gain, which results in a higher growth rate of walking speed close to the transition point of . In this range of microclimates the thermoregulatory system has the means to counterbalance the heat gain (primarily through sweating and evaporation of sweat), so the increase of walking speed (to enhance convection and evaporation and minimize time of exposure) is relatively slow. . We define several heat gain/loss bands in terms of kilojoules. For interpretability purposes, we also provide a rough estimate of skin temperature change T skin caused by this heat gain/loss, assuming that all the heat is gained/lost through the skin. Humans are very sensitive to skin temperature stimulation, and can feel the slightest change in skin temperature of as low as C 0.005 (Hardy and Oppel, 1937). The bands shown in Fig. 8a correspond to those from almost undetectable to significant changes in T skin . Fig. 8b demonstrates the curves of S d V , for the considered values of air temperature. It also shows how the bands are defined and corresponding range of V is determined. In Fig. 8a, we can see that the bands result in wider ranges of V in the middle segment of the considered climate (T C [20,42] air ). This is due to the fact that the left and right segments correspond to more thermally stressful conditions and thus less deviation of V is needed for the considered heat gain/loss compared to the central segment. This implies that one should expect greater variation in walking speeds in more moderate climatic conditions (i.e.

Distance and heat-stress-optimal walking speed
In this section we analyze whether the difference in walking distance in the same thermal environment suggests a different level of heat-stress-optimal walking speed. In all our scenarios a 1 km walking distance is used, however, most of the walks performed in urban environments are significantly shorter. For example, the average walking distance in Singapore is 259 m (Erath et al., 2015). This, however, depends on the purpose of walking, and much longer walks are also possible. This is why we simulated the thermally comfortable walking speed for distances from 100 to 3000 m for thermal environments ranging from cool ( C 15 ) to severely hot ( C 45 ), assuming = T T MRT air for a clear comparison. The level of clothing appropriate to each thermal environment was used.
The results are shown in Fig. 9. Fig. 9a shows that the lowest walking speed of V HS * is observed at temperature = T C 20 air , which is in agreement with Fig. 4. As the environment diverges from neutral on both the cooler and hotter side, the level of thermally comfortable walking speed increases. As the walking distance increases, the optimal walking speed level tends to decrease. The optimal speed for 1 km distance in = T C 30 air (found in Section 3.1.1) is 11% lower than the walking speed for a distance of 0.25 km (0.96 versus 1.08 m/s).
There is a difference in the shape between the curves for the  Fig. 9b shows the relationship between heat-stress-optimal walking speed and distance. For all air temperatures two regimes can be observed, for short distances the optimal speed decreases rapidly (e.g., for = T C 45 air going from 1.65 m/s to 1.4 m/s between 100 m and 500 m) then at some distance the speed  happens at 1500 m. Interpreting this observation: walking speed reduction (i.e. reduction of internal heat production) is more efficient for shorter walking distances and more moderate thermal conditions as compared to longer distances and hotter environments.

Empirical results
We have performed an empirical study of walking speeds in Singapore, a city-state with hot and humid tropical climate and population exceeding 5 millions. Singapore's climate is characterized by low variation of air temperature with an annual mean of 27.5 C, and high relative humidity with annual mean of 83.5%. Previous studies of walking speed in this city performed in 1984 estimated average walking speed to be 1.23 m/s (Tanaboriboon et al., 1986). This result is in agreement with the 1999 Levine's study of pace-of-life (Levine and Norenzayan, 1999), which reported a value of 1.24 m/s. Unlike in the previous studies, we have not studied a downtown area of the city, where other urban factors could impact thermal stimulation and could not be singled out. Instead, we chose a walk path leading to Lakeside MRT (subway) station situated in mostly residential area of the city. It is characterized by a straight clearly observable walking path of 30 m long and 2 m wide, so we consider movement is happening in 1 dimension along the pathway. The pedestrians were recorded on a video camera from a distance, so that their entrance and exit from the measurement region could be clearly identified (see Fig. 10).
All the recordings were taken for a duration of 30-40 min and started at around 17:00, so that the effect of diurnal variation of properties of pedestrian flows can be ruled out. Collecting data in the evening ensures that the samples representative of population are less affected by the time constraints people typically have in the morning. We took videos on three days characterized by different air temperatures, spanning a good range of temperatures typical for Singapore (see Table 1). Microclimate parameters were measured by a portable weather station Kestrel 5400 mounted on a tripod near the point of camera installation.
The entrance and exit events were later labeled manually by two researchers to derive the traversing time. The event of entrance and exit were defined as walker crossing the mark on the screen. The entrance time and exit time (in precision of second) of each participant were recorded, their difference was considered the traversing time. Walking speed was calculated by dividing the distance of 30 m by the traversal time. All the pedestrians were labeled with the following attributes: direction (to or from the station), gender, age group by appearance (younger than 12, 12 to 18, 18 to 45, older than 45), level of clothing (short top and bottom, either of top or bottom is long, both top and bottom are long), usage of smartphone (binary), carrying excessive load (binary) and walking in a group (number of co-walkers, only one characteristic person from a group was considered). All the recorded walkers were considered, i.e. no subjective inclusion criteria were Fig. 8. (a) The dependency of heat-stress-optimal walking speed on the microclimate. (b) The heat gain curves for considered microclimates. Here the minimums of the curves correspond to the value of heat-stress-optimal walking speed in a given microclimate. V.R. Melnikov, et al. Environmental Research 186 (2020) 109397 applied. Exclusion criteria were: people appearing performing activity other than walking (e.g. standing and looking around), people entering the area not from the defined ends of a stretch, people walking in a group (of which only one representative walker was recorded). In our primary analysis we have included only those walkers appearing 12-45 years old, not carrying excessive load, not using smartphones, and not walking in a group. The results reported in Table 1 reveal that there is no significant difference in average walking speed between the days (here and hereafter we assume the statistical significance level of 0.05). Thus, we could not find a reactivity of the average walking speed to the change in microclimate conditions typical for Singapore's climate in the range of T [27.5, 32.2] air°C , i.e. the change of up to = T 4.7 air°C ). A detailed analysis of experimental data is summarized in Table 2.
Here we evaluate the influence of other factors on the variation of walking speed. We found no significant difference in walking speeds of people walking in two opposite directions, which suggests that people were experiencing comparable time pressure while going to and from the station. Walking speeds of walkers of different genders were significantly different considering all three days combined, but not each day individually. This observation agrees with the commonly observed higher walking speeds of males compared to females (Tanaboriboon et al., 1986;Willis et al., 2004;Finnis and Walton, 2008). The use of smartphones and walking in groups significantly decreased the walking speed.
In the next section we discuss these empirical results in relation to the computational study reported earlier in this paper.

Discussion
The computational study reported in Section 3 has the following implications: 1. Energy-expenditure-optimal walking speed is estimated to be = V m s 1.21 / E * and is essentially independent of the environmental conditions. 2. Heat-stress-optimal walking speed is predicted to be dependent on climate and walking distance.

Heat stress implications of observed walking speeds
The results of our empirical studies demonstrated that in the range of air temperatures between 27.5 and 32.2°C average walking speeds do not differ significantly, averaging to 1.34 m/s, with a 95% confidence interval of [1.315, 1.368] m/s. This observation contradicts the expectation that walking speed is determined by process of Fig. 10. A frame from the video recording of experimental area. Red cross-sections indicate the boundaries of the measured walking path. The distance between the two entrances is 30 m. (For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Table 1
The results of measurement of average walking speeds on three days with different air temperatures. The results of pair-wise Welch's t-test of samples demonstrate no significant difference in average walking speed on three considered dates.

Table 2
Results of statistical testing of several control parameters. Significantly lower average walking speeds are observed for pedestrians using smartphone or walking in groups, as well as for females compared to males.  Melnikov, et al. Environmental Research 186 (2020) 109397 optimization for certain parameters: 1. The observed walking speed is considerably (10%) higher than the one found to be energy-expenditure-optimal. This finding can serve as a proof of increased pace-of-life in Singapore: the urban environment dictates parameters, other than internal energy expenditure, for people to optimize for. Thus the Singaporeans pay some energy costs in order to maintain the city's pace of life. Remarkably, the value of average walking speed in our experimental study in a mostly residential area of Singapore are considerably higher (by nearly 10%) than those obtained in a busy downtown area in studies dating 1986 and 1999 (Tanaboriboon et al., 1986;Levine and Norenzayan, 1999). Thus, we can see an increase in the pace of life in Singapore in the 21st century.
2. It is unlikely that the microclimate parameter of the urban environment is the one optimized for by Singaporeans. Not only are the observed values much higher than the ones predicted by heat-stressoptimal walking speed, but they also do not demonstrate the responsiveness to variation in microclimate, contrary to the prediction of our computational models.
The latter implies that there is a considerable amount of additional heat stress taken by each person individually. The computational models described earlier in this paper can quantitatively estimate the amount of this additional heat stress for the observed environmental parameters. The results are provided in Table 3. We see that indeed the observed average walking speeds are higher than the heat-stress-optimal walking speeds, but for the hottest conditions (on November 7, 2019) = V m s 1.23 / HS * : • is much higher than for the other two days; • is closer to our observed experimental value of = V m s 1.34 / ; • is close to values found for average walking speeds of Singapore reported in 1986 and 1999; • is very close to energy-expenditure-optimal walking speed The consequences of these elevated average walking speeds in terms of additional increase of skin temperature T skin are also provided in Table 3: we see that on the hottest day they were the lowest and relatively neglectable, whereas on two cooler days they can be considered as significant overheating. Another, seemingly counter-intuitive, observation is that hotter weather leads to less heat gained additionally due to the high walking speed. This is due to the fact that at the higher temperatures higher walking speeds are prescribed as heat-stress-optimal, so while absolute heat gains rise with the temperature, they become more influenced by exposure to the environment, rather than overheating due to selected walking speed. In other words, the hotter the environment is, the smaller is the contribution of the pace of life to the heat stress.

Walking speed variation and factors affecting it
The fact that we did not observe the sensitivity of walking speed to the changes in air temperatures can be explained by the very tight range of considered temperatures. We can suggest that the behavioral adaptation of walking speed does not have a linear response curve (as follows from simulation of our physiological model), but rather has a step or sigmoidal form found in other studies (Semenza et al., 2008;Dutilh et al., 2011). This implies that should a certain threshold be reached, a critical transition may happen, leading to the behavioral adaptation by means of changing the walking speed. We hypothesize that in Singapore the difference could be observed when comparing sun and shade conditions. We plan to test this hypothesis in the upcoming experimental study.
In this paper, we observed the adaptation of walking speed to rather discrete conditions: usage of a smartphone and walking in a group (see Table 2). Average walking speed of those using smartphone was found to be = V m s 1.21 / SP -strikingly equal to the energy-expenditure-optimal walking speed = V m s We can hypothesize that the extra cognitive load of being engaged in interaction with smartphone leads to a cutoff of the environmental stimulation and, as a consequence, to the physiologically optimal walking speed unaffected by the pace of life. Analogously, interaction with others while walking in a group brings average walking speed even lower to the level of = V m s 1.04 / G . As our physiological simulations predict heat-stress-optimal walking speed to be in general lower than usually observed for normal walkers (see Fig. 8b), we can speculate that, for a wide range of warm microclimates, external cognitive load, such as phone usage or walking in a group, may compensate for the pace-of-life pressures and result in an improved thermophysiological experience.

Heat stress due to the high pace of life
We have performed the simulation of heat gain during walking for the 31 countries reported in the pace-of-life study of Levine (Levine and Norenzayan, 1999). We considered the typical walking distance for all the countries to be 500 m. We assigned air temperature of a city equal to the annual average high temperature reported on the Wikipedia pages of the cities. We assumed = T T MRT air , relative humidity of 60%, and clothing level appropriate to the air temperature. The data of temperature and walking speed is presented in Fig. 11a.
For each of the city we calculated the heat-stress-optimal walking speed V HS * and corresponding heat gain S d V , HS * . Additionally we calculated the pace-of-life heat gain S d V , PoL resulting from walking with a speed observed by Levine for a given city. The difference PoL HS * can then be considered a heat stress of citizens of a particular city attributable to the pace of life in this city. The results are presented in Fig. 11b. It follows from simulation that Austria's and Brazil's pace of life has no effect on heat stress; countries like Romania or Bulgaria have relatively low walking speeds, resulting in a cold stress; whereas the pace of life in Japan has the most pronounced effect on additional heat stress resulting in almost C 0. 8 of additional increase in skin temperature.
The computational model used in our study has been shown to accurately reproduce the dynamics of skin temperature and evaporation of sweat in a wide range of air temperatures of [20,48] C. Exact values Table 3 Comparison of experimentally observed average walking speeds V and heat-stress-optimal V HS * . The computationally estimated quantities (5 rightmost columns) assume walking distance = d 500 meters (approximate distance between subway station and surrounding residential buildings) and outer compartment (skin) mass of 7.5 kg.  Melnikov, et al. Environmental Research 186 (2020) 109397 of quantities reported in this study are bound to a model-specific assumptions and simplifications (such as average person assumption). This implies that while comparative analysis of scenarios using the model is a valid approach, the estimated absolute quantities can have a discrepancy with the real-life measurements of individual people or scenarios.

Conclusions
Increased pace of life is an intrinsic characteristic of big cities. It contributes to the city efficiency in economic and social development. On the other hand, it causes a constant stress in our experience of urban environments. One of the main evidences of increased pace of life is the increased average walking speed in cities, which was shown to scale with the city size.
In this work we studied the heat stress implications of increased walking speeds -a critical issue in conditions of global urbanization and climate change. We described the computational model of complex interaction between the thermal environment, human physiology and walking speed. We defined the heat-stress-optimal walking speed V HS * as the one minimizing heat gain or loss in a given thermal environment on a given distance. Simulating walking scenarios for a wide range of air temperatures, we found that one should adapt walking speed if optimizing for thermal comfort (see Fig. 8a). Heat-stress-optimal walking speed takes its minimum of 0.88 m/s in most thermally neutral environment of air temperature around 20 C. It rises rapidly as the environment becomes colder, because the increased internal heat production due to faster walking is the only mechanism of compensation for the heat loss. Heat-stress-optimal walking speed increases more moderately in warmer environments, as there are thermoregulatory mechanisms to cope with heat load that make minimization of time of exposure due to faster walking a secondary heat mitigation mechanism. Minimization of time of exposure becomes the primary means of the heat gain minimization, and V HS * grows fast in air temperatures above 42°C, because the thermoregulatory mechanisms (evaporation of sweat) reach their capacity at this point.
We then applied the developed models to investigate the implications of Singaporean pace of life for the thermal experience of its citizens. The results of empirical measurements showed stable average walking speed of 1.34 m/s, which is not responsive to the change of air temperature in a range typical for Singapore C [27.5; 32.2] . This observation brings us to the conclusion that: 1. Citizens of Singapore do not employ walking speed adaptation as the means of behavioral response to slight change in thermal environment. 2. Singapore has an increased pace of life in terms of walking speed, which grew by approximately 10% since the studies reported in 1986 and 1999.
Modelling results for heat gain in measured conditions of Singapore show that the increased walking speed results in a significant additional heat load in relatively cooler conditions (27.5 and 29.8 C). As environment becomes hotter, less and less heat stress can be attributed to the increased pace of life, since heat-stress-optimal speed for hotter environment is higher and closer to the empirically observed values of walking speed in Singapore.
For the example of Singapore, we have shown with the computational model, that the urban pace of life has an important implication for people's well-being in hot climates: extra heat stress. Our study suggests that people should slow down to improve thermal comfort in warm and hot climates -a suggestion seemingly contradicting the ever growing pace of life. We have observed, however, that the use of smartphones or walking in a group slows down the walking speed to a level close to the thermally optimal -a remarkable example of how the overstimulating urban environment can be compensated for by social interaction.

Funding sources
This research was conducted at the Complexity Institute of the Nanyang Technological University in Singapore and at the Future Cities Laboratory at the Singapore-ETH Centre, which was established collaboratively between ETH Zurich and Singapore's National Research Foundation (FI 370074016) under its Campus for Research Excellence and Technological Enterprise programme. Funding sources had no involvement in research procedures.

Ethics approval
The procedures of observational study reported in this paper have been reviewed by ETH Zurich Ethics Commission (Approval no. EK, 2018-N-94, January 18, 2019).

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.