Comparison of human thermal loads on foggy and cloudless mornings

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A customizable clothing thermal resistance-operative temperature model was used. The BMI and M b values of the person in the simulations were 25 kgm − 2 and 40 Wm − 2 , respectively. During the observations, weather data was provided by the automatic station of the HungaroMet company and it was accessible on the company's website. We had 77 observations in foggy weather, while we had 46 observations under clear sky conditions in the period between 2019–2023. The following main results should be highlighted: 1) r cl varied between 0.5–2.5 clo in the case of fog, while in clear-sky cases r cl was between 0.9–3.5 clo. Based on our data analysis, we concluded that the warming effect of the morning fog was around 1-1.5 clo. 3) We also showed that the effect of inter-personal variability on r cl was significant when the heat deficit was high (r cl ≥ 2.5 clo) and at this time it was comparable with the degree of the warming effect of fog. It should be mentioned that the analysis of typical weather situations from the point of view of human thermal load is a new field of research, since there is little information available on this subject. human thermal load foggy mornings and clear sky mornings Hungarian lowland comparison thermal resistance of clothing operative temperature human data Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 1. Introduction The weather in and of itself can be analyzed without taking living beings in regard, that is, objectively, to better understand and discover how the atmosphere works (Radinović, 1968). On the other hand, weather can also be analyzed in terms of its effects on living beings. Planet Earth is living the age of human dominance (Mészáros, 2001 ), our approach is human-centric in everything (Rovelli, 2019 ), so we are mostly interested in finding out how weather affects people’s lives (Lim, 2020 ). This impact can be approached in a broader sense, for instance, by thinking of industries such as tourism (Kovács, 2014 ), health (Motlogeloa and Fitchett, 2023 ), recreation (Schiller, 2001 ), but it can also be narrowed down, directly to the lives’ of people (Blazejczyk and Krawczyk, 1994 ). The thermal load of weather is a direct and obvious effect and determines people's daily lives. The thermal load of the weather can only be fully characterized by analyzing the energy balance of the human body (Blazejczyk and Krawczyk, 1994 ). Energy balance-based methods have mostly been used in two types of studies: human comfort studies (Gulyás et al., 2006 ; Kántor et al., 2012 ) studies dealing with weather situations of extreme thermal load (Bašarin et al., 2018 ). Extreme thermal load can be extreme heat excess (Bašarin et al., 2020 ) and/or extreme heat deficit (Auliciems and de Freitas, 1976 ). Former studies have become more widespread than the latter ones since it was discovered that extreme heat loads could be correlated with deaths (Nastos and Matzarakis, 2012 ) and illnesses (Motlogeloa and Fitchett, 2023 ; Yard et al., 2010 ). The study of human reactions induced by heat stress (e.g. thermal perception, sweating) is less widespread, as this would involve examining many people due to the high individual variability. Measuring and observing reactions requires a careful procedure even in the case of one person (Ács et al., 2023 , Ács et al., 2024 ). To avoid having to investigate a lot of people, the concept of "reference human" is used in human biometeorological modeling. In this study, we focus on weather situations that cause a lack of heat. This is during anticyclonic weather conditions in continental areas in the autumn and winter mornings. This is when the continental areas are the coldest. Mornings can be foggy, cloudy and completely cloudless with clear skies. We focus on fog and cloudless situations in order to compare the thermal loads of these situations. These thermal loads are estimated for not one, but three different persons, so we can compare the effect of individual human variability with the effect caused by weather differences. To the best of our knowledge, no one has yet conducted such an investigation. The aim of this study is to estimate the human thermal load 1) under clear sky conditions and 2) in fog during autumn and winter mornings and 3) to estimate the heating effect of fog based on a comparison of the thermal loads obtained in the former situations, as well as to 4) test the sensitivity of human thermal load to interpersonal variability among people. The model we used in our study is a clothing thermal resistance (r cl ) – operative temperature (T o ) model. The r cl -T o model was chosen due to its simplicity and also because it is suitable for investigating the effect of human interpersonal variability on human thermal load. The observations were carried out in the lowland region of the Carpathian Basin. 2. Materials and methods In the following, we briefly describe the model and the parameterizations of the clear sky emissivity used, as well as provide basic information about documenting morning weather situations (fog or clear sky). 2.1. The clothing thermal resistance-operative temperature model The basic equations of the model are the equations of the thermal resistance of clothing and the operative temperature, which can be derived from the energy balance of the human body covered with clothing, $${r}_{cl}= \rho \bullet {c}_{p}\bullet \frac{{T}_{S}- {T}_{o}}{M- \lambda {E}_{sd}- \lambda {E}_{r}-{H}_{r}- W}- {r}_{Hr},$$ 1 $${T}_{o}= {T}_{a}+ \frac{{R}_{ni}}{\rho \bullet {c}_{p}}\bullet {r}_{Hr}, \left(2\right)$$ where ρ is air density [kgm − 3 ], c p is specific heat at constant pressure [Jkg − 1 °C − 1 ], T S is skin temperature (34°C) (Campbell and Norman, 1997), r Hr is combined resistance for expressing thermal radiative and convective heat exchange effect [sm − 1 ], M is metabolic heat flux density [Wm − 2 ], it refers to a person walking at a speed of 1.1 ms -1 . λE sd is latent heat flux density of dry skin [Wm -2 ], λE r is respiratory latent heat flux density [Wm − 2 ], H r is respiratory sensible heat flux density [Wm − 2 ], and W is mechanical work flux density [Wm − 2 ], T a is air temperature at a height of 2 m [°C] and R ni is isothermal net radiation [Wm − 2 ]. It should be mentioned that r cl is usually expressed in units of [clo], 1 [clo] = 0.155 m 2 ·K·W -1 . If r cl /(ρ· c p ) = 1 [clo], then r cl = 1.2 [kgm -3 ] · 1004 [Jkg -1 K -1 ] · 0.155 [m 2 ·K·W -1 ] = 186.74 [sm -1 ]. Both parameters characterize the thermal load of the air, the former through the thermal insulation of clothing, while the latter through an integrated temperature (dimension ℃) value. The parameterization of r Hr , R ni , M, λE sd , λE r , H r and W can be found in the work of Kristóf et al. ( 2024 ). 2.2. Parameterization of clear sky emissivity There are many parameterizations for clear-sky emissivity (Gulyás, 2018 ). There are parameterizations that depend a) only on air temperature, b) only on water vapor pressure and c) on both air water vapor pressure and temperature. We chose a parametrization from the latter two methods, namely Brunt ( 1932 ) (it depends only on partial water vapor pressure), and Konzelmann et al. ( 1994 ) (it depends on both partial water vapor pressure and temperature) formulae, $${ϵ}_{cs}=0.51+0.066\bullet \sqrt{{e}_{a}} , \left(3\right)$$ $${ϵ}_{cs}=0.23+0.4393\bullet {\left( \frac{{e}_{a}}{{T}_{a}}\right)}^{\frac{1}{7}}, \left(4\right)$$ where e a is partial water vapor pressure in air (in Brunt's formula in [hPa), while in Konzelmann et al.’s formula in [Pa]) and T a is air temperature at a height of 2 m in [K]. 2.3. Documenting atmospheric conditions on foggy and clear sky mornings Observations were made between 2019 and 2023 (we have only two observations in 2017 for the fog). Data collection was carried out in the autumn and winter months: October, November, December, January and February. In the case of fog, we also had an observation on September 27. The morning period is from 6 to 10 a.m. in the case of fog, and from 5 to 8 a.m. in the case of clear skies. In the case of clear skies, we had one observation that was between 1 and 2 o'clock. In both cases, the vast majority of the observations took place between 6 and 8 o'clock. The atmospheric conditions are characterized by the following meteorological elements: air temperature, relative sunshine duration, cloud cover, wind gust speed, average wind speed, relative humidity and air pressure. The values of the meteorological elements are average values for a 10 minute time interval. Global radiation was also documented by entering the values of the parameters Q 0 , α (Kristóf et al., 2024 ; Eq. (15)). Q 0 and α values are hourly values, and they refer to the hour interval during which the observation took place. 2.4 Location The region and the location of the observations can be seen in Fig. 1 . Martonvásár is a small lowland town in the Central Transdanubian region of Hungary, about 30 km southwest of Budapest, Hungary. According to Feddema (Ács et al., 2015 ), the climate of Martonvásár is "cool, dry, with extreme temperature fluctuations", the annual clothing thermal resistance value is around 0.4-1.0 clo (Ács et al., 2020 , 2021 ). However, the weather can cause a much greater lack of heat in the winter season, when the thermal resistance values of clothing can be higher than 3 clo (Ács et al., 2023 ). 3. Data We used anthropometric and weather data. These are briefly described below. 3.1 Anthrophometric data There is a Hungarian anthropometric database (Utczás et al., 2015 ; Zsákai and Bodzsár, 2016 ; Fehér et al., 2019) with the anthropometric data of more than 2,000 children and more than 1,000 adults. The dataset is a product of the Department of Biological Anthropology, Eötvös Loránd University, Budapest, Hungary. We also calculated M b and body mass index (BMI) values from the measured and queried data. From the database, we selected the data of three people among whom the individual deviation is quite large, these data (body mass, body length, sex and age) together with the M b values are illustrated in Table 1 . Table 1 Anthropometric data and M b values of the 3 selected persons. Person Sex Age [Years] Body Mass [kg] Body Length [cm] Basal Metabolic Heat Flux Density [W m − 2 ] person 1 male 68 89 190 39.56 person 2 male 53 95 179 41.81 person 3 male 24 120 179 45.93 We chose the persons in such a way that shows individual variability as much as possible. It should be mentioned that the weather observations were made by person 1. 3.2. Weather data When the Carpathian region is dominated by an anticyclone, two opposite weather situations can develop: 1) cloudless weather with a clear sky and 2) fog, weather characterized by fog. We collected data on these two weather types in autumn and winter mornings, when the environmental heat deficit is greatest. As mentioned, we used the following meteorological elements for characterizing thermal load of weather: air temperature, relative sunshine duration, cloud cover, wind gust speed, average wind speed, relative humidity of air and air pressure. The values of the elements, with the exception of relative sunshine duration and cloudiness, were taken from the HungaroMet website ( https://www.met.hu/en/idojaras/aktualis_idojaras/megfigyeles/ ) and transcribed into the database. The beeline distance between the station and the observer’s location (garden of a family house) is shorter than 3 km. Relative sunshine duration and cloudiness were observed. Cloudiness is estimated visually in tenths. Their values refer to the same 10 min period as the HungaroMet data. The radiation parameter (Q 0 and α) values are hourly values and refer to the hour in which the observation took place. The input data are available in Tables S1 and S2 of the Supplementary Material separately for clear skies and fog, respectively. A total of 123 observations were made (77 in the case of fog and 45 in the case of clear skies). Our regular observations lasted from October 26, 2019 to February 21, 2023, and we also have 2 observations from 2017. The most important features of the two weather types are presented below. 3.2.1 Weather on foggy mornings The air temperature varied between − 5.5 and 12.0 ℃, but in the vast majority of cases it occurred between − 2 and 6 ℃. The global radiation was very low, it was never higher than 110 Wm − 2 , and in the vast majority of cases it was lower than 50 Wm − 2 . The relative humidity of the air is by definition 100% or very close to 100%. In fog, wind speeds are usually lower (below 1.5 ms − 1 ), but values higher than 2.5 ms − 1 can occur. Air pressure was less than 1013 hPa in 10% of the cases (8 cases in total). 3.2.2 Weather on cloudless mornings The air temperature varied between − 12.7 and 13.3 ℃. The morning times for these temperatures are 5:00 a.m. and 9:30 a.m., respectively. 65% of the temperature values are less than 0 ℃. The global radiation varied between 0-250 Wm − 2 , but the number of values greater than 200 Wm − 2 was only 2. The global radiation was equal to 0 in 15 cases (33% of the cases). Cloud cover varied between 0 and 0.2. It was 0.2 in three cases and 0.1 twice. The relative humidity of the air varied between 72 and 100 percent. Relative humidity was greater than 90% in 69 percent of the cases (31 cases in total). In the vast majority of the cases, the wind speed was low (less than 1.5 ms − 1 ). Only in 1 case (on February 21, 2023 at 8:30 a.m.) was there a stormy wind (gust speed 12.2 ms − 1 , average wind speed 7.8 ms − 1 ), but even then the weather situation was not anticyclonic. 4. Results We will examine the thermal load of foggy and clear sky mornings by analyzing the r cl and r cl – T o relationship. We will separately analyze a) the thermal load of foggy and b) clear sky mornings, c) the heating effect of fog, d) the sensitivity of thermal loads to human variability and e) the sensitivity of thermal load to the parameterization of clear sky emissivity. Before discussing these subsections, we will also talk about human variability by analyzing the individual M b –BMI relationships. 4.1. The M b –BMI relationship The M b –BMI value pair is unique for each person. Therefore, M b –BMI value pairs can be used to examine human variability. The point clouds of M b –BMI relationships for men and women, based on the use of data from the Hungarian anthropometric database, can be seen in Fig. 2 . The M b –BMI points of the 3 selected persons are marked in black in Fig. 2 . It is clear that small BMI values (values around 15 kgm − 2 ) are represented by children. In the range of BMI ≤ 25 kgm − 2 , 75% of the points refer to children and 25% to adults. Based on these, it is clear that the 3 selected adults are markedly different, even though the difference between their M b values is less than 7 Wm − 2 . However, it is worth noting that the difference of 7 Wm − 2 means a relative difference of 18%. 4.2. Thermal load of foggy and cloud-free mornings The point cloud representing the r cl – T o relationship of foggy and cloud-free mornings can be seen in Fig. 3 . 1.1 ms − 1 as a function of operative temperature on foggy and cloud-free mornings. Foggy cases are marked with dark blue, while clear sky cases are marked with light blue. In foggy situations, r cl varied between 0.5 and 2.5 clo, but in the vast majority of the cases the values were between 1.25 and 2.0 clo. These values refer to the observer (person 1) who is walking at a speed of 1.1 ms − 1 . Note that in only three cases was the r cl smaller than 1 clo. In cloud-free cases, the r cl values varied between 0.9 and 3.5 clo. We had only 2 cases, when r cl was equal to or less than 1 clo. We can see that most of the r cl values are greater than 1.9 clo. We also have a point with a value of 4.1 clo (the associated T o value is -30.7 ℃), this does not refer to Martonvásár, but to the Bükk Mountains. We will refer to this point later in Section 5 . 4.3. The heating effect of fog during mornings The main difference between clear sky and foggy mornings is in the cloudiness values. In both cases, wind is usually weak and the relative air humidity is high or very high. The radiation balance is obviously different: in the case of a clear sky it is much lower (usually between 0 and − 100 Wm − 2 ) than in fog (usually between − 20 and 10 Wm − 2 ) (Tables S1 and S2 of the Supplementary Materials). As a result, air temperature will also be lower in cloudless mornings than in foggy mornings. The resulting difference in radiation and temperature also results in different thermal loads. In our case, thermal load is expressed in terms of r cl . Comparing the r cl values obtained on foggy and cloudless mornings, we can get an insight on how large the heating effect of fog can be. This is obviously an indirect, general estimation of the heating effect of fogs during mornings, which is based on the consideration outlined above. Our reasoning is confirmed by the fact that r cl values obtained on cloudless and foggy mornings are clearly shifted, even if they overlap. The shift of the light-blue points (cloud-free cases) compared to the dark-blue points (foggy cases) is clearly noticeable (Fig. 3 ). This shift can also be interpreted as a warming effect of the fog. It amounts to 1-1.5 clo, or in terms of the absolute values of T o , it is between 10–14 ℃. This is, of course, a rough estimate of the average heating effect of morning fogs. 4.3. Sensitivity of the r cl –T o relationship to human inter-personal variability It is interesting to test the sensitivity of r cl – T o relationship to interpersonal variability of M. We executed this separately for cloudless and foggy mornings, comparing person 1 with persons 2 and 3. These point clouds can be seen in Fig. 4 in the cloudless case, while in Fig. 5 in the foggy case. It is noticeable that as the lack of heat increases, the r cl differences between people also increase. Therefore, the effect of inter-personal variability on r cl values is stronger, even significantly, on cloudless mornings compared to foggy mornings. How big is this effect on the people being tested? In Fig. 4 (cloudless case), the biggest difference is between people 1 and 3, its value is around 1-1.2 clo (the green point representing the biggest heat deficit), which is around 30% of the actual thermal load. At the same extreme point (comparison of persons 1 and 3 for the highest heat deficit) in Fig. 5 (foggy case), the r cl difference is 0.7–0.8 clo, that is, it is around 50% less than in the cloud-free case. It should also be mentioned that the investigated personal r cl difference in the largest heat deficit (Fig. 4 , green point with the largest heat deficit) has a value of 1-1.2 clo and it is comparable to the heating effect of fog, which we estimated to be around 1-1.5 clo. The smallest r cl differences are between people 1 and 2 (blue points), when the heat deficit is the smallest (values around 0.8-1 clo). Its value is 0.1–0.3 clo, which is around 20% of the thermal load. So we can see that the inter-personal r cl differences amount to 10–30% of the actual heat deficits. 4.4. Sensitivity of r cl to ε cs parameterizations The lack of heat in the mornings is mostly determined by cloudiness. In the case of a cloudless sky, the lack of heat is mostly determined by the temperature and humidity of the air, since downward atmospheric radiation strongly depends on these atmospheric state variables. The emissivity of the clear sky also depends on these state variables, so, it can be parameterized only as a function of air humidity (e.g. Brunt's (1932) formula, Eq. (3)) or as a function of air humidity and temperature (e.g. Konzelmann's (1994) formula, Eq. (4)). The question arises: how sensitive is r cl to the parameterization of ε cs , naturally, in the case of a cloudless sky? Fig. 6 illustrates the sensitivity. The results refer to person 1 walking at a speed of 1.1 ms − 1 . The differences between the obtained r cl values are very small, below 0.2 clo, and the r cl values obtained with formula (3) (Brunt, 1932 ) overestimate, albeit minimally, the r cl values obtained with formula (4) (Konzelmann, 1994). 5. Discussion Human biometeorology deals with the effects of climate and/or weather on humans. In the center is the person who is in a state of comfort or discomfort in the given atmospheric environment. The weather itself is not the subject of investigation, but a person's sense of comfort or discomfort. In this study, the weather is the subject of investigation, more precisely, it is the thermal load of weather on humans. This issue was discussed from the point of view of human comfort (Honjo, 2009 ; Milošević et al., 2016 ) and/or discomfort (Blazejczyk et al., 2012 ; Nastos and Matzarakis, 2012 ), and not or less discussed in relation to typical (Kristóf et al., 2024 ) or selected weather situations. There are studies where the focus was on the study of reactions caused by thermal load, such reactions are, for example, thermal sensation (Krüger et al., 2021 ; Ács et al., 2023 ) or sweating (Havenith et al., 2013). Human thermal load depends on both environmental and human factors and since it depends on both factors, it must be calculated from the energy balance of the human body (Katić et al., 2016 ). The calculation requires both human (at least 4 types of data: body mass, body length, sex and age) and meteorological (at least 4 types of data: radiation, air temperature, air humidity and wind speed) data, so we can say that the calculation is data intensive. Collecting human data is more difficult than meteorological data. Human data does not only mean anthropometric data, but also includes data characterizing clothing and activity. It should be emphasized that the variability of data characterizing clothing and activity is enormous. Thus, the "reference human" was introduced into human biometeorological studies. However, the definition of this "reference human" varies by method (Ács et al., 2023 ). This reduced the data requirements of the models, but made it impossible to examine the sensitivity of thermal load to human variability. However, this is not the case for models based on the use of individual human data (Ács et al., 2021 ). In many cases, the use of meteorological data was also reduced (Bröde et al., 2012 ). This may even be justified in special cases (windchill), but it can also lead to large errors in estimating thermal load (Ács et al., 2023 ). The full use of data is very important when estimating the thermal load of the weather, especially if the weather is extreme in some respect. In the Carpathian region, there are extreme thermal loads in anticyclonic weather situations. Then, the mornings of the cold season can be dominated by two completely different weather types: cloudless, mostly calm, but very cold weather with clear skies, or fog, in which the air movement is also weak, and the air is warmer and more humid than in the former weather type. To the best of our knowledge, no one has yet investigated the thermal load of these two opposite weather types or compared their thermal loads. Since, based on our model, we can estimate changes in r cl values due to changes in atmospheric and human factors, we can compare these two effects, such as the warming effect of fog, and r cl changes resulting from human variability. As far as we know, such comparisons have not yet been done, although they are intriguing. We could see that the shift between the r cl values of cloudless (clear sky) and foggy morning point clouds is around 1-1.5 clo (Fig. 3 ), and this is comparable to the largest r cl value deviations caused by human variability (Fig. 4 , green dots). Similarly, in the case of a cloudless sky, we can compare the deviations of the r cl values obtained by different ε cs parameterizations (Fig. 6 ) with the deviations of r cl values obtained by using individual anthropometric data (Fig. 4 ). In this case, the r cl value changes caused by human variability are always larger than the r cl value changes caused by parameterizations. We can say that inter-personal differences cannot be neglected when estimating human thermal load on cloudless mornings. In our opinion, these human thermal load data can be extended to the entire Great Plain. What are these thermal load values in the mountains of Hungary? In the case of fog, we cannot give an estimate, so we assume that the lack of heat in mountain fogs is not greater than in lowland fogs. However, we can give an estimate of thermal load for cloudless mornings. The biggest differences are in the air temperature, the differences between the values of solar radiation (around zero or zero), air humidity (close to saturation) and wind speed (close to calm conditions) values are very small and negligible. HungaroMet stations have already recorded temperatures of around − 20 ℃ in the Bükk Mountains in winter in the morning hours. We selected such a case (February 13, 2021, 6:30 a.m.), at which time the heat deficit was 4.1 clo (Fig. 3 ). In the sinkholes of Bükk-plateau, temperatures could go down to -30 ℃ (Dobos et al., 2024 ), in this case the heat deficit is already around 4.8 clo. These thermal deficit values were experienced by person 1 walking at a speed of 1.1 ms − 1 . We can state that the greatest heat deficit values in Hungary are around 5 clo. This experience is extremely individual, subjective, as it is shown in the study. 7 Conclusion The main conclusions of the study are as follows: 1) based on the shift in the r cl values of cloudless and foggy mornings, it can be concluded that the warming effect of fogs is around 1-1.5 clo in the morning hours. This heating effect, expressed in T o values, is 10–14 ℃. 2) As the heat deficit increases, the inter-personal differences of r cl increase, too. 3) In extreme heat deficit situations (r cl ≥ 2.5 clo), the effect of inter-personal variability on r cl is comparable to the warming effect of fogs during morning. 4) In the given environmental heat deficit, it may also happen that the r cl change caused by inter-personal variability is greater than the r cl change caused by the variability of the physical parameter (in our case clear sky emissivity). Declarations Conflicts of Interest: The authors declare no conflict of interest. Funding: This research received no external funding. Author Contributions: Conceptualization: F.Á.; methodology: F.Á., A.Z.; software: F.Á and E.K.; validation: F.Á.; formal analysis: F.Á., E.K., A.Z.; investigation: F.Á.; resources: F.Á, A.Z.; data curation: F.Á. and A.Z.; writing—original draft preparation: F.Á.; writing—review and editing: F.Á.; visualization: E.K.; supervision: F.Á.; project administration: A.Z. All authors have read and agreed to the published version of the manuscript. References Auliciems A, de Freitas CR (1976) Cold stress in Canada. A human climatic classification. Int J Biometeorol 20:287–294. https://doi.org/10.1007/BF01553585 Ács F, Breuer H, Skarbit N (2015) Climate of Hungary in the twentieth century according to Feddema. Theor Appl Climatol 119:161–169. https://doi.org/10.1007/s00704-014-1103-5 Ács F, Zsákai A, Kristóf E, Szabó AI, Breuer H (2020) Carpathian Basin Climate according to Köppen and a clothing resistance scheme. 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BSc Thesis, Eötvös Loránd University, 42 pp. Havenith G, Bröde P, Hartog E, Kuklane K, Holmer I, Rossi R, Richards M, Farnworth B, Wang X (2013) Evaporative cooling: effective latent heat of evaporation in relation to evaporation distance from the skin. J Appl Physiol 114: 778–785. https://doi.org/10.1152/japplphysiol.01271.2012 Honjo T (2009) Thermal Comfort in Outdoor Environment. Glob Environ Res 13:43–47. Katić K, Li R, Zeiler W (2016) Thermophysiological models and their applications: A review. Building and Environ 106:286–300. https://doi.org/10.1016/j.buildenv.2016.06.031 Kántor N, Égerházi L, Unger J (2012) Subjective estimation of thermal environment in recreational urban spaces-Part 1: Investigations in Szeged, Hungary. Int J Biometeorol 56:1089–1101. Konzelmann T, van de Wal RSW, Greuell W, Bintanja R, Henneken EAC, Abe-Ouchi A (1994) Parameterization of global and longwave incoming radiation for the Greenland Ice Sheet. Global Planet Change 9:143–164. https://doi.org/10.1016/0921- 8181(94)90013-2 Kovács A (2014) Modification of the Tourism Climatic Index to Central European climatic conditions – examples. Időjárás 118(2): 147–166. Kristóf E, Ács F, Zsákai A (2024) On the Human Thermal Load in Fog. Meteorology 3:83– 96. https://doi.org/10.3390/meteorology3010004. Krüger EL, Vieira Silva TJ, Silveira Hirashima SQ, Cunha EG, Rosa LA (2021) Calibrating UTCI'S comfort assessment scale for three Brazilian cities with different climatic conditions. Int J Biometeorol 65:1463–1472. https://doi.org/10.1007/s00484-020-01897-x Lim CL (2020) Fundamental Concepts of Human Thermoregulation and Adaptation to Heat: A Review in the Context of Global Warming. Int J Environ Res Public Health 17, 7795, https://doi.org/10.3390/ijerph17217795 Mészáros E (2001) A Brief History of Earth. Past, Present. Future. Vince Publishing, Budapest, 167 pp (in Humgarian). Milošević D, Savić S, Marković V, Arsenović D, Šećerov I (2016) Outdoor human thermal comfort in local climate zones of Novi Sad (Serbia) during heat wave period. Hung. Geogr. Bull. 65(2): 129–137. https://doi.org/0.15201/hungeobull.65.2.4 Motlogeloa O, Fitchett JM (2023) Climate and Human Health: a review of publication trends in the International Journal of Biometeorology. Int J Biometeorol 67: 933–955, https://doi.org/10.1007/s00484-023-02466-8 Nastos PT, Matzarakis A (2012) The effect of air temperature and human thermal indices on mortality in Athens, Greece. Theor Appl Climatol 108: 591–599. https://doi.org/10.1007/s00704-011-0555-0. Radinović D (1969) Weather analaysis. Institute for Publishing Textbooks of the Socialist Republic of Serbia, Belgrade, 367 pp (in Serbian) Rovelli, C (2019) Reality is not what we see it to be, 2nd edition, Park Book Publishing, Budapest, 239 pp (in Hungarian). ISBN 978-963-633-107-8 Schiller G (2001) Biometeorology and recreation in east Mediterranean forests. Landsc Urban Plan 57(1):1–12, https://doi.org/10.1016/S0169-2046(01)00182-7 Utczás K, Zsákai A, Muzsnai Á, Fehér VP, Bodzsár É (2015) The analysis of bone age estimations performed by radiological and ultrasonic methods in children aged between 7–17 years (in Hungarian). Anthrop Közl 56:129–138. https://doi.org/10.20330/AnthropKozl.2015.56.129 Zsákai A, Bodzsár É (2016) The relationship between reproductive ageing and the changes of bone structure in women (in Hungarian). Anthrop Közl 57:77–84. https://doi.org/10.20330/AnthropKozl.2016.57.77. Yard EE, Gilchrist J, Haileyesus T, Murphy M (2010) Heat illness among high school athletes—U.S., 2005–2009. J Safety Res 41(6):471–474 Supplementary Files SupplementaryMaterialinputoutputdataclearskyfog.xlsx Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4085090","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":288699200,"identity":"11917293-5fbf-4ff9-b72d-57709c19b209","order_by":0,"name":"Ferenc Ács","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA0klEQVRIiWNgGAWjYHACxgdwJohlQIQWZoSihATitLBJkKaFv/34s4ofNTb2/LMPMD5I/GHDYC6RgF+LxJkcs5s9x9ISZ5xLYDZISEhjsJxBQAvDDR622wxshxMYzgBdmJBwmMHgBgEt8jfYnxUz/PtvL3+Ggf1HQsJ/wloMbjCYMTO2HWDcALQF6P0DhLUYnskxluztS07ceIaxWSIhLZnH4MwD/Frkjh9/+OHHNzt7uTPMBz98sLGTMzhOwBYkwNgAInmIVj8KRsEoGAWjADcAAExGQi57n3NqAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0000-0002-1611-6839","institution":"Eötvös Loránd Tudományegyetem: Eotvos Lorand Tudomanyegyetem","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Ferenc","middleName":"","lastName":"Ács","suffix":""},{"id":288699201,"identity":"6f76965a-d028-4c37-889a-45ff8f5566b0","order_by":1,"name":"Erzsébet Kristóf","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Erzsébet","middleName":"","lastName":"Kristóf","suffix":""},{"id":288699202,"identity":"4cb53b06-ff79-430a-9443-5c6cc1aff437","order_by":2,"name":"Annamária Zsákai","email":"","orcid":"","institution":"","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Annamária","middleName":"","lastName":"Zsákai","suffix":""}],"badges":[],"createdAt":"2024-03-12 15:22:12","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4085090/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4085090/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":54521563,"identity":"4d724d28-a6cc-4ca6-a90d-8603e3990d83","added_by":"auto","created_at":"2024-04-11 18:15:45","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":952834,"visible":true,"origin":"","legend":"\u003cp\u003eTopographical map of Hungary and Martonvásár (47.31⁰ N, 18,79⁰ E), the location of weather observations during foggy and clear sky mornings\u003c/p\u003e","description":"","filename":"FIG1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/ee57922c3b4a8fde7335f9b5.jpg"},{"id":54520953,"identity":"c24b17e8-c396-461c-b1fd-a621e9e05a73","added_by":"auto","created_at":"2024-04-11 18:07:45","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":250876,"visible":true,"origin":"","legend":"\u003cp\u003ePoint cloud representing the dependence of the basal metabolic heat flux density of men (blue) and women (red) on body mass index BMI. The points of persons 1 (circle), 2 (triangle), and 3 (cross) (Table 1) are marked in black. Sources of the data: Utczás et al. (2015), Zsákai and Bodzsár (2016), and Fehér et al. (2019).\u003c/p\u003e","description":"","filename":"FIG2.png","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/c6eedf5f450896b2b4ccbad5.png"},{"id":54521562,"identity":"00762594-7411-41d1-a629-76d510e630dc","added_by":"auto","created_at":"2024-04-11 18:15:45","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":151389,"visible":true,"origin":"","legend":"\u003cp\u003eScatter chart of the clothing thermal resistance of person 1 walking at a speed of 1.1 ms\u003csup\u003e-1\u003c/sup\u003e as a function of operative temperature on foggy and cloud-free mornings.\u003c/p\u003e","description":"","filename":"FIG3.png","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/3aba7215f38bea7c55364d4b.png"},{"id":54520951,"identity":"5e4396eb-cabc-40ad-8725-2205551541cc","added_by":"auto","created_at":"2024-04-11 18:07:45","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":290815,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of clothing thermal resistance values referring to persons 2 and 1 (blue) and persons 3 and 1 (green) on cloud-free mornings. Their walking speed is 1.1 ms\u003csup\u003e-1\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"FIG4.png","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/dd44bc0c62038bb593fd5d38.png"},{"id":54520956,"identity":"a8b14236-45dd-457b-87d0-765e428ca97f","added_by":"auto","created_at":"2024-04-11 18:07:46","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":253747,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of clothing thermal resistance values referring to persons 2 and 1 (blue) and persons 3 and 1 (green) on foggy mornings. Their walking speed is 1.1 ms\u003csup\u003e-1\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"FIG5.png","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/3ece85bc2df1f87b441e6bf0.png"},{"id":54520955,"identity":"4e808c7d-11d3-4e0a-b75e-6308756c8136","added_by":"auto","created_at":"2024-04-11 18:07:46","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":296481,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of clothing thermal resistance values obtained on the basis of ε\u003csub\u003ecs\u003c/sub\u003e values estimated by the parameterization of Brunt (1932) and Konzelmann (1994) in the case of clear skies. Anthropometric data refer to person 1 walking at a speed of 1.1 ms\u003csup\u003e-1\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"FIG6.png","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/7b890c1479b815292321a0b6.png"},{"id":58821509,"identity":"3232cb6d-454d-4125-bc5c-9712ad69c690","added_by":"auto","created_at":"2024-06-21 14:46:47","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2984179,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/47e3124b-00b9-4f4e-b78c-b1448090328d.pdf"},{"id":54520957,"identity":"11e71819-d8e9-4658-843f-9bd2da023073","added_by":"auto","created_at":"2024-04-11 18:07:46","extension":"xlsx","order_by":10,"title":"","display":"","copyAsset":false,"role":"supplement","size":25449,"visible":true,"origin":"","legend":"","description":"","filename":"SupplementaryMaterialinputoutputdataclearskyfog.xlsx","url":"https://assets-eu.researchsquare.com/files/rs-4085090/v1/a8cf8818e1b0d7c17a18187b.xlsx"}],"financialInterests":"","formattedTitle":"Comparison of human thermal loads on foggy and cloudless mornings","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe weather in and of itself can be analyzed without taking living beings in regard, that is, objectively, to better understand and discover how the atmosphere works (Radinović, 1968). On the other hand, weather can also be analyzed in terms of its effects on living beings. Planet Earth is living the age of human dominance (M\u0026eacute;sz\u0026aacute;ros, \u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), our approach is human-centric in everything (Rovelli, \u003cspan citationid=\"CR79\" class=\"CitationRef\"\u003e2019\u003c/span\u003e), so we are mostly interested in finding out how weather affects people\u0026rsquo;s lives (Lim, \u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e2020\u003c/span\u003e). This impact can be approached in a broader sense, for instance, by thinking of industries such as tourism (Kov\u0026aacute;cs, \u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e2014\u003c/span\u003e), health (Motlogeloa and Fitchett, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2023\u003c/span\u003e), recreation (Schiller, \u003cspan citationid=\"CR81\" class=\"CitationRef\"\u003e2001\u003c/span\u003e), but it can also be narrowed down, directly to the lives\u0026rsquo; of people (Blazejczyk and Krawczyk, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). The thermal load of weather is a direct and obvious effect and determines people's daily lives. The thermal load of the weather can only be fully characterized by analyzing the energy balance of the human body (Blazejczyk and Krawczyk, \u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e1994\u003c/span\u003e). Energy balance-based methods have mostly been used in two types of studies: human comfort studies (Guly\u0026aacute;s et al., \u003cspan citationid=\"CR42\" class=\"CitationRef\"\u003e2006\u003c/span\u003e; K\u0026aacute;ntor et al., \u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) studies dealing with weather situations of extreme thermal load (Bašarin et al., \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). Extreme thermal load can be extreme heat excess (Bašarin et al., \u003cspan citationid=\"CR23\" class=\"CitationRef\"\u003e2020\u003c/span\u003e) and/or extreme heat deficit (Auliciems and de Freitas, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1976\u003c/span\u003e). Former studies have become more widespread than the latter ones since it was discovered that extreme heat loads could be correlated with deaths (Nastos and Matzarakis, \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2012\u003c/span\u003e) and illnesses (Motlogeloa and Fitchett, \u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e2023\u003c/span\u003e; Yard et al., \u003cspan citationid=\"CR89\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). The study of human reactions induced by heat stress (e.g. thermal perception, sweating) is less widespread, as this would involve examining many people due to the high individual variability. Measuring and observing reactions requires a careful procedure even in the case of one person (\u0026Aacute;cs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e, \u0026Aacute;cs et al., \u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e2024\u003c/span\u003e). To avoid having to investigate a lot of people, the concept of \"reference human\" is used in human biometeorological modeling.\u003c/p\u003e \u003cp\u003eIn this study, we focus on weather situations that cause a lack of heat. This is during anticyclonic weather conditions in continental areas in the autumn and winter mornings. This is when the continental areas are the coldest. Mornings can be foggy, cloudy and completely cloudless with clear skies. We focus on fog and cloudless situations in order to compare the thermal loads of these situations. These thermal loads are estimated for not one, but three different persons, so we can compare the effect of individual human variability with the effect caused by weather differences. To the best of our knowledge, no one has yet conducted such an investigation.\u003c/p\u003e \u003cp\u003eThe aim of this study is to estimate the human thermal load 1) under clear sky conditions and 2) in fog during autumn and winter mornings and 3) to estimate the heating effect of fog based on a comparison of the thermal loads obtained in the former situations, as well as to 4) test the sensitivity of human thermal load to interpersonal variability among people. The model we used in our study is a clothing thermal resistance (r\u003csub\u003ecl\u003c/sub\u003e)\u003cb\u003e\u0026ndash;\u003c/b\u003eoperative temperature (T\u003csub\u003eo\u003c/sub\u003e) model. The r\u003csub\u003ecl\u003c/sub\u003e-T\u003csub\u003eo\u003c/sub\u003e model was chosen due to its simplicity and also because it is suitable for investigating the effect of human interpersonal variability on human thermal load. The observations were carried out in the lowland region of the Carpathian Basin.\u003c/p\u003e"},{"header":"2. Materials and methods","content":"\u003cp\u003eIn the following, we briefly describe the model and the parameterizations of the clear sky emissivity used, as well as provide basic information about documenting morning weather situations (fog or clear sky).\u003c/p\u003e \u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. The clothing thermal resistance-operative temperature model\u003c/h2\u003e \u003cp\u003eThe basic equations of the model are the equations of the thermal resistance of clothing and the operative temperature, which can be derived from the energy balance of the human body covered with clothing,\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${r}_{cl}= \\rho \\bullet {c}_{p}\\bullet \\frac{{T}_{S}- {T}_{o}}{M- \\lambda {E}_{sd}- \\lambda {E}_{r}-{H}_{r}- W}- {r}_{Hr},$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equa\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equa\" name=\"EquationSource\"\u003e\n$${T}_{o}= {T}_{a}+ \\frac{{R}_{ni}}{\\rho \\bullet {c}_{p}}\\bullet {r}_{Hr}, \\left(2\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003ewhere ρ is air density [kgm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e], c\u003csub\u003ep\u003c/sub\u003e is specific heat at constant pressure [Jkg\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e\u0026deg;C\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e], T\u003csub\u003eS\u003c/sub\u003e is skin temperature (34\u0026deg;C) (Campbell and Norman, 1997), r\u003csub\u003eHr\u003c/sub\u003e is combined resistance for expressing thermal radiative and convective heat exchange effect [sm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e], M is metabolic heat flux density [Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e], it refers to a person walking at a speed of 1.1 ms\u003csup\u003e-1\u003c/sup\u003e. λE\u003csub\u003esd\u003c/sub\u003e is latent heat flux density of dry skin [Wm\u003csup\u003e-2\u003c/sup\u003e], λE\u003csub\u003er\u003c/sub\u003e is respiratory latent heat flux density [Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e], H\u003csub\u003er\u003c/sub\u003e is respiratory sensible heat flux density [Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e], and W is mechanical work flux density [Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e], T\u003csub\u003ea\u003c/sub\u003e is air temperature at a height of 2 m [\u0026deg;C] and R\u003csub\u003eni\u003c/sub\u003e is isothermal net radiation [Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e]. It should be mentioned that r\u003csub\u003ecl\u003c/sub\u003e is usually expressed in units of [clo], 1 [clo]\u0026thinsp;=\u0026thinsp;0.155 m\u003csup\u003e2\u003c/sup\u003e\u0026middot;K\u0026middot;W\u003csup\u003e-1\u003c/sup\u003e. If r\u003csub\u003ecl\u003c/sub\u003e/(ρ\u0026middot; c\u003csub\u003ep\u003c/sub\u003e)\u0026thinsp;=\u0026thinsp;1 [clo], then r\u003csub\u003ecl\u003c/sub\u003e = 1.2 [kgm\u003csup\u003e-3\u003c/sup\u003e] \u0026middot; 1004 [Jkg\u003csup\u003e-1\u003c/sup\u003eK\u003csup\u003e-1\u003c/sup\u003e] \u0026middot; 0.155 [m\u003csup\u003e2\u003c/sup\u003e\u0026middot;K\u0026middot;W\u003csup\u003e-1\u003c/sup\u003e]\u0026thinsp;=\u0026thinsp;186.74 [sm\u003csup\u003e-1\u003c/sup\u003e]. Both parameters characterize the thermal load of the air, the former through the thermal insulation of clothing, while the latter through an integrated temperature (dimension ℃) value. The parameterization of r\u003csub\u003eHr\u003c/sub\u003e, R\u003csub\u003eni\u003c/sub\u003e, M, λE\u003csub\u003esd\u003c/sub\u003e, λE\u003csub\u003er\u003c/sub\u003e, H\u003csub\u003er\u003c/sub\u003e and W can be found in the work of Krist\u0026oacute;f et al. (\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Parameterization of clear sky emissivity\u003c/h2\u003e \u003cp\u003eThere are many parameterizations for clear-sky emissivity (Guly\u0026aacute;s, \u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e2018\u003c/span\u003e). There are parameterizations that depend a) only on air temperature, b) only on water vapor pressure and c) on both air water vapor pressure and temperature. We chose a parametrization from the latter two methods, namely Brunt (\u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1932\u003c/span\u003e) (it depends only on partial water vapor pressure), and Konzelmann et al. (\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e1994\u003c/span\u003e) (it depends on both partial water vapor pressure and temperature) formulae,\u003cdiv id=\"Equb\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equb\" name=\"EquationSource\"\u003e\n$${ϵ}_{cs}=0.51+0.066\\bullet \\sqrt{{e}_{a}} , \\left(3\\right)$$\u003c/div\u003e\u003c/div\u003e\u003cdiv id=\"Equc\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equc\" name=\"EquationSource\"\u003e\n$${ϵ}_{cs}=0.23+0.4393\\bullet {\\left( \\frac{{e}_{a}}{{T}_{a}}\\right)}^{\\frac{1}{7}}, \\left(4\\right)$$\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003ewhere e\u003csub\u003ea\u003c/sub\u003e is partial water vapor pressure in air (in Brunt's formula in [hPa), while in Konzelmann et al.\u0026rsquo;s formula in [Pa]) and T\u003csub\u003ea\u003c/sub\u003e is air temperature at a height of 2 m in [K].\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. Documenting atmospheric conditions on foggy and clear sky mornings\u003c/h2\u003e \u003cp\u003eObservations were made between 2019 and 2023 (we have only two observations in 2017 for the fog). Data collection was carried out in the autumn and winter months: October, November, December, January and February. In the case of fog, we also had an observation on September 27. The morning period is from 6 to 10 a.m. in the case of fog, and from 5 to 8 a.m. in the case of clear skies. In the case of clear skies, we had one observation that was between 1 and 2 o'clock. In both cases, the vast majority of the observations took place between 6 and 8 o'clock. The atmospheric conditions are characterized by the following meteorological elements: air temperature, relative sunshine duration, cloud cover, wind gust speed, average wind speed, relative humidity and air pressure. The values of the meteorological elements are average values for a 10 minute time interval. Global radiation was also documented by entering the values of the parameters Q\u003csub\u003e0\u003c/sub\u003e, α (Krist\u0026oacute;f et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e; Eq.\u0026nbsp;(15)). Q\u003csub\u003e0\u003c/sub\u003e and α values are hourly values, and they refer to the hour interval during which the observation took place.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e2.4 Location\u003c/h2\u003e \u003cp\u003eThe region and the location of the observations can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eMartonv\u0026aacute;s\u0026aacute;r is a small lowland town in the Central Transdanubian region of Hungary, about 30 km southwest of Budapest, Hungary. According to Feddema (\u0026Aacute;cs et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2015\u003c/span\u003e), the climate of Martonv\u0026aacute;s\u0026aacute;r is \"cool, dry, with extreme temperature fluctuations\", the annual clothing thermal resistance value is around 0.4-1.0 clo (\u0026Aacute;cs et al., \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2020\u003c/span\u003e, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). However, the weather can cause a much greater lack of heat in the winter season, when the thermal resistance values of clothing can be higher than 3 clo (\u0026Aacute;cs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Data","content":"\u003cp\u003eWe used anthropometric and weather data. These are briefly described below.\u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Anthrophometric data\u003c/h2\u003e \u003cp\u003eThere is a Hungarian anthropometric database (Utcz\u0026aacute;s et al., \u003cspan citationid=\"CR83\" class=\"CitationRef\"\u003e2015\u003c/span\u003e; Zs\u0026aacute;kai and Bodzs\u0026aacute;r, \u003cspan citationid=\"CR86\" class=\"CitationRef\"\u003e2016\u003c/span\u003e; Feh\u0026eacute;r et al., 2019) with the anthropometric data of more than 2,000 children and more than 1,000 adults. The dataset is a product of the Department of Biological Anthropology, E\u0026ouml;tv\u0026ouml;s Lor\u0026aacute;nd University, Budapest, Hungary. We also calculated M\u003csub\u003eb\u003c/sub\u003e and body mass index (BMI) values from the measured and queried data. From the database, we selected the data of three people among whom the individual deviation is quite large, these data (body mass, body length, sex and age) together with the M\u003csub\u003eb\u003c/sub\u003e values are illustrated in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eAnthropometric data and M\u003csub\u003eb\u003c/sub\u003e values of the 3 selected persons.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePerson\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSex\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAge\u003c/p\u003e \u003cp\u003e[Years]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eBody Mass\u003c/p\u003e \u003cp\u003e[kg]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eBody Length\u003c/p\u003e \u003cp\u003e[cm]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBasal Metabolic Heat Flux Density\u003c/p\u003e \u003cp\u003e[W\u0026nbsp;m\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eperson 1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e68\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e39.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eperson 2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e41.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eperson 3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003emale\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e24\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e120\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e179\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e45.93\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWe chose the persons in such a way that shows individual variability as much as possible. It should be mentioned that the weather observations were made by person 1.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.2. Weather data\u003c/h2\u003e \u003cp\u003eWhen the Carpathian region is dominated by an anticyclone, two opposite weather situations can develop: 1) cloudless weather with a clear sky and 2) fog, weather characterized by fog. We collected data on these two weather types in autumn and winter mornings, when the environmental heat deficit is greatest. As mentioned, we used the following meteorological elements for characterizing thermal load of weather: air temperature, relative sunshine duration, cloud cover, wind gust speed, average wind speed, relative humidity of air and air pressure. The values of the elements, with the exception of relative sunshine duration and cloudiness, were taken from the HungaroMet website (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://www.met.hu/en/idojaras/aktualis_idojaras/megfigyeles/\u003c/span\u003e\u003cspan address=\"https://www.met.hu/en/idojaras/aktualis_idojaras/megfigyeles/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e) and transcribed into the database. The beeline distance between the station and the observer\u0026rsquo;s location (garden of a family house) is shorter than 3 km. Relative sunshine duration and cloudiness were observed. Cloudiness is estimated visually in tenths. Their values refer to the same 10 min period as the HungaroMet data. The radiation parameter (Q\u003csub\u003e0\u003c/sub\u003e and α) values are hourly values and refer to the hour in which the observation took place. The input data are available in Tables S1 and S2 of the Supplementary Material separately for clear skies and fog, respectively. A total of 123 observations were made (77 in the case of fog and 45 in the case of clear skies). Our regular observations lasted from October 26, 2019 to February 21, 2023, and we also have 2 observations from 2017. The most important features of the two weather types are presented below.\u003c/p\u003e \u003cdiv id=\"Sec10\" class=\"Section3\"\u003e \u003ch2\u003e3.2.1 Weather on foggy mornings\u003c/h2\u003e \u003cp\u003eThe air temperature varied between \u0026minus;\u0026thinsp;5.5 and 12.0 ℃, but in the vast majority of cases it occurred between \u0026minus;\u0026thinsp;2 and 6 ℃. The global radiation was very low, it was never higher than 110 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, and in the vast majority of cases it was lower than 50 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. The relative humidity of the air is by definition 100% or very close to 100%. In fog, wind speeds are usually lower (below 1.5 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), but values higher than 2.5 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e can occur. Air pressure was less than 1013 hPa in 10% of the cases (8 cases in total).\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section3\"\u003e \u003ch2\u003e3.2.2 Weather on cloudless mornings\u003c/h2\u003e \u003cp\u003eThe air temperature varied between \u0026minus;\u0026thinsp;12.7 and 13.3 ℃. The morning times for these temperatures are 5:00 a.m. and 9:30 a.m., respectively. 65% of the temperature values are less than 0 ℃. The global radiation varied between 0-250 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, but the number of values greater than 200 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e was only 2. The global radiation was equal to 0 in 15 cases (33% of the cases). Cloud cover varied between 0 and 0.2. It was 0.2 in three cases and 0.1 twice. The relative humidity of the air varied between 72 and 100 percent. Relative humidity was greater than 90% in 69 percent of the cases (31 cases in total). In the vast majority of the cases, the wind speed was low (less than 1.5 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e). Only in 1 case (on February 21, 2023 at 8:30 a.m.) was there a stormy wind (gust speed 12.2 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e, average wind speed 7.8 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), but even then the weather situation was not anticyclonic.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cp\u003eWe will examine the thermal load of foggy and clear sky mornings by analyzing the r\u003csub\u003ecl\u003c/sub\u003e and r\u003csub\u003ecl\u003c/sub\u003e\u003cb\u003e\u0026ndash;\u003c/b\u003eT\u003csub\u003eo\u003c/sub\u003e relationship. We will separately analyze a) the thermal load of foggy and b) clear sky mornings, c) the heating effect of fog, d) the sensitivity of thermal loads to human variability and e) the sensitivity of thermal load to the parameterization of clear sky emissivity. Before discussing these subsections, we will also talk about human variability by analyzing the individual M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI relationships.\u003c/p\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.1. The M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI relationship\u003c/h2\u003e \u003cp\u003eThe M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI value pair is unique for each person. Therefore, M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI value pairs can be used to examine human variability. The point clouds of M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI relationships for men and women, based on the use of data from the Hungarian anthropometric database, can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe M\u003csub\u003eb\u003c/sub\u003e\u0026ndash;BMI points of the 3 selected persons are marked in black in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. It is clear that small BMI values (values around 15 kgm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) are represented by children. In the range of BMI\u0026thinsp;\u0026le;\u0026thinsp;25 kgm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, 75% of the points refer to children and 25% to adults. Based on these, it is clear that the 3 selected adults are markedly different, even though the difference between their M\u003csub\u003eb\u003c/sub\u003e values is less than 7 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e. However, it is worth noting that the difference of 7 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e means a relative difference of 18%.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Thermal load of foggy and cloud-free mornings\u003c/h2\u003e \u003cp\u003eThe point cloud representing the r\u003csub\u003ecl\u003c/sub\u003e\u003cb\u003e\u0026ndash;\u003c/b\u003eT\u003csub\u003eo\u003c/sub\u003e relationship of foggy and cloud-free mornings can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e1.1 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e as a function of operative temperature on foggy and cloud-free mornings.\u003c/h2\u003e \u003cp\u003eFoggy cases are marked with dark blue, while clear sky cases are marked with light blue. In foggy situations, r\u003csub\u003ecl\u003c/sub\u003e varied between 0.5 and 2.5 clo, but in the vast majority of the cases the values were between 1.25 and 2.0 clo. These values refer to the observer (person 1) who is walking at a speed of 1.1 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. Note that in only three cases was the r\u003csub\u003ecl\u003c/sub\u003e smaller than 1 clo.\u003c/p\u003e \u003cp\u003eIn cloud-free cases, the r\u003csub\u003ecl\u003c/sub\u003e values varied between 0.9 and 3.5 clo. We had only 2 cases, when r\u003csub\u003ecl\u003c/sub\u003e was equal to or less than 1 clo. We can see that most of the r\u003csub\u003ecl\u003c/sub\u003e values are greater than 1.9 clo. We also have a point with a value of 4.1 clo (the associated T\u003csub\u003eo\u003c/sub\u003e value is -30.7 ℃), this does not refer to Martonv\u0026aacute;s\u0026aacute;r, but to the B\u0026uuml;kk Mountains. We will refer to this point later in Section \u003cspan refid=\"Sec19\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.3. The heating effect of fog during mornings\u003c/h2\u003e \u003cp\u003eThe main difference between clear sky and foggy mornings is in the cloudiness values. In both cases, wind is usually weak and the relative air humidity is high or very high. The radiation balance is obviously different: in the case of a clear sky it is much lower (usually between 0 and \u0026minus;\u0026thinsp;100 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) than in fog (usually between \u0026minus;\u0026thinsp;20 and 10 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) (Tables S1 and S2 of the Supplementary Materials). As a result, air temperature will also be lower in cloudless mornings than in foggy mornings. The resulting difference in radiation and temperature also results in different thermal loads.\u003c/p\u003e \u003cp\u003eIn our case, thermal load is expressed in terms of r\u003csub\u003ecl\u003c/sub\u003e. Comparing the r\u003csub\u003ecl\u003c/sub\u003e values obtained on foggy and cloudless mornings, we can get an insight on how large the heating effect of fog can be. This is obviously an indirect, general estimation of the heating effect of fogs during mornings, which is based on the consideration outlined above. Our reasoning is confirmed by the fact that r\u003csub\u003ecl\u003c/sub\u003e values obtained on cloudless and foggy mornings are clearly shifted, even if they overlap. The shift of the light-blue points (cloud-free cases) compared to the dark-blue points (foggy cases) is clearly noticeable (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). This shift can also be interpreted as a warming effect of the fog. It amounts to 1-1.5 clo, or in terms of the absolute values of T\u003csub\u003eo\u003c/sub\u003e, it is between 10\u0026ndash;14 ℃. This is, of course, a rough estimate of the average heating effect of morning fogs.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Sensitivity of the r\u003csub\u003ecl\u003c/sub\u003e\u0026ndash;T\u003csub\u003eo\u003c/sub\u003e relationship to human inter-personal variability\u003c/h2\u003e \u003cp\u003eIt is interesting to test the sensitivity of r\u003csub\u003ecl\u003c/sub\u003e\u003cb\u003e\u0026ndash;\u003c/b\u003eT\u003csub\u003eo\u003c/sub\u003e relationship to interpersonal variability of M. We executed this separately for cloudless and foggy mornings, comparing person 1 with persons 2 and 3. These point clouds can be seen in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e in the cloudless case, while in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e in the foggy case.\u003c/p\u003e \u003cp\u003eIt is noticeable that as the lack of heat increases, the r\u003csub\u003ecl\u003c/sub\u003e differences between people also increase. Therefore, the effect of inter-personal variability on r\u003csub\u003ecl\u003c/sub\u003e values is stronger, even significantly, on cloudless mornings compared to foggy mornings. How big is this effect on the people being tested? In Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e (cloudless case), the biggest difference is between people 1 and 3, its value is around 1-1.2 clo (the green point representing the biggest heat deficit), which is around 30% of the actual thermal load. At the same extreme point (comparison of persons 1 and 3 for the highest heat deficit) in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e (foggy case), the r\u003csub\u003ecl\u003c/sub\u003e difference is 0.7\u0026ndash;0.8 clo, that is, it is around 50% less than in the cloud-free case. It should also be mentioned that the investigated personal r\u003csub\u003ecl\u003c/sub\u003e difference in the largest heat deficit (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, green point with the largest heat deficit) has a value of 1-1.2 clo and it is comparable to the heating effect of fog, which we estimated to be around 1-1.5 clo. The smallest r\u003csub\u003ecl\u003c/sub\u003e differences are between people 1 and 2 (blue points), when the heat deficit is the smallest (values around 0.8-1 clo). Its value is 0.1\u0026ndash;0.3 clo, which is around 20% of the thermal load. So we can see that the inter-personal r\u003csub\u003ecl\u003c/sub\u003e differences amount to 10\u0026ndash;30% of the actual heat deficits.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.4. Sensitivity of r\u003csub\u003ecl\u003c/sub\u003e to ε\u003csub\u003ecs\u003c/sub\u003e parameterizations\u003c/h2\u003e \u003cp\u003eThe lack of heat in the mornings is mostly determined by cloudiness. In the case of a cloudless sky, the lack of heat is mostly determined by the temperature and humidity of the air, since downward atmospheric radiation strongly depends on these atmospheric state variables. The emissivity of the clear sky also depends on these state variables, so, it can be parameterized only as a function of air humidity (e.g. Brunt's (1932) formula, Eq.\u0026nbsp;(3)) or as a function of air humidity and temperature (e.g. Konzelmann's (1994) formula, Eq.\u0026nbsp;(4)). The question arises: how sensitive is r\u003csub\u003ecl\u003c/sub\u003e to the parameterization of ε\u003csub\u003ecs\u003c/sub\u003e, naturally, in the case of a cloudless sky? Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e illustrates the sensitivity.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe results refer to person 1 walking at a speed of 1.1 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. The differences between the obtained r\u003csub\u003ecl\u003c/sub\u003e values are very small, below 0.2 clo, and the r\u003csub\u003ecl\u003c/sub\u003e values obtained with formula (3) (Brunt, \u003cspan citationid=\"CR34\" class=\"CitationRef\"\u003e1932\u003c/span\u003e) overestimate, albeit minimally, the r\u003csub\u003ecl\u003c/sub\u003e values obtained with formula (4) (Konzelmann, 1994).\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Discussion","content":"\u003cp\u003eHuman biometeorology deals with the effects of climate and/or weather on humans. In the center is the person who is in a state of comfort or discomfort in the given atmospheric environment. The weather itself is not the subject of investigation, but a person's sense of comfort or discomfort. In this study, the weather is the subject of investigation, more precisely, it is the thermal load of weather on humans. This issue was discussed from the point of view of human comfort (Honjo, \u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e2009\u003c/span\u003e; Milošević et al., \u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e2016\u003c/span\u003e) and/or discomfort (Blazejczyk et al., \u003cspan citationid=\"CR31\" class=\"CitationRef\"\u003e2012\u003c/span\u003e; Nastos and Matzarakis, \u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e2012\u003c/span\u003e), and not or less discussed in relation to typical (Krist\u0026oacute;f et al., \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e2024\u003c/span\u003e) or selected weather situations. There are studies where the focus was on the study of reactions caused by thermal load, such reactions are, for example, thermal sensation (Kr\u0026uuml;ger et al., \u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e2021\u003c/span\u003e; \u0026Aacute;cs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e) or sweating (Havenith et al., 2013).\u003c/p\u003e \u003cp\u003eHuman thermal load depends on both environmental and human factors and since it depends on both factors, it must be calculated from the energy balance of the human body (Katić et al., \u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e2016\u003c/span\u003e). The calculation requires both human (at least 4 types of data: body mass, body length, sex and age) and meteorological (at least 4 types of data: radiation, air temperature, air humidity and wind speed) data, so we can say that the calculation is data intensive. Collecting human data is more difficult than meteorological data. Human data does not only mean anthropometric data, but also includes data characterizing clothing and activity. It should be emphasized that the variability of data characterizing clothing and activity is enormous. Thus, the \"reference human\" was introduced into human biometeorological studies. However, the definition of this \"reference human\" varies by method (\u0026Aacute;cs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). This reduced the data requirements of the models, but made it impossible to examine the sensitivity of thermal load to human variability. However, this is not the case for models based on the use of individual human data (\u0026Aacute;cs et al., \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). In many cases, the use of meteorological data was also reduced (Br\u0026ouml;de et al., \u003cspan citationid=\"CR26\" class=\"CitationRef\"\u003e2012\u003c/span\u003e). This may even be justified in special cases (windchill), but it can also lead to large errors in estimating thermal load (\u0026Aacute;cs et al., \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe full use of data is very important when estimating the thermal load of the weather, especially if the weather is extreme in some respect. In the Carpathian region, there are extreme thermal loads in anticyclonic weather situations. Then, the mornings of the cold season can be dominated by two completely different weather types: cloudless, mostly calm, but very cold weather with clear skies, or fog, in which the air movement is also weak, and the air is warmer and more humid than in the former weather type. To the best of our knowledge, no one has yet investigated the thermal load of these two opposite weather types or compared their thermal loads. Since, based on our model, we can estimate changes in r\u003csub\u003ecl\u003c/sub\u003e values due to changes in atmospheric and human factors, we can compare these two effects, such as the warming effect of fog, and r\u003csub\u003ecl\u003c/sub\u003e changes resulting from human variability. As far as we know, such comparisons have not yet been done, although they are intriguing. We could see that the shift between the r\u003csub\u003ecl\u003c/sub\u003e values of cloudless (clear sky) and foggy morning point clouds is around 1-1.5 clo (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e), and this is comparable to the largest r\u003csub\u003ecl\u003c/sub\u003e value deviations caused by human variability (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e, green dots). Similarly, in the case of a cloudless sky, we can compare the deviations of the r\u003csub\u003ecl\u003c/sub\u003e values obtained by different ε\u003csub\u003ecs\u003c/sub\u003e parameterizations (Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e) with the deviations of r\u003csub\u003ecl\u003c/sub\u003e values obtained by using individual anthropometric data (Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e). In this case, the r\u003csub\u003ecl\u003c/sub\u003e value changes caused by human variability are always larger than the r\u003csub\u003ecl\u003c/sub\u003e value changes caused by parameterizations. We can say that inter-personal differences cannot be neglected when estimating human thermal load on cloudless mornings.\u003c/p\u003e \u003cp\u003eIn our opinion, these human thermal load data can be extended to the entire Great Plain. What are these thermal load values in the mountains of Hungary? In the case of fog, we cannot give an estimate, so we assume that the lack of heat in mountain fogs is not greater than in lowland fogs. However, we can give an estimate of thermal load for cloudless mornings. The biggest differences are in the air temperature, the differences between the values of solar radiation (around zero or zero), air humidity (close to saturation) and wind speed (close to calm conditions) values are very small and negligible. HungaroMet stations have already recorded temperatures of around \u0026minus;\u0026thinsp;20 ℃ in the B\u0026uuml;kk Mountains in winter in the morning hours. We selected such a case (February 13, 2021, 6:30 a.m.), at which time the heat deficit was 4.1 clo (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). In the sinkholes of B\u0026uuml;kk-plateau, temperatures could go down to -30 ℃ (Dobos et al., \u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e2024\u003c/span\u003e), in this case the heat deficit is already around 4.8 clo. These thermal deficit values were experienced by person 1 walking at a speed of 1.1 ms\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e. We can state that the greatest heat deficit values in Hungary are around 5 clo. This experience is extremely individual, subjective, as it is shown in the study.\u003c/p\u003e"},{"header":"7 Conclusion","content":"\u003cp\u003eThe main conclusions of the study are as follows: 1) based on the shift in the r\u003csub\u003ecl\u003c/sub\u003e values of cloudless and foggy mornings, it can be concluded that the warming effect of fogs is around 1-1.5 clo in the morning hours. This heating effect, expressed in T\u003csub\u003eo\u003c/sub\u003e values, is 10\u0026ndash;14 ℃. 2) As the heat deficit increases, the inter-personal differences of r\u003csub\u003ecl\u003c/sub\u003e increase, too. 3) In extreme heat deficit situations (r\u003csub\u003ecl\u003c/sub\u003e \u0026ge; 2.5 clo), the effect of inter-personal variability on r\u003csub\u003ecl\u003c/sub\u003e is comparable to the warming effect of fogs during morning. 4) In the given environmental heat deficit, it may also happen that the r\u003csub\u003ecl\u003c/sub\u003e change caused by inter-personal variability is greater than the r\u003csub\u003ecl\u003c/sub\u003e change caused by the variability of the physical parameter (in our case clear sky emissivity).\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eConflicts of Interest:\u003c/h2\u003e \u003cp\u003eThe authors declare no conflict of interest.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding:\u003c/h2\u003e \u003cp\u003eThis research received no external funding.\u003c/p\u003e\u003ch2\u003eAuthor Contributions:\u003c/h2\u003e \u003cp\u003eConceptualization: F.\u0026Aacute;.; methodology: F.\u0026Aacute;., A.Z.; software: F.\u0026Aacute; and E.K.; validation: F.\u0026Aacute;.; formal analysis: F.\u0026Aacute;., E.K., A.Z.; investigation: F.\u0026Aacute;.; resources: F.\u0026Aacute;, A.Z.; data curation: F.\u0026Aacute;. and A.Z.; writing\u0026mdash;original draft preparation: F.\u0026Aacute;.; writing\u0026mdash;review and editing: F.\u0026Aacute;.; visualization: E.K.; supervision: F.\u0026Aacute;.; project administration: A.Z. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eAuliciems A, de Freitas CR (1976) Cold stress in Canada. A human climatic classification. Int J Biometeorol 20:287\u0026ndash;294. https://doi.org/10.1007/BF01553585\u003c/li\u003e\n\u003cli\u003e\u0026Aacute;cs F, Breuer H, Skarbit N (2015) Climate of Hungary in the twentieth century according to Feddema. Theor Appl Climatol 119:161\u0026ndash;169. https://doi.org/10.1007/s00704-014-1103-5 \u003c/li\u003e\n\u003cli\u003e\u0026Aacute;cs F, Zs\u0026aacute;kai A, Krist\u0026oacute;f E, Szab\u0026oacute; AI, Breuer H (2020) Carpathian Basin Climate according to K\u0026ouml;ppen and a clothing resistance scheme. 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Vince Publishing, Budapest, 167 pp (in Humgarian). \u003c/li\u003e\n\u003cli\u003eMilo\u0026scaron;ević D, Savić S, Marković V, Arsenović D, \u0026Scaron;ećerov I (2016) Outdoor human thermal comfort in local climate zones of Novi Sad (Serbia) during heat wave period. Hung. Geogr. Bull. 65(2): 129\u0026ndash;137. https://doi.org/0.15201/hungeobull.65.2.4 \u003c/li\u003e\n\u003cli\u003eMotlogeloa O, Fitchett JM (2023) Climate and Human Health: a review of publication trends in the International Journal of Biometeorology. 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J Safety Res 41(6):471\u0026ndash;474\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"human thermal load, foggy mornings and clear sky mornings, Hungarian lowland, comparison, thermal resistance of clothing, operative temperature, human data","lastPublishedDoi":"10.21203/rs.3.rs-4085090/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4085090/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eWe investigated the human thermal load in Martonv\u0026aacute;s\u0026aacute;r (Hungarian lowland, Carpathian region) in anticyclonic weather conditions in the morning, when a) the sky was completely clear and on the other hand, when b) there was fog. A customizable clothing thermal resistance-operative temperature model was used. The BMI and M\u003csub\u003eb\u003c/sub\u003e values of the person in the simulations were 25 kgm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e and 40 Wm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, respectively. During the observations, weather data was provided by the automatic station of the HungaroMet company and it was accessible on the company's website. We had 77 observations in foggy weather, while we had 46 observations under clear sky conditions in the period between 2019\u0026ndash;2023. The following main results should be highlighted: 1) r\u003csub\u003ecl\u003c/sub\u003e varied between 0.5\u0026ndash;2.5 clo in the case of fog, while in clear-sky cases r\u003csub\u003ecl\u003c/sub\u003e was between 0.9\u0026ndash;3.5 clo. Based on our data analysis, we concluded that the warming effect of the morning fog was around 1-1.5 clo. 3) We also showed that the effect of inter-personal variability on r\u003csub\u003ecl\u003c/sub\u003e was significant when the heat deficit was high (r\u003csub\u003ecl\u003c/sub\u003e \u0026ge; 2.5 clo) and at this time it was comparable with the degree of the warming effect of fog. It should be mentioned that the analysis of typical weather situations from the point of view of human thermal load is a new field of research, since there is little information available on this subject.\u003c/p\u003e","manuscriptTitle":"Comparison of human thermal loads on foggy and cloudless mornings","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-04-11 18:07:40","doi":"10.21203/rs.3.rs-4085090/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"ca2ff802-81f7-4a02-b653-36f3605cb898","owner":[],"postedDate":"April 11th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-06-07T18:17:25+00:00","versionOfRecord":[],"versionCreatedAt":"2024-04-11 18:07:40","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4085090","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4085090","identity":"rs-4085090","version":["v1"]},"buildId":"7rjqhiLT3MXkJMwkYKINL","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}