Human thermal climate of the Carpathian Basin

A human body–clothing–atmosphere environment system energy balance model is constructed to evaluate individual human thermal climates in the Carpathian Basin. The analysis is performed in terms of clothing resistance and operative temperature for the period 1971–2000. The model's main strength is that it simulates the metabolic activity rate M as simply as possible taking into account interpersonal variations. Non‐sweating, walking humans are considered in natural outdoor conditions at a walking speed of 4 km⋅h−1. Atmospheric data are used from the CarpatClim dataset; human data are taken from a Hungarian human dataset. The dataset reveals that the interpersonal variations of M of walking humans can reach 40–50 W⋅m−2. According to the results, the variability of individual human thermal climates can be significant. This variability increases towards cold climates and is less in the comfortable thermal zone, when the operative temperature is between 23 and 28°C. It should be mentioned that summer is thermally neutral in the Little Hungarian Plain, the Great Hungarian Plain and in larger parts of the Transylvanian Plateau, irrespective of the person considered. The warmest areas in the Carpathian Basin can be found in Bačka and Banat. In terms of thermal sensation, the results obtained agree well with the results referring to the human considered in the Physiological Equivalent Temperature index model.

In this study, we will focus on the Carpathian Basin because of its unique ecological and climate features (Metzger et al., 2005;Borhidi et al., 2013;Acs et al., 2015). Its climate is mostly investigated by means of vegetation based methods (e.g., Réthly, 1933;Acs and Breuer, 2013;Szelepcsényi et al., 2014). The vast majority of humanbased methods consider human body energy balance equations characterizing the environmental thermal load as simply as possible via thermal indices as, for instance, PMV (Predicted Mean Vote) (Fanger, 1970), PET (Physiological Equivalent Temperature) (Mayer and Höppe, 1987;Höppe, 1999), UTCI (Universal Thermal Climate Index) Fiala et al., 2011), PT (Perceived Temperature) , HL (Heat Load Index) (Błażejczyk and Krawczyk, 1994). Among these PET (Matzarakis et al., 1999) obtained great popularity. PET is used in the Pannonian Basin for its Hungarian (Matzarakis and Gulyás, 2006;Gulyás and Matzarakis, 2009) and Serbian (Basarin et al., 2014) parts. It should be mentioned that in addition to PET (Stoji cevi c et al., 2016), UTCI (Basarin et al., 2018) and HL (Heat Load) indices are also applied (Pecelj et al., 2017) in Serbia's mountainous regions. Similar human bioclimate analyses are also made in mountainous and coastal regions of Croatia (Zaninovi c et al., 2006;Zaninovi c and Matzarakis, 2007;Zaninovi c and Matzarakis, 2009). Energy balance based human bioclimate analyses referring to the whole Carpathian Basin, including the Carpathians are very rare ( Acs et al., 2020). The study of Acs et al. (2020) is a comparative analysis. The Köppen climate map and the maps representing the annual mean and fluctuation of clothing resistance are compared and discussed in detail. The Serbian (e.g., Stoji cevi c et al., 2016;Pecelj et al., 2017;Basarin et al., 2018) and Croatian (e.g., Zaninovi c et al., 2006) studies mentioned above discussed only human thermal climate aspects at different locations (cities or mountains). In these studies, in the vast majority PET and UTCI indices are used. Many of these studies aim to apply human bioclimatological information in the industry of human health, well-being (e.g., recreation) and tourism, so, there was a rapid rise in the appearance of energy balance based methods after 2010 (Potchter et al., 2018). PET is the most popular bioclimatic index, followed by PMV (Predicted Mean Vote) and UTCI (Potchter et al., 2018). Software calculating PET  can consider different humans, but PET is always calculated for a 35 year old man with a body weight of 75 kg, a body length of 175 cm, who possesses a typical indoor setting of 0.9 (clo) and has metabolic heat production of about 80 WÁm −2 (Yang and Matzarakis, 2016). It should be mentioned that the human chosen in PET is very similar to the UTCI-Fiala model human in UTCI (Błażejczyk et al., 2010;Fiala et al., 2011;Błażejczyk et al., 2013). The main difference between them is in their garments and metabolic heat production. To our knowledge, the interpersonal variability effect on human thermal load has not been considered to date.
In our days, there are more than 100 registered human thermal climate indices (e.g., de Freitas and Grigorieva, 2015;Potchter et al., 2018). The principles that guided us in choosing the model are as follows: (a) it should take into account the effects of all relevant environmental variables, (b) it should take into account interpersonal variations as much as possible, (c) it should be as simple as possible. Along these requirements, we decided to use two human thermal climate indicators: the operative temperature T o and the clothing resistance r cl . The problems related to the estimation of clothing resistance are avoided by using it as model output. The aims of this study are as follows: (a) to characterize the Carpathian Basin climate in terms of operative temperature and clothing resistance, (b) to present the physics of the human body-clothing-air environment energy balance model due to its novel characteristics and (c) to show the importance of the interpersonal variability effect on the formation of clothing resistance. Atmospheric and human data are used in the analysis. Atmospheric data are taken from the CarpatClim dataset referring to the 1971-2000 period. Their brief description is given in Section 2.2. Human data are provided from a Hungarian human dataset (Utczás et al., 2015;Zsákai et al., 2015;Bodzsár et al., 2016). The dataset is briefly presented in Section 2.3. The physics of the model together with the first preliminary thermal perception results are presented in the Appendix. The results are presented in Section 3; the r cl -T o relationships in Section 3.1, the area distributions of r cl in Section 3.2 and the comparison of r cl with PET in Section 3.3. Short discussion can be found in Section 4. Concluding remarks are given in Section 5.

| METHODS AND DATA
There are many methods for characterizing the human thermal climate (Potchter et al., 2018). All of them try to be as simple as possible, therefore they use different indices. In this work, a clothed human body-air environment energy balance model is used for characterizing the human thermal environment in terms of clothing resistance and operative temperature. The model and the first thermal sensation estimations are presented in the Appendix.

| Basic equations
The main outputs of the model, namely clothing resistance r cl (sÁm −1 ) and operative temperature T o ( C) can be treated as indices because they are good indicators of thermal load. They are as follows: where ρ is air density (kgÁm −3 ), c p is specific heat at constant pressure (JÁkg −1 ÁC −1 ], r Hr is combined resistance for expressing the thermal radiative and convective heat exchanges (sÁm −1 ), T S is skin temperature ( C) (a constant, 34 C), T a is air temperature ( C), R ni is isothermal net radiation flux density (WÁm −2 ), M is metabolic heat flux density (WÁm −2 ), λE sd is the latent heat flux density of dry skin (WÁm −2 ), λE r is respiratory latent heat flux density (WÁm −2 ) and W is mechanical work flux density (WÁm −2 ) referring to the activity under consideration. M refers to a walking human in outdoor conditions with a reference speed of 1.1 mÁs −1 (4 kmÁh −1 ). The effect of radiation and convection on human thermal load can be expressed in one parameter, the operative temperature. As it can be seen, there are two expressions for this: in the first, T o depends only upon environmental variables, in the second it depends upon both the human (e.g., clothing resistance) and environmental variables. Of course, both expressions give the same result. In this study, r cl is viewed as a thermal regulator. Note that in previous studies (e.g., De Freitas, 1979;Havenith et al., 2012) r cl is treated as a thermal insulation rate parameter. Viewing r cl as a thermal regulator means the following: if there is heat excess, the human body needs cooling to reach energy balance. In this case, r cl values are negative. Inversely, if there is heat deficit, the human body needs warming to reach energy balance. In this case, r cl values are positive. When the human body is in energy balance, needing neither cooling nor warming and sensing this state as comfortable. In this case r cl is very close or equal to zero. In this sense, r cl can be called a 'Thermal Equilibrium Clothing Index'. This interpretation of r cl is new.

| Region and climatic data
The region studied is the region of the CarpatClim dataset ( Figure 1) located between the 17 and 27 /44 and 50 longitude/latitude lines. The data chosen refer to the period 1971-2010; the temporal and spatial resolutions used are 1 day and 0.1 × 0.1 (about 10 km × 10 km).
The observed data collected from 643 stations (288 climatological stations and 355 precipitation stations) are quality controlled and homogenized. The region contains 6,161 grid points representing the Carpathian Basin almost completely. A Carpathian-Basin region climate analysis from the point of view of the CarpatClim dataset can be found in the work of Spinoni et al. (2015). In this study, the CarpatClim data used are as follows: global radiation, cloud cover, air temperature, vapour pressure and 10 m wind speed. Monthly data are calculated from daily data; 30-year means are created from the monthly data of the period 1971-2000.
In lowland areas of the region, the prevailing climate according to Köppen is the Cfb climate type (C, temperate climate; f, without dry season; b, warm summer). In the Carpathians, the most frequent climate type is Dfb (D, boreal climate), but there are also areas with the climate type ET (ET, polar tundra climate).
F I G U R E 1 The region of the CarpatClim dataset and its basic elevation data and major geographical designations used in the study

| Human datasets
To date, human characteristics are represented by the characteristics of an 'average human' (e.g., Auliciems and Kalma, 1979;Błażejczyk et al., 2010). In this study, we used human data of 4 persons; these data are represented in Table 1. Human 1 represents an extreme Hungarian female. Human 2 is a female whose characteristics are as close as possible to an 'average Hungarian female'. Human 3 is the first author of this study. Human 4 is the 'standardized human' used in the calculation of the PET index.
Except for the 'standardized human' used in PET, human characteristics (age, gender, body mass [M bo ] and body length [L bo ]) are taken from a Hungarian human dataset (Utczás et al., 2015;Zsákai et al., 2015;Bodzsár et al., 2016) created at the Department of Biological Anthropology, Eötvös Loránd University, Budapest, Hungary. The dataset contains data of about 1,000 Hungarian adults. The participation was voluntary and anonymous. The database contains the ID code, gender, chronological age, body structure and physiological parameters of the participants. Written informed consent was obtained from the participants. The data collection was conducted according to the principles expressed in the Declaration of Helsinki. Characteristics of the 'standardized human' used in PET are taken from work of Yang and Matzarakis (2016).

| RESULTS
The clothing resistance-operative temperature relationships for the humans considered, the spatial distribution of annual r cl and T o values and the spatial distribution of the summer and winter values of r cl are analysed. Summer values are formed by averaging the values for June, July, August, and the winter values are obtained by averaging the values for December, January, February. Thirty-year annual, summer and winter means are calculated for the central period 1971-2000.

| Clothing resistance-operative temperature relationships
Individual r cl -T o relationships can be constructed for each person in the climate and/or weather considered. T o represents the environment's thermal load; among human characteristics it depends only upon D (Equation (A9)), but since this dependence is weak, T o can be treated as a human-independent thermal indicator. r cl (Equation (1)) depends upon both the environment and the human characteristics via M. Since M can vary by as much as 40-50 WÁm −2 from human to human, the dependence of r cl on human characteristics cannot be neglected. The r cl -T o link is fundamental since it represents a unique person-environment relationship. The r cl -T o scatter chart is compared for humans 1 and 2 in the Carpathian Basin for the summer/winter seasons (Figure 2), the spring/autumn seasons ( Figure 3) and the year (Figure 4). The point-cloud contains 6,161 points as this is the number of grid points being considered in the region.
Inspecting Figure 2 we see that the point-clouds are separated for winter and summer as well as for humans 1 and 2. The r cl values of human 1 are unequivocally lower than the r cl values of human 2, since the M value of human 1 is larger than the M value of human 2 ( Table 1). The difference in M between humans 1 and 2 is 39.6 WÁm −2 . The r cl differences decrease towards warmer T o values. The largest differences (about 0.6 clo) refer to T o ≈ −9 C, the smallest (less than 0.05 clo) refer to T o ≈ 33 C. For r cl = 0 clo, T o of human 1 is around 24 C, while for human 2 it is around 27 C. This shift of 3 C is not negligible knowing that deviations in human thermal reactions in the comfortable zone are less. All these differences in r cl between humans 1 and 2 are caused by difference in M. The r cl -T o points for humans 1 and 2 in spring and autumn represent one unified point-cloud ( Figure 3). As in the former case, the point-cloud of human 1 is below the point cloud of human 2. The largest inter-human r cl differences are about 0.45 clo, when T o ≈ 1 C. The smallest inter-human r cl differences are about 0.2-0.25 clo for T o = 18-19 C.
The annual r cl -T o point-clouds for the humans considered are very similar to those obtained for spring and autumn (Figure 4). In this case, the separate localisations of the point-clouds are more obvious than in the springautumn case. The largest inter-human r cl differences appear for T o = 1-2 C and amount to about 0.45 clo. The smallest differences amount to about 0.25-0.3 clo for T o = 15-17 C.

| Spatial distributions
The spatial distribution of annual r cl and T o values is considered only for human 2 since her characteristics closely represent the characteristics of the 'average adult Hungarian female'. This is presented in Figure 5. In Hungary, except on mountains, r cl varies between 0.8 and 1.0 clo.
According to the thermal sensation of human 3, this thermal load is sensed as 'cool' or 'cold'. These values can also be found on the Transylvanian Plateau. Banat and the Wallachian Plain are somewhat warmer with r cl values of 0.6-0.8 clo. The warmest areas are located in Oltenia on the southern slopes of the Southern Carpathians (0.4 < r cl < 0.6 clo). The thermal contrasts (large r cl differences between adjacent pixels) seem to be especially high in the Retezat Mountains and the F ag aras Mountains, where r cl deviations can be above 1 clo. The territorial structure of T o distribution is somewhat more detailed than the territorial structure of r cl distribution. For instance, Bačka and Banat are somewhat warmer (14 < T o < 16 C) than the Little Hungarian Plain and central and northern parts of the Great Hungarian Plain (12 < T o < 14 C). Oltenia and the Wallachian Plain are as warm as Bačka and Banat. The thermal diversity on Mount Papuk and the Apuseni Mountains is conspicuous, where T o deviations between two adjacent pixels can reach 10 C. However, the greatest thermal contrasts (above 10 C) can be found in the Retezar Mountains, the F ag aras Mountains, the Maramures Mountains and the High Tatras.
The area distribution of the summer mean r cl values of humans 1 and 2 for the CarpatClim dataset region is presented in Figure 6.
Inspecting r cl distributions, it is conspicuous that both humans are comfortable from the point of view of thermal load (r cl values vary between −0.2 and 0.2 clo) almost over the entire territory of Hungary. This is in accordance with the thermal sensation of person 3 and with the thermal sensation results obtained in the work of Gulyás and Matzarakis (2009). For human 1, Bačka, Banat, many parts of the Transylvanian Plateau and the Wallachian Plain are warmer (−0.2 > r cl > −0.4) than Hungary. For human 2, only the Wallachian Plain and some southern areas of Bačka and Banat are warmer than Hungary. For human 1, many parts of the Transylvanian Plateau are warmer than the Great Hungarian Plain, but this is not valid for human 2. For both humans, the warmest locations (−0.4 > r cl > −0.6) are in Oltenia on the southern slopes of the Southern Carpathians. The largest thermal contrasts can be found in the region of Mount Papuk, the Retezat Mountains, the F ag aras Mountains, the Maramures Mountains and in the High Tatras. At these locations the thermal contrast is at least 0.6 clo. The highest thermal contrasts (about 1 clo) are in the regions of the High Tatras, Maramures Mountains and in the F ag aras Mountains. There is no observable difference between humans 1 and 2 regarding thermal contrast. The area distribution of the winter mean r cl values of humans 1 and 2 is presented in Figure 7.
Note that the spatial distribution structures are very similar. Taking a look at the scales used we can observe a 0.55-0.6 clo shift between them. Since human 1 possesses larger M than human 2, the r cl scale of human 1 ranges from 1 to 2 clo, to the contrast of the r cl scale of human 2, where the scale ranges from 1.5 to 2.6 clo. r cl values for humans 1 and 2 on the Great Hungarian Plain and the Little Hungarian Plain are 1.2-1.4 and 1.8-2 clo, respectively. For human 2 (person representing 'average adult Hungarian female') r cl values in winter range from 1.4 to 2.2 clo over the entire territory of Hungary. According to the thermal sensation of human 3, this thermal load is sensed as 'cold' or 'very cold'. According to the work of Gulyás and Matzarakis (2009), the sensation of the thermal climate in Hungary during winter is denoted as 'very cold'. Just like in summer, Bačka, Banat, Oltenia and the Wallachian Plain are warmer (1 < r cl < 1.2 clo for human 1; 1.4 < r cl < 1.6 clo for human 2) than the Great Hungarian Plain. Note that many locations on the Transylvanian Plateau are as warm as Banat and Oltenia. The greatest thermal contrasts are in the High Tatras, the Maramures Mountains, the F ag aras Mountains and in the Retezat Mountains. At these locations, the r cl differences between adjacent pixels can reach 1 clo.

| Comparisons with Physiological Equivalent Temperature
It is interesting to relate T o and r cl to some other thermal indices. Since PET is the most frequently used human thermal index in the region considered, we compared it with T o and r cl in three different sub-regions (Banat, Great Hungarian Plain and Apuseni Mountains) of the Carpathian Basin for the summer and winter seasons. PET values are taken from the work of Gulyás and Matzarakis (2009). The results together with thermal sensation estimations are presented in Table 2. All results refer to the period 1971-2000. PET values are obtained by using the dataset of the Climatic Research Unit (University of East Anglia, Norwich, UK), while T o and r cl values are simulated by using the CarpatClim dataset. It should be mentioned that the spatial distribution structures of all three indices in Hungary (not presented here) are similar. The thermal contrast between the North Hungarian Mountains and the Great Hungarian Plain regions can be easily observed. Note that T o is higher than PET for 2-6 C.
The most important human characteristic, metabolic activity M is represented in both PET and r cl . In PET, M refers to a standing human, in r cl to a walking human. In r cl , thermal sensation results are given according to person 3. Although there are great differences in terms of model physics and concept, human representation and thermal sensation grade, there is good agreement between the thermal sensation results referring to PET and r cl .

| DISCUSSION
The model is constructed for individual use. The human is represented as much as possible following the principle of 'individualisation'. To date, it is 'standardized humans' that have been treated in the scientific literature (e.g., Höppe, 1999;. So, we have changed the treatment of clothing, human characteristics and metabolic activity rate. Clothing is very variable parameter, it is not only determined thermally but also on a personal and social basis. Therefore, we decided to use this as model output parameter, viewing it only as thermal regulator neglecting its personal and social dependence. Regarding human characteristics, the actual individual characteristics are used as inputs ignoring the concept of the 'average human'. Metabolic activity rate is parameterised as simply as possible via human state variables ignoring treatment of physiological processes, so, the model is unable to physiologically characterize the effects of heat and cold stresses. The first and only attempt to date to relate the heat load results in terms of r cl to thermal sensation results is presented in this study. The model is intended to be used on both climate and weather data. To be user-friendly (Essenwanger, 2001), it needs drastic simplification in its environmental physics part, in the treatment of operative temperature. Without this simplification it cannot be competitive, for instance, with the Köppen method in climate classification applications. Carrying out this simplification is a task for the future.
According to the results obtained, the human thermal load in the Pannonian Plain part of the Carpathian Basin ( Acs et al., 2015) during summer is approximately equal regardless of the personal differences. However, in winter the relevance of personal differences upon human thermal load can be significant. This is unequivocally shown by comparing the area distribution of the clothing resistance parameters of two adult Hungarian females. The model suggests that the relevance of personal differences increases not only in cold stress but also in heat stress. Unfortunately, these statements have not been confirmed so far by independent observations. Lastly, the subject investigated can be traced back to Humboldt (von Humboldt, 1845;Hantel and Haimberger, 2016). Here is a text of his interpretation of climate: 'Der Ausdruck Klíma bezeichnet in seinem allgemeinsten Sinne alle Veränderungen in der Atmosphäre, die unsere Organe merklich afficieren: die Temperatur, die Feuchtigkeit,…die Heiterkeit des Himmels; welcher nicht bloss wichtig ist für…die organische Entwicklung der Gewächse und die Reifung der Früchte, sondern auch für die Gefühle und ganze Seelenstimmung des Menschen'. Translation: The expression climate denotes in its most general sense all changes in the atmosphere that noticeably affect our organs: temperature, humidity,…, serenity of the sky, that is not only important for…the organic development of plants, the ripening of fruits, but also for feelings and state of mind. The results confirm Humboldt's thoughts regarding the subjectivity of the climate-human soul relationship.

| CONCLUSION
A new human thermal load model based on energy balance considerations is presented to estimate individual human thermal climates in the Carpathian Basin. Human thermal climate is characterized in terms of clothing resistance parameter and operative temperature. The metabolic activity rate is simulated as simply as possible but still being able to take into account interpersonal differences. A non-sweating human walking at a speed of 4 kmÁh −1 is considered. The results suggest that the interpersonal variability effect in human thermal load simulation cannot be neglected. Consequently, human datasets should also be used in describing human thermal load variability. According to a Hungarian human dataset, interpersonal variations of M can reach 40-50 WÁm −2 causing variations in r cl of about 0.6-0.8 clo in

CLOTHED HUMAN BODY-ATMOSPHERE ENVIRONMENT MODEL
A clothed human body-air environment model is used. The human body is represented as simply as possible with a one-node model (Kati c et al., 2016), that is there is no treatment of physiological processes (M is a function of human state variables); consequently stress categories and the related physiological responses cannot be characterized. The human body T b and skin T S temperatures are 37 and 34 C, respectively. Clothing exchanges heat with the air environment and it obtains heat from the human body, and so its surface temperature T cl changes. We supposed that garments cover the human body completely, it adheres strongly to the skin surface. The clothing albedo agrees with the skin albedo. The human is walking without sweating, the latent heat of walking. Both terms can be parameterised knowing the most important human body features: gender, age (year), body mass, M bo (kg) and body length, L bo (cm). According to Frankenfield et al. (2005) Mifflin et al.'s (1990 To be able to obtain M b in (WÁm −2 ), the surface of the human body A (m 2 ) has also to be estimated. Dubois and Dubois (1915) parameterisation is used taking M bo and L bo as inputs, Formula (1) in Weyand et al. (2010) refers to a walking distance of 1 m. Since the reference walking speed in our model is 1.1 mÁs −1 , Weyand et al.'s (2010) formula (1) is multiplied by a factor of 1.1. Dividing this by A, we will get M w in (WÁm −2 ).
The λE r + λE sd sum can be expressed as a function of M according to Campbell and Norman (1998). In this work, this sum is taken as 10% of M. W also depends upon M. According to Auliciems and Kalma (1979) W is expressed as APPENDIX B.

THERMAL SENSATION AND THE r cl PARAMETER VALUES
There are many studies (e.g., Cohen et al., 2013;Hamzah et al., 2018) presenting and discussing methods for determining the thermal index-thermal sensation relationship. These relationships are given for the most frequently used indices (e.g., Błażejczyk et al., 2012;Zare et al., 2018). To the best of our knowledge, there has been no study discussing the r cl -thermal sensation relationship to date. In this study, a preliminary estimation is given by concurrent observation of weather and subjective thermal sensation carried out by person 3 in Table 1