An Approach for Quantifying a Regional Haze Stress: Case Study in Three Cities of Taiwan

: This study proposes an approach of evaluating the haze stress index (HSI) and quantifying people’s feelings for haze stress. The three special municipalities in Taiwan were selected as representative cities of slightly, moderately, and heavily contaminated with ﬁne particulate matter (PM 2.5 ) to evaluate the adaptability of the proposed approach. Equations with weightings of parameters to evaluate four temporal HSIs—hourly, daily, monthly, and yearly HSIs—were established. The parameters were measured PM 2.5 , relative humidity, and secondary organic aerosol (represented by the sum of measured O 3 and NO 2 ). The results of evaluating the HSIs in the three cities demonstrated that the inverse-variance weighting method is the best because the haze stress sensitivities in the four temporal periods were higher than those obtained using the unit and variance weighting methods to respond to the real situation of air quality. Variation in the four temporal HSIs for the three cities demonstrates that the variation increases with an increasing level of air pollution. When comparing between 2015 and 2018, the fractional reductions in HSIs in the slightly, moderately, and heavily contaminated cities were ≤ 18.4%, ≤ 10.8%, and ≤ 11.3%, respectively. It is recommended that the HSIs are categorized into ﬁve haze stress groups based on the haze stress level. The people’s feelings in the three cities on the haze stresses were represented using the established quantifying descriptors in detail. The results show that the proposed approach can provide quantiﬁcation indices of haze stress and people’s feelings in a regional haze, thereby ﬁrmly establishing the governmental improvement policy.


Introduction
A number of environmental indices are used to state regional air quality. The air quality index (AQI) was developed by government agencies to communicate the degree to which air pollutants affect human health at a given time. The AQI is based on the maximum values of the subindices of pollutants-fine particulate matter (PM 2.5 ), sulfur dioxide (SO 2 ), nitrogen dioxide (NO 2 ), carbon monoxide (CO), and ozone (O 3 ). The air quality health index is a multipollutant index model that is based on the observed relationship between the 3-h average concentrations of O 3 , NO 2 , and PM 2.5 that are harmful to health [1,2]. Plaia et al. [3] proposed a multipollutant-multisite air quality index approach for considering the combined effect of various pollutants in the environmental quality over time. Thach et al. [4] aggregated the subindices of PM 10 , SO 2 , NO 2 , and O 3 by using the root-mean-power function to construct an overall AQI on health. Gorai et al. [5] proposed the fuzzy air quality health

Target Cities and Selected Representative Air Quality Monitoring Stations
Taiwan is an island with an area of 35,883 km 2 and mostly comprises rugged mountains that include five high ranges with an altitude higher than 3000 m from the northern to the southern tip of the island and the flat to gently rolling plains in the west (Figure 1). Taiwan has a high-income advanced economy and a highly urbanized island, with more than 70% of its residents living in the urbanized area. The estimated population in 2018 was 23.58 million. New Taipei City, Taichung City, and Kaohsiung City, which are three special municipalities in Taiwan, were selected as target cities in which to evaluate the adaptability of this approach. New Taipei City, Taichung City, and Kaohsiung City are located in northern, central, and southern Taiwan, respectively. New Taipei City has the highest population of any city in Taiwan, with 3.99 million residents; followed by Taichung City, with 2.81 million; and Kaohsiung City, with 2.77 million (2018). In terms of geographic location, New Taipei City and Taichung City are located in basins (the Taipei Basin and Taichung Basin). Kaohsiung City is located on a large plain (the Kaohsiung Plain) ( Figure 1). In this study, for each city, a representative air quality monitoring station (AQMS) was selected, from which to draw air quality data for the calculation of haze stress in Xinghuang, Xitun, and Siaogang in New Taipei City, Taichung City, and Kaohsiung City, respectively ( Figure 1). These representative AQMSs were selected because they are located in the densely populated downtown of each city.
Atmosphere 2020, 11, x FOR PEER REVIEW 3 of 17 urbanized area. The estimated population in 2018 was 23.58 million. New Taipei City, Taichung City, and Kaohsiung City, which are three special municipalities in Taiwan, were selected as target cities in which to evaluate the adaptability of this approach. New Taipei City, Taichung City, and Kaohsiung City are located in northern, central, and southern Taiwan, respectively. New Taipei City has the highest population of any city in Taiwan, with 3.99 million residents; followed by Taichung City, with 2.81 million; and Kaohsiung City, with 2.77 million (2018). In terms of geographic location, New Taipei City and Taichung City are located in basins (the Taipei Basin and Taichung Basin). Kaohsiung City is located on a large plain (the Kaohsiung Plain) (Figure 1). In this study, for each city, a representative air quality monitoring station (AQMS) was selected, from which to draw air quality data for the calculation of haze stress in Xinghuang, Xitun, and Siaogang in New Taipei City, Taichung City, and Kaohsiung City, respectively ( Figure 1). These representative AQMSs were selected because they are located in the densely populated downtown of each city. Monitoring data (https://taqm.epa.gov.tw/taqm/tw/default.aspx) of air pollutants and meteorology from the three selected representative AQMSs were used to calculate the hourly, daily, monthly, and yearly HSIs in the three target cities. In Taiwan, AQI has been adopted since December 1, 2016 as the basis for determining air quality standards. Table 1 lists the pollutant concentration breakpoints and AQI index of Taiwan, which is similar to that of U.S. and most Asian countries. In this study, some AQI standards of PM2.5, O3, and NO2 will be used to establish regional HSIs as the recommended reference limits.  Monitoring data (https://taqm.epa.gov.tw/taqm/tw/default.aspx) of air pollutants and meteorology from the three selected representative AQMSs were used to calculate the hourly, daily, monthly, and yearly HSIs in the three target cities. In Taiwan, AQI has been adopted since 1 December 2016 as the basis for determining air quality standards. Table 1 lists the pollutant concentration breakpoints and AQI index of Taiwan, which is similar to that of U.S. and most Asian countries. In this study, some AQI standards of PM 2.5 , O 3 , and NO 2 will be used to establish regional HSIs as the recommended reference limits.

Weighting Methods
The following four methods were used to obtain the weight: unit, statistical, variance, and inverse-variance weighting methods.
(1) Unit weighting: In this method, the weights between n indicators are not considered. Each indicator has equal importance in the evaluation. The formula of unit weighting is as follows: (2) Statistical weighting: In this method, the weights are set inversely proportional to the score. The purpose of this method is to retain information on low-level indicators. The formula of statistical weighting is as follows: where c i is the concentration of indicator i.
(3) Variance weighting: This method is used when the variation in data is inconsistent to reduce the data importance of larger variation indicators. Therefore, indicators with a smaller variation in data have greater weight. The formula of variance weighting is as follows: where 1/σ i 2 is the variance, which can be calculated using the following equation: where N and µ are the number of terms in the distribution and the mean of data, respectively. (4) Inverse-variance weighting: This method is exactly opposite to the variance weighting method, which reduces the data importance of lower variation indicators. The formula of inverse-variance weighting is as follows: Each indicator in the regional HSI is a sufficiency condition rather than a necessity condition. Moreover, variance is used to quantify the variation in a set of data, which is applicable when apparent variations appear during air pollutant monitoring. In this study, the unit, variance, and inverse-variance weighting methods were investigated and compared to obtain an optimal weighting method. Moreover, the weights were normalized to make the established regional HSI equations more regular. The formula of the normalized weight W i of indicator i is as follows: where the denominator is the sum of the original weights.

Establishing Regional HSIs
Many countries in Asia have experienced severe haze pollution [5,25,26]. Some previous studies used various analytic methods and tools, such as the inductively coupled plasma mass or atomic emission spectrometer for heavy metals, ion chromatography for water-soluble ions, the thermal or optical carbon analyzer for organic and elemental carbons, and the microvolume spectrophotometer for microbial deoxyribonucleic acid in haze, to determine the chemical and microbial components of haze [26][27][28][29]. These fine analytical results cannot be used as parameters to establish HSIs because they are not items monitored by AQMSs. Haze, like smog, has tiny suspended solid or liquid particles [30] that reduce horizontal visibility to less than 10 km [31]. Hunova [32] presented a visualization method for measured air quality data that uses ambient air pollution (the rank average of annual median 24-h average concentrations of SO 2 , NO x , CO, PM 10 , Cd, and Pb), ground-level ozone, and wet atmospheric deposition as factors. Kim et al. [33] indicated that the oxygenated organic component in interstitial aerosol is similar to that in fog water (r 2 > 0.95), which is attributable to the moderately oxidized low-volatility dissolved organic matter under humid conditions. Some previous studies have investigated the formation of a secondary organic aerosol (SOA) from various organic compounds [33][34][35] and determined that the level of SOA is usually underestimated [36]. Ren et al. [37] indicated that high-molecular-weight n-alkanes and fatty acids dominated the particles with an aerodynamic diameter greater than 1.1 µm in terms of their concentration during severe haze days. Ultrafine particles (aerodynamic diameter: 0.001-0.1 µm) are typically present in a high concentration in an urban environment [38]. SOA is an important component of ultrafine aerosols in the ambient atmosphere and is a gas phase product of atmospheric oxidation and condensation of volatile organic compounds [39]. Photochemical reactions are the main formation pathways of SOAs [40], and the concept of odd oxygen (O x = O 3 + NO 2 ) is often used to study the photochemical formation of SOAs [41][42][43]. Zhu et al. [44] indicated that SOA was the largest contributor to the scattering coefficient of PM 1 during haze episodes, accounting for 45.5%. In our previous study, a method was established to quantify accurately the source apportionment of ambient haze from measured PM 2.5 , moisture, and SOA [45]. In Taiwan, the height of sampling ports of most AQMSs is 3-15 m from the ground. Therefore, the measured data of PM 2.5 does not represent all the haze in the sky. In addition, high air moisture can affect people's feelings, causing them to feel particularly uneasy and discomfort [46]. The strongly enhanced aerosol extinction coefficient is due to hygroscopic growth at high moisture conditions [47]. Liu et al. [48] indicated that RH was related to the high particle concentrations in haze episodes. Moisture is often mixed in haze, so moisture must also be considered for haze stress.
Sulfate, nitrate, and ammonium are the dominant species in secondary inorganic aerosol (SIA) [49,50]. Some gaseous species (such as NO 2 , SO 2 , and NH 3 ) can be adsorbed on to the existing particles and then undergo chemical transformation to produce SIA [51] or acid rain [52]. The formation of SIA plays a key role in the increasing PM 2.5 concentration [53], especially on the days with high relative humidity [54]. Therefore, SIA (the sum of NH 4 + , NO 3 − , and SO 4 2− ) mainly exists on PM 2.5 [50]. In addition, general air quality monitoring stations do not monitor the SIA concentration so that no SIA data can be used directly. Thus, SIA is not considered separately in the evaluation of ambient HSI. Some meteorological parameters, such as wind speed, temperature, solar irradiance, and pressure, can affect the formation of haze, but this study does not discuss the cause of formation of haze. Therefore, the real existing haze was estimated by three main components (PM 2.5 , moisture, and SOA) that can be measured by AQMS. The concentrations of fine particles (PM 2.5 ), RH (represented moisture), and SOA (represented by [O 3 + NO 2 ]) were used to establish the relationship between equations of the HSI during various periods: (1) Hourly HSI (HSI hourly ): (2) Daily HSI (HSI daily ): (3) Monthly HSI (HSI monthly ): (4) Yearly HSI (HSI yearly ): where the denominators are the recommended reference limits of the selected air pollutants or meteorological parameters for hourly, daily, monthly, or yearly HSIs. These limits are based on the AQI and health implications in Table 1 and suitable conditions with respect to the weather in Taiwan. For PM 2.5 and odd oxygen ([O 3 + NO 2 ]), the recommended limits of hourly, daily, monthly, and yearly periods are the concentrations corresponding to their AQI of 100, 75, 50, and 50 (Table 1), respectively. These recommended limits are based on the hourly, daily, and monthly/yearly AQIs, which can be "good", "between good and moderate", and "moderate", respectively. In Taiwan, the annual average concentration standard of each criteria pollutant is its concentration corresponding to AQI of 50. Therefore, the concentration corresponding to AQI of 50 was recommended as the limits of monthly and yearly periods. People tend to feel most comfortable at an RH range of 30-50%, and the range of about 30-70% is healthy for humans [55]. The higher the RH, the less the sweat evaporates, which seriously affect the body's thermoregulation [56] and people's emotions. People feel stuffy and uncomfortable when RH is about 80%, and it is very sticky when RH is higher than 90%. The range of monthly average RH in Taiwan was 73-81%, and those for which the maximum and minimum are in February and in July, respectively. This RH range occurs widely in some major cities, such as Los Angeles, Chicago, Singapore, Bangkok, and Shanghai [57][58][59]. According to the factors mentioned above, the recommended RH limits of hourly, daily, monthly, and yearly periods are RHs of 70%, 70%, 60%, and 60%, respectively. However, the selection of suitable denominator values is important for an administrator, which can be changed according to the regional environmental characteristics.

Spatial and Temporal Variations in PM 2.5 , RH, and ([O 3 ] + [NO 2 ])
In Taiwan, the daily average limit (DAL) and annual average limit (AAL) of PM 2.5 are 35.5 and 15 µg m −3 , respectively. The southwest and northeast monsoon periods are from mid-April to mid-September and from mid-September to mid-April, respectively. Figure 2 displays the monthly average concentrations of PM 2.5 in New Taipei City, Taichung City, and Kaohsiung City during 2015-2017. The monthly average concentrations of PM 2.5 in the three cities are in the following sequence: Kaohsiung City > Taichung City > New Taipei City. This sequence reveals that the concentration of PM 2.5 increases from north to south in Taiwan. The results show that New Taipei City, Taichung City, and Kaohsiung City are slightly, moderately, and heavily contaminated with PM 2.5 , respectively, especially during the northeast monsoon period. This is because Taiwan experiences the northeast monsoon for seven months, thus pollutants are transmitted mainly from the north to south. From 2015 to 2018, the monthly average concentrations of PM 2.5 in Kaohsiung City were higher than the AAL during the northeast monsoon season (November to March). In addition, Kaohsiung City is located in the south of Jianan Plain, the largest in Taiwan. Therefore, Kaohsiung's air pollutants are relatively easy to dissipate during the southwest monsoon season (April to September), with a clear annual cycle for PM 2.5 than other two cities.
Atmosphere 2020, 11, x FOR PEER REVIEW 7 of 17 2017. The monthly average concentrations of PM2.5 in the three cities are in the following sequence: Kaohsiung City > Taichung City > New Taipei City. This sequence reveals that the concentration of PM2.5 increases from north to south in Taiwan. The results show that New Taipei City, Taichung City, and Kaohsiung City are slightly, moderately, and heavily contaminated with PM2.5, respectively, especially during the northeast monsoon period. This is because Taiwan experiences the northeast monsoon for seven months, thus pollutants are transmitted mainly from the north to south. From 2015 to 2018, the monthly average concentrations of PM2.5 in Kaohsiung City were higher than the AAL during the northeast monsoon season (November to March). In addition, Kaohsiung City is located in the south of Jianan Plain, the largest in Taiwan. Therefore, Kaohsiung's air pollutants are relatively easy to dissipate during the southwest monsoon season (April to September), with a clear annual cycle for PM2.5 than other two cities.

Comparison Between the Three Weighting Methods
Because the units and scales of PM2.5, RH, and [O3] + [NO2] are different, the statistical weighting method is not suitable for this study. As mentioned previously, the unit, variance, and inverse variance weighting methods are applicable when the variations in the data of each indicator have equal importance, thus reducing the importance of larger variation indicators and enhancing the importance of larger variation indicators. Figure 3 displays the results of computing the hourly HSI (HSIh) in New Taipei City, Taichung City, and Kaohsiung City by using the three weighting methods during 2017. The computation results of unit weighting demonstrate that the mean values and variations in HSIh in the three cities were all approximately constant and low throughout the day. Although the variance in HSIh in Kaohsiung City was higher than that in the other two cities, the mean values of HSIh were the lowest throughout the day. This is unreasonable because Kaohsiung City is heavily contaminated with PM2.5, thus the unit weighting method is not applicable for the evaluation of haze stress.

Comparison Between the Three Weighting Methods
Because the units and scales of PM 2.5 , RH, and [O 3 ] + [NO 2 ] are different, the statistical weighting method is not suitable for this study. As mentioned previously, the unit, variance, and inverse variance weighting methods are applicable when the variations in the data of each indicator have equal importance, thus reducing the importance of larger variation indicators and enhancing the importance of larger variation indicators. Figure 3 displays the results of computing the hourly HSI (HSI h ) in New Taipei City, Taichung City, and Kaohsiung City by using the three weighting methods during 2017. The computation results of unit weighting demonstrate that the mean values and variations in HSI h in the three cities were all approximately constant and low throughout the day. Although the variance in HSI h in Kaohsiung City was higher than that in the other two cities, the mean values of HSI h were the lowest throughout the day. This is unreasonable because Kaohsiung City is heavily contaminated with PM 2.5 , thus the unit weighting method is not applicable for the evaluation of haze stress. The mean values of HSIhourly in the three cities are in the following sequence: Kaohsiung City > Taichung City > New Taipei City, which matches the monitoring results of PM2.5 ( Figure 2). However, the variance in HSIh for the three cities was low throughout the day (Figure 3), which is different from the fact that the concentration of pollutants in highly polluted areas varies greatly. Therefore, the variance weighting method is also not applicable for the evaluation of haze stress. The inverse variance weighting method is applicable because the mean values and variations in HSIh in the three cities are in line with the corresponding monitoring data (Figures 2 and 3).
Moreover, because the responses of people to haze are subjective and sometimes strong, the two larger variation indicators-PM2.5 and [O3] + [NO2]-are more important in the haze stress evaluation. Therefore, inverse variance weighting is recommended for the evaluation of the regional HSI. Here, the follow-up work uses the inverse variance weighting method. Figure 4 displays the box-whisker plots of HSIh obtained using the inverse variance weighting method in the three cities during 2015-2018. The results demonstrate that the values of HSIh in the three cities are consistent with their pollution situations-New Taipei City, Taichung City, and Kaohsiung City are slightly, moderately, and heavily contaminated cities, respectively. The values and variations in HSIh in the three cities exhibited slight and small decreases by year. The HSIh patterns of each city in different years are similar; however, the pattern differences between cities are large. Kaohsiung City has the largest value and variability of HSIh, especially at midnight (00:00-04:00) and early morning (04:00-08:00). The means of HSIh in New Taipei City and Taichung City are similar, but the variability of HSIh in Taichung City is greater than that in New Taipei City. The lowest HSIh of all three cities appeared in the afternoon (10:00-18:00). This may be due to the higher The mean values of HSI hourly in the three cities are in the following sequence: Kaohsiung City > Taichung City > New Taipei City, which matches the monitoring results of PM 2.5 ( Figure 2). However, the variance in HSI h for the three cities was low throughout the day (Figure 3), which is different from the fact that the concentration of pollutants in highly polluted areas varies greatly. Therefore, the variance weighting method is also not applicable for the evaluation of haze stress. The inverse variance weighting method is applicable because the mean values and variations in HSI h in the three cities are in line with the corresponding monitoring data (Figures 2 and 3).

Hourly Haze Stress
Moreover, because the responses of people to haze are subjective and sometimes strong, the two larger variation indicators-PM 2.5 and [O 3 ] + [NO 2 ]-are more important in the haze stress evaluation. Therefore, inverse variance weighting is recommended for the evaluation of the regional HSI. Here, the follow-up work uses the inverse variance weighting method. Figure 4 displays the box-whisker plots of HSI h obtained using the inverse variance weighting method in the three cities during 2015-2018. The results demonstrate that the values of HSI h in the three cities are consistent with their pollution situations-New Taipei City, Taichung City, and Kaohsiung City are slightly, moderately, and heavily contaminated cities, respectively. The values and variations in HSI h in the three cities exhibited slight and small decreases by year. The HSI h patterns of each city in different years are similar; however, the pattern differences between cities are large. Kaohsiung City has the largest value and variability of HSI h , especially at midnight (00:00-04:00) and early morning (04:00-08:00). The means of HSI h in New Taipei City and Taichung City are similar, but the variability of HSI h in Taichung City is greater than that in New Taipei City. The lowest HSI h of all three cities appeared in the afternoon (10:00-18:00). This may be due to the higher temperature during this period, which increases the mixed layer height and reduces hourly HSIs. In particular, the HSI h pattern of Kaohsiung City exhibits a strong wave-like variation from 08:00 to 20:00, with the lowest value at approximately 14:00.

Hourly Haze Stress
Atmosphere 2020, 11, x FOR PEER REVIEW 9 of 17 temperature during this period, which increases the mixed layer height and reduces hourly HSIs. In particular, the HSIh pattern of Kaohsiung City exhibits a strong wave-like variation from 08:00 to 20:00, with the lowest value at approximately 14:00.

Daily Haze Stress
The box-whisker plots of HSId obtained using the inverse variance weighting method in the three cities during 2015-2018 are displayed in Figure 5. The number of days per month is different, so the amount of data calculated from 29 to 31 is also different in the calculation of HSId. The variations in HSId do not have certain criteria and are mainly affected by the daily weather. Therefore, the changes in HSId in the three cities are all messy. The results demonstrate that the values of HSId for the three cities can present their pollution statuses, which is the same as HSIh-slight, moderate, and heavy contamination, respectively. The values and variations in HSIdaily in the three cities are decreasing year by year, showing an improvement in their air quality with each passing year, which is important for the government environmental protection decision makers. However, for people in the same city, there is no significant change in the daily haze stress in a month.

Daily Haze Stress
The box-whisker plots of HSI d obtained using the inverse variance weighting method in the three cities during 2015-2018 are displayed in Figure 5. The number of days per month is different, so the amount of data calculated from 29 to 31 is also different in the calculation of HSI d . The variations in HSI d do not have certain criteria and are mainly affected by the daily weather. Therefore, the changes in HSI d in the three cities are all messy. The results demonstrate that the values of HSI d for the three cities can present their pollution statuses, which is the same as HSI h -slight, moderate, and heavy contamination, respectively. The values and variations in HSI daily in the three cities are decreasing year by year, showing an improvement in their air quality with each passing year, which is important for the government environmental protection decision makers. However, for people in the same city, there is no significant change in the daily haze stress in a month.  Figure 6 shows the box-whisker plots of HSIm obtained using the inverse variance weighting in the three cities during 2015-2018. The HSIm patterns of the three cities present the low-and highpolluted seasons in a year. The variation in HSIm increases strongly by increasing the degree of air pollution in a region or city. In particular, the difference between the lowest and highest polluted month is very large in Kaohsiung City, with a maximum deviation of approximately 0.9 in the mean HSIm. For the slightly contaminated city, New Taipei City, the difference between the low-and highpolluted months is approximately 0.3 in terms of the mean HSIm. The lowest and highest polluted months of the three cities were June and July and January and February, which are the same as the results in Figure 2a,c, respectively. Therefore, RH is not the main cause of high haze stress. High RH occurs from June to September in Taiwan (Figure 2b). For a highly polluted region, effectively improving air quality, especially in terms of PM2.5, can significantly reduce the HSIm in the highly polluted months (Figure 2a).  Figure 6 shows the box-whisker plots of HSI m obtained using the inverse variance weighting in the three cities during 2015-2018. The HSI m patterns of the three cities present the low-and high-polluted seasons in a year. The variation in HSI m increases strongly by increasing the degree of air pollution in a region or city. In particular, the difference between the lowest and highest polluted month is very large in Kaohsiung City, with a maximum deviation of approximately 0.9 in the mean HSI m . For the slightly contaminated city, New Taipei City, the difference between the low-and high-polluted months is approximately 0.3 in terms of the mean HSI m . The lowest and highest polluted months of the three cities were June and July and January and February, which are the same as the results in Figure 2a,c, respectively. Therefore, RH is not the main cause of high haze stress. High RH occurs from June to September in Taiwan (Figure 2b). For a highly polluted region, effectively improving air quality, especially in terms of PM 2.5 , can significantly reduce the HSI m in the highly polluted months (Figure 2a).

Yearly Haze Stress
The bar charts of HSIy obtained using the inverse variance weighting method in the three cities during 2015-2018 are displayed in Figure 7. In the yearly haze stress evaluation, the regional variation significantly increases with the degree of contamination. The results indicate that the change in HSIy of Kaohsiung City is up and down, which is different from the trends of HSIh, HSId, and HSIm in the years (Figures 3c, 4c, and 5c). The change in HSIy of Taichung City is small. By contrast, the change in HSIy of New Taipei City exhibits a significant decrease each year. The HSIy values of the three cities were all greater than 1.0, which indicate that improvements of the air quality are still needed.

Yearly Haze Stress
The bar charts of HSI y obtained using the inverse variance weighting method in the three cities during 2015-2018 are displayed in Figure 7. In the yearly haze stress evaluation, the regional variation significantly increases with the degree of contamination. The results indicate that the change in HSI y of Kaohsiung City is up and down, which is different from the trends of HSI h , HSI d , and HSI m in the years (Figures 3c, 4c and 5c). The change in HSI y of Taichung City is small. By contrast, the change in HSI y of New Taipei City exhibits a significant decrease each year. The HSI y values of the three cities were all greater than 1.0, which indicate that improvements of the air quality are still needed.  Table 2 presents the mean and variance (SD) of hourly, daily, and monthly HSIs in the three cities during 2015-2018. The results show that the means and standard deviation of hourly, daily, and monthly HSIs in the three cities have been decreasing year by year, which is due to the effort of  Table 2 presents the mean and variance (SD) of hourly, daily, and monthly HSIs in the three cities during 2015-2018. The results show that the means and standard deviation of hourly, daily, and monthly HSIs in the three cities have been decreasing year by year, which is due to the effort of each city's environmental protection bureau to improve air quality in recent years. However, the effect of improvement is still small and needs to be further enhanced. Comparing between 2015 and 2018, the fractional reductions in the hourly, daily, and monthly HSIs in 2018 were 12.5%, 16.2%, and 18.4% in New Taipei; 7.3%, 8.8%, and 10.8% in Taichung; and 6.7%, 9.5%, and 11.3% in Kaohsiung, respectively. Thus, the effects of improvement in the three cities are in the following sequence: New Taipei > Kaohsiung > Taichung. It accurately reflects the current situation of the haze problem in the three cities. Many countries experience severe haze pollution, especially in Asia. Li et al. [60] quantitatively examined the impact of public concern over haze by the utilization of an econometric model. However, people's feelings of haze stress are typically not quantified. There is still a lack of evidence on how haze stress affects people's mental and physical health [61]. Therefore, this study does not explore that people of different ages, genders, and living in different locations may have different feelings of haze stress. The values of four temporal HSIs were all distributed in a range between 0 and 2, and only a few values were greater than 2 (Figures 4-6). Additionally, their average values were between 0.5 and 1.0. So, a reasonable categorical method of people's feelings for determining haze stress is recommended, such as using an HSI grade with five scales (Table 3). Further, HIS = 1 is considered as the criteria between fair and anxious. The grade point ranges of the first four scales are all 0.5, and the grade point of the last scale is greater than two. Five descriptors of people's feelings were used (good, fair, anxious, uncomfortable, and very uncomfortable) to correspond to the individual HSI grades. The categorical method may help policy makers to understand the quantitative influence of haze, on the basis of which they may devise some effective countermeasures. The percentages of five people's feelings for the hourly, daily, and monthly haze stresses in the three cities during 2015-2018 are shown in Table 4, which can be summarized as follows: (1) Different haze stress conditions caused by the degree of contaminated situations of city lead to a systematic variability of people's hourly, daily, and monthly feelings; (2) the sum of the three temporal people's feelings in good and fair in New Taipei City and in Taichung City were higher than 75% and 83%, respectively; (3) the lowest sum of the three temporal people's feelings in good and fair occurred in the monthly haze stress of Kaohsiung City (50.0% in 2015, 2016, and 2018); (4) people's hourly, daily, and monthly feelings in uncomfortable occurred most frequently in Kaohsiung City, especially in 2018; and (5) a low probability of people's hourly feeling in uncomfortable appeared in Taichung City in 2015-2018 (≤0.4%). Comparing the results with the frequency of people's struggles on the haze stresses in Taiwan, the data in Table 4 can truly reflect the feelings of people in the three cities.  The results in Tables 2 and 4 demonstrate that the HSI estimated using the inverse variance weightings method is highly consistent with the monitoring data and fully agrees with people's feelings.

Conclusions
Ambient haze mainly includes PM 2.5 , SOA, and moisture. Therefore, the concentration of PM 2.5 cannot be used to express haze. Both government managers and people need a quantitative method to understand the effectiveness of improvement strategies and the public's feelings in the haze stress. This study proposed an approach for evaluating the HSI to quantify the effect of haze and the feelings of people in a region. The established evaluation method integrates three parameters-PM 2.5 , RH, and O 3 + NO 2 -with inverse-variance weighting to estimate the values of four temporal HSIs. The applied results for the slightly, moderately, and heavily contaminated cities in term of haze stress show that this method can achieve the goals. The estimated results of the improvement effects in regional haze can successfully reflect the current situation of the three cities according to their fractional reductions of ambient PM 2.5 ( Figure 2) and HSIs (Table 2). Based on the frequency of people's struggles with the haze stress, it can also truly reflect the feelings of people in the three cities (Table 4). Therefore, the proposed method can successfully provide a quantification index of haze stress, thereby helping policy makers to understand the phenomenon of haze so that more stringent strategies can be implemented. This study presented a categorical method to analyze the effect of haze stress, which makes the quantitative results easier for people to understand.