Environ Eng Res > Volume 28(5); 2023 > Article
Kim, Kwoun, Lee, and Jo: Air Quality Index through Inverse Evaluation of Hazard Quotient for Public Indoor Facilities - schools, child daycare centers and elderly nursing homes

### Abstract

Indoor air quality indices (IAQI-S, IAQI-C and IAQI-E) were developed to manage air quality in public facilities for vulnerable groups such as schools, child daycare centers, and elderly nursing homes, respectively. In this study, hazard quotient (HQ) was first designated, then the concentrations of each pollutant were calculated by adding the exposure factor of residents. The presented index was more stringent than comprehensive air quality index (CAI) for outdoor atmosphere. Also, composite indices that integrate individual indices for each pollutant were developed for quick and convenient recognition of the current air quality by administration officers or teachers and to take remedial actions. Among all data collected in field measurements, 75.4%, 71.2% and 35.6% were classified as ‘Good’ or ‘Moderate’ in school classrooms, child daycare centers and elderly nursing homes, respectively

### 1. Introduction

Public schools, child daycare centers and elderly nursing homes are indoor spaces designed for growing children and the elderly, which are classified as vulnerable age groups. In particular, children are at higher risk of exposure to pollutants heavier than air because they are smaller than adults and have a high respiration rate relative to their body weight [1,2]. According to the National Report (NIER), elderly people living in nursing homes spend nearly 24 hours of the day in the facility, and are exposed to indoor pollutants throughout the day. In the elderly, the volume of the lungs decreases and respiratory infections occur frequently. For example, the lung capacity of a 70-year-old is reduced to 50% of that of a 50-year-old, and respiratory function is deteriorated, allowing frequent bronchial disease. Thus, the Korean government has specified strict air quality standards for public facilities used by these sensitive groups. The daily average concentrations of PM10, PM2.5 and CO2 for the maintenance guideline are 75 μg/m3, 35 μg/m3 and 1,000 ppm, respectively.
Indoor air pollutants increase the risk of various diseases, including asthma, in school-aged and preschool children and the elderly. In particular, long-term exposure to fine dust (PM10, PM2.5) causes respiratory diseases, decreased lung function, heart disease, and lung cancer [3,4]. In addition to drowsiness, headache and dizziness, CO2 concentration is related to asthma diagnosis [5,6].
At present, the government grades the current outdoor air quality using the Comprehensive Air Quality Index (CAI) and delivers it to the public (https://www.airkorea.or.kr). This index alerts people to the outdoor air quality and provides health effects. However, there is no official index that occupants or managers can use to quantify the real-time air quality for public indoor spaces in most countries including Korea. In the case of Taiwan suffering from air pollution, the IAQI was proposed by referring to the cancer risk and hazard quotient (HQ) values calculated through carcinogenicity and non-carcinogenicity assessment [7]. Saad et al.(2017) presented an IAQI by combining various regulations from US EPA, WHO, HKPED (Hong Kong Environmental Protection Department), IEESC (Institute of Environmental Epidemiology in Singapore) and Malaysian DOSH (Department of Occupational Safety & Health) [8]. In addition, EIAQI (Environment Indoor Air Quality Index) was made by adding thermal control index (TCI) to the IAQI value. Since the IAQI pollution level has a higher impact than the TCI, the hazard of the IAQI was given a higher weight than the TCI.
Air quality indices (AQIs) are mostly formulated according to health-based recommendations for short-term or long-term exposure. The composite or overall AQI that is used to communicate the real-time air quality to the public is usually prepared from sub-indices for individual pollutants. Most countries have designed their AQIs based on the US EPA model, in which pollutant concentrations are transformed onto a normalized numerical scale of 0 to 500. Unlike the outdoor environment, the occupants or users of these facilities are constantly exposed to consistent air quality. In addition, health effects by index grade were presented so that occupants and managers can quickly identify and respond to indoor air quality levels.
In accordance, this study emphasizes the importance of indoor air quality for public spaces by introducing a new approach to design the index for customized indoor air quality control. The index for each facility was defined as IAQI-S (Indoor Air Quality Index-School), IAQI-C (Indoor Air Quality Index - Child daycare center) and IAQI-E (Indoor Air Quality Index - Elderly nursing home). In methodology, while other studies find the HQ at the final stage because they aim to hazard assessment of pollutants, this study inserted the HQ first, then the CA could be calculated by adding the exposure factor of users. In addition, since some field measurements revealed low levels of Rn, VOCs (volatile organic compounds) and O3, the current IAQI was designed focusing on pollutants of interest present in relatively high concentration such as PM10, PM2.5 and CO2.

### 2.1. Development of Customized Indoor Air Quality Index for Each Facility

The present indoor air quality indices (IAQI-S, IAQI-C, IAQI-E) were developed with a focus on health effects based on the hazard quotient (HQ) of occupants of each facility. The hazard quotient was defined such that adverse health effects are unlikely to occur for values less than or equal to 1 [9]. Former studies used an exposure factor (EF)with an average value of the population, and calculated HQ by substituting the concentration of pollutants (CA) as the breakpoint for each grade [7, 10]. However, in this study, EF was evaluated by adding twice the standard deviation to the average value in order to include the case where the main users of each facility were relatively vulnerable to a given pollutant [11]. In addition, an inverse calculation method was chosen, in which the designated HQ was first inserted and then CA was calculated by substituting the exposure factors of the main users for each facility. In this case, the worst-case exposure factor was applied in order to include potential cases sensitive to pollutants. The existing method obtained the HQ value at the final calculation step, such that the health effect at only that concentration might be defined. The inverse calculation finds the concentration of the pollutant at the final step, so the breakpoint can be determined based on health effects, making it more convenient to define the health effect for each grade.
##### (1)
$HQ=CA×IR×ET×EF×EDBW×ATRfC×IRS/BWs$
In Eq. (1)., HQ indicates the hazard quotient, and CA is the concentration of the pollutant (mg/m3). RfC represents the reference concentration of each pollutant for indoor air quality standards of public facilities (PM10 75 μg/m3, PM2.5 35 μg/m3, CO2 1,000 ppm). IRS (Standard Inhalation Rate) and BWS (Standard Body Weight) are standard respiration rate and standard body weight, respectively. US EPA defines them as 20 m3/day and 70 kg, respectively [12]. This study used exposure factors defined in the ‘Korean Exposure Factors Handbook’ and ‘Korean Exposure Factors Handbook for Children’ released by the National Institute of Environmental Research (NIER). The variables, ET, EF and ED are exposure time (hr/day), exposure frequency (day/yr), and exposure duration (yr), respectively, and AT (averaging time) is the cumulative exposure time (day) for the facility [10].

### 2.2. Field Data Collection

To verify the indices developed through this study, field data were collected at 46 elementary schools located in metropolitan areas including Seoul, Gyeonggi-do, Incheon, and Chungcheong-do and Jeollabuk-do, as depicted in Fig. 1, and 78 daycare centers and 9 elderly nursing homes mainly in Gyeonggi-do, Korea. The used data for school classrooms were PM10, PM2.5, and CO2 measured by a device based on light scattering monitor (11D, Grimm Aerosol Technik, Germany) during school semesters from 2019 to 2020. Mini-volume air samplers (Model BMW 2500, Total Eng., Seoul, Korea) with an impactor classifying 2.5 μm- or 10 μm-particles were placed at 30 cm from the back wall and 1.2–1.5 m above the floor. IoT sensors (R-AQM, RM tech, Korea) were used for indoor PM10 and PM2.5 in daycare centers and nursing homes during the period from Nov. 2020 to Feb. 2021, the winter season in Korea. CO2 was measured in real time by non-dispersive infrared spectrometer (NDIR, TR-76i, T&D, Japan). More detailed monitoring specifications and analysis are provided in our previous publication [13].

### 3. Results and Discussion

The method of establishing the index for each facility is explained step by step in the following section. Values were comparatively evaluated with the existing indoor air quality index proposed in Taiwan (T-IAQI) and the domestic outdoor air quality index (CAI) of Korea.

### 3.1. Hazard Quotient by Facility

The hazard quotient (HQ) for potential effect on human health was calculated according to the definition derived by the US EPA (Eq. (1)) [14]. According to the national statistics for Korean exposure factors, exposure time (ET), exposure frequency (EF) and exposure duration (ED) are 8 hours, 190 days and 1 year for schools; 10.5 hours, 250 days and 1 year for child daycare centers; and 24 hours, 365 days and 5 years for elderly nursing homes, respectively [15]. The relative values of IR to BW for Korean people of different ages also were taken from the handbook [16]. Average time (AT) was determined by multiplying ED by 365 days. Reference concentration (RfC) indicates the base level for health effect of each pollutant. The EPA guidelines calculated the relative ratio of standard inhalation rates to body weight (IRs/BWs) of a general person using values of 20 m3/day and 70 kg, respectively [17].
The value of IRs/BWs was calculated by the Three-Sigma Rule based on the ‘Korean Factors Handbook’. Exposure factors for students varied with ages; for example, IR/BW was 0.56 m3/day.kg for a third year elementary school student, whereas according to the working manual of child daycare centers, IR/BW was 1.48 m3/day.kg for infants and 0.63 m3/day.kg for 5-years old-children. The ages of seniors staying in nursing homes ranged from 65 years to greater than 80. Their IR/BW ranged from 0.32 to 0.38 m3/day.kg.
In Table 1, the hazard quotient for each facility depending on air quality ratings was defined as noted. Based on the relevant references [10, 17], the grade ‘Good’ was designated as 0.1, which is very unlikely to have harmful effects. A range of 0.1 to 1.0 indicates a low level of health effects [11], and the potential impact is very high above 1.0. In IAQI-S, the health standard defined by law for schools (0.34) was designated as ‘Moderate’; indoor air quality standard levels for IAQI-C and IAQI-E were set at ‘Caution’ (0.986) and ‘Unhealthy’ (1.688) levels, respectively, in consideration of residence time. In order to designate high concentration values rarely found at each facility as ‘Hazardous’, the HQ value was determined by multiplying the difference between the standard value and a lower grade value by 6 for IAQI-S and IAQI-C and by 7 for IAQI-E. In order to gradually increase the HQ value as the grade increases, the gradients were designated as 1.5, 3 and 4.5 for school, 2, 4 and 6 for child daycare center, and 3.5 and 7 for elderly nursing home, respectively.
To establish the breakpoints of each pollutant for rating, CA values were obtained by inserting HQ values defined in Table 1 into Eq. (1), and the results are summarized by grade in Table 2 for each facility.

### 3.2. Establishment of Indoor Air Quality Index

The breakpoints were summarized in Tables 3 to 5 to be clearly visible according to the EPA-AQI and the Korean (CAI). The air quality index rating from 0 to 500 was determined by dividing the concentration range of each pollutant (PM10, PM2.5, CO2) into six descriptive categories from ‘Good’ to ‘Hazardous’ based on the HQ. Higher scores indicate air quality that is harmful to health. The general air quality index is rated from 0 to 500 with four grades in the Korean CAI and six grades in the EPA-AQI [18]. Since the HQ values of elderly nursing homes for ‘Very Unhealthy’ and ‘Hazardous’ are significantly higher than those of school and child daycare centers, the indices for each grade in the IAQI-E were designated as 50, 100, 150, 200, 350 and 500 respectively.
The index value (Ip) for a target pollutant (p) was calculated through linear interpolation (Eq. (2)) which is frequently used by the Korean Ministry of Environment and US EPA for outdoor AQIs [18]. Here, Cp is the atmospheric concentration of the pollutant, and BPHI and BPLO are the maximum and minimum pollution levels for the relevant regime, respectively, corresponding to the concentration breakpoints. IHI and ILO are the IAQI values corresponding to BPHI and BPLO, respectively, i.e. indicating the highest and lowest index values of each regime.
##### (2)
$IP=IHI-ILOBPHI-BPLO×(CP-BPLo)+ILO$
Tables S1 to S3 summarize the index description for each facility. By designating the National Air Quality Maintenance Standard for public indoor spaces (PM10 75 μg/m3, PM2.5 35 μg/m3, CO2 1,000 ppm) as ‘Caution’ for daycare centers and ‘Unhealthy’ for senior care facilities, occupants and managers could simply monitor indoor air quality in real time. Considering ambient level, the CO2 reference concentration started as ‘Good’ with a value of 300 ppm. The health effect of each index was restructured according to the HQ values obtained by substituting each reference concentration into Eq. (1) through comprehensive literature review as referred in Table 2.

### 3.3. Composite Index

The composite index developed in this study is a single numerical value used to express the air quality in consideration of the combined health effects of individual pollutants (PM10, PM2.5, CO2). It follows the definition for each category presented in Tables 3 to 5. Based on the CAI calculation step, indoor air quality index (IAQI-CI(C)2) could be determined by adding an additional point (EP1) according to the number of grades above ‘Caution’ to the maximum index value (IAQI-CI(C)1) among the individual index of PM10, PM2.5 and CO2. In case the grade above ‘Caution’ is two or three, the additional points of 50 or 75 depending on facility were added to the maximum index value, respectively (Eq. (3) and (4)). Then, an additional point (EP2) depending on the individual grade of each pollutant was added as shown in Eq. (5). In contrast to AQI, the introduction of EP2 emphasizes the significance of indoor air quality.
##### (3)
$IAQI-CI (C)1=Maximum index value$
##### (4)
$IAQI-CI (C)2=IAQI-CI (C)1+EP1$
##### (5)
$IAQI-CI (Composite Index)=IAQI-CI (C)2+EP2$
• EP1 : 50, in cases with more than two ‘Caution’ grades among PM10, PM2.5, and CO2

• EP1 : 75, in cases with more than two ‘Caution’ grades among PM10, PM2.5, and CO2

• EP2 : (5, 10, 20, 40) × n, depending on number of grades (n) for ‘Caution’, ‘Unhealthy’, ‘Very Unhealthy’, or ‘Hazardous’ among PM10, PM2.5, and CO2

### 3.4. Comparison of Air Quality Indices

Outdoor air quality indices are often designated by national policies [19, 20], whereas indoor air quality index levels are only suggested in the literature [7, 8, 12, 21]. Thus, the CAI applied to air quality or the AQI of the US EPA is sometimes used as a reference value for evaluation of indoor air quality. However, since the composition of fine dust and exposure intensity vary greatly between indoor and outdoor sources, the impact on human health will also be very different [22]. Accordingly, this study compared the reference concentration levels of the air quality index and the indoor air quality index, in order to determine whether the air quality index can be applied to evaluate indoor air quality. For this purpose, the CAI of Korea, composed of the same grades ranging from 0 to 500 as the existing index, and AQI of US EPA, AQI of UK and a proposed IAQI in Taiwan (T-IAQI) were compared. Since CAI, AQI of US EPA and UK AQI, which are atmospheric air quality indices do not include CO2, total bioaerosols and VOCs which belong to indoor air quality guidelines, only the breakpoints of PM10 and PM2.5, and the conversion value of CO2 were compared.
When comparing the breakpoints of PM10 (Fig. 2), EPA-AQI had higher PM10 values than other indices for a given index value, and T-IAQI also had relatively high PM10 values despite being the only indoor air quality index. On the other hand, CAI for atmosphere was located below other indices, which means that when the same concentration of pollutants was applied to all the indices, CAI yields the highest index value and grade accordingly. However, in the graph on the right, which is enlarged to show index values below 150, the breakpoint values of CAI corresponding to the index values of 50 and 100 were higher than those of the T-IAQI. Since most of the pollutant concentrations found in indoor spaces appear in the index range of 50 to 100, CAI is expected to have a higher index value than T-IAQI on average.
A similar trend was observed in PM2.5, as seen in Fig. 3. However, at the index value of 100, the AQIs of CAI and EPA were lower than that of T-IAQI. Since this did not reflect the guideline for classifying PM2.5 as a Class 1 carcinogen by the International Agency for Research on Cancer (IARC) in 2013, T-IAQI was calculated as a relatively high breakpoint in this regime. Therefore, establishment of breakpoints corresponding to the index values of 50 and 100 along with the comparison result of PM10 can be considered an important part in the development of the indoor air quality index.
As a consequence, if the air quality index standard presented in this study is applied, a high index value will be derived even for a relatively low PM concentration, and indoor air quality could be controlled more strictly.

### 3.5. Evaluation of Indoor Air Quality for Each Facility

To increase the accuracy for exposure concentration and to respond quickly to changes in concentration, real-time hourly concentrations of PM10, PM2.5 and CO2 were predicted using a moving-average method (Eq. (6)). C8hr avg in Eq. (6) was obtained as a prediction of the concentration of the next period by weighting the average concentration of the past 1 hour more heavily for data from the past 4 hours to the present. C4 and C1 are the average concentrations for the past 4 hours and 1 hour from the reference time, respectively. In schools and daycare centers, the 8-hour average was thought be more reasonable than 24-hour average because the concentration was relatively low in the absence of children.
##### (6)
$C8hr avg=(C4×4+C1×4)÷8$

#### 3.5.1. Comparative analysis of IAQI-S with T-IAQI and CAI

The index-based indoor air quality was evaluated by applying the IAQI-S developed in this study to concentration data (n=110,189) measured in 52 schools (46 elementary schools, 4 middle schools and 2 high schools) (138 classrooms). The average concentrations of classrooms for PM10 and PM2.5 were 30.93 μg/m3 and 14.82 μg/m3, respectively (Table S4). The average CO2 was 715.81 ppm throughout the study duration. In 2020, during the field measurement period, a relatively low average concentration was found due to frequent ventilation and refraining from vigorous activities to prevent the spread of Covid-19. This could be evidenced by contrast to the high concentrations measured between 2017 and 2019 [23].
The maximum concentration values for each pollutant (Table 6) are lower than the breakpoints corresponding to the ‘Hazardous’ grade of the IAQI-S presented in this study. Therefore, it can be confirmed that the IAQI-S sufficiently includes the concentration range actually shown in school classrooms. As a result of the cumulative frequency analysis of PM10, PM2.5 and CO2 concentrations in the classroom, approximately 97.6% of the total data for PM10 found in the classroom and 96.8% for PM2.5 met the maintenance standards of the School Health Act., and 73.1% of classrooms satisfied the standard for CO2.
As summarized in Table 3, the composite index of IAQI-S was distributed from ‘Good’ to ‘Very Unhealthy’, with 27.6%, 47.8%, 19.1%, 4.8% and 0.7% of data in the ‘Good,’ ‘Moderate,’ ‘Caution,’ ‘Unhealthy,’ and ‘Very Unhealthy’ grades, respectively. Compared to the percentage of Total, which represents the percentile sum of the data for each grade of PM10, PM2.5 and CO2, the grade ‘Good’ was lower than ‘Total’ and the grades over ‘Moderate’ showed higher values.
On the other hand, the T-IAQs of PM10 and PM2.5 for ‘Good’ and ‘Moderate’ were 89.9% and 98.1%, respectively, slightly higher than the IAQI-S. Since CAI using a 24-hour predicted moving average for PM10 and PM2.5 was obtained from the measurements at schools from 07:30 to 15:30 for elementary schools and 07:30 to 18:00 for middle and high schools, it was not possible to compute a 24-hour forecast moving average, which requires measurements from the preceding 12 hours. Therefore, in the same way as IAQI-S, CAI was applied to the data calculated by the 8-hour predicted moving average, and compared with IAQI-S. In addition, in order to compare the data distributions, since IAQI-S and CAI are composed of six and four grades, respectively, the grades were classified as ‘Good’, of which both belonged to the same index values (0–50), ‘Moderate’ (50–100), and higher than 100.
Since there is no index for CO2 in CAI, breakpoints of CO2 in IAQI-S were applied to the index values (50, 100, 250, 500) for the CAI grade, resulting in ‘Good’(700 ppm), ‘Moderate’(1,000 ppm), ‘Unhealthy’(2,500 ppm) and ‘Very unhealthy’(5,000 ppm). As a result, CAI and IAQI-S showed 56.5% and 37.9% for ‘Good’ respectively. The sum of ‘Unhealthy’ and ‘Very Unhealthy’ for PM10 in CAI was 3.8% which was lower than the sum of values above ‘Caution’ in IAQI-S (4.9%). For PM2.5, CAI was higher than IAQI-S (39.7%) for the ‘Good’ grade (59.0%), and was 35.0% in ‘Moderate’, which was lower than IAQI-S (54.3%). The sum of ‘Unhealthy’ and ‘Very Unhealthy’ grades in CAI was 6.0%, which was the same as the sum of ‘Caution’ and higher grades in IAQI-S. Looking at the Total value, while the ‘Good’ grade of CAI was 60.8%, higher than the IAQI-S (48.1%), ‘Moderate’ was 29.3%, lower than IAQI-S (41.6%).
On the other hand, for the composite index for IAQI-S and comprehensive index for CAI, a higher value (40.3%) was found in ‘Good’ than when using IAQI-S alone (27.6%). For grades with an index value of 100 or higher, the CAI was 24.5%, which was slightly higher than the IAQI-S (24.6%). On the whole, it was confirmed that the CAI could evaluate the air quality of the school classroom more positively than the IAQI-S. Thus, the composite index evaluates the general air quality level somewhat more strictly than does the sum of individual indices of pollutants.

#### 3.5.2. Comparative analysis of IAQI-C with T-IAQI and CAI

Results of the cumulative frequency analysis for child day-care centers (Table S5) indicated that approximately 99.9%, 99.6% and 91.5% of the total data for indoor PM10, PM2.5 and CO2, respectively, satisfied the IAQ standard of public child daycare center.
When comparing the PM10 data evaluated by applying T-IAQI and IAQI-C (Table 4), the ‘Good’ grade in T-IAQI accounted for 30.5% of data, which was higher than that of IAQI-C (6.9%), and ‘Moderate’ accounted for 65.2% of data, which was lower than that of IAQI-C (80.5). PM2.5 showed similar tendencies, although the detailed data are not presented, the 0% PM2.5 ‘Unhealthy’ and ‘Very unhealthy’ obviously were lower than those of IAQI-C (data number: 25,520 and 880 respectively). Also, IAQI-C and T-IAQI showed similar increase/decrease patterns in PM10 and PM2.5. This might be because daycare centers maintain relatively lower concentrations than schools. For CO2, T-IAQI decreased by 0.0% (#132 data) in the ‘Good’ grade compared to the IAQI-C (47.5%), but showed a higher ratio of 65.6% in the ‘Moderate’ grade than IAQI-C (34.4%). In conclusion, the T-IAQI more positively expressed the health effect than the IAQI-C for PM10 and PM2.5, but CO2 has a greater impact on the air quality rating at low concentrations than at high concentrations.
Whether the IAQI-C properly reflects indoor air pollution and data distribution for each index was investigated by comparing the 8-hour moving-average data of 78 child daycare centers with those of CAI, as shown in Table 9. Because IAQI-C and CAI have six and four grades, respectively, values were divided into three corresponding index ranges: ‘Good’, ‘Moderate’ and ‘index value 100 or higher’ for comparison. Additionally, since CAI does not consider CO2, four grades for CO2 breakpoints were added for relative comparison: ‘Good’(500 ppm), ‘Moderate’(800 ppm), ‘Unhealthy’(1,500 ppm) and ‘Very unhealthy’(4,000 ppm).
The comparison showed that CAI classified 68.9% of all data as ‘Good’, which was 39.2% higher than that with IAQI-C. The sum of the data percentages above ‘Very Unhealthy’ was 9.9%, which was 3.8% lower than the ‘Caution’ grade of the IAQI-C developed in this study. These findings confirmed that CAI better expressed indoor air quality than IAQI-C.
The composite index value of T-IAQI was relatively high in ‘Unhealthy for Sensitive groups’ compared to ‘Caution’ of IAQI-C due to the high dependency on CO2, but other grades showed lower values than IAQI-C. In accordance, the CO2 index of T-IAQI needs to be reestablished with consideration of the background concentration of CO2 in the air. In addition, since T-IAQI does not include data for ‘Very Unhealthy’ and ‘Hazardous’, it seems insufficient to evaluate high concentration areas.
The comparison between the composite index of IAQI-C and comprehensive index of CAI indicated a large difference in ‘Good’, between 4.0% and 38.1% for IAQI-C and CAI, respectively, ‘Moderate’ showed closer values of 67.2% and 34.5%. There was no significant difference in the sum of ‘Good’ and ‘Moderate’, which was 72.6% for CAI and 71.2% for IAQI-C. However, this difference is expected to increase if the actual CAI is used with a 24-hour average. Thus, indoor air quality could be expressed more accurately because CAI could be calculated at lower concentration than IAQI-C for the same period. Above all, CAI did not include the CO2 index, and was limited in expressing indoor air quality.

#### 3.5.3. Comparative analysis of IAQI-E with T-IAQI and CAI

Nine elderly nursing homes revealed average concentrations were 12.86 μg/m3, 10.12 μg/m3 and 706.51 ppm for PM10, PM2.5 and CO2, respectively (Table S6). Although measurements were performed at the same time as in schools and daycare centers, they showed relatively low concentration levels. Maximum PM10 and CO2 concentrations were lower due to less indoor activity, while PM2.5 was high probably due to winter heating. The maximum measured concentration was lower than the breakpoint of the ‘Hazardous’ grade of IAQI-E. Considering that concentrations of pollutants are expected to increase after the Covid-19 pandemic, it could be concluded that the IAQI-E sufficiently analyzed concentration ranges in elderly nursing homes.
The sum of ‘Good’ and ‘Moderate’ in IAQI-E summarized in Table 5 was 81.5% and 65.7% for PM10 and PM2.5, respectively. CO2 was 40.6% at highest in ‘Moderate’. The composite index was only 4.0% in ‘Good’ which was lower than Total (35.2%), but a value of 1% was also seen in ‘Hazardous’.
In T-IAQI, the grade ‘Good’ for PM10 was 71.6%, higher than that of IAQI-E (55.1%) despite the small difference in ‘Moderate’ between 27.4% and 26.4%. PM2.5 also showed high proportions of ‘Good’ and ‘Moderate’ in T-IAQI (65.7% and 32.8% respectively). However, CO2 in T-IAQI was lower for ‘Good’ (0.3%) and ‘Very Unhealthy’ (7.3%) than those of IAQI-E (12.5% and 20.3%, respectively). Furthermore, ‘Good’ in Total was 45.9% higher than that of IAQI-E (35.2%). In other words, as in other facilities’ indices, T-IAQI better assesses the air than IAQI-E both for PM10 and PM2.5.
On the other hand, the sum of grades ‘Good’ and ‘Moderate’ in the composite index was lower in T-IAQI (0.3% and 29.4%, respectively) than in IAQI-E (4.3% and 31.3%). This likely is due to significant dependency on CO2. Similar results were found in the ‘Unhealthy for sensitive groups’, which contained a much larger proportion of CO2 (62.8%) than PM10 (1.0%) and PM2.5 (1.5%). Thus, T-IAQI should be modified to consider CO2, particularly in low ranges.
In CAI, 61.4% of ‘Total’ data which are the sum of all pollutants were ‘Good’, higher than those of IAQI-E and T-IAQI. There was a larger difference between CAI and the presented indices for the grades above ‘Unhealthy’ in elderly nursing homes than in schools and child daycare centers. The indices of this study were developed based on health impacts, and exposure time (ET) and exposure frequency (EF) of elderly nursing homes are much higher than schools and child daycare centers. Thus, for the same pollutant concentration, the index values of elderly nursing homes could be higher than those of schools and child daycare centers. Overall, the sum of data above ‘Caution’ using IAQI-E was distributed more widely than in IAQI-S and IAQI-C.

### 4. Conclusions

Indoor air quality indices (IAQI-S, C, E) for schools, daycare centers, and elderly nursing homes were developed in this study based on the risk index (HQ), which is an assessment method for non-carcinogenic risk. The current IAQI represents indoor air quality more precisely than the atmospheric air index through the HQ value differentiated by facility according to the occupant’s exposure factor. In particular, by applying the 8-hour moving average concentrations of particulate matters and carbon dioxide, it was possible to represent the actual air quality during the presence of people more realistically and respond faster than the 24-hour average including absence of occupants.
As a result of the IAQI-S evaluation, among all the data (n=110,189), 95.1% of PM10, 94% of PM2.5 and 80% of CO2 were classified as ‘Good’ and ‘Moderate’. IAQI-C and IAQI-E showed similar trends, with most measurements satisfying the national IAQ standards. In addition, a Composite Index was developed so that the real-time IAQ of each facility can be easily understood by expressing the air quality as a single numerical value. The Composite Index was obtained by adding additional points to the maximum index value based on the target pollutant causing the most harmful effects. Thus, 75.4% of measurements were classified as ‘Good’ or ‘Moderate’ with IAQI-S, which is lower than the Total (sum of individual pollutants).
In the IAQI developed in this study, the current standards of the Ministry of Environment and the Ministry of Education were used as the reference concentration (RfC) because there were not sufficient data on the health effects of each pollutant concentration. Thus, if the national standard is revised in the future, there is a limitation that it is necessary to reform the reference values for each index.

### Acknowledgments

This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT, MOE) (No. 2019M3E7A1113077).

### Notes

Conflict-of-Interest Statement

The authors declare no conflict of interests.

Authors Contributions

Based on Contribution Roles Taxonomy: D.Y.K. (MA student) conducted data curation. J.K. (PhD student) supported data analysis. T.J.L. (Associate Professor) wrote an original manuscript. Y.M.J. (Professor) wrote and revised the manuscript.

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##### Fig. 1
Location of study facilities.
##### Fig. 2
Comparison of PM10 breakpoints in US EPA AQI, UK AQI, CAI and T-IAQI for index values from 0 to 500 (left), and from 0 to 150 (right).
##### Fig. 3
Comparison of PM2.5 breakpoints in US EPA AQI, UK AQI, CAI and T-IAQI for index values from 0 to 500 (left), and from 0 to 150 (right).
##### Table 1
HQ values for each facility and their description.
Category HQ value
School Child daycare center Elderly nursing home
Value Basis Value Basis Value Basis
Good 0.100 Base line of HQ 0.100 Base line of HQ 0.100 Base line of HQ
Moderate 0.340 Standard level of school health law 0.543 0.100 + (0.986 – 0.100)×0.5 0.550 0.100 + (1.000 – 0.100)×0.5
Caution 0.700 0.340 + (0.340 – 0.100)×1.5 0.986 Level of indoor air quality standard 1.000 Level of HQ evaluation
Unhealthy 1.060 0.340 + (0.340 – 0.100)×3 1.872 0.986 + (0.986 – 0.543)×2 1.688 Level of indoor air quality standard
Very unhealthy 1.421 0.340 + (0.340 – 0.100)×4.5 2.758 0.986 + (0.986 – 0.543)×4 4.096 1.688 + (1.688 – 1.000)×3.5
Hazardous 1.781 0.340 + (0.340 – 0.100)×6 3.643 0.986 + (0.986 – 0.543)×6 6.504 1.688 + (1.688 – 1.000)×7
##### Table 2
Calculated breakpoints (CA) from Eq. (1) by grade.
Grade Facility PM10(μg/m3) PM2.5(μg/m3) CO2 (ppm) References
Good School 22 10 294 WHO(2005)
Jeon et al.(2020)
Wu et al. (2021)
Child daycare center 8 4 101
Elderly nursing home 4 2 59

Moderate School 75 35 1,000 UK AQI (2011)
Zhu and Li (2017)
Lee el al., (2018)
IAQMG (2019)1)
School Health Law of Korea (2021)
IAQM Act in Korea (2021)2)
Child daycare center 41 19 551
Elderly nursing home 24 11 326

Caution School 154 72 2,059 IEES (1996)3)
US EPA (2006)
Wang et al. (2008)
Lahrz et al. (2008)
Zhu and Li (2017)
Jeon et al.(2020)
Child daycare center 75 35 1,000
Elderly nursing home 44 21 592

Unhealthy School 234 109 3,118 Wang et al. (2008)
DOSH (2010)4)
US EPA (2020)
Child daycare center 142 66 1,899
Elderly nursing home 75 35 1,000

Very Unhealthy School 313 146 4,177 AEC Act in Korea (2021)5)
School Health Law of Korea (2021)
Child daycare center 210 98 2,797
Elderly nursing home 182 85 2,427

Hazardous School 393 183 5,236 HSE in UK (2005)6)
NIOSH (2019)
OSHA (2019)
ACGIS (2019)
AEC Act in Korea (2021)5)
Child daycare center 277 129 3,696
Elderly nursing home 289 135 3,853

1) Indoor Air Quality Management Group in Hong Kong

2) Indoor Air Quality Management Act in Korea

3) Institute of Environmental Epidemiology in Singapore

4) Department of Occupational Safety and Health in Malaysia

5) Air Environment Conservation Act in Korea

6) Health and Safety Executive in U.K.-EH40 Workplace Exposure Limits

##### Table 3
Distribution of index grades for school classroom data.
Pollutant INDEX Good Moderate Caution1) Unhealthy Very Unhealthy Hazardous
PM10 IAQI-S 37.9% 57.2% 4.8% 0.1% 0.0% 0.0%
T-IAQI 27.0% 62.9% 10.0% 0.1% 0.0% 0.0%
CAI 56.5% 39.7% - 3.7% 0.1% -

PM2.5 IAQI-S 39.7% 54.3% 6.0% 0.0% 0.0% 0.0%
T-IAQI 39.7% 58.4% 1.9% 0.0% 0.0% 0.0%
CAI 59.0% 35.0% - 6.0% 0.0% -

CO22) IAQI-S 66.8% 13.2% 17.5% 2.3% 0.2% 0.0%
T-IAQI 7.3% 52.6% 20.1% 20.0% 0.0% 0.0%
CAI1 66.8% 13.2% - 19.2% 0.8% -

Total3) IAQI-S 48.1% 41.6% 9.4% 0.8% 0.1% 0.0%
T-IAQI 24.7% 58.0% 10.6% 6.7% 0.0% 0.0%
CAI 60.8% 29.3% - 9.6% 0.3% -

Composite Index IAQI-S 27.6% 47.8% 19.1% 4.8% 0.7% 0.0%
T-IAQI 0.6% 56.3% 18.9% 18.5% 5.7% 0.0%
Comprehensive Index CAI 40.3% 35.2% - 22.6% 1.9% -

1) Corresponding to ‘Unhealthy for sensitive groups’ for T-IAQI

2) Based on CO2 index of IAQI-S.

3) Sum of data for each grade of PM10, PM2.5 and CO2.

##### Table 4
Distribution of index grades for child daycare center data.
Pollutant INDEX Good Moderate Caution1) Unhealthy Very Unhealthy Hazardous
PM10 IAQI-C 6.9% 80.5% 10.6% 2.1% 0.0% 0.0%
T-IAQI 30.5% 65.2% 4.3% 0.0% 0.0% 0.0%
CAI 77.2% 21.2% - 1.6% 0.0% -

PM2.5 IAQI-C 34.7% 54.5% 7.8% 2.9% 0.1% 0.0%
T-IAQI 67.1% 31.6% 1.3% 0.0% 0.0% 0.0%
CAI 82.1% 14.9% - 2.9% 0.0% -

CO22) IAQI-C 47.5% 34.4% 8.7% 9.0% 0.3% 0.0%
T-IAQI 0.0% 65.6% 25.1% 9.3% 0.0% 0.0%
CAI 47.5% 27.6% - 23.1% 1.9% -

Total3) IAQI-C 29.7% 56.5% 9.0% 4.6% 0.1% 0.0%
T-IAQI 32.6% 54.1% 10.2% 3.1% 0.0% 0.0%
CAI 68.9% 21.2% - 9.2% 0.7% -

Composite Index IAQI-C 4.0% 67.2% 15.7% 12.3% 0.8% 0.0%
T-IAQI 0.0% 62.7% 24.6% 12.0% 0.7% 0.0%
CAI 38.1% 34.5% - 25.1% 2.3% -

1) Corresponding to ‘Unhealthy for sensitive groups’ for T-IAQI

2) Based on CO2 index of IAQI-S.

3) Sum of data for PM10, PM2.5 and CO2.

##### Table 5
Distribution of index grades for elderly nursing home data.
Pollutant INDEX Good Moderate Caution1) Unhealthy Very Unhealthy Hazardous
PM10 IAQI-E 55.1% 26.4% 14.5% 3.6% 0.4% 0.0%
T-IAQI 71.6% 27.4% 1.0% 0.0% 0.0% 0.0%
CAI 91.7% 8.1% - 0.2% 0.0% -

PM2.5 IAQI-E 37.8% 27.9% 22.1% 8.8% 3.4% 0.0%
T-IAQI 65.7% 32.8% 1.5% 0.0% 0.0% 0.0%
CAI 79.9% 16.7% - 3.3% 0.1% -

CO22) IAQI-E 12.5% 40.6% 19.3% 20.3% 7.3% 0.0%
T-IAQI 0.3% 29.6% 62.8% 7.3% 0.0% 0.0%
CAI 12.5% 40.6% - 46.9% 0.0% -

Total3) IAQI-E 35.2% 31.6% 18.6% 10.9% 3.7% 0.0%
T-IAQI 45.9% 29.9% 21.8% 2.4% 0.0% 0.0%
CAI 61.4% 21.8% - 16.8% 0.0% -

Composite Index IAQI-E 4.0% 67.2% 15.7% 12.3% 0.8% 0.0%
T-IAQI 0.3% 29.4% 58.9% 10.6% 0.8% 0.0%
CAI 10.8% 41.2% - 47.6% 0.4% -

1) Corresponding to ‘Unhealthy for sensitive groups’ for T-IAQI

2) Based on CO2 index of IAQI-S.

3) Sum of data for grades PM10, PM2.5 and CO2.

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