Novel index to comprehensively evaluate air cleanness: the "Clean

Air quality on our planet has been changing in particular since the industrial revolution (1750s) because of anthropogenic emissions. It is becoming increasingly important to visualize air cleanness, since clean air deserves a valuable resource as clean water. Global standard to quantify the level of air cleanness is swiftly required, and we defined a novel concept, namely "Clean aIr Index, CII." The CII is a simple index defined by the normalization of the amount of individual air pollutants. A CII value of 1 indicates completely clean air (no air pollutants), and 0 indicates the presence of air pollutants up to numerical 5 environmental criteria for the normalization. In this time, the air pollutants used in the CII were taken from the Air Quality Guidelines (AQG) set by the World Health Organization (WHO), namely O3, particulate matters, NO2 and SO2. We chose Japan as a study area to evaluate CII because of the following reasons: i) accurate validation data, as the in situ observation sites of the Atmospheric Environmental Regional Observation System (AEROS) provide highly accurate values of air pollutant amounts, ii) obvious numerical criteria, namely the Japanese Environmental Quality Standards given by the Ministry of the 10 Environment (MOE). We quantified air cleanness in terms of the CII for the all 1896 municipalities in Japan, and used Seoul and Beijing to evaluate Japanese air cleanness. The amount of each air pollutant was calculated using a model that combined the Weather Research and Forecasting (WRF) and Community Multiscale Air Quality (CMAQ) models for 1 April 2014 to 31 March 2017. The CII values calculated by the WRF-CMAQ model and the AEROS measurements showed good agreement with a correlation coefficient of 0.66±0.05, averaging 498 municipalities where the AEROS measurements have operated, 15 which was higher than that of Air Quality Index (AQI) of 0.57±0.06. The CII values averaged for the study period was 0.67, 0.52 and 0.24 in Tokyo, Seoul and Beijing, respectively, thus, the air in Tokyo was 1.5 and 2.3 times cleaner, i.e., less amounts of air pollutants, than those in Seoul and Beijing, respectively. The average CII value for the all Japanese municipalities was 0.72 over the study period. The extremely clean air, CII ≈ 0.90, occurred in southern remote islands of Tokyo and around west of the Pacific coast, i.e., Kochi, Mie and Wakayama Prefectures during summer with transport of clean air from the ocean. 20 We presented "Top 100 clean air cities" in Japan as one example of application using CII in society. We confirmed that the CII enabled the quantitative evaluation of air cleanness. The CII can be useful value in various scenarios, such as encouraging sightseeing and migration, investment and insurance company business, and city planning. The CII is a simple and fair index that can be applied to all nations.

as the overall AQI. Hu et al. (2015) performed a comparison study of several indices for air quality using the measurements in China, and showed AQI underestimates the severity of the health risk associated with the exposure to multi-pollutant air pollution because AQI does not appropriately represent the combined effects of exposure to multiple pollutants. An index to quantify the air quality is still under development, and the global standard has not been established yet.
In this study, we propose a novel concept of index to quantify air cleanness, "Clean aIr Index (CII)" to establish the global 45 standard for quantifying air cleanness. The purpose of CII is to comprehensively evaluate air cleanness by normalizing the amounts of common air pollutants with numerical environmental criteria. In this time, we selected surface O 3 , particulate matter (PM), NO 2 , and SO 2 from the Air Quality Guidelines (AQG) set by the World Health Organization (WHO) (WHO, 2005). As a first approach, we chose Japan for evaluating the CII because of i) the validation data, as the in situ observation sites of the Atmospheric Environmental Regional Observation System (AEROS) provide highly accurate air pollutant amounts, and 50 ii) the obvious numerical criteria, i.e., the Japanese Environmental Quality Standards given by the Ministry of the Environment (MOE).
In this paper, Sect. 2 defines the CII. Section 3 describes the model for calculating the CII for all Japanese municipalities, and validates the CII values by comparing with those derived from AEROS measurements. In Sect. 4, air cleanness in each municipality is quantified and the area and season of high air cleanness in Japan is identified using the CII. 55 Table 1. Value of numerical criteria (s), O3, suspended particulate matter (SPM), NO2, and SO2 used in this study. We used the criteria of the Japanese Environmental Quality Standards (JEQS) given by the Ministry of the Environment (MOE) of Japan. Average of air pollutant amount calculated by the model for all Japanese municipalities over the study period is shown. The CII is a simple index defined by the normalization of each air pollutant amount. The definition of CII is given by where x[i] is the amount of ith air pollutant, s[i] is the numerical criteria for the normalization of x [i], and N is the number of air pollutants considered in the CII. In this equation, a higher CII value indicates cleaner air, with a maximum of 1 indicating 60 the absence of air pollutants. The CII value decreases as the amount of air pollutant increases, with a value of 0 indicating that the amount of air pollutant is equal to the numerical criteria and a negative value indicating that the amount of air pollutant is larger than the numerical criteria.
In this study, the air pollutants used in the CII are O 3 , PM, NO 2 and SO 2 following the WHO AQG (WHO, 2005) as mentioned above, i.e., N = 4. The field of this study is Japan, thus, we set the values of s according to the Japanese Environmental pollutant. It mostly originates from anthropogenic sources, especially fossil fuel combustion (e.g., power plants and vehicles).
The environmental SO 2 level was severe in 1970s in Japan. But the SO 2 concentration has been decreasing owing to the 80 use of desulfurization technologies and low-sulfur heavy oil, and JEQS for SO 2 was satisfied at most AEROS sites in 2012 (Wakamatsu et al., 2013).

Model simulation
A model simulation was performed to calculate the amounts of O 3 , SPM, NO 2 , and SO 2 of all Japanese municipalities (1896 in total; note that wards in megacities, such as Tokyo, Osaka, and Fukuoka were counted as independent municipalities). The

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AEROS measurement network does not cover the all municipalities, thus we employed the model simulation. We combined two

WRF-CMAQ settings
We used the WRF model version 3.7 (Skamarock et al., 2008)  water vapor mixing ratio as well as two-dimensional grid nudging for sea surface temperature were performed every six hours.

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The CMAQ model version 5.1 was used as a chemical transport model in this study. Byun and Schere (2006)  formations (Pye and Pouliot, 2012;Pye et al., 2013;Appel et al., 2017), ISORROPIA algorithms (Fountoukis and Nenes, 2007) and binary nucleation (VehkamäKi et al., 2002) has been implemented. 45 kinds of aerosols components, including sulfate, ammonium, black carbon, organic carbon and sea salt, have been considered in this model.
The molecules and aerosols were provided by the emissions (anthropogenic, biogenic and sea salt) from surface or transports from the boundaries of domains, and were transported by the wind fields calculated in the WRF model and the parameteri-120 zations of horizontal/vertical diffusions, dry deposition and gravitational settling (see Byun and Schere, 2006;Appel et al., 2017). Anthropogenic emissions were defined using the MIX Asian emission inventory version 1.1 which included emissions by power, industry, residential, transportation and agriculture (Li et al., 2017). This inventory of SO 2 , NO X , PM, VOC, CO and The MOZART provided the distributions of more than 80 kinds of chemical species and aerosols for the inputs of our model calculations. The amount of pollutants in each Japanese municipality were defined at the longitude/latitude of the municipal office, with the weighted average of the outputs at model grid points near the municipal office using the following equation: (2). We also derived the amount of pollutants in Seoul and Beijing for the comparisons with that inside Japan from the model outputs of Domain 1.

Spatial-temporal variation of CII
The spatial-temporal variations of CII based on the WRF-CMAQ model is shown in Fig. 2 (a). The horizontal and vertical axes correspond to the date and municipal number, respectively. The lower municipal number corresponds approximately to 150 the municipalities in northeast Japan and vice versa, and the major cites in Japan are shown in the vertical axis. The CII value clearly depended on both area and season. The CII value tended to be higher in summer because of transportation of unpolluted air mass from the Pacific Ocean. In August 2014, July 2015 and September 2016, the CII values of almost all municipalities were higher than 0.9 for a few weeks. However, the local CII values decreased to below 0.5 over a short period from May because of local air pollutant emissions and the enhancement due to photochemical reactions induced by strong UV sunlight.

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The CII value was moderate (0.7-0.8) and stable from November to February over Japan but gradually decreased from February to May or June because polluted air was transported from East Asia (e.g., Park et al., 2014), and the sunlight strengthened.
These spatial-temporal features were reproduced by the AEROS measurements. Figures 2 (b) and (c) show the time series variations in the daily CII value derived from the AEROS measurements and the difference (WRF-CMAQ − AEROS), respec-  tively. AEROS is operated by the MOE of Japan and has 1901 observation sites for monitoring air pollutants in FY2016. The

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AEROS data were obtained from the atmospheric environment database of the National Institute for Environmental Studies (Kankyosuchi database (in Japanese)). We used the AEROS observation sites that cover more than 80 % of days in the study period, and 498 in 1896 municipalities were covered by the AEROS measurements. The AEROS measurement results were averaged for all observation sites in each municipality in case that there were several observation sites in one municipality. In this comparison, the AEROS Ox data were compared to the WRF-CMAQ O 3 data because the composition ratio was larger 165 than 90-95 % O 3 in Ox (Akimoto, 2017).
The CII value depends not only on the amount of O 3 , SPM, NO 2 , and SO 2 (x), but also on their numerical criteria (s), see Eq.
(1). A partial differentiation analysis was performed to determine the sensitivities of the s values of O 3 , SPM, NO 2 , and SO 2 to CII. Figure 3 shows the weighting function for the numerical criteria (K s ) given by 170 As shown in Eq. (3), K s positively correlates with x, and the CII value monotonically increases with increasing s. The temporal variation in CII primarily corresponded with the variation in O 3 . The average K s for O 3 was highest among the species used to calculate the CII in this study, because the x/s value of O 3 was higher than those of SPM, NO 2 , and SO 2 ( Table 1). The value of K s for SPM in western Japan was higher than that in eastern Japan during winter and spring because of the effect of transboundary pollution from East Asia (e.g., Park et al., 2014). The spatial distribution of CII corresponded to those of K s for 175 NO 2 and SO 2 , which explicitly reflected local emission sources, such as megacities and industrial areas. Typical lifetime of NO 2 is approximately a few hours (e.g., Kenagy et al., 2018), and the transport effect was therefore less for these species. We ignored SO 2 emissions from volcanic eruptions, and the SO 2 distribution consequently corresponded to industrial activities.
The spatial distribution of O 3 was negatively correlated to that of NO 2 primarily because of the reactions (R1-R3).

Evaluation of spatial and temporal bias 180
We discuss the spatial and temporal bias in our calculation to clarify magnitude of significant differences in the CII value. We compared the CII mean of all days in the study period between WRF-CMAQ and AEROS for each municipality to investigate the spatial bias in Fig. 4 (a). The histogram of the CII difference showed an asymmetric distribution, thus we fitted the histogram by using the Johnson SU function, which is a probability distribution transformed from the Normal distribution to cover the asymmetry of the sample distribution (Johnson, 1949

Comparison of CII and AQI
In Sect. 3.4, we discuss difference between CII and AQI as a representative of the other indices. We compared these indices calculated from the WRF-CMAQ model and the AEROS measurements. The correlation coefficient (r) of mean for the study period between WRF-CMAQ and AEROS was calculated for each municipality. Figure  In this case, NO 2 is underestimated because of the following reactions:

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where M is a third body for the ozone formation reaction. This discrepancy is less affected for CII than for AQI because the amounts of air pollutants are averaged with being normalized by the numerical criteria.

Visualization of air cleanness in Japan
In Sect. 4, we discuss the area and season of high air cleanness in Japan. Figure 6 shows the average CII over the study period (FY2014-2016) for each Japanese municipality. The average CII of 85 % of municipalities were higher than that of Tokyo (23 210 wards), and those of all the municipalities were higher than those of Seoul and Beijing. Here the JEQS values were employed to the s values to calculate the CII values in Seoul and Beijing to directly compare with those in Japanese municipalities.
The average and standard deviation (1 σ) of CII was 0.67±0.10, 0.52±0.18, and 0.24±0.32 in Tokyo, Seoul, and Beijing, respectively. The value of 1 − CII monotonically increases with air pollutant amounts increase, and the air in Tokyo was 1.5 and 2.3 times cleaner, i.e., less air pollutant amounts, than those in Seoul and Beijing, respectively. The location of the 215 municipalities discussed hereafter is shown in Fig. 7.

Area and season of high air cleanness
We discuss the area and season of highest air cleanness over Japan using the CII in Sect. 4.1. First, the CII average over the study period, FY2014-2016, in each municipality was compared in Fig. 8 (a). The CII averages in northern Japan were higher, and those in municipalities around megacities and industrial areas were lower than the average of all municipalities, 0.72±0.04    (1 σ). Table 2 shows the 10 municipalities with the highest average CII values, which located in eastern Hokkaido and southern remote island in Tokyo. The average CII was approximately 0.81 in these 10 municipalities and the standard deviation (1 σ) over the study period was lower than that in other areas, see Fig. 8 (b), which means the CII remained high throughout the year.

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average CII values on these 30 days for each municipality are displayed in Fig. 8 (c), and Table 3 shows the 10 municipalities with the highest average CII values on these days. These 10 municipalities located in southern remote islands of Tokyo and western Pacific coast area, i.e., Kochi, Mie and Wakayama Prefectures. The average CII of Aogashima-mura municipality in southern remote islands of Tokyo Prefecture was the highest. The average CII of these 10 municipalities was approximately 0.90, which was 0.06, by CII, higher than that of all Japanese municipalities on high-CII days (0.84). Therefore, the highest 235 CII value occurred on the Pacific coast during summer with the condition of few local pollution.
The average CII in these municipalities was 0.84-0.86, which was approximately 0.30-0.32, by CII, higher than that of all municipalities on low-CII days (0.54). The selected 30 days occurred especially at the end of spring and beginning of summer.
Generally, the transboundary pollution effect is large in the cold season, and heavy local pollution occurs in summer because of photochemical reactions induced by strong sunlight (e.g., Nagashima et al., 2010). These pollution effects are less pronounced 245 in the remote islands, thus the CII maintained higher values.
We selected "Top 100 clean air cities" in Japan as one example of use in society of CII by the following method. The average of 30 highest daily CII values in the study period was calculated for each municipality. The 30 days were selected for each municipality, not as the case of Fig. 8 (c) and (d). Table 5 shows the 100 municipalities with the highest average CII values. The municipalities in remote islands of Tokyo, around western Japan, especially around the Pacific coast, and Okinawa Prefectures, 250 were selected.

Air cleanness and human activities
Industrial activities, particularly fossil fuel combustion such as vehicles and power plants, are major sources of air pollutants, and air cleanness is strongly related with human activities. In Sect. 4.2, we discuss the municipalities in Japan with not only air cleanness but also human activity, i.e., 1) clean air with high human activity, 2) clean air with low human activity, 3) dirty 255 air with high human activity, and 4) dirty air with low human activity. In this study, the common logarithm of population density (n), log 10 (n), was employed to quantify human activities following e.g., Kerr and Currie (1995). The n data were obtained from the 2015 Japanese national census (NSTAC, 2016). Figure 9 (a) shows the scatter plot of log 10 (n) and average Average of all Japanese municipalites 0.544  CII for the study period derived from the WRF-CMAQ model and the AEROS measurements for each municipality. A clear negative correlation between log 10 (n) and the CII was observed and the r values were −0.74 and −0.71 for WRF-CMAQ and 260 AEROS, respectively. This negative correlation was formulated by the linear regression with the objective variable of CII and the explanatory variable of log 10 (n), as shown by the dashed lines in Fig. 9 (a).
Approximated CII = a × log 10 (n) + b (4) The parameters of a and b were estimated to be −0.034±0.001 and 0.801±0.002 for WRF-CMAQ, and −0.033±0.001 and 0.796±0.005 for AEROS, respectively. The negative correlation between log 10 (n) and the CII value derived from WRF-CMAQ 265 was reproduced from AEROS, and the parameters of a and b were agreed within their errors.
The CII value showed negative correlation with the human activity, thus the municipalities in groups 2 and 3 are in normal situation. The municipalities in group 1 is ideal case because such municipalities are expected to be industrially advanced as well as to succeed to maintain clean air environment. There are some issues in the municipalities in group 4 because such municipalities can not save clean air in spite of smaller population. It might indicate that there are large air pollution sources, 270 such as large power plant, or air pollutants are transported from the outside. The degree of this categorizing is quantified by difference between the CII and the linear regression line, Eq. (4), (∆CII).
The positive ∆CII value means that the municipality is categorized in group 1, and the negative ∆CII value does group 4. The distribution of ∆CII in the average for the study period is shown in Fig. 9 (b), and Table 6 shows the 10 municipalities with 275 the highest average ∆CII values. All of these municipalities were in Hokkaido and Okinawa prefectures. The higher ∆CII values were observed in northeastern Japan and coastal area. There are many industrial areas in western Japan (Li et al., 2017), which might be one reason for the lower ∆CII values. A combination of CII and ∆CII could be a useful way of evaluating air cleanness in municipality.

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We defined a novel concept of index for quantifying air cleanness, namely CII. This index comprehensively evaluates the level of air cleanness by normalizing the amounts of common air pollutants. A CII value of 1 indicates the absence of air pollutants, and 0 indicates that the amounts of air pollutants are the same as the normalization numerical criteria.  by CII, higher than that of all municipalities on low-CII days (0.54). Furthermore, "Top 100 clean air cities" in Japan was presented as one example of CII to be used in society.
We quantified the air cleanness in municipality with respect to human industrial activities. Population density was used to quantify human activities in this study. A negative correlation between CII and the population density was observed by both the 310 WRF-CMAQ model and the AEROS measurement. The CII was approximated by a linear function of the common logarithm of population density. The differences of CII from this approximation line (∆CII) indicates the CII normalized by human activity. The municipalities with positive ∆CII values are expected to maintain clean air and to be industrially advanced. Those with negative ∆CII values are expected to have certain issues such as large air pollution source and air pollutants transported from the outside. A combination of CII and ∆CII could be a useful way of evaluating air cleanness in municipality.

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The CII can be used in various scenarios, such as encouraging sightseeing and migration, investment and insurance company business, and city planning. The CII can be used for an advertisement of clean air for promoting sightseeing and migration for local governments. The CII is also effective to measure the potential of local brands and tourism resources. Private company can be expected to use CII for ESG (Environmental, Social and Governance) investment. If the CII could be associated with life expectancy, the CII can be applied to insurance business especially in Asian region where urban air pollution is a serious 320 problem. City planning is also a possible use of CII because air cleanness is related to urban form (e.g., McCarty and Kaza, 2015). As mentioned above, the CII has a potential to be applied to policy as well as company business in cities and countries around the world.
Data availability. The WRF-CMAQ model data in this publication can be accessed by contacting the authors. The AEROS measurement data are available through the following link: https://www.nies.go.jp/igreen. Japanese population density data are available through the following in Ministry of Internal Affairs and Communications to give us an idea "TOP 100 clean air cities". TOS thanks to Seidai Nara for his polite technical support.