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Data of major pollutant concentrations such as PM₁₀ and NO₂, and precipitation data were collected from national air monitoring sites and from the Korean Meteorological Administration (KMA, 2012) for the period of 1999 to 2008. PM₁₀ concentration is measured by the β-ray absorption method and NO₂ concentration is measured by the chemiluminescent method at the air monitoring sites (MOE, 2012). The NO₂ data for 1999, which has a lower reliability, however, were excluded. PM₁₀ data during Asian dust periods, as designated by the National Weather Service of Seoul, were also excluded to remove the effect of Asian Dust from our analysis. Asian Dust was observed for 114 days during our analysis period of ten years. Most of the precipitation patterns showed “local” characteristics such as rainfall occurring on the east side of Seoul, but not on the west. So it was determined that spatial averaging would only confuse our analysis. Therefore, for this research, the Seosomun urban air monitoring site and the Seoul-station roadside air monitoring site, which are located in the central part of Seoul and are close to the weather monitoring site about 2 km away from where we obtained the meteorological information, were selected as the target sites. The selected sites are shown in Fig. 1.

Fig. 1. 
Location of air and weather monitoring sites: (a) Seosomun urban air monitoring site, (b) Seoul-station roadside air monitoring site, (c) Seoul weather monitoring site.

In this study, the IETD, which is obtained from serial correlation analysis (Adams et al., 2000), was applied to define a precipitation event. As illustrated in Fig. 2, if the non-precipitation time duration between two rainfall events is greater than that of the determined IETD, the first and second precipitation events are considered to be independent. On the other hand, if non-precipitation time is smaller than that of the determined IETD, it is considered to be a continuous event, not two separate events.

Fig. 2. 
Example of separation of two precipitation events.

The volume, duration, non-precipitation time interval and average intensity of rainfall can then be determined for the independent precipitation events. An event volume is defined as the sum of the hourly reported amount of precipitation for the separate event as determined by the IETD, and the duration of rainfall is the period from the start to the end of one precipitation event. The non-precipitation time interval is the time period from the end point of the previous precipitation event to the starting point of the next. The average event intensity can be calculated by dividing the event volume by the duration. The assumption that there is uniform rainfall volume distribution throughout the duration of an event is applied (Joksimovié, 1999).

To separate out independent rainfall events from continual precipitation, the IETD needs to be defined initially. The methods used for this definition are autocorrelation, coefficient of variation (Nix, 1994), and average annual number of rainfall events (Nix, 1994; Heaney et al., 1977). The autocorrelation method uses the lag time, when the coefficient of autocorrelation levels off near 0, as the IETD. The autocorrelation coefficient of Seoul weather station is close to 0.06 for a 12 hour lag time, as presented in Fig. 3. The method using average annual number of rainfall events, on the other hand, showed a relatively constant variation after the 6 hr IETD (Fig. 4).

Fig. 3. 
Autocorrelation coefficients for Seoul weather station, Korea.

Fig. 4. 
Average annual number of rainfall events, in Seoul, Korea.

Seoul is a megacity with a population of over 10 million, so air pollutant emissions should change dramatically during periods of heavy commuting. Looking at the average hourly concentrations of PM₁₀ and NO₂ for a sample year of 2006 measured at 27 air monitoring sites in Seoul we can see that there seems to be a fluctuation period of about six hours, as shown in Fig. 5, due to the impact of daily commuting pattern. Adams et al. (1986) and Kauffman (1987) also recommended that the IETD should be 6 hours for urban areas, in general. Therefore, the IETD in Seoul was determined to be 6 hours for this study.

Fig. 5. 
Hourly variation of PM₁₀ and NO₂ in Seoul in 2006, average concentrations of 27 air monitoring sites.

Concentration data of PM₁₀ and NO₂ for the 10 year period were separated according to conditions of precipitation and non-precipitation by using the pre-determined IETD. For a more accurate analysis, in general, concentration variation attributable to other parameters such as the emission amount, wind direction, and wind speed, should be excluded. Analyzing the reduction effect on the air pollutants due to precipitation scavenging effect only is also very difficult, as the concentration sometimes increases after the onset of precipitation. In this study, therefore, the determination of whether the concentration variation of pollutants was caused by primarily precipitation or by a variation in emission pattern was performed as follows:

1) Calculation of the “time-of-day” hourly average concentration of pollutants during non-precipitation events from the data for ten years, i.e. the 10-year concentration average for 1 am, 2 am, ···, 11 pm, 12 am, all 24 excluding hours with precipitation.

2) Subtraction of the concentration one hour prior to the beginning of precipitation from that at the termination of rainfall for each independent precipitation event as determined by IETD.

3) Thus, the effect of precipitation scavenging can be defined as the difference between the concentration variation under the conditions of the precipitation event calculated from Step 2 and the difference in the 10-year average concentrations calculated from Step 1 for the two times specified in Step 2.

where,

• CV_pre=Concentration variation under condition of precipitation event
• C_pre-end=Concentration at termination of precipitation event
• C_pre-beg-1=Concentration at 1 hour prior to beginning of precipitation event
• ACV_non-pre=Difference in 10-year average concentrations under condition of non-precipitation between the two times specified in Eq. 1 event
• AC_non-pre-end=10-year average non-precipitation conc. for time specified by event Cpre-end
• AC_{non-pre-beg-1}=10-year average non-precipitationconc. for time specified by event Cpre-beg-1
• E_pre=Effect of precipitation event on PM₁₀ and NO₂ concentration

The effect of precipitation scavenging on PM₁₀, as mentioned above, can also be illustrated using a sample as in Fig. 6. Precipitation was observed at 6 am, 9 am and 12 pm with an interval of 3 hours each. Therefore, the period from 6 am to 12 pm is defined as a single precipitation event, because the IETD was set to be 6 hours. The difference in the 10-year average concentrations for 12 pm and 6 am under conditions of non precipitation (ACV_non-pre) is +14 μg/m³ which, by definition, is the difference between 73 μg/m³, the 10-year average at 12 pm, signifying the time of rainfall termination of the event (AC_non-pre-end), and the concentration of 59 μg/m³ at 5 am, representing the 10-year average one hour prior to the beginning of the event (AC_{non-pre-beg-1}). On the other hand, the concentration variation during the precipitation event at the monitoring site (CV_pre) can be calculated as 58-65=-7 μg/ m³ (Fig. 6). Finally, the effect of precipitation on PM₁₀ (E_pre) for this sample event can be defined as (-7)-(+14)=-21 μg/m³. Such calculations were carried out for all precipitation events during the 10 year period as defined by the IETD. The utilization of long-term averages and the fact that atmospheric concentrations of most air pollutants in urban areas, including PM₁₀ and NO₂, usually follow a general repetitive diurnal pattern helps validate such an approach as the one explained above.

Fig. 6. 
Example of method for analysis of effect of precipitation scavenging on pollutant concentrations.

Goodness-of-fit tests are generally used to identify the appropriate probability distribution model that best fits the data (Bentler et al., 1980). In this study, the Stat::Fit software (Benneyan, 1998) was utilized for the goodness-of-fit test, and the results of the goodness-of-fit tests are shown in Fig. 7.

Fig. 7. 
Examples of CDF (Cumulative Density Function): (a) Normal distribution of Group 1 for PM₁₀, (b) Weibull distribution of Group 1 for NO₂.

The characteristics of precipitation events derived by application of the IETD in Seoul are presented in Fig. 8. Precipitation events occurred in Seoul 946 times during our ten-year period, and the duration of precipitation ranged from 1 to 71 hours. The amount of precipitation also ranged from 0.1 to 483.3 mm during the entire period. Precipitation cases with a duration of less than one hour had the highest frequency with 22.6 % (214 times), and a duration of 1 to 2 hours was next with 10.4% (99 times). Overall, precipitation events with a duration of less than 12 hours occurred a total of 775 times, and this accounted for 80% of the total. Therefore, it should be noted that short duration precipitation events were much more prevalent in Seoul.

Fig. 8. 
Characteristics of precipitation during 10 years in Seoul: (a) amount of rainfall, (b) duration of rainfall.

The amount of precipitation less than 1 mm had a ratio of 32.1% (304 times) while amounts between 1 to 10 mm accounted for 36.7% (347 times) during the 10-year period. Thus, precipitation events of less than 10 mm in Seoul over these 10 years accounted for about 70% of the total, whereas precipitation cases of over 200 mm were mainly concentrated in July, August, and September when our peninsula is affected by the monsoon season and multiple typhoons.

The hourly concentration variations of PM₁₀ and NO₂ at urban and roadside air monitoring sites during conditions of precipitation and non-precipitation, respectively, are shown in Fig. 9 and Fig. 10. Fig. 9(a) shows that the average difference of average hourly concentrations of PM₁₀ between the wet and dry cases was 24.5 μg/m³ at our urban air monitoring sites. The average PM₁₀ concentration at these sites during precipitation events was about 63% of non-precipitation conditions. The pattern of hourly PM₁₀ concentration variation under non-precipitation conditions was similar with that of typical urban areas. However, PM₁₀ concentrations under precipitation conditions during daytime did not increase but stayed relatively constant in spite of increasing number of vehicles. This may be explained by a combination of the following factors:

1) wash-out effect of precipitation, 2) low PM₁₀ production caused by reduction of photo-chemical reactions during rainfall, and 3) activity reduction of emission sources such as construction sites.

Fig. 9. 
PM₁₀ hourly variations under conditions of precipitation and non-precipitation: (a) urban air monitoring sites, (b) roadside air monitoring sites.

Fig. 10. 
NO₂ hourly variations under conditions of precipitation and non-precipitation: (a) urban air monitoring sites, (b) roadside air monitoring sites.

Fig. 9(b) also shows that the average difference of average PM₁₀ concentrations between precipitation and non-precipitation events were 19.9 μg/m³ at roadside air monitoring sites. The average PM₁₀ concentration at road-side air monitoring sites during precipitation events were about 72% of non-precipitation conditions. At road-side air monitoring sites, the pattern of hourly PM₁₀ concentration variation under conditions of precipitation and non-precipitation were similar with each other. This may mean that the hourly PM₁₀ concentration at road-side sites increase by a relatively stronger direct effect of vehicle emissions despite the rainfall. Consequently, the reduction effect of precipitation scavenging at urban sites was higher than that at road-side air monitoring sites. The ratio of wet to dry concentrations for PM₁₀ at background sites in Canada was 0.66 (Veira et al., 2013). This ratio was similar to our value for the urban air monitoring site while that of the road-side air monitoring site was much closer to one. This also supports the argument that on-road emissions somewhat negate the wash-out effect of precipitation.

As shown in Fig. 10(a), the average differences of average NO₂ concentration between precipitation and non-precipitation events were 7.8 ppb at the monitoring sites. The average NO₂ concentration during precipitation events was about 80% of non-precipitation conditions. Therefore, we could confirm that the reduction effect of precipitation scavenging on NO₂ was lower than that of PM₁₀ at our urban and road-side sites. Under non-precipitation conditions, the NO₂ concentration at urban sites increased in proportion to the traffic in the morning, while decreasing presumably due to photochemical reaction during the daytime. NO₂ concentration variation during daytime under precipitation conditions was not observed. At roadside sites, as shown in Fig. 10 (b), the NO₂ concentration variation under the conditions of non-precipitation were similar with the case of precipitation, just like PM₁₀, because the amount of NO emissions/NO₂ production by vehicles was presumably larger than NO₂ reduction by photochemical reaction.

The amount of rainfall was classified into six groups; less than 1 mm, 1.1~5 mm, 5.1~10 mm, 10.1~20 mm, 20.1~50 mm, and over 50 mm. Then, distributions of concentration reduction by precipitation for each group were estimated through the goodness-of-fit test. Estimates are Maximum Likelihood Estimation (MLE), Lower Bound unknown, Interval Type equal probability, Accuracy of fit 0.0003, Level of Significance 0.05, Distribution Type continuous distributions, and the parameter is unbounded. The Normal distribution was selected in preference regardless of rank among the results of accepted distribution types. After that, a CDF (Cumulative Density Function) for each type was applied to estimate the probability that the concentration will be decrease over 0 after precipitation relative to non-precipitation times.

Table 1 presents distribution types and probabilities for the six groups of precipitation amount classification, as mentioned above. In group 1, less than 1 mm, we were not able to fit any distribution to the PM₁₀ and NO₂ reductions. The “No fit” in group 1 means that the fluctuation of PM₁₀ and NO₂ concentrations after precipitation changes randomly. On the other hand, the other groups showed mostly Normal distributions, except for the NO₂ in group 2 which showed a Weibull distribution.

Most cases in group 1 were drizzle events with shortterm light rain averaging 2.2 hours. Because reduction mechanisms such as collision or absorption between pollutants and rain drops could not be very active, washout by precipitation appeared to have little effect on pollutant removal. When the amount of precipitation is less than 1 mm, alternatively, an increase of PM₁₀ concentration in the atmosphere may be observed, because the effect of traffic and other emissions can be higher than the washout effect of the rain. Castro et al. (2010) also reported that if the rain intensity is about 0.6 mm/h or lower, the result may be a considerable increase in the number of aerosols measured - up to 89% more - with an increase in the number of particles smaller than 1.3 μm and a decrease in the number of particles larger than 1.3 μm.

The probability of PM₁₀ concentration reduction increased with amount of rainfall with a high of 80.5% in group 6 when the amount of rainfall was greater than 50 mm. From the results of Castro et al. (2010), the detected number of particles decreased 20%, and large- and small-sized particles also decreased all together during rain events with intensities of over 3.2 ±1.5 mm/h. However, correlations between the probabilities of NO₂ concentration reduction and amount of rainfall was not observed, as the probability of NO₂ concentration reduction decreased from 56.8% in group 2 to 53.9% in group 6.

The average pollutant concentration reduction of each group classified by amount of rainfall was calculated (Table 2). The PM₁₀ concentration reduction, in general, increased with amount of rainfall for both urban and roadside air monitoring sites: group 1 (0.5 mm average precipitation), group 2 (2.7 mm average precipitation), group 3 (7.3 mm average precipitation), group 4 (14.3 mm average precipitation), group 5 (31.8 mm average precipitation), group 6 (112.9 mm average precipitation), had concentration reductions of -0.3 μg /m³, -8.6 μg/m³, -8.1 μg/m³, -19.6 μg/m³, -21.3 μg /m³, -25.6 μg/m³, respectively.

The PM₁₀ concentration reductions for the two group pairs 2, 3 and 4, 5 were quite similar, even with a significant difference in the amount of average precipitation. The concentration reduction difference of PM₁₀ between groups 3 and 4, however, was 11.5 μg/m³. PM₁₀ concentration reduction due to precipitation scavenging seems to have a significant critical point, maybe even a shift in dominant mechanism, around a rainfall amount of 10 mm.

The log regression equations for effect of PM₁₀ concentration reduction by precipitation are as follows:

Seosomun urban air monitoring site:

Seoul-station road-side air monitoring site:

where,

• y=concentration reduction of PM₁₀(μg/m³)
• x=amount of rainfall (mm)

A log-shaped regression equation was most suitable for the expression of pollutant reduction by precipitation scavenging, as can be seen by the R² value for the reduction of PM₁₀ concentration at the urban air monitoring site being 0.920. From the estimated log-shaped regression equation, the nonlinear correlation between precipitation and reduction of PM₁₀ concentration is well represented (Fig. 11(a)). It has been reported that PM₁₀ levels reduce significantly for precipitation amounts up to around 5 mm/day, whereas for larger values of precipitation amounts its relative effect diminishes (Barmpadimos et al., 2011).

Fig. 11. 
Regressions of concentration reduction of PM₁₀ and NO₂ according to amount of precipitation: (a) PM₁₀ at urban air monitoring sites, (b) PM₁₀ at roadside air monitoring sites, (c) NO₂ at urban air monitoring sites, (d) NO₂ at roadside air monitoring sites.

The R² on the reduction of PM₁₀ concentration at the road-side air monitoring site was 0.792 (Fig. 11(b)) which was lower than that of the urban air monitoring site. For NO₂ concentrations at road-side air monitoring sites (Fig. 11(d)), a much lower correlation between precipitation and concentration reduction was observed, most likely due to the mobile emission effect. Plaude et al. (2012) also reported that the reduction effect of precipitation scavenging on air pollutants was low due to the sources on the surface layer.

These regression equations give us a quantitative analysis regarding PM₁₀ concentration reduction with increase of precipitation. Through comprehensive analysis of this and the previous section, there is greater probability of large reductions in PM₁₀ concentration with increase in precipitation amount. The correlation between average concentration reduction and amount of rainfall is quite high for PM₁₀, but, there is an inherent numerical error because of using averages. The presence of this error between the actually reduced concentrations and the estimated concentration reductions using regression equations needs to be recognized.

The ranges of NO₂ concentration reduction by precipitation at urban and road-side air monitoring sites were 1~4 ppb, 2~5 ppb, respectively (Table 2). The NO₂ concentrations were reduced under precipitation but the NO₂ concentration reduction and rainfall at both site types had extremely low correlation (Fig. 11 (c) and (d)). Lim et al. (2013), however, analyzed that the NO₂ concentration gradually decreases with increased rainfall, and especially showed the largest reduction efficiency to be events with over 100 mm of rainfall. Finally, we need to realize that the selected sites in this study were centrally located in Seoul, so the reduction effect of precipitation should be underestimated due to the influence of emissions from the mobile sector being a major NO₂ source.