# Spatio-temporal analysis of particulate matter extremes in Seoul: use of multiscale approach

- 259 Downloads

## Abstract

This paper considers a problem of analyzing temporal and spatial structure of particulate matter (PM) data with emphasizing high-level \(\text {PM}_{10}\).
The proposed method is based on a combination of a generalized extreme value (GEV) distribution and a multiscale concept from scaling property theory used in hydrology. In this study, we use hourly \(\text {PM}_{10}\) data observed for 5 years on 25 stations located in Seoul metropolitan area, Korea. For our analysis, we calculate monthly maximum values for various duration times and area coverages at each station, and show that their distribution follows a GEV distribution. In addition, we identify that the GEV parameters of \(\text {PM}_{10}\) maxima hold a new scaling property, termed ‘piecewise linear scaling property’ for certain duration times. By using this property, we construct a 12-month return level map of hourly \(\text {PM}_{10}\) data at any arbitrary *d*-hour duration. Furthermore, we extend our study to understand spatio-temporal multiscale structure of \(\text {PM}_{10}\) extremes over different temporal and spatial scales.

## Keywords

Generalized extreme value distribution Kriging Particulate matter Return level Scaling property## Notes

### Acknowledgements

This paper is based on author’s report awarded at “The Seoul Institute Research Competition 2015” and the data provided by The Seoul Institute. This work was supported in part by the National Research Foundation of Korea (NRF) Grant funded by the Korea government (MSIP) (Nos. 20110030811 and 2015R1D1A1A01056854).

## References

- Blanchet J, Davison AC (2011) Spatial modeling of extreme snow depth. Ann Appl Stat 5:1699–1725CrossRefGoogle Scholar
- Ceresetti D, Anquetin S, Molinié G, Leblois E, Creutin J-D (2012a) Multiscale evaluation of extreme rainfall event predictions using severity diagrams. Weather Forecast 27:174–188Google Scholar
- Ceresetti D, Ursu E, Carreau J, Anquetin S, Creutin J-D, Gardes L, Girard S, Molinie G (2012b) Evaluation of classical spatial-analysis schemes of extreme rainfall. Nat Hazards Earth Syst Sci 12:3229–3240Google Scholar
- Coles S (2001) An introduction to statistical modeling of extreme values. Springer, New YorkCrossRefGoogle Scholar
- Cooley D, Cisewski J, Erhardt J, Jeon S, Mannshardt E, Omolo BO, Sun Y (2012) a survey of spatial extremes: measuring spatial dependence and modeling spatial effects. Revstat 10:135–165Google Scholar
- Davison AC, Padoan SA, Ribatet M (2012) Statistical modeling of spatial extremes. Stat Sci 27:161–186CrossRefGoogle Scholar
- De Michele C, Kottegoda NT, Rosso R (2001) The derivation of areal reduction factor of storm rainfall from its scaling properties. Water Resour Res 37:3247–3252CrossRefGoogle Scholar
- Dey DK, Yan J (2015) Extreme value modeling and risk analysis: methods and applications. CRC Press, Boca RatonCrossRefGoogle Scholar
- Friedman JH (1991) Multivariate adaptive regression splines. Ann Stat 19:1–67CrossRefGoogle Scholar
- Gupta VK, Waymire E (1990) Multiscaling properties of spatial rainfall and river flow distribution. J Geophys Res 95:1999–2009CrossRefGoogle Scholar
- Heffernan JE, Stephenson AG (2016) ismev: an introduction to statistical modeling of extreme values. R package version 1.41. http://www.ral.ucar.edu/ericg/softextreme.php
- Hosking JRM (1990) L-moments: analysis and estimation of distributions using linear combinations of order statistics. J R Stat Soc Ser B 52:105–124Google Scholar
- Huser R, Davison AC (2014) Space-time modelling of extreme events. J R Stat Soc Ser B 76:439–461CrossRefGoogle Scholar
- Kim U, Kim J, Hong J (2014) A study on establishing \(\text{ PM }_{2.5}\) advisory criteria with emission source management system in Seoul (written in Korean). Research Report of The Seoul Institute, Seoul. http://www.si.re.kr/node/49968 Google Scholar
- Kim U, Kim J (2011) A study of building customized management strategies based on local \(\text{ PM }_{10}\) emission inventory in Seoul (written in Korean). Research Report of Seoul Development Institute, Seoul. http://www.si.re.kr/node/24705 Google Scholar
- Laio F (2004) Cramer-von Mises and Anderson-Darling goodness of fit tests for extreme value distributions with unknown parameters. Water Resour Res 40:W09308. doi: 10.1029/2004WR003204 CrossRefGoogle Scholar
- Lu H-C, Fang G-C (2003) Predicting the exceedances of a critical \(\text{ PM }_{10}\) concentration-a case study in Taiwan. Atmos Environ 37:3491–4399CrossRefGoogle Scholar
- Masseran N, Razall AM, Ibrahim K, Latif MT (2016) Modeling air quality in main cities of Peninsular Malaysia by using a generalized Pareto model. Environ Monit Assess 188:1–12CrossRefGoogle Scholar
- Menabde M, Seed A, Pegram G (1999) A simple scaling model for extreme rainfall. Water Resour Res 35:335–339CrossRefGoogle Scholar
- Nychka D, Furrer R, Paige J, Sain S (2016) Fields: tools for spatial data. R package version 8.4-1. http://www.image.ucar.edu/fields
- Paciorek CJ, Yanosky JD, Puett RC, Laden F, Suh HH (2009) Practical large-scale spatio-temporal modeling of particulate matter concentrations. Ann Appl Stat 3:370–397CrossRefGoogle Scholar
- Padoan SA, Ribatet M, Sisson SA (2010) Likelihood-based inference for max-stable processes. J Am Stat Assoc 105:263–277CrossRefGoogle Scholar
- Panthou G, Vischel T, Lebel T, Blanchet J, Quantin G, Ali A (2012) Extreme rainfall in West Africa: a regional modeling. Water Resour Res. doi: 10.1029/2012WR012052 Google Scholar
- Panthou G, Vischel T, Lebel T, Quantin G, Pugin A-C, Blanchet J, Ali A (2013) From pointwise testing to a regional vision: an integrated statistical approach to detect nonstationarity in extreme daily rainfall. Application to the Sahelian region. J Geophys Res: Atmos 118:8222–8237Google Scholar
- Qin S, Liu F, Wang C, Song Y, Qu J (2015) Spatial-temporal analysis and projection of extreme particulate matter (\(\text{ PM }_{10}\) and \(\text{ PM }_{2.5}\)) levels using association rules: a case study of the Jing-Jin-Ji region, China. Atmos Environ 120:339–350CrossRefGoogle Scholar
- Rodríguez R, Navarro X, Casas MC, Redaño A (2013) Rainfall spatial organization and areal reduction factors in the metropolitan area of Barcelona (Spain). Theor Appl Climatol 114:1–8CrossRefGoogle Scholar
- Van de Vyver H (2015) On the estimation of continuous 24-h precipitation maxima. Stoch Environ Res Risk Assess 29:653–663CrossRefGoogle Scholar
- World Health Organization (2006) Air quality guidelines: global update 2005: particulate matter, ozone, nitrogen dioxide, and sulfur dioxide. p 12. http://apps.who.int/iris/bitstream/10665/69477/1/WHO_SDE_PHE_OEH_06.02_eng
- Yanosky JD, Paciorek CJ, Laden F, Hart JE, Puett RC, Liao D, Suh HH (2014) Spatio-temporal modeling of particulate air pollution in the conterminous United States using geographic and meteorological predictors. Environ Health. doi: 10.1186/1476-069X-13-63 Google Scholar
- Yoon P, Kim T-W, Yoo C (2013) Rainfall frequency analysis using a mixed GEV distribution: a case study for annual maximum rainfalls in South Korea. Stoch Environ Res Risk Assess 27:1143–1153CrossRefGoogle Scholar