Journal of Korea Water Resources Association (한국수자원학회논문집)

Korea Water Resources Association (한국수자원학회)
권호 표지
DOI QR코드

DOI QR Code

Evaluating the contribution of calculation components to the uncertainty of standardized precipitation index using a linear mixed model

선형혼합모형을 활용한 표준강수지수 계산 인자들의 불확실성에 대한 기여도 평가

  • Shin, Ji Yae (Research Institute of Engineering Technology, Hanyang University) ;
  • Lee, Baesung (Department of Civil and Environmental System Engineering, Hanyang University) ;
  • Yoon, Hyeon-Cheol ( National Integrated Drought Center, National Disaster Management Research Institute) ;
  • Kwon, Hyun-Han (Department of Civil and Environmental Engineering, Sejong University) ;
  • Kim, Tae-Woong (Department of Civil and Environmental Engineering, Hanyang University)
  • 신지예 (한양대학교(ERICA) 공학기술연구소) ;
  • 이배성 (한양대학교 대학원 건설환경시스템공학과) ;
  • 윤현철 (국립재난안전연구원 국가통합가뭄센터) ;
  • 권현한 (세종대학교 건설환경공학과) ;
  • 김태웅 (한양대학교(ERICA) 건설환경공학과)
  • Received : 2023.06.30
  • Accepted : 2023.08.16
  • Published : 2023.08.31
Download PDF
⟨ Previous Next ⟩

Abstract

Various drought indices are widely used for assessing drought conditions which are affected by many factors such as precipitation, soil moisture, and runoff. The values of drought indices varies depending on hydro-meteorological data and calculation formulas, and the judgment of the drought condition may also vary. This study selected four calculation components such as precipitation data length, accumulation period, probability distribution function, and parameter estimation method as the sources of uncertainty in the calculation of standardized precipitation index (SPI), and evaluated their contributions to the uncertainty using root mean square error (RMSE) and linear mixed model (LMM). The RMSE estimated the overall errors in the SPI calculation, and the LMM was used to quantify the uncertainty contribution of each factor. The results showed that as the accumulation period increased and the data period extended, the RMSEs decreased. The comparison of relative uncertainty using LMM indicated that the sample size had the greatest impact on the SPI calculation. In addition, as sample size increased, the relative uncertainty related to the sample size used for SPI calculation decreased and the relative uncertainty associated with accumulation period and parameter estimation increased. In conclusion, to reduce the uncertainty in the SPI calculation, it is essential to collect long-term data first, followed by the appropriate selection of probability distribution models and parameter estimation methods that represent well the data characteristics.

가뭄은 강수량, 토양수분 그리고 유출량 등 여러 가지 요인으로부터 영향을 받으며, 가뭄의 상황 판단을 위하여 다양한 가뭄지수가 널리 활용되고 있다. 가뭄지수의 산정에 활용되는 수문기상학적 자료와 가뭄지수 산정공식에 따라서 지수값은 달라지며, 가뭄 상황에 대한 판단에도 차이가 발생 할 수 있다. 본 연구에서는 국내외에서 널리 활용되는 표준강수지수(SPI)의 산정과정에서 결정해야 하는 강수량의 자료길이, 누적기간, 확률분포 모형, 매개변수 추정기법 등을 불확실성 영향 요인으로 가정하고, 각각의 조합에 대한 불확실성을 평균제곱근오차와 선형혼합모형(LMM)을 활용하여 평가하였다. 평균제곱오차는 SPI 산정과정에 발생되는 전반적인 오차를 추정하며, LMM은 영향 요인들의 상대적인 불확설성을 평가하는데 활용되었다. 그 결과, SPI 산정에 활용된 자료의 기간과 누적기간이 길어질수록 평균제곱오차가 감소하였다. LMM을 통하여 불확실성 영향요인들의 기여도를 비교한 결과, SPI의 불확실성에는 자료기간의 영향이 가장 크게 나타났다. 또한, 자료기간이 증가하면, 자료기간에 의한 불확실성은 감소하고 누적기간과 매개변수 추정기법에 의한 불확실성이 상대적으로 증가하였다. 본 연구 결과, SPI 산정과정에서 발생되는 불확실성을 줄이기 위해서는 장기간의 자료 확보가 우선이며, 자료의 특성을 적절히 반영하는 확률분포모형과 매개변수 추정기법이 적용되어야 한다.

Keywords

Acknowledgement

이 논문은 행정안전부 재난안전 공동연구 기술개발사업 (2022-MOIS63-001(RS-2022-ND641011))의 지원을 받아 수행된 연구입니다.

References

  1. Bae, D.-H., Son, K.-H., Ahn, J.-B., Hong, J.-Y, Kim, G.S., Chung, J.-S., Jung, U.S., and Kim, J.-S. (2012). "Development of real-time drought monitoring and prediction system on Korea & east Asia region, atmosphere." Korean Meteorological Society, Vol. 22, No. 2, pp. 267-277 (in Korean).
  2. Blain, G.C., de Avila, A.M.H., and Pereira, V.R. (2018). "Using the normality assumption to calculate probability based standardized drought indices: selection criteria with emphases on typical events." International Journal of Climatology, Vol. 38, pp. e418-e436. https://doi.org/10.1002/joc.5381
  3. Carbone, G.J., Lu, J., and Brunetti, M. (2018). "Estimating uncertainty associated with the standardized precipitation index." International Journal of Climatology, Vol. 38, pp. e607-e616. https://doi.org/10.1002/joc.5393
  4. Guttman, N.B. (1999). "Accepting the standardized precipitation index: A calculation algorithm." Journal of the American Water Resources Association, Vol. 35, No. 2, pp. 311-322. https://doi.org/10.1111/j.1752-1688.1999.tb03592.x
  5. Jeung, S., Park., J., Jang, D., and Kim, B. (2019). "Modified standardized precipitation index and evaluation of its effectiveness using past extreme drought cases." Journal of the Korean Society of Hazard Mitigation, Vol. 19, No. 7, pp. 117-124 (in Korean). https://doi.org/10.9798/KOSHAM.2019.19.7.117
  6. Kim, B.K., Kim, S., Lee, J.S., and Kim, H.S. (2006). "Spatio-temporal characteristics of droughts in Korea: Construction of drought severity-area-duration curves." Journal of the Korean Society of Civil Engineers B, Vol. 26, No. 1B, pp. 69-78 (in Korean).
  7. Kim, G.S., and Lee, J.W. (2011). "Evaluation of indices using the drought records." Journal of Korea Water Resources Association, Vol. 44, No. 8, pp. 639-652 (in Korean). https://doi.org/10.3741/JKWRA.2011.44.8.639
  8. Kwon, M., Sung, J.H., Kim, T.-W., and Ahn, J. (2018). "Drought assessment by bivariate frequency analysis using standardized precipitation index and precipitation deficit: Focused on Han River basin." Journal of Korea Water Resources Association, Vol. 51, No. 10, pp. 875-886 (in Korean). https://doi.org/10.3741/JKWRA.2018.51.10.875
  9. Laimighofer, J., and Laaha, G. (2022). "How standard are standardized drought indices? Uncertainty components for the SPI & SPEI case." Journal of Hydrology, Vol. 613, 128385.
  10. McKee, T.B., Doesken, N.J., and Kleist, J. (1993). "The relationship of drought frequency and duration to time scales." Proceedings of the 8th Conference on Applied Climatology, Anaheim, CA, U.S., Vol. 17, pp. 179-184.
  11. Mishra, A.K., and Singh, V.P. (2010). "A review of drought concepts." Journal of Hydrology, Vol. 391, No. 1-2, pp. 202-216. https://doi.org/10.1016/j.jhydrol.2010.07.012
  12. Okpara, J.N., Afiesimama, E.A., Anuforom, A.C., Owino, A., and Ogunjobi, K.O. (2017). "The applicability of standardized precipitation index: drought characterization for early warning system and weather index insurance in west Africa." Natural Hazards, Vol. 89, pp. 555-583. https://doi.org/10.1007/s11069-017-2980-6
  13. Paulo, A., Martins, D., and Pereira, L.S. (2016). "Influence of precipitation changes on the SPI and related drought severity. an analysis using long-term data series." Water Resources Management, Vol. 30, pp. 5737-5757. https://doi.org/10.1007/s11269-016-1388-5
  14. Pieper, P., Dusterhus, A., and Baehr, J. (2020). "A universal standardized precipitation index candidate distribution function for observations and simulations." Hydrology and Earth System Sciences, Vol. 24, No. 9, pp. 4541-4565. https://doi.org/10.5194/hess-24-4541-2020
  15. Pinheiro, J., and Bates, D. (2006). Mixed-effects models in S and S-PLUS. Springer Science & Business Media, New York, NY, U.S.
  16. Ryoo, S., and Yoo, C. (2004) "A modified standardized precipitation index and its application." Journal of Korea Water Resources Association, Vol. 27, No. 7, pp. 553-567 (in Korean). https://doi.org/10.3741/JKWRA.2004.37.7.553
  17. Shukla, S., and Wood, A.W. (2008). "Use of a standardized runoff index for characterizing hydrologic drought." Geophysical Research Letters, Vol. 35, No. 2, pp. 41-46. https://doi.org/10.1029/2007GL032487
  18. Sienz, F., Bothe, O., and Fraedrich, K. (2012). "Monitoring and quantifying future climate projections of dryness and wetness extremes: SPI bias." Hydrology and Earth System Sciences, Vol. 16, No. 7, pp. 2143-2157. https://doi.org/10.5194/hess-16-2143-2012
  19. Stagge, J.H., Tallaksen, L.M., Gudmundsson, L., Van Loon, A.F., and Stahl, K. (2015). "Candidate distributions for climatological drought indices (SPI and SPEI)." International Journal of Climatology, Vol. 35, No. 13, pp. 4027-4040. https://doi.org/10.1002/joc.4267
  20. Stahl, K., Kohn, I., Blauhut, V., Urquijo, J., De Stefano, L., Acacio, V., Dias, S., Stagge, J.H., Tallaksen, L.M., Kampragou, E., Van Loon, A.F., Barker, L.J., Melsen, L.A., Bifulco, C., Musolino, D., de Carli, A., Massarutto, A., Assimacopoulos, D., and Van Lanen, H.A.J. (2016). "Impacts of European drought events: Insights from an international database of text-based reports." Natural Hazards and Earth System Sciences, Vol. 16, No. 3, pp. 801-819. https://doi.org/10.5194/nhess-16-801-2016
  21. Svoboda, M., LeComte, D., Hayes, M., Heim, R., Gleason, K., Angel, J., Rippey, B., Tinker, R., Palecki, J., Stooksbury, D., Miskus, D., and Stephens, S. (2002). "The drought monitor." Bulletin of the American Meteorological Society, Vol. 83, No. 8, pp. 1181-1190. https://doi.org/10.1175/1520-0477(2002)083<1181:TDM>2.3.CO;2
  22. Thai, H.T., Mentre, F., Holford, N.H., Veyrat Follet, C., and Comets, E. (2013). "A comparison of bootstrap approaches for estimating uncertainty of parameters in linear mixed effects models." Pharmaceutical Statistics, Vol. 12, No. 3, pp. 129-140. https://doi.org/10.1002/pst.1561
  23. Vicente-Serrano, S.M., Begueria, S., and Lopez-Moreno, J.I. (2010). "A multiscalar drought index sensitive to global warming: The standardized precipitation evapotranspiration index." Journal of Climate, No. 23, No. 7, pp. 1696-1718. https://doi.org/10.1175/2009JCLI2909.1
  24. Wang, W., Wang, J., and Romanowicz, R. (2021). "Uncertainty in SPI calculation and its impact on drought assessment in different climate regions over China." Journal of Hydrometeorology, Vol. 22, No. 6, pp. 1369-1383. https://doi.org/10.1175/JHM-D-20-0256.1
  25. Wilhite, D. (2006). Drought monitoring and early warning: Concepts, progress and future challenges. WMO-No.1006, World Meteorological Organization, Geneva, Switzerland.
  26. World Meteorological Organization (WMO) and Global Water Partnership (GWP). (2016) Handbook of drought indicators and indices. Geneva, Switzerland.
  27. Yoo, J., Song, H.Y. , Kim, T.-W., and, An, J.-H. (2013). "Evaluation of short-term drought using daily standardized precipitation index and ROC Analysis." KSCE Journal of Civil and Environmental Engineering Research, Vol. 33, No. 5, pp. 1851-1860 (in Korean). https://doi.org/10.12652/Ksce.2013.33.5.1851
  28. Zhang, X., Park, M., Kim, H., Cho, J., and Joo, J. (2019) "Comparison of drought assessment results according to three drought indices." Journal of the Korean Society of Hazard Mitigation, Vol. 19, No. 7, pp. 95-104 (in Korean). https://doi.org/10.9798/KOSHAM.2019.19.7.95
  29. Zhang, Y., and Li, Z. (2020). "Uncertainty analysis of standardized precipitation index due to the effects of probability distributions and parameter errors." Frontiers in Earth Science, Vol. 8, 76.
  30. Zhao, R., Wang, H., Zhan, C., Hu, S., Ma, M., and Dong, Y. (2020). "Comparative analysis of probability distributions for the standardized precipitation index and drought evolution in China during 1961-2015." Theoretical and Applied Climatology, Vol. 139, pp. 1363-1377. https://doi.org/10.1007/s00704-019-03050-0
  31. Zhu, Y., Liu, Y., Wang, W., Singh, V. P., Ma, X., and Yu, Z. (2019). "Three dimensional characterization of meteorological and hydrological droughts and their probabilistic links." Journal of Hydrology, Vol. 578, 124016.