Spatial Extreme Value Analysis of Extreme Rainfall Using the Extremal-t Process

Husna Mir'atin Nuroini, Sutikno Sutikno, Purhadi Purhadi

Abstract


Indonesia’s diverse topography, consisting of coasts, lowlands, highlands, and mountains, results in a wide range of weather and climate conditions, enabling various hydrological phenomena such as extreme rainfall, hurricanes, high temperatures, and storms. In recent years, global warming has emerged as a major environmental concern, with one of its significant impacts being climate change. This, in turn, increases the frequency and intensity of extreme hydrological events, potentially causing floods, transportation and communication disruptions, infrastructure damage, agricultural losses, and threats to human life. This study aims to identify the best model and estimate the return levels of extreme rainfall in Ngawi Regency from March 1990 to November 2022 using spatial extreme value analysis with max-stable processes and the extremal-t process. Daily rainfall data from 1990 - 2018 were used for model training, while data from 2018 - 2022 were allocated for model testing to validate predictive performance. Parameter estimation was conducted using Maximum Likelihood Estimation (MLE) and Maximum Pairwise Likelihood Estimation (MPLE), solved through the Broyden-Fletcher-Goldfarb-Shanno (BFGS) Quasi-Newton numerical iteration method. The analysis shows that the best trend surface model has average rainfall and variance influenced by latitude, while the distribution shape is unaffected by latitude or longitude, indicating isotropy. Furthermore, the return level prediction demonstrates higher accuracy when applied over a three-year period.

Keywords


Extremal-t Process, Extreme Rainfall; Maximum Pairwise Likelihood Estimation; Max-Stable Processes; Return Level

Full Text:

PDF

References


BMKG, “Prakiraan Musim Hujan 2021/2022 di Indonesia,” Jakarta, 2021.

E. Surmaini and A. Faqih, “Kejadian Iklim Ekstrem Dan Dampaknya Terhadap Pertanian Tanaman Pangan Di Indonesia,” Jurnal Sumberdaya Lahan, vol. 10, no. 2, 2016, doi: 10.2017/jsdl.v10n2.2016.%p.

BMKG, “Leaflet Hidrometeorologi: Mengenal Bencana Hidrometeorologi,” 2019, Jakarta. [Online]. Available: https://iklim.bmkg.go.id/publikasi-klimat/ftp/brosur/Leaflet%20Hidrometeorologi.pdf

M. G. Donat, A. L. Lowry, L. V. Alexander, P. A. O’Gorman, and N. Maher, “More extreme precipitation in the world’s dry and wet regions,” Nat Clim Chang, vol. 6, no. 5, pp. 508–513, May 2016, doi: 10.1038/nclimate2941.

M. Marzuki et al., “Long‐Term Spatial–Temporal Variability, Trends and Extreme Rainfall Events Over Indonesia Based on 43 Years of CHIRPS Data,” International Journal of Climatology, vol. 45, no. 14, Nov. 2025, doi: 10.1002/joc.70107.

A. Kurniadi, E. Weller, J. Salmond, and E. Aldrian, “Future projections of extreme rainfall events in Indonesia,” International Journal of Climatology, vol. 44, no. 1, pp. 160–182, Jan. 2024, doi: 10.1002/joc.8321.

M. Gilli and E. këllezi, “An Application of Extreme Value Theory for Measuring Financial Risk,” Comput Econ, vol. 27, no. 2–3, pp. 207–228, May 2006, doi: 10.1007/s10614-006-9025-7.

L. De Haan, “A Spectral Representation for Max-stable Processes,” The Annals of Probability, vol. 12, no. 4, pp. 1194–1204, 1984, [Online]. Available: http://www.jstor.org/stable/2243357

R. L. Smith, “Max-stable processes and spatial extremes,” Unpublished manuscript, vol. 205, pp. 1–32, 1990.

T. Opitz, “Extremal t processes: Elliptical domain of attraction and a spectral representation,” J Multivar Anal, vol. 122, pp. 409–413, Nov. 2013, doi: 10.1016/j.jmva.2013.08.008.

L. Yang, C. L. E. Franzke, and W. Duan, “Evaluation and projections of extreme precipitation using a spatial extremes framework,” International Journal of Climatology, vol. 43, no. 7, pp. 3453–3475, Jun. 2023, doi: 10.1002/joc.8038.

A. Kurniadi, E. Weller, S. Min, and M. Seong, “Independent ENSO and IOD Impacts on Rainfall Extremes Over Indonesia,” International Journal of Climatology, vol. 41, no. 6, pp. 3640–3656, May 2021, doi: 10.1002/joc.7040.

E. Y. Shchetinin and N. D. Rassakhan, “Modeling of Extreme Precipitation Fields on the Territoryof the European Part of Russia,” RUDN Journal of Mathematics, Information Sciences and Physics, vol. 26, no. 1, pp. 74–83, 2018, doi: 10.22363/2312-9735-2018-26-1-74-83.

H. Schellander and T. Hell, “Modeling snow depth extremes in Austria,” Natural Hazards, vol. 94, no. 3, pp. 1367–1389, Dec. 2018, doi: 10.1007/s11069-018-3481-y.

A. Boluwade, “Stochastic modeling of spatial dependency structures of extreme precipitation in the Northern Great Plains using max-stable processes,” Journal of Water and Climate Change, vol. 14, no. 9, pp. 3131–3149, Sep. 2023, doi: 10.2166/wcc.2023.187.

S. A. Padoan, M. Ribatet, and S. A. Sisson, “Likelihood-Based Inference for Max-Stable Processes,” J Am Stat Assoc, vol. 105, no. 489, pp. 263–277, Mar. 2010, doi: 10.1198/jasa.2009.tm08577.

S. Coles, “Classical Extreme Value Theory and Models,” 2001, pp. 45–73. doi: 10.1007/978-1-4471-3675-0_3.

E. Omey, F. Mallor, and E. Nualart, “An introduction to statistical modelling of extreme values. Application to calculate extreme wind speeds,” 2009.

M. Ribatet, “A user’s guide to the SpatialExtremes package,” EPFL, Lausanne, Switzerland, vol. 200, 2009.

M. Ribatet, “Spatial extremes: Max-stable processes at work,” Journal de la société française de statistique, vol. 154, no. 2, pp. 156–177, 2013, [Online]. Available: https://www.numdam.org/item/JSFS_2013__154_2_156_0/

R. A. Fisher and L. H. C. Tippett, “Limiting forms of the frequency distribution of the largest or smallest member of a sample,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 24, no. 2, pp. 180–190, Apr. 1928, doi: 10.1017/S0305004100015681.

B. Gnedenko, “Sur La Distribution Limite Du Terme Maximum D’Une Serie Aleatoire,” The Annals of Mathematics, vol. 44, no. 3, p. 423, Jul. 1943, doi: 10.2307/1968974.

A. C. Davison, S. A. Padoan, and M. Ribatet, “Statistical Modeling of Spatial Extremes,” Statistical Science, vol. 27, no. 2, May 2012, doi: 10.1214/11-STS376.

M. A. Stephens, “EDF Statistics for Goodness of Fit and Some Comparisons,” J Am Stat Assoc, vol. 69, no. 347, p. 730, Sep. 1974, doi: 10.2307/2286009.

A. Bechler, L. Bel, and M. Vrac, “Conditional simulations of the extremal t process: Application to fields of extreme precipitation,” Spat Stat, vol. 12, pp. 109–127, May 2015, doi: 10.1016/j.spasta.2015.04.003.

D. Cooley, P. Naveau, and P. Poncet, “Variograms for spatial max-stable random fields,” in Dependence in Probability and Statistics, P. Bertail, P. Soulier, and P. Doukhan, Eds., New York, NY: Springer New York, 2006, pp. 373–390. doi: 10.1007/0-387-36062-X_17.

L. Anselin, Spatial econometrics: methods and models, vol. 4. Springer Science & Business Media, 1988.

P. Asadi, S. Engelke, and A. C. Davison, “Optimal regionalization of extreme value distributions for flood estimation,” J Hydrol (Amst), vol. 556, pp. 182–193, Jan. 2018, doi: 10.1016/j.jhydrol.2017.10.051.

E. Aldrian and R. Dwi Susanto, “Identification of three dominant rainfall regions within Indonesia and their relationship to sea surface temperature,” International Journal of Climatology, vol. 23, no. 12, pp. 1435–1452, Oct. 2003, doi: 10.1002/joc.950.




DOI: http://dx.doi.org/10.12962%2Fj27213862.v8i3.23351

Refbacks

  • There are currently no refbacks.


Bookmark and Share


Creative Commons License
Inferensi by Department of Statistics ITS is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Based on a work at https://iptek.its.ac.id/index.php/inferensi.

ISSN:  0216-308X

e-ISSN: 2721-3862

Web Analytics Made Easy - StatCounter View My Stats