Return Level Estimation in Spatial Extreme Value Modeling of Bali Sea Currents Velocity using The Smith and Brown-Resnick Max-Stable Process Approach

Nyoman Gede Trisna  Sanjaya; Pratnya Paramitha  Oktaviana; Galuh Oktavia  Siswono

doi:10.20956/j.v20i1.27436

Authors

Nyoman Gede Trisna Sanjaya Departemen Aktuaria, Fakultas Sains dan Analitika Data, Institut Teknologi Sepuluh Nopember
Pratnya Paramitha Oktaviana Departemen Aktuaria, Fakultas Sains dan Analitika Data, Institut Teknologi Sepuluh Nopember
Galuh Oktavia Siswono Departemen Aktuaria, Fakultas Sains dan Analitika Data, Institut Teknologi Sepuluh Nopember

DOI:

https://doi.org/10.20956/j.v20i1.27436

Keywords:

Brown-Resnick Model, Max-Stable Process, Return Level, Sea Currents Velocity, Smith Model

Abstract

Bali is the world's second most popular tourist destination in 2023. One of the best tourisms is the beauty of its coasts. Even though it is the best tourism destination, it is not uncommon for disasters to occur in the coastal areas of Bali. One important factor in the occurrence of coastal disasters from waters such as tidal flooding and abrasion is ocean currents. Spatial analysis of sea currents velocity was carried out using the Smith and Brown-Resnick Max-Stable Process Approach. The purpose of this study was to determine parameter estimation and comparison of the results of Spatial Extreme Value modeling with the Smith and Brown-Resnick Max-Stable Process approach, and to determine the Return Level of Bali Sea current velocity for the same period after data testing with the best model. The data used is daily data for the period March 2, 2017 to December 30, 2020. Extreme data selection with Block Maxima uses 14 daily blocks, so there are 100 blocks for each water location. The proportion of training and testing data is 80:20. The training data follows the Generalized Extreme Value distribution and has no pattern trend (stationary). The results of the extremal coefficient measurements ranged from 1.18604 to 1.59485 indicating a fairly strong dependency between locations. The best trend surface model is a model that only has longitude coordinates on the location parameter and latitude on the scale parameter. The estimated value of the spatial parameters of the Smith model tends to be greater than that of the Brown-Resnick model. The Root Mean Square Error and Mean Absolute Percentage Error for the Smith model are 0.15503 and 7.75076%. Meanwhile, the Brown-Resnick model is 0.29576 and 14.12131%. Return Level values for the same period after data testing are classified as strong currents and are respectively 1.20586 m/s, 1.63592 m/s, 1.51322 m/s and 2.13233 m/s for Serangan, Gianyar, Nusa Dua, and Nusa Lembongan Waters. Information on estimated Return Levels is expected to be a consideration that can be used by related agencies such as the Coastal and Marine Resources Management Agency (BPSPL) and the Bali Province Regional Disaster Management Agency (BPBD) as a coastal disaster mitigation effort to make it more effective, efficient and on target.

References

Chan, S. C., Kendon, E. J., Fowler, H. J., Youngman, B. D., Dale, M., & Short, C. 2023. New extreme rainfall projections for improved climate resilience of urban drainage systems. Climate Services Journal, Vol. 30, No. 3, 1-42.

Cooley, D., Nychka, D., & Naveau, P. 2012. Bayesian Spatial Modeling of Extreme Precipitation Return Levels. Journal of the American Statistical Association, Vol. 102, No. 479, 824-840.

Davison, A. C., Padoan, S. A., & Ribatet, M. 2012. Statistical Modeling of Spatial Extremes. Statistical Science, Vol. 27, No. 2, 161-186.

Dinaryanti, N. A. & Darwis, S. 2021. Estimasi Parameter Distribusi Generalized Extreme Value (GEV) dengan Maximum Likelihood Estimation (MLE) dan L-Moments pada Data Vibrasi Akselerasi Bearing. Prosiding Statistika, Vol. 7, No. 1, 113-120.

Gautama, I. W., Putra, I. K., & Sukarsa, I. M. 2016. Aplikasi Pemetaan Objek Wisata Pantai Bali Selatan Berbasis Android. Jurnal Ilmiah Merpati, Vol. 4, No. 1, 43-51.

Global Ocean Physics Reanalysis. 2022. E.U. Copernicus Marine Environment Monitoring Service (CMEMS). Marine Data Store (MDS). https://data.marine.copernicus.eu/product/GLOBAL_MULTIYEAR_PHY_001_030/. [28 Februari 2023]

Hakim, A. R. 2016. Pemodelan Spatial Extreme Value dengan Pendekatan Max-Stable Process (Studi Kasus: Pemodelan Curah Hujan Ekstrem di Kabupaten Ngawi). ITS Repository, Surabaya. http://repository.its.ac.id/id/eprint/75290. [2 Januari 2023]

Hatanti, Y. D. 2016. Perbandingan Model Smith, Schlather, Brown-Resnick dan Geometric Gaussian pada Pemodelan Curah Hujan (Studi Kasus: Curah Hujan Ekstrem di Kabupaten Lamongan). ITS Repository, Surabaya. http://repository.its.ac.id/id/eprint/41654. [2 Januari 2023]

Indonesia, Pemerintah Pusat. 2010. Peraturan Pemerintah (PP) Nomor 64 Tahun 2010 tentang Mitigasi Bencana di Wilayah Pesisir Dan Pulau Pulau Kecil. https://peraturan.bpk.go.id/Home/Details/5088. [15 Februari 2023]

Karami, H., Ghazvinian, H., & Dadrasajirlou, Y. 2023. Application of statistical and geostatistical approaches in temporal and spatial estimations of rainfall. Water and Climate Change Journal, Vol. 14, No. 5, 1696–1722.

Maitriani, C. 2023. Analisis Spasial Tinggi Muka Air Wilayah Jakarta untuk Mitigasi Bencana Banjir Menggunakan Extreme Vaue Max Stable Process Model Brown-Resnick. ITS Repository, Surabaya. http://repository.its.ac.id/id/eprint/95529. [22 Februari 2023]

Mathieu, R. & Mohammed, S. 2013. Extreme value copulas and max-stable processes. Journal de la Société Française de Statistique, Vol. 154 No. 1, 138-150.

Modalo, R. J., Rampengan, R. M., Opa, E. T., Djamaluddin, R., Manengkey, H. W., & Bataragoa, N. E. 2018. Arah dan Kecepatan Arus Perairan Sekitar Pulau Bunaken pada Periode Umur Bulan Perbani di Musim Pancaroba II. Jurnal Pesisir dan Laut Tropis, Vol. 1, No. 1, 61-68.

Pramesti, D. D., Novitasari, D. C., Setiawan, F., & Khaulasari, H. 2022. Long-Short Term Memory (LSTM) For Predicting Velocity and Direction Sea Surface Current on Bali Strait. Jurnal Ilmu Matematika dan Terapan, Vol. 16, No. 2, 451-462.

Putri, N. M. 2023. Bali Didapuk Jadi Destinasi Wisata Terpopuler Kedua di Dunia, Susul Dubai. detikBali, Denpasar. https://www.detik.com/bali/bisnis/d-6539108/bali-didapuk-jadi-destinasi-wisata-terpopuler-kedua-di-dunia-susul-dubai. [30 Mei 2023]

Ramadani, I. R. 2015. Spatial Extreme Value Modeling dengan Max-Stable Processes Model Smith dan Brown-Resnick. ITS Repository, Surabaya. http://repository.its.ac.id/id/eprint/41635. [2 Januari 2023]

Sebille, Q., Fougères, A.-L., & Mercadier, C. 2017. A comparison of spatial extreme value models. Application to precipitation data. HAL Open Science, Vol. 21, Part A, 187-208.

Skahill, B., Smith, C. H., Russell, B. T., & England, J. F. 2023. Impacts of Max-Stable Process Areal Exceedance Calculations to Study Area Sampling Density, Surface Network Precipitation Gage Extent and Density, and Model Fitting Method. Hydrology Journal, Vol. 10, No. 6, 121-152.

Suryanto, J., & Krisbiyantoro, J. 2018. Analisis Kecenderungan Curah Hujan Kabupaten Magelang Menggunakan Uji Mann-Kendall dan Variasi Modifikasi Mann-Kendall. Jurnal AGRIFOR, Vol. 17, No. 2, 293-304.

Triwidiyanti. 2022. Dihantam Gelombang dan Arus, Abrasi di Pantai Kuta Makin Parah. detikBali, Badung. https://www.detik.com/bali/berita/d-6098303/dihantam-gelombang-dan-arus-abrasi-di-pantai-kuta-makin-parah. [29 Mei 2023]

Yogaswara, G. M., Indrayanti, E., & Setiyono, H. 2016. Pola Arus Permukaan di Perairan Pulau Tidung, Kepulauan Seribu, Provinsi DKI Jakarta pada Musim Peralihan (Maret-Mei). Jurnal Oseanografi, Vol. 5, No. 2, 227-233.