Spatial Extreme Value Modeling of Seawater Wave Height in Banyuwangi with Smith and Geometric Gaussian Models

Banyuwangi faces serious challenges related to Coastal Disasters, with a high risk of extreme waves and abrasion by 2022. Therefore, an understanding of wave characteristics and behavior is essential for disaster mitigation. Spatial analysis was conducted in four coastal disaster-prone locations in Banyuwangi Sea using the Spatial Extreme Value method with the Max-Stable Process approach of Smith and Geometric Gaussian models. The data analyzed is seawater wave height data for the period January 1, 2019 - December 31, 2023. The Block Maxima method was used to select extreme values, with 80% of the data allocated for training data and 20% for testing data. The training data follows a stationary Generalized Extreme Value distribution, with no trend. Then, the training data is transformed to frechet margin units and the extremal coefficients are calculated. The resulting extremal coefficients indicate a fairly strong dependency between locations. The best trend surface model is a model with location parameters that have a latitude coordinate factor and scale that has a longitude coordinate factor. The estimation of the spatial parameters of the Smith and Geometric Gaussian models for each location was carried out using the Nelder-Mead and BFGS Quasi Newton numerical iteration methods, and the frechet and GEV margin unit level returns were calculated. Model evaluation is done by calculating the MAPE, SMAPE, and RMSE values for each model and iteration method. The MAPE, SMAPE, and RMSE values of the Smith model with the Nelder-Mead iteration method are 0.23912%, 0.23873%, and 0.01575, while the Geometric Gaussian model is 0.32274%, 0.32212%, and 0.02001. The estimated return level of the Sea Wave Height in the next five years at the four water locations is classified in the extreme category.