Max-stable processes with geometric Gaussian model on ocean wave height data

Abstract

In Spatial extreme value (SEV) is a method used to model an extreme event in several locations where there are dependencies between these locations. This method is a development of the Extreme Value Theory which is used in univariate cases. One of the approaches used in SEV is the max-stable process. Several models used in the max-stable process are the Smith, Schlater, Brown Resnick and Gaussian Geometric models. In general, these models have a Generalized Extreme Value (GEV) distribution. This study uses rainfall data in Central Java, then the extreme data is selected by the Maxima block method. The basic principle of maxima block is that extreme data is selected from the maximum data in each predefined block. The next step is modeling the extreme data with a geometric-Gaussian model. This method is a development of the Smith and Schlater models. The model obtained is then used to predict extreme rainfall using the return level. The result is that the maximum extreme rainfall in the next two periods is Pekalongan Station 1.16, Rembang station 0.8 and Semarang station 1.29 with an RMSE of 1.9.