Parameter Estimation of Smith Model Max-Stable Process Spatial Extreme Value (Case-Study: Extreme Rainfall Modelling in Ngawi Regency)

Abstract

The unpredictable extreme rainfall can affect flood. Prediction of extreme rainfall is needed to do, so that the efforts to preventing the flood can be effective. One of the methods that can predict the extreme rainfall is the Spatial Extreme Value (SEV) with the Max-Stable Process (MSP) approach. The important purpose of SEV is calculated of return level (the extreme value prediction). The calculation of return level depends on parameter estimation in that method. This research discusses about parameter estimation of the Spatial Extreme Value Max-Stable Process especially Smith model. Parameter estimation was performed using Maximum Composite Likelihood Estimation (MCLE) method and Maximum Pairwise Likelihood Estimation (MPLE) method. The result of estimation using this method is not closed form, it must be continued by using numerical iteration method. The iteration method used in this research is Broyden-Fletcher Goldfarb-Shanno (BFGS) Quasi Newton, which is faster than other methods to achieve convergence. The result of parameter estimation applied to the rainfall data of Ngawi Regency which is the Regency with the largest rice production in East Java Province (the province with the largest rice farm in Indonesia). Based on the results of data analysis obtained trend surface model (s) = 2,794 + 0,242 v(s); (s) = 1,8196 + 0,1106 v(s); (s) = 1,012 with goodness criterion model Takeuchi Information Criterion (TIC) 26237,62. Root Mean Square Error (RMSE) based on 20 testing data is 32,078 and Mean Absolute Percentage Error (MAPE) is 27,165%