The Linear Combination of ARIMA Models in Constructing The Areal Rainfall Using Thiessen Polygon Weighted Method
Utriweni Mukhaiyar1, Muhammmad Rozzaq Hamidi2 , Elizabet Sri Rezeki3 , Naila Ratu Dianti4, Abdan Maulana Rohat5

1 Statistics Research Division, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
2,5 Master Program in Actuarial Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia
3,4 Master Program in Mathematics Science, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Bandung, Indonesia

Abstract

The construction of areal rainfall is crucial aspects in water resource management and disaster risk mitigation. The areal rainfall can be constructed as the linear combination of the actual rainfall in each stasion in the respected area. Thus, the rainfall modeling also be crucial. This research explores the integration of ARIMA models for temporal rainfall analysis and Thiessen polygon method for spatial analysis in constructing the areal rainfall. The ARIMA was used to model the monthly cumulative rainfall of eight rain gauge stations in Tasikmalaya area. The areal rainfall was subsequently constructed using the Thiessen polygon method based on actual rainfall, taking into account the spatial heterogeneity of the observation stations. It is obtained that the AR(1) is the appropriate model for the actual rainfall in each rain gauge station. Further analysis showed that a linear combination of AR(1) model from the rain gauge stations resulted in a consistent AR(1) model for areal rainfall. This research successfully provided practical and analytical evidence that a linear combinations of multiple AR(1) models result in a consistent AR(1) model.

Keywords: Rainfall Modeling, Areal Rainfall, ARIMA, Thiessen Polygon, Temporal and Spatial Analysis.

Topic: Probability and Stochastic Analysis