Spatio-Temporal Median Polish Kriging with ARIMA Integration for Monthly Precipitation Interpolation in East Kalimantan

Precipitation can lead to disasters like droughts and floods, necessitating accurate interpolation methods. Traditional spatio-temporal kriging often struggles with outliers, which can reduce estimation reliability. This study develops spatio-temporal median polish kriging, which separates spatial and temporal components to improve interpolation accuracy, particularly in handling outliers. Unlike conventional kriging, this method integrates median polish kriging for robust spatial interpolation and ARIMA for capturing temporal trends, making it more effective in dynamic precipitation pattern estimation. The study utilizes precipitation data from seven observation posts in East Kalimantan (2021–2023). The data is processed using a combination of spatial, temporal, and spatial-temporal modeling approaches to capture precipitation variations accurately. For spatial interpolation, the study applies kriging in median polish spatial effects. The best semivariogram model for spatial effects is exponential, which is used to characterize spatial dependencies. To capture temporal effects of median polish, the study employs ARIMA(1,2,0), which models precipitation trends over time and helps manage temporal fluctuations. For residuals of median polish interpolation, the study applies spatio-temporal kriging, using a simple sum-metric model as the best approach to integrate both spatial and temporal dependencies. The semivariograms selected for spatial, temporal, and joint dependencies follow a gaussian structure. The interpolation results reveal that precipitation increases toward the west, with precipitation patterns also showing an increasing trend over time. These findings demonstrate the model’s capability in capturing spatial and temporal precipitation variations while addressing potential outliers through the median polish approach. By utilizing a robust statistical framework, the model reduces the influence of extreme values, leading to more reliable precipitation estimates. However, this study utilizes only seven observation posts. The limited number of observation posts may introduce uncertainty in regions distant from measurement stations and affect the model's accuracy. Therefore, further research should test this model by applying it to different geographical regions with a more extensive dataset.