Performance of Bayesian Kriging under Different Levels of Spatial Autocorrelation: A Simulation Study of Rainfall Interpolation

Abstract

This study investigates the influence of spatial autocorrelation on the performance of Bayesian kriging for interpolating daily rainfall in East Java, Indonesia, using both empirical observation data and controlled simulation experiments. Daily rainfall records from multiple monitoring stations were analyzed to assess spatial dependence via Global Moran’s I, revealing that the onset phase of the rainy season exhibits moderate to strong positive spatial autocorrelation, whereas the peak phase shows weak or negligible spatial structure dominated by local-scale variability. Cross-validation results indicate that stronger spatial autocorrelation significantly improves Bayesian kriging performance, as evidenced by lower RMSE and MAE. Simulation results further corroborate that Bayesian kriging yields substantial predictive gains when Moran’s I exceeds approximately 0.30–0.40, while predictive improvement is marginal when Moran’s I falls below 0.15–0.20. Under weak spatial dependence, the model effectively reduces to a nugget-driven process with limited spatial continuity. These findings underscore that the effectiveness of Bayesian kriging for daily rainfall interpolation is fundamentally contingent upon the magnitude of spatial autocorrelation, highlighting the necessity of preliminary spatial diagnostics to guide appropriate methodological choices in geostatistical applications.