Geographically Weighted Random Forest Model for Addressing Spatial Heterogeneity of Monthly Rainfall with Small Sample Size

Random Forest (RF) is a flexible machine learning algorithm that does not rely on linearity. The use of the RF method for spatial analysis is referred to as Geographically Random Forest (GRF), which can capture the effects of spatial heterogeneity. Therefore, GRF is well-suited for modeling rainfall, which exhibits spatial heterogeneity characteristics. However, the limited sample size in rainfall data presents a challenge. The aim of this study is to apply and explore the performance of the GRF model in monthly rainfall modeling in East Java. The GRF model is applied with different numbers of trees in the forest to achieve an optimal model. The performance evaluation of the GRF model is assessed based on the smallest RMSE, AIC, and AICc values. The analysis results indicate that the model exhibits an overestimation of Out-of-Bag (OOB) Error across all variations in the number of trees, with the smallest RMSE obtained at 750 trees. Based on variable importance values, humidity is identified as the most important variable in determining monthly rainfall in East Java.