Rainfall Forecasting Using Gaussian Process Regression with Brownian Motion Prior (Case Study: Special Region of Yogyakarta Province)

Climate variability significantly impacts the agricultural sector, necessitating accurate forecasting methods to support agricultural planning. This study aims to develop a rainfall forecasting model using the Gaussian Process Regression (GPR) method with Brownian motion prior. Monthly climate data from the Yogyakarta Geophysics Station for the period January 2015 to December 2024 were utilized, comprising predictor variables (air humidity and wind speed) and response variable (rainfall). The posterior GPR model was developed for parameter estimation using the marginal log-likelihood approach, with missing data handled through seasonal mean imputation that preserves temporal patterns. The results demonstrate that the GPR model achieves reasonable forecasting performance with a Mean Absolute Percentage Error (MAPE) of 36.84% and strong correlation (r = 0.94) between predicted and actual values. The highest predicted rainfall occurred in March 2024 (20.148 mm) and the lowest in June 2024 (0.022 mm), consistent with the seasonal patterns of Indonesia's tropical climate.