Spatio-Temporal Forecasting and Continuous Spatial Reconstruction of Fire Radiative Power Using Sequential GSTARX-IDW and Ordinary Kriging

Abstract

This study presents a sequential hybrid spatio-temporal forecasting framework combining the Generalized Space-Time Autoregressive with Exogenous Variables (GSTARX-IDW) model and Ordinary Kriging (OK) to model and map weekly Fire Radiative Power (FRP) dynamics in West Kalimantan from January 2021 to October 2025. A strong dominance of spatial contagion was observed, with the spatial autoregressive parameter (p1) being statistically significant across 95.56% of operational grid centroids, providing empirical validation of Tobler's First Law of Geography. Locally, Land Surface Temperature (LST) serves as a key exogenous forcing variable, exhibiting geographical dichotomies driven by localized microclimatic conditions and peatland hydrology. To overcome the limitation of discrete point forecasts at grid centroids, Ordinary Kriging was applied directly to the k-step ahead GSTARX-IDW point forecasts, successfully reconstructing continuous spatial risk surfaces for October 2025. Evaluated through robust out-of-sample metrics, the framework achieved a Root Mean Squared Error (RMSE) of 1.1380, a Mean Absolute Error (MAE) of 0.8736, and a Mean Absolute Scaled Error (MASE) of 1.0008, demonstrating competitive temporal point forecasting on par with baseline dynamics while offering superior spatial continuous risk mapping. This sequential framework provides a mathematically grounded baseline for short-term spatio-temporal risk assessment in highly fragmented tropical landscapes.