RESIDUAL-GUIDED MULTI-RESOLUTION REFINEMENT OF FOUNDATION MODELS - A CASE STUDY IN DROUGHT FORECASTING

Regional climate prediction presents unique challenges for time series foundation models, which typically process temporal patterns through a single-pass inference. Expert climatologists, in contrast, employ multi-scale temporal analysis and iterative refinement based on systematic error diagnosis. We present RGMR (Residual-Guided Multi-Resolution Refinement), an inference-time framework that adapts pre-trained foundation models to perform structured multi-scale reasoning for climate forecasting without parameter modification. Our approach combines hierarchical coarse-to-fine prediction refinement with residual-guided error correction; together, they systematically address prediction failures at each resolution level. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR consistently enhances foundation model performance across diverse climate regions within an Australian regional area. Experimental results demonstrate substantial improvements over direct foundation model application, achieving up to 18.9\% reduction in mean squared error, 10.2\% reduction in root mean squared error, and 21.1\% relative gain in $R^2$ when applied to TimesFM, with the largest benefits observed in climatologically complex regions where multi-scale temporal dynamics are most pronounced. The framework's inference-time operation enables immediate deployment on existing operational climate prediction systems without model retraining, offering a practical solution for enhancing foundation model capabilities in specialized forecasting domains.