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 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 coarse-to-fine refinement for climate forecasting without updating backbone parameters. Applied to drought forecasting using the Standardized Precipitation Evapotranspiration Index (SPEI), RGMR is architecture-agnostic across the three TSFM backbones evaluated per site (TimesFM, TimeGPT, TabPFN) and consistently lowers test-set MSE on three South Australian sites and three additional regions outside South Australia. Applied to TimesFM, the wrapper reduces one-month-ahead SPEI MSE by up to 18.9\% across the three South Australian sites (mean reduction $\approx$18.7\%). Overall, RGMR provides a practical route for deploying frozen TSFMs in regional climate forecasting workflows.

Accurate drought forecasts help communities plan water use, agriculture, and emergency responses. Many modern AI forecasting systems make predictions in one pass: they look at past data and immediately output a future forecast. Human climate experts often work differently. They examine patterns over several time scales, such as yearly cycles, longer dry periods, and sudden extreme events, and then revise their judgement when they identify likely mistakes. This paper introduces RGMR, a method that gives existing AI forecasting models a similar step-by-step correction process. Instead of retraining the original model, RGMR runs the model at several time scales and uses patterns from past forecasting errors to adjust the prediction from coarse to fine detail. We test this idea on drought forecasting using a standard drought index that reflects both rainfall and water loss through evaporation. Across several South Australian sites and additional regions, RGMR consistently improves forecasts from three existing AI forecasting models. For one widely used model, it reduces one-month-ahead prediction error by up to 18.9% in the South Australian tests, while adding only a small amount of extra computation. These results suggest that existing AI forecasting tools can be made more useful for regional drought monitoring without rebuilding or retraining them.