A Meta Learning Approach to Enhance Resolution in Uncertainty Space of Hydro- Climatic Artificial Intelligence Models

Enhancing uncertainty space resolution in hydro-climatic models improves in-bound feature interpretation and supports more confident project decisions. This study introduces a novel meta-learning framework, Intelligent Nonlinear Integration (INI), for refining uncertainty space in hydro-climatic simulations. The INI method combines multiple Artificial Intelligence and Machine Learning (AI/ML) models—including Artificial Neural Networks (ANN), Adaptive Neuro-Fuzzy Inference Systems (ANFIS), and Support Vector Regression (SVR)—through two dedicated ANN-based architectures optimized by a metaheuristic algorithm to estimate uncertainty space. Prediction Intervals (PIs) were estimated using the Lower–Upper Bound Estimation (LUBE) approach to assess uncertainty in modeling pan evaporation ( Et ), the Standardized Precipitation Index (SPI), and the Standardized Precipitation Evapotranspiration Index (SPEI). The method was applied to two climatically diverse stations in Iran, Tabriz and Ahvaz. These two stations were selected to reflect contrasting hydro-climatic conditions in Iran, where water stress is a major concern due to their climatic settings. Compared to individual models, the INI framework improved PI resolution by up to 29% for SPEI in Ahvaz, over 15% and 12% for SPI and Et in Tabriz, respectively. The proposed integration framework outperformed standalone models in capturing and refining uncertainty boundaries. SPEI consistently yielded lower uncertainty than SPI. Based on the optimal PIs, local climatic extremes such as heat stress in Ahvaz and transitional moisture states in Tabriz often widen the PIs, reflecting their distinct climate sensitivities.