Hybrid Physics-Informed Transformers vs. Traditional Machine Learning for Operational Snow Water Equivalent Forecasting: A Multi-Basin Evaluation

Foundation models for climate science must encode physical structure and conservation laws to achieve reliable generalization beyond training distributions. We present a Hybrid Physics-Informed Transformer (HPIT) demonstrating three core principles for building scientific foundation models: (1) integrating differentiable physical constraints (mass balance, energy balance, elevation effects) directly into model architectures, (2) designing inductive biases appropriate for spatiotemporal scientific data through multi-scale attention, and (3) maintaining interpretability and uncertainty quantification essential for operational decision-making. Evaluated on snow water equivalent (SWE) forecasting across five climate basins with 20+ years of data, HPIT achieves R² = 0.876 ± 0.023, representing 6.3\% improvement over traditional machine learning baselines. Physics constraints contribute 2.9\% performance gain while ensuring predictions respect conservation laws. The model provides well-calibrated uncertainty (89.3\% coverage at 90\% intervals) and maintains real-time inference ($<$50ms), demonstrating how hybrid physics-ML systems can advance climate forecasting for the 1.2 billion people dependent on snowmelt.