From Conceptual Hydrologic Models to Conceptually Interpretable Neural Networks: A Snow-Water Mass-Conserving-Perceptron Framework for Discovering Catchment-Scale Precipitation-Storage-Runoff Representations

Machine learning models can achieve high predictive accuracy in hydrological applications but often lack physical interpretability. The Mass-Conserving Perceptron (MCP) provides a physics-aware artificial intelligence (AI) framework that enforces conservation principles while allowing hydrological process relationships to be learned from data. In this study, we investigate how progressively embedding physically meaningful representations of hydrological processes within a single MCP storage unit improves predictive skill and interpretability in rainfall-runoff modeling. Starting from a minimal MCP formulation, we sequentially introduce bounded soil storage, state-dependent conductivity, variable porosity, infiltration capacity, surface ponding, vertical drainage, and nonlinear water-table dynamics. The resulting hierarchy of process-aware MCP models is evaluated across 15 catchments spanning five hydroclimatic regions of the continental United States using daily streamflow prediction as the target. Results show that progressively augmenting the internal physical structure of the MCP unit generally improves predictive performance. The influence of these process representations is strongly hydroclimate dependent: vertical drainage substantially improves model skill in arid and snow-dominated basins but reduces performance in rainfall-dominated regions, while surface ponding has comparatively small effects. The best-performing MCP configurations approach the predictive skill of a Long Short-Term Memory benchmark while maintaining explicit physical interpretability. These results demonstrate that embedding hydrological process constraints within AI architectures provides a promising pathway toward interpretable and process-aware rainfall-runoff modeling.

Geospatial foundation models compress multispectral observations into dense embeddings increasingly used in natural-language environmental reasoning systems. A single planetary-scale model, e.g. Google AlphaEarth, handles broad characterization well but may compromise on specialized hydrologic signals. Such generalist models are also often inaccessible, expensive, and require large-scale compute. We propose Mini-JEPAs: a fleet of small sensor-specialized Joint Embedding Predictive Architecture (JEPA) foundation models consulted by a routing agent for specialized questions. We pretrained five 22M-parameter Mini-JEPAs sharing an identical Vision Transformer backbone, JEPA recipe, and 64-d output space, using Sentinel-2 optical, Sentinel-1 SAR, MODIS thermal, multi-temporal Sentinel-2 phenology, and a topography-soil stack. Each Mini-JEPA reconstructs the variable matched to its sensor, with cross-validated $R^2$ reaching 0.97 for elevation, 0.97 for temperature, and 0.81 for precipitation. The five manifolds differ in geometric structure, with global participation ratios from 8.9 to 20.2 and local intrinsic dimensionalities from 2.3 to 9.0. Joint topography-soil and phenology models add predictive value beyond AlphaEarth alone for soil moisture, aridity, and precipitation ($ΔR^2$ up to 0.031). A router LLM reads per-modality references and selects appropriate sensors with a perfect hit rate over a curated question set. In paired LLM-as-Judge evaluation, dual retrieval over AlphaEarth and the routed fleet outperforms AlphaEarth alone on physics-matched questions (Cohen's $d = 1.10$, $p = 0.031$). Locally-trained Mini-JEPAs can be operationalized for hydrologic intelligence with modest compute.

Extreme ocean phenomena are challenging not only to predict but to diagnose, as accurate forecasts alone do not reveal the underlying physical drivers. While recent machine learning approaches achieve strong predictive skill, they remain largely opaque and provide limited guarantees of fidelity to ground-truth physics. We introduce OceanCBM, the first concept bottleneck model (CBM) for spatiotemporal prediction and mechanistic interrogation of ocean dynamics. OceanCBM uses mixed supervision to predict mixed layer heat content, a key precursor of marine heatwaves, while routing information through an intermediate layer of prescribed concepts derived from geophysical fluid dynamics and a 'free' concept. This design imposes soft physical structure without over-constraining the model, and the free concept both regularizes concept predictions and captures residual physical processes. Across ensemble initializations, we show that mixed supervision yields consistent mechanistic representations, whereas prediction-only and prescription-only baselines learn highly variable latent structures despite similar predictive performance. OceanCBM achieves interpretable, physically grounded representations without sacrificing skill, explicitly characterizing the interpretability-performance trade-off.