Towards CONUS-Wide ML-Augmented Conceptually-Interpretable Modeling of Catchment-Scale Precipitation-Storage-Runoff Dynamics

Technical Summary: Towards CONUS-Wide ML-Augmented Conceptually-Interpretable Modeling of Catchment-Scale Precipitation-Storage-Runoff Dynamics

Problem Statement
While recent large-sample hydrology (LSH) studies have successfully applied deep learning (DL), particularly Long Short-Term Memory (LSTM) networks, to achieve state-of-the-art predictive accuracy across diverse catchments, these "universal" models often function as black boxes. They offer limited physical interpretability and fail to explicitly encode how hydrological process dominance varies geographically. Conversely, traditional conceptual rainfall-runoff (CRR) models are physically interpretable but often struggle to match the predictive skill of data-driven approaches, particularly when a single fixed structure is applied across regions with vastly different hydro-climatic regimes. The central challenge addressed is how to bridge the gap between predictive performance and physical understanding by developing models that are both data-driven and conceptually interpretable, while acknowledging that the optimal model structure is not universal but depends on local process dominance.

Methodology
The study employs a large-sample analysis across 513 minimally disturbed catchments in the Continental United States (CONUS) using the CAMELS dataset. The core methodology relies on the Mass-Conserving Perceptron (MCP), a machine learning unit that enforces mass conservation at the nodal level while learning gating functions from data.

1. Model Architecture: The authors constructed a hierarchy of MCP-based models of varying complexity:
   • Single-State Models:
     • HMCP: A generic single-state model representing total water storage (soil moisture) without distinguishing snow. Variants included mass-relaxation ($HMCP(1, MR)$) and augmented loss ($HMCP(1, AL)$).
     • SNOWMCP: A single-state model where the state variable represents Snow Water Equivalent (SWE), trained initially against observed SWE data. Variants included basic temperature-based formulations and augmented versions incorporating vapor pressure deficit, solar radiation, and temperature extremes.
   • Two-State Coupled Models (HYDROMCP): These explicitly couple a SNOWMCP module and a SOILMCP module. Two coupling configurations were tested:
     • Series: Snowmelt enters the soil storage before generating runoff.
     • Parallel: Snowmelt bypasses the soil module and routes directly to the outlet.
2. Training Strategy: Models were trained individually for each catchment (catchment-by-catchment) rather than using a single universal architecture trained on all data simultaneously. This allowed for the systematic exploration of how optimal model structure varies with climate, topography, and vegetation.
3. Evaluation and Selection: Performance was evaluated using the Kling-Gupta Efficiency skill score ($KGE_{ss}$). Model selection was guided by the Akaike Information Criterion (AIC) to balance predictive fit with structural parsimony.
4. Benchmarks: The MCP-based models were compared against:
   • A mass-conserving, distributed-state MCP network ($NMCP^{DS}(5)$) with 5 cell states.
   • A standard 5-state LSTM network ($LSTM(5)$).

Key Results

• Process Dominance and Complexity: No single architecture performed optimally across all catchments. The study found that model complexity requirements are strongly tied to hydro-climatic regimes.
  • In snow-dominated regions, explicitly representing snow dynamics (via SNOWMCP or HYDROMCP) was critical. Simple temperature-based snow formulations performed remarkably well in these areas.
  • In non-snowy or low-elevation regions, the simplest single-state HMCP models were often sufficient and preferred by the AIC criterion.
  • Two-state models (HYDROMCP) were selected less frequently (22% of catchments) and primarily in complex mountainous or transitional zones where both soil moisture and snow dynamics were significant.
• Predictive Performance:
  • The "optimal" parsimonious MCP framework (OPTMCP), which selects the best architecture per catchment (typically 1–2 cell states), achieved a median $KGE_{ss}$ of 0.85 across the CONUS.
  • This performance was comparable to the more complex 5-state mass-conserving NMCP benchmark (median $KGE_{ss} \approx 0.85$) and slightly lower than the non-mass-conserving 5-state LSTM benchmark (median $KGE_{ss} = 0.89$).
  • Crucially, the OPTMCP framework outperformed the mass-conserving benchmark in nearly half of the catchments (240 out of 513).
• Interpretability: The study demonstrated that physically interpretable, mass-conserving architectures can achieve near-optimal predictive skill with substantially fewer parameters (8–27 parameters) compared to generic DL approaches (often 64–256 states).
• Geographical Patterns: The selection of model architecture revealed distinct spatial patterns. SNOWMCP models were selected in snow-influenced regions, while HYDROMCP models appeared in specific western mountainous and southeastern non-snowy regions, suggesting missing process representations in simplified models for those specific contexts.

Significance and Claims
The paper positions itself as a necessary step toward "models of everywhere" that do not rely on a single universal architecture but instead acknowledge spatial and temporal variability in process dominance.

• Theory-Informed ML: The study argues that the future of hydrologic science lies in synthesizing theory-driven, hypothesis-based modeling with data-driven ML. By using MCP units, the authors show that models can be "ML-augmented" to learn process dynamics directly from data while retaining the structural interpretability of traditional CRR models.
• Parsimony over Universality: The authors claim that striving for a single universal model may obscure regional process differences. Instead, developing families of models tailored to specific process dominance (e.g., snow vs. soil moisture) allows for better mechanistic understanding and robust predictive skill.
• Foundation for Future Work: The study concludes that while current MCP-based models are not fully process-resolving physical models (e.g., internal states may act as "informational" states when trained only on streamflow), they provide a strong foundation. The authors suggest that future work should focus on embedding these parsimonious, interpretable architectures into broader ML frameworks to create next-generation models that explicitly account for geo-hydro-climatic variability, thereby grounding predictive power in improved theoretical understanding.

The authors maintain a modest tone, acknowledging that while their approach improves interpretability and performance, it does not yet fully resolve the trade-off between accuracy and physical realism, particularly in complex transitional regimes where mass-energy coupling and vegetation interactions remain challenging to represent.