Domain-Informed Neural Networks for Remote Sensing-Based Hydrology: Insights from Finland’s Digital Waters Flagship

Getnet Jenberia, University of Oulu. getnet.jenberia@oulu.fi

The effective management of water resources under accelerating climate change, particularly in complex cryosphere-influenced environments like Finland, necessitates accurate and timely hydrological information. Earth observation (EO) provides vast datasets, yet converting indirect satellite measurements into quantitative hydrological variables remains challenging. Traditional process-based hydrological models are grounded in physics but face issues with computational cost and data requirements. Purely data-driven AI models, while efficient, can produce physically inconsistent results, especially when extrapolating.

Finland’s Digital Waters (DIWA) Flagship initiative is addressing this by pioneering Domain-Informed Neural Networks (DINNs). DINNs integrate physical principles into AI architectures, combining the strengths of process-based and data-driven modeling to improve accuracy, reliability, and physical consistency in remote sensing-based hydrology.

Challenges and the need for domain knowledge

Finland’s diverse hydrology, with extensive lakes, dynamic snow cover, and peatlands, makes it an ideal testbed. Satellite missions (e.g., Sentinel-1/2, SMAP, GPM) provide data (SAR backscatter, passive microwave brightness temperature, optical/NIR reflectance) that are indirect proxies for hydrological states. Retrieving variables like Snow Water Equivalent (SWE), soil moisture, or river discharge is non-trivial due to factors like signal penetration limitations, complex interactions with land cover (forests, peat), snowpack properties (density, grain size, stratigraphy), and the inherent spatial heterogeneity of hydrological processes. Purely data-driven models often struggle to capture these complex, non-linear relationships robustly or generalize to unobserved conditions without physical guidance.

Domain-Informed neural networks: approaches

DINNs incorporate domain knowledge via several technical avenues:

1. Physics-Informed Neural Networks (PINNs): Embed governing physical equations (e.g., mass conservation) directly into the neural network’s loss function. The network learns to satisfy both data constraints and physical laws simultaneously.
2.  Hybrid Modeling: Couple AI components with physical models. AI can preprocess EO data, estimate physical model parameters, replace computationally expensive model components (e.g., using a neural network surrogate for a complex sub-model), or facilitate data assimilation to update model states.
3. Physically Guided Loss Functions/Regularization: Incorporate terms in the loss function that penalize outputs violating known physical constraints (e.g., non-negativity, monotonicity, adherence to physical bounds) or exhibiting non-physical spatio-temporal patterns. This acts as regularization, directing the model towards physically plausible solutions.

These methods enhance the physical consistency and generalization capabilities of AI models in hydrological applications.

DIWA case studies

DIWA research exemplifies DINN applications in the Finnish context:

1. Snow Water Equivalent Mapping (FMI & Aalto University): CNNs fusing passive microwave data (sensitive to SWE) and in-situ observations are used for SWE estimation. Integrating physically guided loss terms that enforce mass balance principles (e.g., penalizing unphysical SWE changes given temperature and precipitation) improves the spatio-temporal consistency and realism of SWE maps, particularly during snowmelt.
2. Peatland Soil Moisture Monitoring (SYKE): Hybrid models leverage Sentinel-1 SAR (sensitive to dielectric constant/moisture) and potentially Sentinel-2 data. An AI component processes these inputs, coupled with or constrained by simplified physical models of subsurface flow in peatlands. This integrates remote sensing signals with hydrological processes specific to peat, enabling higher resolution and more physically interpretable moisture mapping in complex, often restored, peat ecosystems.
3. Streamflow Forecasting (Kemijoki Basin): Recurrent CNN-LSTM models are applied to assimilate satellite-derived precipitation and snow cover data for streamflow forecasting in large northern basins. CNNs capture spatial features from gridded inputs, while LSTMs handle temporal dynamics. Hydrological domain knowledge can be incorporated via architecture design (e.g., topography-aware processing) or physically guided loss functions that penalize deviations from water balance, improving forecast accuracy and lead times during crucial periods like snowmelt floods.

Uncertainty quantification and operationalization

Quantifying uncertainty is vital. DIWA explores approaches like Bayesian Neural Networks for estimating parameter uncertainty and Monte Carlo dropout for predictive intervals. Error propagation through embedded physical constraints also contributes to robust uncertainty estimation, crucial for risk-informed decision-making in areas like lake ice phenology forecasting.

DIWA is building a cloud-based platform for operationalizing these models, featuring automated EO data pipelines, a repository of validated DINN models (“model zoo”), and APIs for integration into national water management systems. This infrastructure aims to enable scalable applications, including transboundary issues like Baltic Sea nutrient modeling.

Future directions

Upcoming EO missions (SWOT, NISAR, CHIME) offer new data types. Future DINN developments in DIWA will explore:

• Graph Neural Networks (GNNs): To explicitly model hydrological connectivity in river networks and catchments.
• Neural Operators: For learning mappings between function spaces, potentially offering computationally efficient ways to solve or approximate hydrological PDEs from data.
• Transfer Learning: To adapt models trained in data-rich areas or conditions to data-scarce regions or non-stationary climate regimes.
• Differentiable Simulators: To enable end-to-end training of coupled physical-AI models, facilitating parameter inference and model refinement based on observations.

Finland serves as an important testbed for these innovations under changing environmental conditions.

Conclusion

Integrating domain knowledge into neural networks is crucial for reliable remote sensing-based hydrology. DINNs offer a pathway to scalable, physically consistent hydrological modeling using EO data. Finland’s Digital Waters Flagship is actively advancing these hybrid approaches, translating research into operational capabilities and contributing significantly to the field by developing and applying cutting-edge AI techniques to address critical water challenges in a changing world.

Read Jenberia’s more extensive blog post here  

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References

Finnish Meteorological Institute. (2018). The total product error is demonstrated here for Northern Europe by applying the GlobSnow Snow Extent (SE) product on fractional snow cover(FSC% -units). Clouds are depicted in brown-grey colour. Improved uncertainty characterization for satellite-based mapping of Earth’s snow cover – Finnish Meteorological Institute

21.5.2025.