In this blog we present Aquanty's recent research into the use of next-generation hybrid "delta models". Delta models combine the advantages of data-driven/machine learning techniques and traditional physics-based hydrologic models. A delta-model retains the conceptual structure of a hydrologic model, including state variables such as snow water equivalent and soil moisture, while using differentiable, data-driven training to learn model parameters and improve streamflow simulation performance.
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Canadian Lake River Hydrofabric (CLRH)
Tolson, B. A., J. R. Craig, S. Lin, P. Aberi, M. Han, J. Wiebe, S. Babra, S. Kolev, M. Stapleton, H. Shen (2023). Canadian Lake and River Hydrofabric (CLRH) version 1. 2023 Canadian Water Resources Association Annual Conference, June 19-21, 2023, Halifax, Canada.
The Bighorn dam is located in the foothills of the Canadian Rockies in Alberta and is one of TransAlta's major hydroelectric facilities, with a capacity of 120 MW and an average annual generation of approximately 408,000 MWh (Bighorn - TransAlta). Reservoir planning is important for hydropower operations because operators must balance water availability, storage constraints, generation demand, flood risk, and downstream flow requirements. In snowmelt dominated basins (like this one), reservoir inflow relies on both current streamflow and upstream watershed conditions which determine future water volumes over coming days, weeks, and months. These conditions include the amount of water stored as snowpack, the timing/rate of snowmelt, antecedent soil wetness, incoming precipitation, and changes in temperature. Therefore, hydrologic modelling can provide support by mapping meteorological inputs and watershed states into expected inflow timing and volume. A streamflow simulation provides an estimate of incoming water volume, while diagnostic state variables such as snow water equivalent (SWE) and soil wetness help explain whether the basin is primed for sustained runoff. This context can help distinguish between short-lived flow responses and broader watershed conditions that may support persistent flow. In this case study, we examine the North Saskatchewan River at Whirlpool Point (05DA009, 1920 km²), a primary upstream tributary contributing to Lake Abraham. The objective is to demonstrate how hydrologic streamflow simulations, paired with physically meaningful watershed state diagnostics can support reservoir inflow interpretation and planning to help answer questions such as:
Is the basin storing above normal snow going into the freshet?
Has the basin transitioned from stored snow into active melt?
Is inflow likely to persist after the initial rise?
Are inflows likely snowmelt-driven or rainfall driven?
This case study also highlights an emerging capability within HydroSphereAI. While HydroSphereAI currently provides AI-based streamflow forecasting, this work demonstrates how next-generation hybrid "delta models" can extend the platform by combining the predictive performance of machine learning with the interpretability of process-based hydrologic models. The result is a forecasting approach that not only predicts reservoir inflows but also provides insight into the watershed conditions driving those forecasts, making them more transparent and actionable for operational decision-making.
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Simulated and Observed Streamflow and SWE at Station 05DA009 (2014-2024)
Hydrologic inflow forecasting for reservoir operations is commonly executed through process-based models or data-driven machine learning models. Classical process-based models (e.g., HBV) represent hydrologic processes such as snow accumulation, snowmelt, soil moisture storage, runoff generation, and routing through explicit conceptual or physically based equations. These models are valuable because their internal states can be interpreted, but they often require careful calibration, basin-specific assumptions, and manual effort across many watersheds. In contrast, machine learning models (e.g., LSTM) can learn complex relationships between meteorological inputs, basin specific attributes, and streamflow across numerous watersheds simultaneously from data. These models can achieve strong predictive performance, often better than process-based models, especially when sufficient historical observations are available. However, purely data-driven models are often more difficult to interpret (i.e., a black-box model) because their internal representations do not directly correspond to recognizable hydrologic states such as snowpack or soil moisture. For reservoir operators, this can make it harder to determine why a forecast is changing.
On the HydroClimateSight platform, we are improving our HydroSphereAI machine learning based forecasting capabilities through hybrid delta-models, which combine the advantages of both of these modelling approaches (Feng et al, 2023).
A delta-model retains the conceptual structure of a hydrologic model, including state variables such as snow water equivalent and soil moisture, while using differentiable, data-driven training to learn model parameters and improve streamflow simulation performance. As a result, the model can provide strong predictive performance, similar to LSTM models, while preserving hydrologically interpretable states and the mass-conserving structure. This makes the model useful not only for streamflow prediction, but also as a watershed state diagnostic tool for reservoir planning.
In this case study, we use δHBV, a differentiable version of the widely-used HBV model that has demonstrated strong regional performance, including in ungauged basins (Song et al, 2025). By combining the interpretability of the HBV hydrological model with the trainability of modern data-driven approaches, δHBV provides a useful framework for examining both reservoir inflow simulations and the upstream watershed states that help explain those flows.
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Using Watershed State Diagnostics for Reservoir Operations at Station 05DA009 (March 14 to September 30, 2021)
Model Setup and Simulation
In this application, the model was trained across more than 500 basins in Canada, using only streamflow observations as the calibration target (Water Survey of Canada - Canada.ca). The model demonstrated strong performance for station 05DA009 (North Saskatchewan River at Whirlpool Point in Alberta) when evaluated on unseen test period data, indicating that it was able to reproduce the streamflow dynamics at this upstream reservoir tributary. In addition to streamflow, the extracted δHBV SWE storage showed strong agreement with ERA5-Land SWE, an independent land-surface reanalysis product. Although ERA5-Land is not a direct observation of snowpack, this comparison provides supporting evidence that the δHBV's internal snow state is physically plausible and useful as a diagnostic tool.
Watershed Aggregated Diagnostics
To illustrate how these diagnostic states can support reservoir inflow interpretation, we focus on the 2021 freshet period as a case-study window. The 2021 freshet produced the highest daily peak flow at 05DA009 during the 2014–2024 test period, making it a useful example for examining how the model represents a reservoir-relevant high-inflow year. The objective is not only to evaluate the simulated hydrograph, but to demonstrate how modelled SWE storage, soil wetness, precipitation, and temperature can be interpreted together to explain the upstream basin conditions that contributed to the sustained inflow response.
For 05DA009, the 2021 freshet is better interpreted as a stored-water-volume event rather than a short-duration peak-flow event. During the accumulation and pre-melt period, observed inflow remained low, but δHBV diagnosed roughly 400-490 mm of upstream SWE storage, with SWE in the upper quartile of the day-of-year percentile range. This provided an early indication that the basin contained substantial water available for future inflow before the reservoir observed a major hydrograph response.
During active melt, the model diagnosed rapid snow depletion and a sharp increase in soil wetness. Between active melt and the peak inflow periods, δHBV active SWE storage decreased approximately 382 mm, equivalent to roughly 733 million m³ of water over the basin. Observed inflow over the same period was about 723 million m³. This comparison is a key interpretability result: the model states connect the observed inflow volume to a physically meaningful depletion of upstream snow storage, rather than treating the hydrograph as an isolated discharge signal. Nevertheless, the close agreement in SWE depletion volume and observed inflow volume should only be interpreted as a diagnostic consistency check, not a closed basin water balance proof.
The peak flow on July 2 was important, but it does not fully represent key reservoir relevant decision context for this event. Approximately 63% of the total event inflow volume occurred on and after the peak date, meaning the operational concern was not only the maximum daily discharge, but also the persistence of elevated flows after the peak. The δHBV cumulative-volume curve captured the timing of the incoming volume well, although discrepancies between the simulated and observed cumulative inflow became more apparent during the peak inflow stage.
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Animation showing simulated SWE shows how active snowpack storage evolves across the basin through 2020-2021.
After early July, SWE storage had largely depleted, and the dominant driver of runoff shifted from snow storage to wet-basin rainfall response. From this point onward, inflow variability was better explained by rainfall falling onto an already wet basin rather than by remaining snowmelt supply. For reservoir operations, this distinction matters because snow storage and rainfall-driven runoff imply different planning horizons and release/storage decisions.
Spatial Watershed Diagnostics
In addition to outlet streamflow and basin averaged state variables, δHBV can also provide spatially distributed diagnostics across the upstream watershed. This is important because reservoir inflow at the outlet integrates many upstream subbasins that can differ in snow accumulation, melt timing, runoff generation, and travel time.
The SWE animation shows how modelled active snowpack storage evolves across the basin through 2020-2021 water year. Here, "active" means the snow storage represented within δHBV's hydrologic state: the portion of snowpack that participates in modelled accumulation, melt, and runoff-generation processes. Rather than representing the basin as a single lumped snow reservoir, the semi-distributed structure allows users to inspect where the model stores snow, how spatial accumulation patterns evolve through winter, and which parts of the basin begin depleting during spring freshet. In this case, the animation indicates larger snow storage in the western, higher elevation subbasins, followed by steady depletion as melt conditions develop. This provides context for why inflow can remain elevated after the initial streamflow rise: upstream active snow storage may still be available even after lower elevation areas begin melting.
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A streamflow animation showing how simulated runoff is transferred through the river network toward the 05DA009 outlet.
The routed-flow animation shows how simulated runoff is transferred through the river network toward the 05DA009 outlet. This adds a spatial interpretation to the hydrograph by showing which reaches carry larger flows at different points in the event and how upstream runoff signals propagate downstream. For reservoir operations, this helps distinguish between localized runoff responses from broader basin-wide inflow events. A localized response may create a short-lived rise, whereas widespread high flows across multiple tributaries will generate more sustained reservoir inflow.
Together, these spatial diagnostics demonstrate that δHBV is not limited to producing a single outlet forecast and single basin averaged state. This model can provide an interpretable spatial view of the upstream watershed storage, runoff generation, and downstream routing. This helps users evaluate not only how much inflow may occur, but where that water is coming from and how it moves through the basin. For reservoir planning, this spatial context can make inflow forecasts more transparent and operationally useful, especially during snowmelt events where differences in elevation, aspect, and timing can strongly influence peak flow and inflow persistence.
Conclusion
The streamflow hydrograph tells operators what happens at the gauge; the δHBV state diagnostics help explain why it happens and whether similar inflow conditions are likely to persist. In this case, the model suggests that the basin entered the freshet period with above-normal, but not extreme, SWE conditions. A subsequent warming period triggered the transition to active melt, contributing directly to reservoir inflow as well as basin wetness, which helped to sustain inflows throughout the summer.
This case study demonstrates how HydroSphereAI can evolve beyond streamflow prediction by incorporating process-informed, data-driven delta models that provide both accurate forecasts and interpretable watershed diagnostics for reservoir operations. Instead of relying only on forecasted discharge, reservoir managers can inspect the watershed state diagnostics to evaluate where the water is coming from, whether the basin is primed for sustained inflow, and whether the future risk is snowmelt-driven, rainfall-driven, or mixed. Physically interpretable model states can improve hydrologic awareness and decision-making by making forecasts more explainable, auditable, and actionable than a "black-box" streamflow prediction.
References
Feng, D., Liu, J., Lawson, K., & Shen, C. (2022). Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy. arXiv. doi.org/10.48550/ARXIV.2203.14827
Song, Y., Bindas, T., Shen, C., Ji, H., Knoben, W. J. M., Lonzarich, L., Clark, M. P., Liu, J., van Werkhoven, K., Lamont, S., Denno, M., Pan, M., Yang, Y., Rapp, J., Kumar, M., Rahmani, F., Thébault, C., Adkins, R., Halgren, J., … Lawson, K. (2025). High‐Resolution National‐Scale Water Modeling Is Enhanced by Multiscale Differentiable Physics‐Informed Machine Learning. Water Resources Research, 61(4). doi.org/10.1029/2024wr038928
Tolson, B. A., J. R. Craig, S. Lin, P. Aberi, M. Han, J. Wiebe, S. Babra, S. Kolev, M. Stapleton, H. Shen (2023). Canadian Lake and River Hydrofabric (CLRH) version 1. 2023 Canadian Water Resources Association Annual Conference, June 19-21, 2023, Halifax, Canada.