To evaluate reservoir routines in a data-rich context, we utilized the ResOpsUS dataset , which provides daily time series of reservoir operations for 679 reservoirs across the CONUS. From this initial pool, we applied a rigorous filtering process to ensure the suitability of the reservoirs for LSHM:

Data Availability: We selected only those reservoirs containing concurrent daily records for all three primary variables: inflow (I), storage (V), and outflow (Q).

Applying these criteria resulted in a final selection of 164 reservoirs. Their geographical distribution, categorized by catchment area and storage capacity, is depicted in Fig. .

To satisfy the input requirements of the diverse reservoir routines, we enriched the ResOpsUS records with supplementary hydrometeorological time series, and catchment and reservoir attributes.

As detailed in Sect. , the routines require time series of direct precipitation and evaporation. These were extracted for each reservoir location from the ERA5 reanalysis dataset .

Static reservoir and dam attributes were primarily sourced from the Global Reservoir and Dam dataset (GRanD) . While we included all GRanD attributes in our dataset, four were critical for the simulations: storage capacity (Vmax⁡), maximum surface area (Amax⁡), dam crest elevation (Zmax⁡), and dam height (Hdam). A comparison of these attributes against observed time series revealed inconsistencies in some attribute values. To rectify this, we cross-referenced GRanD with the Global Dam Watch (GDW) dataset . For instances where the attributes remained inconsistent, we manually updated the records using official data from US authorities, including the U.S. Army Corps of Engineers' National Inventory of Dams (NID), the U.S. Bureau of Reclamation (USBR), and the U.S. Geological Survey (USGS) . Similar errors were reported by .

For the purpose of parameter regionalization or the development of data-driven models, we further included catchment-scale characteristics derived from GloFAS surface fields and climate indices derived from ERA5 .

We named the enriched dataset Reservoir Operations US and CAtchment and Reservoir Static attributes (ResOpsUS+CARS). It is available via 10.5281/zenodo.15978041 . The dataset structure follows the standards defined by the CARAVAN initiative , ensuring it is formatted for immediate use in deep learning and large-sample hydrological studies.

The specific time series and static attributes from ResOpsUS+CARS utilized in this study are summarized in Table . These include model forcing inputs, variables for calibration and evaluation, and geometric parameters used for the estimation of reservoir area or elevation.

Each of the reservoir routines evaluated in this study is governed by the water mass balance equation (Eq. ). At each time step Δt, the model calculates the reservoir storage at the end of the interval (Vt+1) based on the preceding storage state (Vt), the water surface area (At), and three forcing variables: inflow (It), precipitation (Pt), and evaporation (Et): 2Vt+1=Vt+Pt-Et⋅At+It-Qt⋅Δt where Qt is the reservoir outflow (release), the fundamental difference between the four reservoir schemes.

To represent the reservoir's bathymetry, we assume an inverted half-pyramid geometry (Fig. ), following the approach of and subsequent studies .This geometric approximation allows for the continuous estimation of the water surface area (Eq. ), which is required for the mass balance, and the water level (Zt; Eq. ), provided that the dam crest elevation and the dam height are known. We evaluate the validity of this geometric assumption by comparing estimated levels against observed records in a subset of reservoirs where such data is available. 3aAt=Amax⁡(VtVmax⁡)2/33bZt=Zmax⁡-Hdam1-(VtVmax⁡)1/3

To address our research questions, we conducted four distinct simulation experiments designed to evaluate the routines under varying levels of data availability and calibration complexity.

The first run evaluates model performance using default parameters sourced from the literature (see Tables , , and ). This experiment assesses the “out-of-the-box” reliability of the routines, which is particularly relevant for continental or global applications where historical operational data are unavailable.

The remaining three experiments involve local parameter optimization targeting different target variables:

OBJ-Q. Univariate calibration of reservoir outflow. This mirrors the standard calibration procedure for operational systems like EFAS/GloFAS, where model parameters are tuned to match observed streamflow.

Parameter optimization was performed using the Shuffled Complex Evolution (SCEUA) algorithm , implemented via the Spotpy Python library . For each reservoir, the algorithm was executed for up to 1000 iterations using four complexes. Following the recommendations of for large-sample hydrology, we used the full length of the available daily time series for calibration to capture the widest possible range of hydrological conditions.

Performance was quantified using the modified Kling-Gupta Efficiency (KGE^′) , which decomposes performance into correlation, bias, and variability components. For the bivariate experiment, we integrated the individual KGE^′ scores into a single multi-objective metric: 15aKGE′=1-(α-1)2+(β-1)2+(ρ-1)215bKGEbivariate′=1-(1-KGEQ′)2+(1-KGEV′)2 where ρ is the Pearson correlation coefficient, α represents variability (ratio of coefficients of variation), and β is the bias (ratio of means), defined as: 16β=μsimμobs17α=CVsimCVobs

While the LISFLOOD, CaMa-Flood, and mHM routines are optimized using the iterative SCEUA algorithm, STARFIT employs a direct statistical fitting procedure. This approach does not require a heuristic search. Instead, the storage model parameters are estimated in a two-step process: an initial ordinary least squares (OLS) regression provides a first guess for the three harmonic parameters, followed by a non-linear optimization using the L-BFGS-B algorithm to finalize all five parameters, including the upper and lower capping values (V^max⁡,V^min⁡). In contrast, the parameters for the release model are derived exclusively through OLS regression.

Because the original STARFIT formulation inherently requires observations of both storage (to define the NOR) and outflow (to define the release policy), it is only evaluated within the OBJ-QV bivariate experiment. This ensures a consistent comparison between the statistically-derived STARFIT policies and the calibrated rule-based routines.

Figure  illustrates the performance of the three rule-based reservoir routines (LISFLOOD, CaMa-Flood, and mHM) across the four experimental configurations. The results highlight a critical dependency between the calibration objective and the model's ability to represent the dual states of discharge and storage.

The default parameterization (gray) provides a reasonably effective baseline for reservoir outflow across all three routines, with median KGE^′ values of 0.44, 0.52, and 0.60 for LISFLOOD, CaMa-Flood, and mHM, respectively. However, these default parameters fail to capture storage dynamics effectively; median KGE^′ scores for storage drop to 0.30, 0.36, and 0.29, respectively. The significantly larger interquartile range (IQR) in these scores indicates the high variability in storage performance across the 164 reservoirs.

As expected, each routine achieves its peak performance for a specific variable when that variable is the sole target of the calibration. However, there is a clear trade-off when we look at how the models perform on variables they weren't trained on. Calibrating outflow (OBJ-Q) severely degrades storage performance; in LISFLOOD and CaMa-Flood, this configuration yields the lowest median KGE^′ for storage among all experiments; in mHM, while the median is slightly higher than the default parameters, the dispersion between reservoirs is remarkably large. Conversely, calibrating to storage does not result in a similar degradation of outflow performance. In all three routines, OBJ-V maintains outflow KGE^′ values that are superior to the default parameterization.

The bivariate calibration (OBJ-QV) consistently achieves the highest combined performance across all routines. Notably, the performance of the OBJ-QV run is closely mirrored by the storage-only calibration (OBJ-V). These findings suggest that reservoir storage is a more informative variable than outflow for identifying model parameters.

While operational hydrology has traditionally relied on streamflow (outflow) for calibration, our results indicate that storage time series provide a more robust constraint on the internal state of the reservoir. This has significant implications for global hydrology, as it supports the feasibility of using satellite-derived storage products to calibrate reservoir routines in ungauged or data-poor regions .

Figure  compares the performance of the four routines across the different experimental configurations. Note that the outflow-only calibration (OBJ-Q) is excluded here for simplicity, as the previous section demonstrated that it is a suboptimal strategy for capturing overall reservoir behavior.

Among the rule-based schemes, the mHM routine consistently achieves the highest performance across nearly all scenarios. Its primary strength lies in its ability to represent seasonal operations through demand-driven logic. The only exception is the uncalibrated (default) simulation of storage, where CaMa-Flood shows a slight advantage. Note that the CaMa-Flood routine was specifically designed for global applications without site-specific tuning .

The results also highlight the benefits of model complexity: the CaMa-Flood routine, which evolved from the original LISFLOOD scheme by adding quadratic storage logic and inflow-dependency, systematically outperforms LISFLOOD in every experiment. This suggests that even small increases in the physical complexity of the storage-discharge relationship can significantly improve model performance.

Finally, the bivariate calibration results provide the first direct comparison with the STARFIT model. Despite its high parameterization (up to 19 parameters) and seasonal flexibility, STARFIT does not outperform mHM. Its combined performance is generally comparable to CaMa-Flood. This suggests that while seasonal harmonics are valuable, the structured rules in mHM and CaMa-Flood may provide a more robust framework for continuous daily simulations in large-scale hydrological models.

For a detailed analysis of model performance across each routine and variable, Appendix  presents the decomposition of the KGE^′.

To represent the elevation–storage–area relationship in our modeling, we adopted a simplified geometric assumption where all reservoirs are treated as an inverted half-pyramid . Under this assumption, the reservoir geometry is defined by the maximum surface area (Amax⁡) and the dam height (Hdam) (Eq. ). This approximation directly influences the calculation of the instantaneous surface area, which is a critical term for estimating direct precipitation and open-water evaporation.

While in situ observations of reservoir area are often unavailable, we validated this geometric assumption by comparing time series of estimated and observed water elevation. Time series of observed storage were converted into water elevations via Eq. (). These estimates were then compared against in situ observations for a subset of 138 reservoirs where such data were available. The performance of this elevation estimation is summarized in Fig. .

The inverted half-pyramid assumption proved to be a robust approximation for the majority of the study sites. The median KGE^′ for reservoir level estimation is 0.72, with 75 % of the reservoirs achieving a KGE^′ at least 0.44. From the three components of KGE^′, the variability is the main cause of poor performance (median value of 1.25), whereas bias and correlation showed an overall good performance (median values of 1.00 in both cases). The accuracy of the level calculation is highly sensitive to the quality of the static attributes, specifically the crest elevation (Zmax⁡) and dam height (Hdam) (Eq. ). As discussed in Sect. , errors in global databases such as GRanD or GDW can propagate into these elevation estimates; therefore, data cleaning and the use of locally validated attributes are essential for accurate water-level modeling.

This study compared reservoir routines of varying complexity, from the simple storage-dependent logic of LISFLOOD to the demand-driven and statistically-inferred policies of mHM and STARFIT. Our results indicate that model performance generally scales with the number of environmental covariates included in the routine (e.g., inflow or demand).

While mHM emerged as the best-performing routine (Sect. ), its dependence on a demand time series poses a significant operational challenge. In data-rich environments, demand can be inferred via machine learning , but in continental or global systems like EFAS or GloFAS, such data are often unavailable.

A similar constraint applies to STARFIT, although its performance was not markedly superior to the more parsimonious CaMa-Flood routine. A distinct advantage of STARFIT for global applications is its flexibility across different temporal resolutions. The harmonic functions can be fitted at coarse or irregular temporal resolutions (such as those in satellite products) and be executed at daily resolution by adjusting the frequency term (ω). For instance, recently demonstrated a global application of the STARFIT routine within the PCR-GLOBWB2 hydrological model by leveraging satellite-derived storage from the GloLAKES dataset to define the storage normal operating range (NOR). To explore this potential, Appendix  provides a comparative analysis of the four reservoir routines when calibrated using satellite-derived storage estimates.

The CaMa-Flood routine has been selected for implementation in the forthcoming major evolution of the open-source LISFLOOD model (OS-LISFLOOD). This update will form the core of the upcoming EFAS v6 and GloFAS v5 operational systems . These systems undergo regular updates encompassing updated meteorological forcing, revised surface fields, extended river discharge records and model developments. By evolving the reservoir logic to include inflow-dependency and quadratic storage–outflow relationships, we achieve a measurable gain in performance without increasing the data requirements for calibration. Furthermore, the robust default performance of the CaMa-Flood routine supports global applications in regions where historical records are sparse .

A notable limitation across the benchmarked routines is the absence of explicit reservoir purpose (e.g., irrigation, hydropower, or flood control …) . Reservoir operation is fundamentally driven by water demand, which varies significantly by use case. For instance, hydropower reservoirs are often maintained at high levels to maximize hydraulic head, whereas flood control reservoirs are drawn down ahead of wet seasons to maximize storage capacity. Conversely, irrigation reservoirs follow a distinct seasonal filling and release cycle to bridge the gap between wet-season supply and dry-season demand.

While simple schemes like LISFLOOD or CaMa-Flood do not explicitly represent these operational rules, several studies have focused on purpose-specific modeling. This includes routines for water supply in the UK , hydropower in France , and non-consumptive uses . Other approaches differentiate between irrigation and non-irrigation schemes or apply distinct objective functions based on the reservoir's primary use . Although the reservoir routines evaluated in this study do not explicitly consider reservoir purpose, Appendix  shows the model performance disaggregated by the main reservoir use reported in GRanD.

In our comparison, the superior performance of mHM and STARFIT likely stems from their ability to capture these dynamics indirectly. mHM is a demand-driven routine that can infer specific usage patterns directly from demand time series, while STARFIT leverages observed seasonal patterns to learn operational behaviors. The fact that these two models outperformed LISFLOOD and CaMa-Flood, even if by a small margin, suggests that accounting for the temporal variability of human-driven demand is critical for improving global reservoir modeling.

Furthermore, these routines lack a forward-looking component, whereas in practice, reservoir operators rely on meteorological and hydrological forecasts across multiple timescales. While replacing current inflow with forecasted values could address this, it introduces a significant bottleneck for computationally demanding systems. The model would need to simulate the entire upstream catchment for the full forecast horizon before the reservoir release can be determined at any given node. While local or regional systems running simpler lumped models could potentially process these computations sequentially at each reservoir location, this remains a substantial implementation challenge for continental or global distributed systems.

The scarcity of in situ records remains the primary hurdle for large-scale reservoir modeling . Satellite-derived products offering reservoir area, elevation, and storage anomalies provide an opportunity to bridge this gap . Two of the outcomes of this study specifically support the transition toward using satellite products. First, we found that reservoir storage is a more informative calibration target than reservoir outflow, as storage-based calibration yields models that perform well across both state variables (Sect. ). This represents a “lucky coincidence” for the community, as many available satellite products provide direct estimates of reservoir storage or storage variations rather than discharge. Second, our validation of the inverted half-pyramid shape (Sect. ) suggests that even simplified geometric assumptions are sufficient to translate satellite-derived levels into volumes with reasonable accuracy. However, a rigorous analysis of the feasibility of remotely sensed data should consider also spatial and temporal resolution, apart from accuracy.

Recent studies are already leveraging these synergies; for instance, estimated monthly target storage values for 1178 GRanD reservoirs by combining area time series from Global Water Watch (GWW) with area-storage curves from GRDL . This monthly target storage was integrated into an evolved reservoir scheme – based on LISFLOOD and CaMa-Flood – to introduce seasonality into otherwise simple storage–outflow formulations.

The flexibility of STARFIT's harmonic formulation is particularly well-suited for satellite data, as emphasized by . Because the frequency term in the harmonic curves allows the model to be fitted at coarser temporal resolutions (e.g., monthly satellite passes) and then run at a daily time step, it overcomes the temporal sampling limitations of many satellite products.

In line with , we have conducted a preliminary analysis of the potential use of the (GWW) dataset , as detailed in Appendix . Our findings indicate that while satellite-derived storage follows observed historical trends, a persistent bias often exists between in situ and remotely-sensed values. The primary bottleneck for the quality of these products is the availability of accurate elevation-storage-area curves. While several efforts have attempted to provide these curves globally , they frequently show shortcomings when validated against in situ data.

The recent revolution in deep learning has demonstrated that data-driven models can outperform traditional physical models in streamflow prediction . To support a similar transition in reservoir modeling, we have formatted the ResOpsUS+CARS dataset following the CARAVAN standard . This extension of the original ResOpsUS dataset integrates the reservoir operations with meteorological time series, the reservoir attributes from GRanD/GDW, catchment characteristics from GloFAS static maps, and climate indices from ERA5. By consolidating these diverse covariates – encompassing reservoir morphology, catchment physiography, seasonality, meteorology and climate – we provide the necessary information for deep learning models to identify the complex drivers of reservoir release.

Reservoir operations are the product of complex human-natural interactions that process-based routines struggle to capture entirely. While we acknowledge that deep learning offers a path toward superior performance, these models are notoriously data-hungry. This highlights the ongoing necessity of curated, multi-national observational datasets – not just for training, but for the rigorous benchmarking of the hybrid physical-statistical models and the development of global remotely-sensed approaches.