As is common in modelling reservoirs, we consider reservoirs to be zero-dimensional points, where their dynamics are controlled by a mass balance equation. The reservoir mass balance is updated at every time step and represented with the following equation: 1ΔSΔt=It-CFt-ABSt-spillt, where S represents the reservoir storage and t is time. It is the inflow simulated by the hydrological model per unit time, CFt is the volume per unit time of water released into the downstream river to fulfil environmental flow requirements (known as the compensation flow), ABSt is the volume per unit time of water abstracted from the reservoir for public water supply and spillt is the volume of water remaining above the reservoir capacity per unit time which must be released downstream (this is calculated after all other fluxes have been calculated). Equation (1) does not include evaporation as this is not a big component of the mass balance for reservoirs in Great Britain (see Sect. 3.4) (Dobson et al., 2020); however, evaporation could easily be included in the mass balance for reservoirs where this is important.

We use transfer functions to determine the relationships between catchment attributes (e.g. catchment size or mean annual rainfall), reservoir attributes (e.g. capacity or use), and the rates of compensation flow (CF) and abstraction (ABS) as follows: 2ABS=f1(catchmentattributes,reservoirattributes,parameter1…n),3CF=f2(catchmentattributes,parameter1…n). The catchment and reservoir attributes used within these functions will vary depending on what data are available, and a selection of attributes may have to be tested before a sensible relationship is established. In some cases attributes may be combined (e.g. by normalizing reservoir storage by catchment area). In this study, we calibrate the parameters in the transfer functions above both in a catchment-by-catchment manner and nationally, identifying one parameterization for the entire sample of catchments. The development of the transfer functions for our study area (Great Britain) is described in more detail in Sect. 3.5.1. The compensation flow and abstraction fluxes at each time step, CFt and ABSt, are then calculated (in m3 d-1) based on the current reservoir storage as follows: 4CFt=CFifSt>Smin+CF⋅Δt,(St-Smin)/ΔtifSmin<St<Smin+CF⋅Δt,0ifSt≤Smin,5ABSt=ABSifSt>Smin+CF⋅Δt+ABS⋅Δt,(St-Smin)/Δt-CFifSmin<St<Smin+CF⋅Δt+ABS⋅Δt,0ifSt≤Smin+CF⋅Δt. In this instance, CFt is given priority and removed before ABSt; hence, the calculation of ABSt must ensure there is enough storage for the CFt to be removed first. This step ensures there is sufficient storage for these fluxes to be removed and prevents the reservoir from being drained below its minimum capacity Smin (which can be either specified using site-specific data or estimated as a percentage of total reservoir capacity). Note that whilst in this study we use fixed values for CF and ABS over time, seasonal or sub-seasonal transfer functions could be developed to vary these parameters over time if appropriate.

To implement these operating rules into a hydrological model, the user will need data describing reservoir use (in this case the reservoir ought to be designed for water supply), capacity (to represent storage) and location (to locate the reservoir on the river network). These data can be obtained nationally, from datasets such as the UK Reservoir Inventory (Durant and Counsell, 2018), Inventory of dams in Germany (Speckhann et al., 2021) or National Inventory of Dams in the USA (U.S. Army Corps of Engineers, 2023), or globally, from datasets such as GRanD (Lehner et al., 2011b) and GeoDAR (Wang et al., 2022). In order to define the transfer functions used in the operating rules above, a small sample of observed compensation flow and abstraction data are needed (ideally for at least 10 reservoirs). These data can be found in documents published by water companies (e.g. water resource management plans (WRMPs) or drought plans) and academic literature, or (where a gauge is located close to a reservoir outflow) they can be inferred from the downstream flow time series.

DECIPHeR (Dynamic fluxEs and ConnectIvity for Predictions of HydRology) is a flexible, semi-distributed hydrological modelling framework which has previously been implemented across a range of scales (e.g. catchment to national scales) and locations (e.g. Europe, Asia, Africa) and has both been coupled to other models and had additional modules incorporated (Shannon et al., 2023; Dobson et al., 2020; Devitt, 2019; Fadhliani et al., 2021). The model has been applied nationally in Great Britain and demonstrated good performance (Lane et al., 2021; Coxon et al., 2019a), with generally better model performance in wetter catchments in the north and west of GB. However, since the model has no reservoir representation, performance is usually poor in catchments downstream of reservoirs. At present, in these locations the model has no knowledge of reservoir locations, and flow in these catchments is simulated as if reservoirs were natural.

DECIPHeR uses hydrological response units (HRUs) to split the landscape into non-contiguous spatial elements that share similar characteristics in landscape attributes (e.g. soil, topography or geology) and spatially varying inputs (e.g. rainfall). Each HRU then acts as a separate model store capable of having different spatial inputs, model parameter values, and/or model structures to represent different and localized processes. In this study, HRUs were classified using a 2.2 km input grid (consistent with national climate projection data) and were further subdivided by gauged sub-catchments (which include those defined by reservoir nodes) and percentiles of slope and upslope accumulated area (i.e. the area of land draining to a particular point in the landscape). This ensures that HRUs cascade downslope to the bottom of the valley and that the spatial variability of the climatic inputs is appropriately represented.

To drive the hydrological model, precipitation and potential evapotranspiration (PET) time series are needed. In this study, we use observation-based gridded daily precipitation and PET data derived from the HadUK-Grid dataset, which provides a number of climate variables on a 1 km × 1 km grid across the UK (Hollis et al., 2019). Daily precipitation data from HadUK-Grid are available from 1891 to the present and derived from the Met Office UK rain gauge network. The observed precipitation data from the rain gauge network are quality-controlled, and then inverse-distance-weighted interpolation is used to generate the daily rainfall grids (Hollis et al., 2019). Daily PET was calculated using the Penman–Monteith equation applied to climate variables available from HadUK-Grid (Robinson et al., 2023). These data are available from 1969–2021. While the climatic variables are available on a 1 km × 1 km grid, these were upscaled to a 2.2 km grid for use in the hydrological modelling. This was chosen to align with the existing model setup and the grid used for national climate projections (Robinson et al., 2021; Lane and Kay, 2022).

In this study, we run the model from 1970–2020 since it encompasses a variety of climatic conditions. The first 5 years of the time window was used as a spin-up period where no model evaluation is carried out. Simulations are evaluated from 1975 onwards (or from the date the reservoir construction was completed) using daily streamflow time series from the UK National River Flow Archive (NRFA) (https://nrfa.ceh.ac.uk/, last access: 9 September 2024). Since 96 % of reservoirs in GB were built by 1980, we can evaluate the model performance across most of the simulated period (where the flow data are available at the relevant gauge).

In this study, we calibrate the parameters in the reservoir operating rules independently from the natural model parameters. This avoids unrealistic parameterizations or equifinality, where natural parameters might mimic reservoir processes (Dang et al., 2020).

DECIPHeR has seven natural model parameters which describe how much water the soils can store and how permeable they are, the river channel velocity, and the transmissivity of the sub-surface (Coxon et al., 2019a). To generate nationally consistent parameter fields for DECIPHeR's natural model parameters, we use multiscale parameter regionalization (MPR), following the method introduced by Samaniego et al. (2010) and applied in DECIPHeR by Lane et al. (2021). High-resolution parameter fields are generated by linking model parameters to spatial catchment characteristics via transfer functions and subsequently using MPR to upscale the parameter fields to the model resolution. Transfer functions were defined for each natural model parameter (see Lane et al., 2021), and the transfer function parameters were calibrated simultaneously across all non-reservoir (or near-natural) catchments. Catchments with reservoirs were excluded from this calibration, as the purpose was to find parameter fields which resulted in good model performance for natural catchments before the addition of any reservoir component.

We calibrated the transfer function parameters using a set of simulations in near-natural catchments selected from the UK benchmark network (Fig. 2b). The UK benchmark network (Harrigan et al., 2018) consists of 137 catchments chosen for their lack of human influence and near-natural flow regime. In each catchment, we ran 5000 simulations sampling the transfer function parameters between set bounds. The top 10 natural transfer function parameter combinations were then chosen by calculating the non-parametric Kling–Gupta efficiency (KGE) (Pool et al., 2018) (see Sect. 3.6) in all near-natural catchments. The 10 combinations with the highest average non-parametric KGE across all the near-natural catchments were subsequently used to determine the natural model parameters in reservoir catchments.

To integrate new reservoir representation into DECIPHeR, we modified the river routing and represent each reservoir as a zero-dimensional point on the river network. Channel flow routing in DECIPHeR is modelled using a set of time delay histograms for the points on the river network where river flow time series are required. A fixed channel wave velocity is applied throughout the network to account for delay and attenuation in the simulated flows. The reservoir points are placed at their outflow locations as nodes on the river network. These nodes break up the river reach such that, during a simulation, incoming river flow is manipulated according to the operating rules described in Sect. 2.1 before it continues downstream. Reservoir storage is also simulated, and the time series can be obtained as an output. In this study, we do not consider evaporation from the reservoirs; this is partly because the flux is small in GB and partly because we model reservoirs as zero-dimensional points, and so we already simulate evaporation from the underlying area. We do not have evaporation relationships or surface area data, and we note that other studies also opted to exclude evaporation from reservoirs across Great Britain, where even the largest reservoir (Kielder Water) only has evaporation equal to 3 % of its inflow (Dobson et al., 2020).

We use a 50 m gridded digital elevation model (Intermap Technologies, 2009) to generate the river network in DECIPHeR, extracting headwater cells from an open-access river network which maps the rivers across GB, generated by the Ordinance Survey (Ordnance Survey, 2023). These cells are then routed downstream to generate a river network. Once the river network has been generated, reservoir locations and capacities were extracted for water supply reservoirs from the UK Reservoir Inventory (Durant and Counsell, 2018), which contains data on UK reservoirs with storage exceeding 1.6×106 m3 (or MCM for million cubic metres) and a selection of smaller ones. After cross-referencing the UK Reservoir Inventory with the Global Reservoir and Dam Database (Lehner et al., 2011a), we found that some of the Scottish reservoirs in GRanD were not included in the UK Reservoir Inventory, and in several locations the capacities were significantly different. Consequently, in Scotland, the UK Reservoir Inventory has been supplemented with data from the Scottish Environment Protection Agency (SEPA). This provided an additional four water supply reservoirs, and where mismatches in capacities were identified, the UK Reservoir Inventory has been updated using the supplementary SEPA data.

In total, 207 reservoirs from the UK Reservoir Inventory were classified as water supply. We excluded 47 of the UK Reservoir Inventory water supply reservoirs from this analysis, either because there was no gauge downstream of the reservoir and thus results could not be evaluated (11); because they were outside of Great Britain (2); or because they could not be placed on the river network (34), which was usually because the reservoir appeared to be disconnected from the river channel.

Simulations in reservoir catchments are carried out for all gauges located downstream of one or more water supply reservoirs. This is a total of 264 catchments (Fig. 2b). In each catchment, the model is run both with and without reservoir representation. The no-reservoir scenario runs 10 simulations in each reservoir catchment using the top 10 natural transfer function parameter combinations (Sect. 3.3). In the reservoir scenario, for each of the same 10 parameter combinations, we sample the reservoir parameters 500 times, resulting in 5000 simulations per catchment. The minimum capacity of each reservoir (Smin) is set to 10 % of the maximum capacity (which is obtained from relevant databases). At the very start of a simulation, St is set to 90 % of the reservoir's maximum capacity (since simulations begin in winter when reservoirs are usually full).

To evaluate the flow simulations in the both the benchmark and reservoir catchments, we use the non-parametric KGE (Pool et al., 2018; Gupta et al., 2009). The non-parametric KGE metric is comprised of three diagnostically meaningful components considering the errors in mean flow, flow variability, and the correlation between observed and simulated flow. The non-parametric KGE uses the flow duration curve to investigate flow variability instead of the standard deviation and the Spearman rank correlation instead of the Pearson correlation coefficient. Since previous work (Ferrazzi and Botter, 2019; Salwey et al., 2023) has shown that reservoirs can have a significant impact on the flow duration curve and water balance, we considered this to be a suitable metric to investigate the flow components in both benchmark and reservoir catchments. We also calculated the normalized mean absolute error (nMAE) to complement the Spearman rank correlation, which was more informative in catchments with little variability in river flows (see Sect. 4.3).

Flow time series are only evaluated at gauges where there is more than 20 years of observed data between 1975 (or the reservoir construction date if this is later) and 2020. After these criteria have been enforced, we are able to evaluate the model in 205 out of 264 catchments. The model is evaluated for both the catchment-by-catchment calibration and the nationally consistent calibration by comparing simulations with and without reservoir representation.

For completeness, in a few selected catchments we also compared our operating rules to the widely used non-irrigation reservoir rule introduced by Hanasaki et al. (2006). However, since the Hanasaki rule assumes that no abstractions are taken directly from the reservoir, this rule is not well suited to water supply reservoirs in our domain (see Sects. 4.3 and S8). We could not compare our operating rules to any of the data-driven approaches in the literature (e.g. Turner et al., 2020), since their high data requirements could not be fulfilled at the national scale in GB. Comparing the simulations which use our new operating rules to the simulations of the pre-existing hydrological model without reservoir representation thus remains the most feasible and relevant way to evaluate the new proposed model.

Model performances from simulations in near-natural catchments with the top (highest median non-parametric KGE across 137 catchments) nationally consistent calibration are displayed in Fig. 3. When considering the top 10 near-natural simulations across all 137 catchments, the median KGE score ranges from 0.83–0.84. While the model generally captures the mean flow, flow variability and correlation well, there are some catchments which have poor performance. For example, the Aldbourne at Ramsbury (39101) and the Ewelme at Ewelme Brook (39065) (which are both chalk catchments) have non-parametric KGE scores of -0.69 and -0.11 in the best-performing simulation, respectively. In general, the poorer-performing catchments are largely chalk catchments, since here the model is not able to capture flow losses from inter-catchment groundwater flows, which has also been noted in previous studies (Coxon et al., 2019a; Lane et al., 2021, 2019). While this is an area of model improvement for future studies (see, for example, Oldham et al., 2023), it is less significant for this study as reservoirs are typically not constructed in groundwater-dominated catchments in GB.

We tested a number of catchment/reservoir attributes to define the reservoir transfer functions used in this study (see Sect. S1), relying on data from a small sample of catchments (see Sect. 3.5.1). We found that catchment area was the most appropriate attribute to identify the compensation flow (CF), and the upstream reservoir capacity was best for identifying the abstraction volume (ABS) (see Fig. 4 and Eqs. 6 and 7 below). Since the observations (Fig. 4) do not show any evidence of non-linearity, we chose to use a linear (and hence more parsimonious) relationship for both transfer functions: 6ABS=ResCapacity⋅p1,7CF=CatchArea⋅p2. The top nationally consistent calibration associated with the ABS parameter (marked in Fig. 4a with a dashed grey line) generates parameters which are similar to those observed in the literature. However, the top nationally consistent transfer function selected for estimating the CF parameter (marked in Fig. 4b with a dashed grey line) lies close to the upper end of the sampling limits (Table 1) and does not match the observations. To investigate the sensitivity of the model to each of the reservoir parameters (CF and ABS), Fig. 4 also shows the variability in the transfer functions associated with the top 5 % of nationally consistent simulations (this is displayed in Fig. 4 with darker shading). The top 5 % of simulations are those with the highest average non-parametric KGE (calculated across the full sample of reservoir catchments). This shows that the model's predictive performance is more sensitive to ABS (p1) than CF (p2). The regional differences in the transfer function parameters selected by the catchment-by-catchment calibration can be seen in Sect. S9.

After running DECIPHeR both with and without reservoir representation across GB, we produced 5000 flow simulations with reservoir representation and 10 simulations without reservoir representation in 205 reservoir catchments.

The following results have been split into two sections. The first (Sect. 4.3.1) presents the results from a catchment-by-catchment calibration, identifying the optimum set of transfer function parameters in each catchment (considering there are two calibrated transfer function parameters and 205 catchments, this approach identifies 410 parameters). The second section (Sect. 4.3.2) presents the results from a nationally consistent calibration (a total of two transfer function parameters assuming the same relationship between catchment and reservoir attributes in every catchment).

After integrating a set of simple operating rules into a national-scale hydrological model, we found that large gains in model performance are possible with only two additional calibrated parameters. The best results were produced when these parameters were calibrated at each downstream gauge, but amongst reservoirs with a single purpose (water supply), a nationally consistent calibration can also make significant improvements.

The improvements we have achieved in simulating streamflow with reservoir representation are similar to others seen in the literature (Turner et al., 2020; Yassin et al., 2019; Coerver et al., 2018). However, what makes this study unique is twofold. Firstly, it is the simplicity of our operating rules. Many of the alternative sets of calibrated reservoir operating rules introduced in the literature have far more calibrated parameters than the two we have introduced here (e.g. Yassin et al. (2019) recommend six parameters that are determined for every month of the year, leaving 72 total parameters; Turner et al. (2021) introduce a data-driven scheme with 19 parameters). Most of these rules are, to some extent, attempting to recreate specific operating policies or rule curves and by extension introduce significant additional complexity compared to our flux-based approach. A second key advantage of our operating rules is their minimal data requirement. It is not uncommon for a set of reservoir operating rules to require storage, inflow and release data to calibrate their parameters, which are rarely available over large scales (Yassin et al., 2019; Turner et al., 2020; Ehsani et al., 2017). Contrastingly, our rules (which only require a reservoir's location, capacity and catchment area) ought to be more transferable to large-scale modelling, particularly in regions where inflow, outflow and storage time series are unavailable (such as GB).

To our knowledge, this is also the first time water supply reservoirs have been the focus of a large-scale study. Unlike hydropower (Abeshu et al., 2023) or irrigation (Hanasaki et al., 2006) reservoirs, water supply reservoirs are rarely the focus of large-scale studies, despite the fact that 22 % of reservoirs globally (according to the GRanD database) play a role in water supply. Instead, in many uncalibrated models, this type of reservoir is often collated into one “non-irrigation” category (Hanasaki et al., 2006; Wisser et al., 2010). In this case, reservoir rules usually aim to (where possible) release mean flow at all times of the year or reduce intra-annual variability. Since these rules facilitate no abstractions or compensation flow requirement, we consider them unsuitable for most of the reservoirs in our sample. Although we have only tested our approach at water supply reservoirs, a similar set of transfer functions and simple rules could be designed to suit reservoirs of other purposes. While we do not expect our rules to outperform more complex approaches, our rules provide a simple and practical starting point as a benchmark for incorporating reservoir representation into hydrological modelling where, due to data limitations, none of the pre-existing approaches can be applied.

Overall, a nationally consistent calibration across most of the reservoirs in our sample worked well, where 49 % of gauges (with a contributing area higher than 25 %) saw the non-parametric KGE increase by more than 0.1 after the inclusion of the nationally consistent operating rules. This is promising given this approach uses only two parameters (compared with 410 in the catchment-by-catchment approach) and open-access catchment and reservoir attributes, thus reducing computational requirements (where a model no longer needs to be calibrated in every catchment) and facilitating the application of our operating rules to ungauged basins or to reservoirs located in countries with fewer data available for calibration. We find that, within our sample of reservoirs, catchment area and reservoir capacity are reasonable predictors of the compensation flow and abstraction volume across most water supply reservoirs.

There are very few examples of calibrated operating rules which undertake a similar nationally consistent calibration. Yassin et al. (2019) introduce rules which may be applied in a similar, nationally consistent manner, but the parameters are extracted from inflow, storage and release data which are not available in GB (or many other locations). Turner et al. (2021) extrapolate their rules to data-scarce reservoirs, but the calibration varies from location to location and rules are fitted to observed data. We suggest that our approach can act as an informative lower benchmark (Seibert et al., 2018) to compare to more complex approaches that involve more detailed calibration, more parameters or higher data requirements.

However, while the nationally consistent calibration worked well for many of the reservoirs in our sample, there were some catchments where a nationally consistent calibration did not work well, particularly those which contained reservoirs fulfilling multiple purposes or regulating downstream flow. Although we included only reservoirs classified as water supply reservoirs (from the UK Reservoir Inventory) in our sample, in practice some of these reservoirs fulfil multiple objectives (e.g. Cow Green Reservoir plays a role in flood management, and Kielder Water is used for hydropower). Furthermore, approximately seven of the reservoir catchments in our sample contained upstream reservoirs which play a different role in the water supply system than the rest of the sample. In these locations, reservoirs focus on facilitating downstream abstractions (rather than those taken directly from the reservoir). It is no surprise that our rules do not work well here, where they are likely to miss some crucial coordination with the downstream river and misrepresent the purpose of the reservoir (Rougé et al., 2021). However, future work might consider defining new transfer functions to describe the operating rules at reservoirs in this sample (see Sect. 5.4 for more detail).

Although much of the literature assessing reservoir operating rules evaluates their success with metrics such as RMSE (or nRMSE) (Turner et al., 2020), KGE (both parametric and non-parametric) (Yassin et al., 2019) and Nash–Sutcliffe efficiency (NSE) (Voisin et al., 2013), we advise that this is interpreted and carried out with caution.

Standard metrics such as the non-parametric KGE worked well in our near-natural catchments; however, when used to evaluate reservoir-impacted hydrographs, their shape and distribution meant that the correlation component of the metric was not informative. The Spearman's rank was not able to characterize correlations between two time series with low variability (i.e. when the compensation flow dominates the regime), which is often the case in reservoir-impacted time series. Although the Spearman's rank was chosen for the non-parametric KGE over the Pearson correlation for its lower sensitivity to extreme values and focus on mean and low flows (Pool et al., 2018), in many reservoir-impacted catchments it was this portion of the hydrograph which the metric could not evaluate properly.

Although several other metrics were tested to look at the timing, or correlation, of our simulated flow, these were often very influenced by the high flows. Whilst matching the timing of these high flows is an important component of simulating reservoir-impacted flows, we were interested in where a reservoir absorbed a peak in inflow (releasing only the compensation flow) or spilled in broadly the right week/month rather than on the exact day. The Pearson correlation and RMSE put too much emphasis on the daily peaks, giving more weight to larger errors. Comparatively, the nMAE was less influenced by the peaks in flow and large errors, providing a better evaluation of a time series dominated by the compensation flow.

We suggest that future studies should seek to develop new signatures which replace the correlation component of the KGE evaluation metric and can better capture behaviour in human-influenced catchments (Kiraz et al., 2023). Standard metrics like the KGE should be calculated on impacted time series with caution, where their ability to evaluate natural time series does not always translate.

A limitation of this study was our inability to capture reservoir operations at gauges where upstream reservoirs fulfil multiple purposes as well as facilitating water supply. Future work might investigate whether this second cluster of multi-purpose or river-regulating reservoirs could be represented by a similar set of simple rules. By extension, national-scale inventories could benefit from sub-categories for reservoir purpose, including a multi-purpose category. Furthermore, although these rules have only been tested at water supply reservoirs in Great Britain, they may be useful for simulating reservoirs in other locations. Whilst operations will vary country by country, this simple approach could be used to design rules and transfer functions for application elsewhere. Where a nationally consistent approach is not appropriate (perhaps due to multi-purpose reservoirs or more complex coordination), transfer functions could be useful in defining the parameter bounds for calibration and establishing relationships between reservoir and catchment attributes and model parameters.