Runoff generation in Xanthos-original is based on the abcd model. First developed by Thomas (1981), abcd is a simple water balance model effective for capturing key hydrologic processes, and their interactions, in diverse climatic and landscape settings (Martinez and Gupta, 2010, 2011). Liu et al. (2018) introduced the abcd model into Xanthos as its runoff module for simulating direct runoff, baseflow, evapotranspiration, and soil moisture at a monthly time step. The sum of direct runoff and baseflow is denoted as total runoff, which feeds into the river-routing module. The five parameters in the abcd model are described in Table 2. Parameters a and b pertain to runoff characteristics, while c and d relate to shallow soil moisture and deeper groundwater storage. The fifth parameter is a snowmelt coefficient, denoted as m. Since Xanthos-original is a distributed model, each grid cell has its own set of abcd parameters, though these parameters can optionally have the same values for all grid cells within a given river basin. Xanthos classifies the global water system into 235 large water basins.

In Xanthos, the routing of water through river networks is simulated using a simple cell-to-cell river-routing scheme, a modified version of the river transport model (Branstetter and Erickson, 2003) and hereinafter denoted as MRTM. MRTM is essentially based on the linear reservoir-routing method. The channel flow rate is estimated as a function of channel water storage, channel velocity, and flow distance from one grid cell to another (Zhou et al., 2015). MRTM uses spatially variable but temporally constant channel velocities, which were derived by averaging the long-term channel velocity simulations from Li et al. (2015). The flow distance values were derived by tracing the natural dominant river channel between grid cells to account for the meandering nature of rivers (Wu et al., 2011). Here we add a channel velocity adjustment coefficient (Table 2) to account for the uncertainties in our channel velocity field. For more details about MRTM, please refer to Zhou et al. (2015).

To enhance Xanthos, we add a water management module on top of the river-routing module. The water management module represents the two most common surface water management activities of local surface water extraction and reservoir operation. Local surface water extraction is water that is locally consumed within a particular grid cell. For example, some fraction of the water applied to irrigated agricultural land may evaporate and effectively become unavailable for use in a given grid cell. This local consumptive water use is subtracted from the total runoff produced by the abcd model. The remaining runoff is discharged into the channels and routed downstream using MRTM. If the consumptive water use is greater than the total runoff in a grid cell, then the remaining runoff is zero. In such a case, the grid cell is considered to have unmet water demand or access to supply from other external sources, such as desalination or groundwater pumping, which are not currently represented in Xanthos. If there is a reservoir in a grid cell, then local runoff (after removing water consumption) and upstream inflow are first intercepted and stored in the reservoir. Reservoir operation is then invoked to estimate the release from the reservoir to the downstream grid cells. Note that a grid cell can contain only one reservoir. That is, if there are multiple individual reservoirs co-located in the same grid cell, we first lump these individual reservoirs into a single reservoir with a storage capacity equivalent to all the combined reservoirs. The primary purpose of this lumped reservoir within a given grid cell is determined in the following two steps: (1) sum up the storage capacities of the individual reservoirs in four categories based on their primary purposes (irrigation, hydropower, flood control, and other); and (2) in each category, sum up the reservoir storage capacities. The aggregated reservoir's primary purpose is assigned to the category with the largest summed storage capacity, while the volume of the single lumped reservoir is equivalent to the sum of all individual reservoir storage capacities across all purposes. The reservoir operation rule is defined for each lumped reservoir based on its primary purpose. For reservoir purposes, if the estimated release is unavailable or less than 10 % of the mean annual inflow, then the monthly release is set to the minimum environmental flow requirement (i.e., 10 % of the mean annual inflow; Tennant, 1976; Hanasaki et al., 2008; Müller Schmied et al., 2021). Next, we provide more details on the operating rule for each reservoir type (Fig. 1).

In total, Xanthos-enhanced now includes seven parameters for the runoff and routing or water management modules. Typically, there are two strategies for determining the parameter values in a hydrologic model, namely calibration and estimation a priori (i.e., without calibration; Beven, 2012). Parameter calibration requires thousands of model runs and is only feasible for computationally inexpensive models. Feasibility can be compromised by parameter calibration efforts that require refactoring a model to run more efficiently, the budget required to scale simulations via high-performance computing resources, and the time needed for a comprehensive run. Furthermore, most hydrological models are subject to concerns surrounding equifinality, since the number of parameters, in most cases, far exceeds the number of observational variables available for calibration (Beven, 2006). Alternatively, parameter estimation a priori requires each parameter to be physically meaningful and have robust relationships with the existing climate or landscape information. These relationships are usually not readily available and have to be identified via sound prior knowledge (e.g., Li et al., 2015) or machine learning techniques (e.g., Abeshu et al., 2022; Li et al., 2021).

This study proposes a new, two-stage parameter determination strategy (described in Fig. 2) that seeks to overcome existing limitations by (1) screening out parameter sets that are not physically meaningful and (2) significantly reducing the overall computational burden associated with identifying optimal parameter sets. We seek to determine seven Xanthos parameters in total, namely five from the runoff module and two from the routing module, including water management. We determine runoff parameters in the first stage and routing parameters in the second stage. The runoff module runs separately from the routing and water management modules and is relatively lightweight, taking a standard personal computer less than 2 h to execute it at a global scale for one million simulations covering a 20-year duration. Meanwhile, the routing and water management modules are much more computationally intensive because they run at a 3 h time step to ensure numerical stability (Li et al., 2011, 2015). The first stage takes advantage of the lightweight runoff module to exhaustively explore the runoff parameter space before handing off favorable subsets of parameters to the second stage, which then limits its focus to the more computationally intensive search for the remaining two (routing) parameters. We describe the parameterization strategy in detail in the remainder of this section, whereas the results of implementing the strategy using a particular set of global data are detailed in Sect. 3.2. This strategy is designed based on the characteristics of the Xanthos modules, but we suggest that it has the potential to be useful in diverse global hydrological modeling contexts.

In the first stage, we determine the optimal values for the five parameters in the runoff-generation module (see Table 2) in four steps. (1) We generate 1 million runoff parameter combinations using a Latin hypercube sampling (LHS) scheme (McKay et al., 1979; Fig. S1 in the Supplement). LHS is a statistical method for multidimensional parameter space sampling. The stratified sampling strategy employed by LHS ensures that all portions of the sampling space are represented (McKay et al., 1979). The user decides on the required number of parameter combinations and the upper and lower bounds of the individual parameters. Based on that, LHS simultaneously stratifies all input dimensions. (2) For each runoff parameter combination, we execute the runoff module to produce the simulated monthly total runoff time series at each grid cell in the study period. In this study, we uniformly apply the same parameter values to all the grid cells in a basin to generate a monthly runoff time series at each grid cell. Parameter values vary among basins, just not across grid cells within a basin. (3) We calculate the simulated annual runoff depth at each grid cell. We then take the spatial average across the grid cells within the upstream drainage area of a gauge station where observed streamflow data are available; this is denoted as Qsim_annual (mm yr-1). (4) At the river gauge station, we calculate the long-term mean of observed streamflow and divide it by the drainage area, Qobs_annual (mm yr-1). We then select the top 100 runoff parameter combinations that produce the smallest normalized root mean square error (NRMSE) between Qsim_annual (the annual water consumption) and Qobs_annual.

Before these 100 runoff parameter combinations are passed onto the second stage, the runoff generated by the top 100 parameters is further evaluated at the mean monthly scale to confirm that the selected parameter combinations yield reasonable runoff simulations in terms of timing. For this purpose, we compare the peak time of the simulated mean monthly runoff (i.e., the calendar month in which the mean monthly runoff is highest; hereafter denoted as simulated peak runoff time) with that of Global Runoff Data Center (GRDC) mean monthly flow (i.e., the calendar month when the mean monthly flow is highest; hereafter denoted as observed peak flow time; Fig. S2). Note that the mean monthly runoff employed here is a simple spatial average with no channel routing. Therefore, a reasonable simulated peak runoff time is expected to be earlier than the observed peak flow time by 0–3 months. The range of 0–3 months is estimated by applying a 1.0 m s-1 travel velocity to the longest river in the world, the Nile River, which yields a total travel time between 2.0 and 3.0 months.

The selected 100 parameter combinations are then passed on to the second stage, where we determine the final optimal parameter set in four steps. (1) We set the reservoir capacity reduction factor (α) to a value of 0.85, following Hanasaki et al. (2006). (2) The channel velocity adjustment coefficient (β) is sampled in a relatively uniform manner within the range of 0.1–10.0. In total, there are 19 possible β values to be considered (i.e., β=0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, and 10.0). (3) For each of the 100 selected runoff parameter combinations, we use the corresponding simulated runoff time series as the inputs and run the river and water management modules 19 times (each time corresponds to one of the 19 β values and α=0.85) at a 3 h time step. (4) We validate the simulated streamflow time series at the grid cell (where the gauge station is located) against the observed monthly streamflow time series. From step (3), there are 1900 simulations for each basin, each corresponding to a combination of five runoff parameters and one routing parameter (a, b, c, d, m, and β). The final optimal parameter set is the one that produces the best model performance (per the performance metrics discussed in the following Sect. 2.5). Note that within each basin, we held the set of parameters constant across the cells, which is a reasonable simplification since, typically, there is no sufficient observational data to effectively capture the spatial heterogeneity of these parameters within each basin.

This new strategy has several benefits. First, it largely alleviates the equifinality issue by effectively sampling the whole parameter space. Our experimental design covers the full theoretical value range for each of the six parameters. Second, it reduces the computational burden to a reasonable level. Our suggested approach includes 1 million model runs for the runoff module at the monthly time step for each river basin and another 1900 runs for the river-routing and water management modules at the 3 h time step. We suggest that this new strategy applies to those hydrologic modeling frameworks where (1) some module(s) is (are) computationally much cheaper than the others, and (2) these modules must run sequentially instead of simultaneously. A demonstration of this parameter determination strategy is provided in Sect. 3.

To evaluate model performance, we use the Kling–Gupta efficiency (KGE; Gupta et al., 2009), which is given by 5KGE=1-r-12+σSimσObs-12+μSimμObs-12, where σsim,σobs,μsim, and μobs are the standard deviation of streamflow value for a given simulation, the standard deviation of observed streamflow, the simulated mean, and the observed mean values, respectively. A higher KGE indicates a better degree of agreement between the simulated and observed variables, and a KGE value of 1.0 indicates perfect agreement. The KGE value is -0.41 if the simulated monthly flow equals the observed long-term mean flow for all months (Knoben et al., 2019).

While KGE is a useful means of evaluating the skill of a particular set of model parameters in reproducing observed streamflow, we also wish to directly compare simulation outputs against one another across multiple model configurations and parameterizations for both reservoir storage and reservoir release. To enable this comparison, we employ the following indices that capture key aspects of the regulation behavior of reservoirs.

Reservoir impact index (RII). RII is the ratio of a reservoir storage capacity (C) in meters cubed to annual mean flow (Qmean; López and Francés, 2013; Wang et al., 2017). RII is similar to the Hanasaki scheme's degree of regulation term, except that RII is computed at the GRDC site instead of the reservoir site. Low and high values of RII indicate that the stream is lightly and heavily regulated, respectively.6RII=CQmean,where Qmean is the observed annual mean flow at the GRDC site (in m3 yr-1).

As we have discussed, equifinality is a crucial issue when calibrating a hydrological model that is highly parameterized. To assess model robustness, it is important to evaluate how sensitive the model's performance is to each model parameter. The sensitivity analysis approach we propose here is moderately different from traditional methods, since we implement a novel parameter determination strategy (see Sect. 2.4). The sensitivity analysis aims to identify the most and least influential model parameters. Such an understanding can help identify priorities of parameter estimation in future works and simplify or improve the model structure. Two separate sensitivity analyses are performed. The first sensitivity analysis is performed before the parameter selection, using results from all 1 million parameter sets. Here, an NRMSE for each of the 1 million parameter sets was computed between simulated annual runoff and observed annual runoff. The annual runoff is observed as annual streamflow converted to an equivalent depth over the upstream contributing basin area. The simulated annual runoff is calculated by subtracting the basin's annual water consumption from the total runoff. The correlation coefficient was then computed between an array of the computed NRMSE and each runoff parameter to evaluate the correlation between the change in parameter values and model performance. We computed five correlation coefficients from the 1 million runs (i.e., between model performance and the five runoff parameters for each basin).

After applying the new parameter selection strategy, the second sensitivity analysis is carried out on 1900 samples (i.e., samples generated from combining the 100 samples from the first stage with 19 discretized β values). Each sample includes the five runoff parameters and the velocity adjustment coefficient employed for streamflow simulation during the second stage. Here, the model performance (KGE) is computed between the monthly observed and simulated streamflow. We switched to KGE for the monthly time series evaluation, as we are interested in metrics that reflect the agreement in both magnitude and patterns of monthly flow. The correlation coefficient is computed between the KGE and each parameter. We obtain six correlation coefficient values for each basin, corresponding to the five abcd model parameters and the routing parameter (i.e., β). As with its interpretation in stage 1 of the sensitivity analysis, here a higher correlation coefficient between a parameter's values and the corresponding performance metric (in this case, KGE) suggests that the variance in model simulation outcomes is more strongly related to the changes in the target parameter and hence more sensitive to this parameter.

For this study, we obtain gridded global monthly climatic data, including precipitation, maximum temperature, and minimum temperature, from the WATer and global CHange (WATCH; Weedon et al., 2011) dataset, which covers the period 1971–2001. We obtain global reservoir data from the GRanD dataset (Lehner et al., 2011; Fig. 3a). Monthly water demand and consumptive water use data for various sectors at a 0.5∘ resolution are from Huang et al. (2018b, a), which are available from 1971 to 2010 (Fig. 3c). Observed streamflow data for model parameter identification and validation are obtained from the GRDC (https://www.bafg.de/GRDC, last access: 1 August 2022). We begin by comparing Xanthos' corresponding MRTM upstream area (after locating each gauge station within a Xanthos grid cell) with the GRDC gauge contributing area. If the drainage area difference is larger than ±20 %, then we look for an option to readjust the station to one of the eight neighboring grid cells. Here, only gauges within ±20 % in area difference (3097 GRDC gauges) are retained for further use in this study. Temporal filtering of these gauges with the availability of 20 years (1971–1990) of continuous data reduced the number of stations to 1178. These gauge stations are located within 91 of the 235 Xanthos basins. For model validation purposes, we select the GRDC gauge with the largest upstream area within each basin, i.e., 91 GRDC gauges in total (Fig. 3b).

The GRanD database we use here only considers reservoirs with storage capacity values greater than 0.1 km3. We also exclude reservoirs with missing storage capacity values and those identified with purposes such as tide control, which reduces the total GRanD reservoirs from 6862 to 6847. For any grid cell with more than one reservoir, we aggregate all of the reservoirs located locally (i.e., within the grid cell) into a single reservoir with a storage capacity equivalent to that of the local reservoirs combined. The purpose of the combined storage is determined by the two steps described in Sect. 2.3. As a result of this process, the 6847 GRanD reservoirs are remapped into 3790 reservoirs. Among the 3790 reservoirs, 1095, 598, and 2097 are categorized as irrigation, hydropower, and flood control and others, respectively (Fig. 1). Furthermore, out of the 3790 global reservoirs, only 1878 of them are located within the 91 basins simulated in this study. Out of these 1878 reservoirs, the primary purpose is hydropower for 296, irrigation for 486, and flood control or others for 1096. The reservoirs across these 91 basins make up approximately 66 % of the total dams within the GRanD dataset. The construction years of these dams pose a critical factor in deciding the starting year of the calibration. Here, we found that ∼ 69.5 % of these dams were constructed before 1971, and an additional ∼ 17.2 % were built between 1971 and 1981. We considered it reasonable to include all dams, regardless of their construction year, in the calibration starting from 1971, mainly for the following two reasons: (i) incrementally aggregating dams built during this period over time, in addition to the dams built before 1971, would significantly complicate the modeling process; and (ii) dams constructed before 1981 account for approximately 84 % of the total storage within these basins.

With the aforementioned data, we carry out three global simulations to explore the performance of the Xanthos-enhanced (see Table 3). These include (1) a simulation with Xanthos-original, denoted Xanthos-original-sim, where the simulated flow is obtained by routing-calibrated runoff data generated by Liu et al. (2018) with calibrated abcd model parameters but no water management; (2) a simulation with Xanthos-enhanced, denoted Xanthos-enhanced-sim, where we run the runoff, river-routing, and water management modules with the final optimal parameter values determined, following the new strategy as outlined in Sect. 2.4; (3) a simulation similar to Xanthos-enhanced-sim but one that treats all the hydropower reservoirs as flood control reservoirs (denoted Xanthos-enhanced-sim2). By comparing Xanthos-enhanced-sim with Xanthos-original-sim, we demonstrate the overall improvement of model performance from Xanthos-original to Xanthos-enhanced, due to a combination of the new parameter determination strategy and new water management module. Note that in Liu et al. (2018), the traditional, brute-force calibration strategy was invoked, since Xanthos-original only consists of a monthly runoff-generation module and runs very quickly. By comparing Xanthos-enhanced-sim with Xanthos-enhanced-sim2, we isolate the net difference between simulating hydropower reservoirs based on Eq. (3) and the traditional approach employed by GHMs (i.e., treating hydropower reservoirs as flood control reservoirs, based on Eq. 4).

We apply the two-stage model parameter determination strategy described in Sect. 2.4, using the global datasets described in Sect. 3.1. The LHS generates a parameter set using defined bounds (see Fig. S1 in the Supplement). Here, we describe the results from the implementation of the two-stage strategy, using the Amazon basin as an example. A subset of 100 good parameter sets (filtered) are identified among the 1 million parameter sets (raw; see Fig. S2a in the Supplement). The mean monthly runoff generated with the subset and the observed mean monthly runoff (see Fig. S2b in the Supplement) showed that the simulated runoff peak time is earlier than the streamflow peak time and within the 1–3-month range established in Sect. 2.4. The model's integrity is contingent upon the theoretical expectation of the streamflow peak trailing the runoff peak by a span of days to months. Any set of parameters resulting in a reversed pattern, where the runoff peak occurs later, is deemed unacceptable due to possible anomalies within the model.

The peak time differences (i.e., the difference between GRDC mean monthly peak flow time minus simulated runoff peak flow time) corresponding to the selected sets of parameters are among the best of the 1 million samples when ranked in an ascending order, based on an absolute value of the peak time difference (see Fig. S2c in the Supplement). The robustness of the implemented procedure is justified by the presence of a range of parameter values between their upper and lower bounds (see Fig. S2d in the Supplement), indicating that the selected parameters are not concentrated within a specific parameter space. These characteristics have also been observed in most of the basins evaluated for this study (figure not shown). We select one parameter combination for each basin that results in the best KGE value. The spatial maps of the final optimal parameter values are shown in Fig. S3 in the Supplement. In most cases, optimal values for parameter a are close to the upper bound, while those of parameter d are closer to the lower bound. Parameter b is low in basins in the high-latitude sub-region; to some degree, this may be attributed to the fact that, in general, evapotranspiration decreases towards most of the high-latitude regions. Parameter c seems to be lower in the eastern hemisphere and has relatively no distinct pattern in the western hemisphere basins. The snowmelt parameter m is only above zero in regions with significant snow contributions. The parameter β is higher in high-latitude basins. β was only introduced to readjust the global velocity data after noticing bias in the monthly flow timing at many sites; hence, applications of our methodology that use more reliable velocity data should consider setting β to a value of 1. The high values of β in the higher-latitude basins could be attributed to the original velocity estimation approach's systematic bias in cold regions (Li et al., 2015).

Overall, Xanthos' performance has improved after adding the water management module. Figure 4 shows violin plots of KGE between the GRDC monthly observed streamflow and those simulated from the Xanthos-original-sim and Xanthos-enhanced-sim simulations for the 91 basins during the calibration (Fig. 4a) and validation (Fig. 4b) periods, respectively. In most cases, during both calibration and validation periods, the Xanthos-enhanced-sim simulation's KGE values are consistently higher than those of the Xanthos-original-sim simulation. For the Xanthos-enhanced-sim simulation, the KGE value is no less than 0.5 and 0.0 for 59 and 89 basins during the calibration period and 39 and 81 basins during the validation period, respectively.

Figure 5 provides a comprehensive comparison of the Xanthos-enhanced-sim and Xanthos-original-sim, emphasizing the impact of water management integration. This is illustrated both spatially, through a map depicting KGE differences, and temporally, via time series plots for selected basins. Overall, by incorporating this element, improvements are noticeable in the KGE values of 75 basins, thus indicating a better simulation accuracy for these basins. The increase in KGE values is substantial and exceeds 0.05 when compared to those of the Xanthos-original-sim. However, it is also crucial to note that the water management integration negatively affected the KGE values (i.e., KGE values decreased by more than 0.05) in seven basins. In the remaining nine basins, KGE did not significantly change. For basins in which performance worsened, the decrease in performance is likely due to factors such as the uncertainties in the climate forcing data and GRDC streamflow observations (Moges et al., 2021) and the lack of spatial heterogeneity in the estimated parameters at the sub-basin scale (i.e., the parameters are uniform across all grid cells in a given basin). The distribution and operational patterns of reservoirs, particularly in relation to their closeness to gauge stations, could also represent a nontrivial contributing factor to this issue.

To further examine Xanthos' performance in more detail, Fig. 5 also shows the monthly time series of simulated and observed streamflow at the 12 GRDC stations (out of the 91 evaluated here) with relatively higher average annual water demand in their geographical region (see Fig. 3c) and hence stronger water management effects. The 12 basins are the Rhine, Po, Siberia north coast, Ziya He interior, Ganges–Brahmaputra, Chao Phraya, Murray–Darling, South Africa south coast, Uruguay–Brazil South Atlantic coast, east Brazil South Atlantic coast, California basin, and mid Atlantic. Compared to Xanthos-original, Xanthos-enhanced-sim better captures the seasonal variations in the streamflow, more closely matching the observed streamflow during the high-flow and low-flow periods. This highlights the importance of the reservoir regulation effect (e.g., attenuating high flows and augmenting low flows) that Xanthos-original has not captured.

To identify which parameters are most critical (i.e., contribute most to the variance in key model outputs), we evaluate the sensitivity of the model's performance to the changes in a, b, c, d, m, and β, as shown in Fig. 6. Note that we fix the value of α at 0.85, following Hanasaki et al. (2006), in this study. We first carry out the sensitivity analysis on the runoff parameters based only on the first-stage parameter determination results (Fig. 6a). The results show a significant sensitivity (correlation coefficient > |±0.4|) only for parameters a (which represents the propensity of runoff to occur before the soil is fully saturated) and b (which represents an upper limit on the sum of evapotranspiration and soil moisture storage). The correlation between parameter a and the model performance is negative, indicating that it is inversely related to the NRMSE computed from annual observed and simulated runoff. Parameter a controls the volume of runoff generation when soil is undersaturated, and the relationship suggests that annual runoff is estimated better when saturation excess runoff is not the primary process. Parameter b controls the soil saturation level. Hence, it is responsible for the memory of the basin. Therefore, the positive correlation indicates that the difference between simulated and observed annual runoff increases as the basin memory increases.

A similar analysis is made for the set of parameters generated by combining the 100 best abcd model parameter sets with the velocity adjustment parameter (β; Fig. 6b). Here, it appears that β has a stronger influence on model performance than the other parameters. This is expected because the differences among the 100 selected runoff parameter combinations are supposed to be small (e.g., see Fig. S2a (filtered) in the Supplement for the Amazon basin). For β, the sensitivity corresponds to an adjustment in the flow timing, leading to improved KGE. Note that this parameter can be avoided with a better estimate of spatially and temporally varying flow velocity. Considering these observations, it becomes evident that an enhanced parameterization of this variable, along with the other variable used to estimate the grid's water residence time (i.e., channel length), warrants increased attention. Hence, in the future, proper generation and integration of these components are crucial for boosting the model's accuracy and robustness, given their pivotal role in the MRTM-flow-routing process.

Among the 91 basins we studied here, 51 have one or more hydropower reservoirs included in GRanD and hence in our simulations. Recall that these reservoir counts reflect our lumping of multiple reservoirs together within any given grid cell, so 296 reservoirs in our methodology reflect 433 actual reservoirs. At each of the 296 reservoirs, the simulated release and storage time series from Xanthos-enhanced-sim2 are compared with those from Xanthos-enhanced-sim to identify the benefit of capturing hydropower operations.

Figure 7 compares Xanthos-enhanced-sim and Xanthos-enhanced-sim2 with regard to intra-annual (Fig. 7a and b) and interannual (Fig. 7c and d) variability. The seasonality index (SI) summarizes the intra-annual variability; weak seasonality (i.e., low SI) indicates that most months contribute significantly to the annual magnitude, and strong seasonality (i.e., high SI) indicates that very few months contribute to the annual flux magnitude. Although SI showed more difference, both the SI and coefficient of variation (CV; which summarizes interannual variability) for release fall on the 1:1 line for most reservoirs (Fig. 7a and c), indicating that in most cases, the two scenarios have less impact on the intra- and interannual variability in the release. On the other hand, both SI and CV values for storage at most reservoirs show a significant difference, indicating that the two experiments significantly disagree in terms of the interannual and intra-annual variability in the storage. We emphasize that the significant takeaway from this comparison is not that one experiment's storage and release simulations are more variable than the other but that the two experiments led to substantially different seasonal and annual patterns. This highlights the drawbacks of representing hydropower reservoirs as flood control reservoirs.

Figure 8 summarizes the reservoir storage and release comparisons between Xanthos-enhanced-sim and Xanthos-enhanced-sim2 with an empirical cumulative distribution function (CDF) that plots R2 (and/or NRMSE) values across all 296 hydropower reservoirs, according to their rank-ordered exceedance probabilities. The spatial map for the comparisons is also shown in Fig. S4. Recall that a high NRMSE value means a significant magnitude difference between the two different time series, and a low R2 value means a significant timing difference. Of the 296 reservoirs, the simulated reservoir releases differ significantly between the two model configurations in ∼ 45 % of reservoirs in terms of magnitude (if we set a threshold at NRMSE > 0.25; Fig. 8b) and at only ∼ 28 % in terms of timing (if we set a threshold at R2<0.5; Fig. 8a). According to Fig. 8a and b, treating hydropower reservoirs as flood control reservoirs does not significantly impact the model simulated reservoir releases from most reservoirs, which partly supports the lack of differentiation between hydropower and flood control reservoirs in previous studies. However, the simulated reservoir storages are significantly different for ∼ 44 % of the 296 reservoirs in terms of magnitude (NRMSE > 0.25; Fig. 8b) and ∼ 90 % in terms of timing (R2<0.5; Fig. 8a). Treating hydropower as flood control reservoirs thus has much more impact on the simulation of reservoir storage than release, particularly in terms of timing. The NRMSE and R2 values in Fig. 8 do not appear to relate to the reservoir sizes (figure not shown).

To explore the dynamics responsible for these broad patterns in Fig. 8, we select the Yenisey basin here to study them in more detail. Here, the Yenisey basin is selected for demonstration because it has a mix of only flood control and hydropower reservoirs and has just six reservoirs upstream of the GRDC site. In the Yenisey basin, the upstream area of the GRDC station is dominated by hydropower reservoirs, i.e., four hydropower reservoirs and two flood control, as shown in Fig. S5a in the Supplement. Note that one of the two flood control reservoirs is located downstream of the hydropower reservoirs (Fig. S5a). This spatial arrangement allows us to evaluate the effects of simulating hydropower reservoirs as flood control reservoirs without interference from the third purpose (i.e., in cases where an irrigation reservoir is located downstream of a hydropower reservoir). Figure S5b (see the Supplement) shows the total simulated storage (sum of all six reservoirs) from Xanthos-enhanced-sim2 and Xanthos-enhanced-sim. The difference in the magnitude of total simulated storage between the two simulations is very significant (KGE between them is 0.44). In Xanthos-enhanced-sim2, where all reservoirs are simulated as flood control, the storage is relatively more variable from month to month, while Xanthos-enhanced-sim changes are more smooth, likely because the release aims to maintain mean annual flow in Xanthos-enhanced-sim2, which leads to releases that exceed inflow during the drier seasons and quick fill-up during the wet seasons. The streamflow comparison at the GRDC site (Fig. S5c in the Supplement) indicates that the difference in the simulated reservoir releases is also significant. The KGE values drop from 0.366 to 0.152 during the calibration period (1971–1980) and from 0.293 to 0.008 during the validation period (1981–1990) when simulating the hydropower reservoirs as flood control.

For those basins where hydropower reservoirs serve a secondary purpose compared to irrigation, flood control, or other types of reservoirs, there is no significant difference in the KGE values between Xanthos-enhanced-sim2 and Xanthos-enhanced-sim, suggesting that treating hydropower reservoirs as flood control reservoirs will not lead to a significant difference in streamflow simulations at the regional or basin level. Figure 9 depicts the RII of the hydropower reservoirs on flow at GRDC stations for basins with one or more hydropower reservoirs (i.e., 51 of the 91 basins). The RII, shown here, corresponds to a hydropower reservoir with the largest storage within the basin. Figure 9 also shows a time series plot of the relative difference between Xanthos-enhanced-sim2 and Xanthos-enhanced-sim storage and release for 10 basins with relatively higher RII within different geographic regions.

The time series plots in Fig. 9 show the storage relative difference (S-RD) and release relative difference (R-RD) between the two scenarios. S-RD represents Xanthos-enhanced-sim storage minus Xanthos-enhanced-sim2 storage scaled by the mean of the two storages. Similarly, R-RD is the scaled difference in the simulated releases. From the time series plots of S-RD, one can see that, in some example basins, S-RD is > 0 (Fig. 9). This characteristic implies that when a reservoir is simulated as a hydropower reservoir, it generally maintains high storage with less variation than when simulated as a flood control reservoir. This can be attributed to our release policy for hydropower simulation, which targets maximum long-term revenue, where reservoir storage level is an essential component. Out of the 296 reservoirs, about 150 of them demonstrate this type of behavior for at least 50 % of the study period (1981–1990).

Flow downstream of hydropower reservoirs is also influenced by the change in the reservoir purpose from hydropower to flood control (Fig. S5c in the Supplement). Similarly, a comparison of simulated releases (Fig. S6 in the Supplement) shows the difference between the simulated monthly releases in the peak and low-flow periods. On the one hand, the release from the flood control reservoirs is high during peak flow periods because they aim to create excess storage capacity to attenuate inflow during the next flood event. On the other hand, the release from the hydropower reservoirs can only go up to the maximum turbine flow plus spillover. The Hanasaki et al. (2006) approach readjusts the mean annual flow, depending on the reservoir's degree of regulation (i.e., capacity ratio to mean annual inflow). Therefore, in Xanthos, given that the readjusted mean annual flow is greater than the environmental flow (10 % of the mean annual flow), release remains constant during the low-flow periods. For hydropower reservoirs, low-flow releases are determined by a release policy intended to maximize revenue. Because of the changes in reservoir purpose, downstream reservoir releases are also modified.

Taken together, Figs. 7–9 and Figs. S4–S6 (in the Supplement) suggest that individual hydropower and flood control reservoirs behave very differently under the same climate and upstream conditions, particularly in terms of the simulated reservoir storage variations. Regarding regional-scale simulations, treating hydropower reservoirs as flood control leads to noticeably different simulated streamflow only in the basins, where hydropower reservoirs dominate over the other types of reservoirs. For instance, for the lower Colorado (RII = 1.92), Caspian Sea southwest coast (RII = 1.2), Yenisey (RII = 1.02), Hudson Bay coast (RII = 1.32), and São Francisco (RII = 0.67) basins, KGE improvement was > 0.1 over the calibration period. The indicated RII corresponds to the total effect of hydropower reservoirs located upstream of the basin's GRDC site. This observation will have critical implications in studies for which freshwater storage is the core interest, since reservoir storage is a critical component of terrestrial freshwater storage. For instance, the number of hydropower reservoirs in many global basins is rapidly increasing (Zarfl et al., 2015). Hence, the potential of simulating them in GHMs is vital, as the water use characteristics in many of these basins with hydropower reservoirs could change in the next decade or two if hundreds of new dams are built. Furthermore, the observed distinct characteristics between hydropower and flood control reservoir storages have substantial implications for reservoir sedimentation, which is another essential feature that the GHMs are increasingly looking to capture.

The results in this paper highlight some promising potential outcomes from accounting explicitly for hydropower objectives and operational behavior in GHMs. However, we note that it is premature to conclude from the above analysis that treating hydropower reservoirs as flood control leads to poor hydrological simulations, and vice versa. Many reservoirs, particularly large ones, serve multiple purposes, so their behavior is controlled by multiple factors. This study takes the same simplification strategy adopted by all existing GHMs, i.e., treating each reservoir as having a single purpose. Overcoming this simplification in a GHM setting is beyond the scope of this study and is left for the future.