Analyzing the Impact of Streamflow Drought on Hydroelectricity Production: A Global‐Scale Study

Electricity production by hydropower is negatively affected by drought. To understand and quantify risks of less than normal streamflow for hydroelectricity production (HP) at the global scale, we developed an HP model that simulates time series of monthly HP worldwide and thus enables analyzing the impact of drought on HP. The HP model is based on a new global hydropower database (GHD), containing 8,716 geo‐localized plant records, and on monthly streamflow values computed by the global hydrological model WaterGAP with a spatial resolution of 0.5°. The GHD includes 44 attributes and covers 91.8% of the globally installed capacity. The HP model can reproduce HP trends, seasonality, and interannual variability that was caused by both (de)commissioning of hydropower plants and hydrological variability. It can also simulate streamflow drought and its impact on HP reasonably well. Global risk maps of HP reduction were generated for both 0.5° grid cells and countries, revealing that 67 out of the 134 countries with hydropower suffer, in 1 out of 10 years, from a reduction of more than 20% of mean annual HP and 18 countries from a reduction of more than 40%. The developed HP model enables advanced assessments of drought impacts on hydroelectricity at national to international levels.

Both hydraulic head and water flows are temporally variable. In case of run-of-river hydropower, lower than normal streamflow, that is, drought, immediately reduces outflow through turbines and thus HP, while in case of reservoir-storage hydropower, lower than normal streamflow flowing into the reservoir may require a reduction of reservoir outflow and thus HP only later. Still, unless streamflow deficit is small compared to the reservoir storage, HP is reduced during streamflow drought for both types of hydropower plants, negatively affecting both hydropower suppliers and consumers. The three consecutive years of drought that began in 2014 had caused severe reductions in hydroelectricity supply with negative effects on daily life and the economy in Venezuela (Hambling, 2016). Two consecutive monsoon failures had reduced reservoir storage in India such that HP was significantly lower than normal in 2015-2016, with 15% less HP than the previous year in some plants, while electricity demand due to a heat wave (often concurrent to less precipitation than normal) was higher than normal (Singh & Sally, 2020). HP reduction due to drought is particularly problematic in countries that strongly rely on hydropower for their electricity supply, which include many countries in Africa and South America (EIA, 2019). For the western United States, it was found that frequent droughts had caused a notable shift toward conventional energy sources, thus leading to increases in air pollutant emissions of around 10% (Herrera-Estrada et al., 2018).
There are a number of continental-or global-scale studies about the impact of climate change on the potential of HP (e.g., Stanton et al., 2016;Van Vliet, van Beek, et al., 2016;. Impact of drought on HP was only investigated for small regions and some countries such as Finland (Jääskeläinen et al., 2018) and Canada (Bonsal et al., 2011) and in one global study of Van Vliet, Sheffield, et al. (2016), HP reduction in selected drought years was quantified.
This paper presents a new comprehensive global hydropower database (GHD) and a global HP model to assess the impact of drought on HP. Combining data from the GHD and hydrological variables simulated by the global hydrological model WaterGAP (Müller Schmied et al., 2021), the HP model computes, with a spatial resolution of 0.5° (55 km × 55 km at the equator), monthly time series of HP between 1975 and 2016 at the global scale. The aim of this paper is to show and discuss the capability of the HP model and to assess HP reduction due to drought, computing HP reduction during spatially extensive historic drought events as well as the HP reduction that can be expected with a probability of 10% in 0.5° grid cells and whole countries. Section 2 describes the methodology consisting of the GHD and HP model development as well as drought and risk analyses. Section 3 validates the performance of the database and HP model, followed by the assessment of HP reduction due to drought. Section 4 discusses the uncertainties of the HP model and the robustness of the results. Section 5 closes with concluding remarks.

Methods and Data
The amount of hydropower electricity t HP (kWh) produced over a time period t H can be quantified using the following equation (El-Hawary & Christensen, 1979;Wan et al., 2020;Zhao et al., 2014): where  is a comprehensive hydropower coefficient (kJ m −4 = kN m −3 ) that combines acceleration of the earth (m s −2 ), density of water (kg m −3 ) and a unitless efficiency term, , t turb Q is rate of water flow through the pipe and turbine (m 3 /s), t H is hydraulic head with respect to the outlets of the pipe (m), that is, the difference between elevations of forebay and tailwater, and installed N is the installed capacity of the hydropower plant (kW = kJ s −1 ), that is, the maximum power output that can be produced by a specific plant. To enable the application of Equation 1 for simulating HP globally from 1975 onward, the location, type, and installed capacity of ideally all but at least a large part of all hydropower plants are required. t H and , t turb Q must be estimated for all hydropower plants and time steps. As daily values of streamflow that are simulated by global-scale hydrological model are much less reliable than monthly values, HP is simulated with a monthly time step based on monthly streamflow simulated by the global hydrological model WaterGAP.
The spatial resolution of the HP model is the spatial resolution of WaterGAP, 0.5° longitude × 0.5° latitude.
WaterGAP streamflow values can be assumed to represent plants is derived from databases, topographic data, and WaterGAP simulation of water storage in reservoirs. Thus, HP model presented and applied in this study relies on two main inputs, the newly developed GHD (Section 2.1) and output of WaterGAP (Section 2.2). The HP model is introduced in Section 2.3.

A New Global Hydropower Database
Despite the recognition of environmentally sustainable hydropower to modern society, there is no reliable, comprehensive, and open-access global database describing hydropower plants and their characteristics. To address this shortcoming, we collated information about currently developed/under-construction hydropower plants in the new GHD.
The GHD contains 8,716 records of hydropower plants distributed across 134 countries worldwide, consisting of 13.1% reservoir-storage plants, 9.9% run-of-river plants, and 3.3% pumped-storage plants. For the remaining 73.7% of plant records, no plant category is available, but we can assume that they are conventional plants (reservoir storage or run-of-river) as the installed capacity of pumped-storage plants fits EIA statistics well. A hydropower plant may be described by more than one record if it is located at the boundary of two countries or its installed capacity varied over time (Section S1). The total number of hydropower plants included in GHD is 8,648. The GHD comprises only hydropower plants with installed capacities above 1 MW or plants of which the associated reservoir has a storage capacity above 0.1 km 3 . The spatial distribution and installed capacities of the hydropower plants included in GHD are shown in Figure 1a. The total installed capacity of all hydropower plants commissioned before 2016 is 1.147 TW, contributing 91.8% of the documented data of EIA (2019). 36.5% of total installed capacity is known to be reservoir-storage hydropower, 10.7% is run-of-river hydropower, and 13.4% is pumped-storage hydropower. For 39.4% of total installed capacity, the primary sources do not provide information on the category of hydropower plant. In some countries, HP accounts for more than 90% of total electricity production in 2016, while only a few countries do not harness hydropower at all (Figure 1b).  Table S1). We also included plants that are not listed in these databases from scattered data sources, such as HTML sources (e.g., Wikipedia), NHA (https://www. hydro.org/map/hydro/), AQUASTAT (http://www.fao.org/aquastat/), CDM (https://cdm.unfccc.int/), or research articles (see Section S1 for more details). In addition to the compilation of data from these sources, GHD also contains estimated values as not all data required to implement Equation 1 were available from the data sources. The GHD contains 44 attributes per hydropower plant. Table 1 provides an overview of key attributes provided in the GHD, while a complete attribute list is found in Table S2.
Each hydropower plant and, if any, the associated reservoir was allocated to the appropriate 0.5° × 0.5° grid cell. This cannot be done by just taking into account latitude and longitude information of the plants but each plant has to be coregistered in accordance with the river network used in WaterGAP, the 0.5° global drainage direction map DDM30 (Döll & Lehner, 2002). Coregistration means that a power plant is assigned to a 0.5° grid cell not simply according to the geographic coordinates but taking into account its location on the actual river network (e.g., whether is located on the mainstem or the tributary entering the mainstem within the grid cell). Coregistration may move the plant to an adjacent cell to make sure that the plant is situated along the correct DDM30 river. It required extensive manual checking. For plants with information on the upstream basin, additional adjustments to the plant geographical location were implemented to ensure reasonable consistency: (1) the upstream catchment area defined by the DDM30 and those collected (partly) in GHD should be consistent or close; (2) compare the reservoir-storage capacities of plants in GHD to GRanD reservoirs, that is, the plants should be located in the outflow cells of GRanD reservoirs. Therefore, geo-locations and upstream and downstream topologies of some plants may be modified a bit as compared to their original sources.
For computing HP according to Equation 1, GHD included WaterGAP-derived attributes like catchment area, routing area, basin ID, the simulated long-term mean highest and lowest monthly streamflow at all 8,716 plant sites, and the simulated mean reservoir storage for 693 plant sites. Also included in GHD is the WAN ET AL.  (Lehner et al., 2006) distinguishing cells with flow direction to its downstream neighbor (i.e., crossflow cells) from those cells without downstream cell (i.e., outflow cell of basin to the ocean or its inland sink). The elevation difference of the cross-flow cell was calculated by assuming streamflow falls from the mean elevation of the considered cell to that of the downstream neighboring cell (i.e.,  Δ ele mean H L , where L is the grid cell elevation in meters). In contrast, the streamflow for the basin-outflow cell is assumed, on average, falls from the mean elevation to the minimum elevation per cell; the elevation difference was then derived as the difference between the two elevations of the basin-outflow cell (i.e.,   ele mean min H L L ). Additionally, for 36 of the 60 largest hydropower plants with an installed capacity of at least 3,000 MW, the hydropower load factor (%) could be included in GHD (Table 1). The load factor, also known as capacity WAN ET AL.  factor or percentage full load hours, is calculated as actual annual HP divided by the theoretical maximum annual HP. The load factor of the 36 plants varies between 36% and 80%. Taking into account the load factor enabled a good reproduction of recorded HP for these large plants.

WaterGAP
WaterGAP 2.2d (Müller Schmied et al., 2021) is a 0.5° (55 km × 55 km at the equator) grid-based global-scale hydrological model that simulates both human water use and freshwater fluxes and water storages on all continents of the Earth except Antarctica with a daily time step. Differentiating surface water bodies and groundwater as sources and sinks of water withdrawals, it estimates water withdrawal and consumption for five sectors: irrigation, livestock farming, domestic use, manufacturing water use, and thermal power plant cooling . Based on the simulated time series of net groundwater, time series of climate data and many physiographical data, daily water balances of up to 10 storage compartments are computed for each of the 67,420 grid cells. For this study, the global daily WFDEI-GPCC data set (Weedon et al., 2014) was used as climate input. Runoff from land is routed through groundwater and surface water bodies (i.e., lakes, reservoirs, wetlands, and rivers) along the drainage direction. WaterGAP simulates water storage dynamics of and outflow from the 1,109 largest reservoirs worldwide (storage capacity 0.5 km 3 ) and 52 regulated lakes (area 100 km 2 ) based on the GRanD database version 1.1 (Lehner et al., 2011;Müller Schmied et al., 2021). Seven hundred and five of the 1,161 large reservoirs/regulated lakes have HP as either the most important or the second most important purpose. Simulation of reservoir operation in WaterGAP distinguishes reservoirs with the main purpose of irrigation from all others (Döll et al., 2009). WaterGAP 2.2d also includes more than 5,000 man-made reservoirs, whose storage capacities are less than 0.5 km 3 . In each grid cell, the water balance of these small reservoirs and of all small lakes is simulated by a lake algorithm (Müller Schmied et al., 2021). Different from other global hydrological models, WaterGAP is calibrated against observed long-term average annual streamflow at 1,309 gauging stations, with the purpose of obtaining meaningful estimates of water resources despite a number of sources for significant uncertainty in global hydrological modeling . This is one of the reasons why WaterGAP has been shown to provide better fits to streamflow observations than most other global hydrological models (Krysanova et  Note. Details on data sources are provided in Section S1 and Table S1. A complete list of attributes is provided in Table S2.

HP Model
The developed HP model takes into account only conventional hydropower plants, that is, reservoir-storage and run-of-river plants. The electricity produced by the pumped-storage plants is not included in this study because (1) pumped-storage plants do not produce net electricity but serve as energy storages (House et al., 2018), and (2) data for calculating pumped-storage HP such as operating period, pumping rate as well as lift and drop heights (Schill & Kemfert, 2011) are lacking.
Based on Equation 1, the HP model simulates monthly time series of HP for each conventional hydropower plant in GHD. It does not distinguish run-of-river plants from reservoir-storage plants as there is no information on plant category for 73.7% of the plants in GHD, corresponding to 39.4% of total installed capacity. Figure 2 provides the flowchart of plant-specific HP simulation. To implement Equation 1, the comprehensive hydropower coefficient , which usually ranges from 6.5 to 8.5 kJ m −4 depending on water conduit and turbine types (Bakis, 2007;Zhou et al., 1997), is set to 8.  is specified for two cases. For the 693 WaterGAP reservoir plants whose reservoir operation processes are explicitly simulated in WaterGAP 2.2d, we assume that all reservoir outflow goes through the turbines unless installed capacity is exceeded, that is,  , , t turb t out Q Q . For all other plants, the turbine release is assumed to be equal to the WaterGAP 2.2d gridded streamflow time series, that is, Estimation of hydraulic head t H also differs between the two plant groups but does not distinguish runof-river plants from those reservoir-storage plants that are not among the 693 plants for which WaterGAP explicitly simulates reservoir storage.  from GHD attributes of installed capacity of plant, gridded elevation difference ele H , and long-term mean highest and lowest monthly streamflow of the grid cell in which the power plant is located. Visual inspection revealed no evidence of multicollinearity among these predictors. The regression model was first fitted for the 4,169 plants with observations of dam/weir height in GHD (correlation coefficient of this model r = 0.6 after removing outliers with studentized residuals that were larger than 3 in absolute value) and then used to assess the dam height for the remaining plants. Due to the low correlation, the minimum value of simulated dam height is set to 2 m, and for plants with installed capacity lower than 100 MW, where t S is WaterGAP 2.2d simulated monthly reservoir storage (10 6 m 3 ), max S is the maximum reservoir storage (listed in GHD) (10 6 m 3 ), and   0.9229 is a regression parameter that relates storage variations to head variations and is taken from the GRanD technical document (Beames et al., 2019). For plants whose reservoirs are not in the WaterGAP simulation, they are implicitly treated as run-of-river plants.
t H is assumed to be temporally constant, with where   0.68 is a globally homogeneous calibrated parameter such that the simulated global gross HP in 2016 is proportional to the EIA statistic, taking into consideration of installed capacity coverage included in GHD.
For any single hydropower plant, the actual time series of electricity generation depends on the operation status of plants. When a plant is reported to be first commissioned/opened from a specific year (see Table 1, i.e., attribute Year_Open in Table S2), we then started to estimate the HP at the plant level. If this attribute is missing, we assume that this plant has already been commissioned before year 1975, which is the starting point of our simulation period. The operation status of plant can vary by time period due to maintenance, decommission, and accidental destruction (i.e., attribute Timeline in Table S2), we excluded the electricity generation during these nonworking years. The HP from plants that were still under refurbishment in 2016 or have been decommissioned/shutdown before 2016 was also excluded. Therefore, the monthly HP to the plant levels that were operational during the time period 1975-2016 was determined.
Changes in HP are mainly due to commissioning and decommissioning of hydropower plants and hydrological variability, and HP data, for example, annual HP country values from EIA reflect both influences.

Evaluation Metrics
Three metrics, Nash-Sutcliffe efficiency (NSE) (Nash & Sutcliffe, 1970), coefficient of determination ( 2 R ), and variability ratio (CVR) (Kling et al., 2012), are adopted to evaluate the performance of simulated time series (e.g., HP and streamflow). NSE and 2 R are traditional metrics in hydrological modeling. Along with the CVR, these metrics provide an integrated measure of modeling performance with respect to different components, that is, correlation, bias, and variability, respectively.
where t O is observed value (e.g., monthly HP), t S is simulated value,  represents mean value,  is standard deviation, and CV is coefficient of variation. Ideal values for all the three metrics are 1, representing a perfect match of simulated series to the observed data.  of −1 indicates the streamflow averaged over the last 3 months was one standard deviation lower than normal (i.e., the mean) for the respective three calendar months.

Three-Dimensional Streamflow Drought Event Identification
As droughts are regional phenomena, it is of interest to quantify drought hazard not only for individual 0.5° grid cell but to also identify large, spatially and temporally contiguous drought patches/events, and characterize them by their spatial extent, duration, severity, and intensity (Andreadis et al., 2005;Dracup et al., 1980). Using the approach proposed by Haslinger and Blöschl (2017), we performed the following four main steps.
(1) Identify the grid cells that are "under drought". Following Agnew (2000), a drought is assumed to occur if SSI3 is less −0.84, which occurs on average once every 5 years (corresponding to an annual probability of nonexceedance F of 0.2). Each F of each SSI3 value smaller than −0.84 is then mapped to the where F is the nonexceedance probability of SSI3 in period t. All grid points with positive , int t q for at least two consecutive months are considered as "under drought" in a temporal dimension of each 0.5° grid cell.
(2) Detect the spatial extent of drought. The 0.5° cells under drought are aggregated into different drought patches by searching their 3  3 neighborhood grids. Once a continuous drought area exceeds a threshold of 25,000 km 2 (around nine grid cells in the equatorial regions), it is considered as a drought event with reasonable size and therefore impact (Liu et al., 2019). With this approach, smaller drought patches are filtered out. In our study, only 13% of all grid cells and months, for which a positive , int t q was determined throughout the study period, were identified to belong to such reasonable large drought patches.
(3) Determine the temporal connection between drought patches. Because one single drought event in a month can break up into multiple smaller drought events, or several small droughts merge into one spatially larger event in the subsequent month, we assume that the drought patches in two consecutive months belong to one drought event if drought area overlap is larger than 50% of the area of the smaller patch while the denominator itself is no less than one quarter of the area of the larger patch. (4) Extract drought features. The duration of the three-dimensional drought event is defined as the months between earliest initial and latest terminal time steps of all related grid points in the same event. For every time step, the monthly intensity is calculated as the sum of the gridded , int t q of the current drought patch. Drought severity is the cumulative monthly intensity over the whole drought duration, with where 3d s and 3d l are the initiation and termination periods of the three-dimensional drought event; t cell indicates all grid cells of the drought patch in period t.

Risk Analysis of Streamflow and HP Reductions
The risk analysis relates the severity of streamflow or HP reduction during a deficit event to its frequency or probability of occurrence. Different from Section 2.5, the deficit event is defined for either individual 0.5° grid cells or whole countries, that is, the sum of all grid cells pertaining to a country. Risks were computed with model variant V1, assuming hydropower plants that existed in 2016 and taking into account monthly values of streamflow and HP during 1975-2016. Both streamflow and HP deficits were derived as compared to the respective long-term mean at each grid, and then the deficit events were ranked according to their severity. A probability distribution was fitted to the ranked severity series to estimate the probability of exceedance of deficit events of a certain severity. WAN ET AL.
10.1029/2020WR028087 9 of 25 For the same reasons as for aggregating streamflow over 3 months (Section 2.5.1), we averaged also HP, for each month in the historical period, over the last 3 months to obtain HP3. For a specific hydropower plant, HP deficit t Def occurs in months where HP3 is less than long-term mean over the same months ( 3 HP ) for each plant, with The symbol Var stands for either HP or streamflow. In case of streamflow, the deficit computation was done per grid cell. For HP risk analyses at the grid cell level and country level, HP3 of each plant within a grid cell or a country was first added to the grid/national total HP3 before applying Equation 10. This aggregation is reasonable for hydropower because HP produced by individual plant is distributed via regional power transmission networks. Deficit events may last for a few months to multiple years. Severity of each identified deficit event was calculated as the sum of the monthly deficits over the event duration as where i s and i l are the first and last time steps of a streamflow or HP deficit event i. In case of HP, it quantifies the amount of hydroelectricity that could not be produced due to dryer than normal conditions. Each deficit event can be described by the probability that its severity is exceeded, applying the threshold method used for flood frequency analysis (Smith, 1984). The severities of all identified deficit events were ranked based on their magnitudes. Subsequently, a lognormal distribution was fitted to the top 42 streamflow severity values while Pareto type II distribution to HP severity values in the 42 years of 1975-2016 (see Section S2 for the distribution test). This step was to estimate the probability that in any year a streamflow/ HP deficit event occurs that does not exceed a given severity. If there were less than 42 historical deficit events, the remaining events were fill by 0, representing ignorable severity of the deficit event. Streamflow/ HP reduction during one event was expressed in terms of the severity value divided by mean annual streamflow/HP, with

Results
In Section 3.1, we test the quality of the new GHD regarding its completeness by comparing the included installed capacities to independent country values. Computed annual time series of HP per country are evaluated against independent historical time series in Section 3.2. In Sections 3.3 and 3.4, we evaluate the performance of simulated streamflow drought and the drought impact on HP. Building upon these validations, the HP reduction during large contiguous droughts is assessed in Section 3.5, while the 1-in-10 year risk of HP reduction in individual grid cells or countries is presented in Section 3.6. Figure 3 compares the total installed capacity in 2016 in GDH to the statistics of EIA (2019) at the country level, for 134 countries. The six world regions are divided according to the International Hydropower Association regional classification (IHA, 2018). For 80% (i.e., 107) of the 134 countries, the differences in conventional installed capacities between EIA and GHD are within 10% or 0.1 GW. The largest absolute discrepancy is found for China, where GHD misses 23.5% of the EIA installed capacity (Figure 3a, the highest green symbol shown refers to China). Countries with relative discrepancy higher than 50% are found equipped with EIA installed capacities of less than 0.2 GW. Figure

Performance of Simulated Annual HP at the Global Scale
For a global-scale validation of the HP model, only annual time series of HP per country were available by EIA starting from 1980 (EIA, 2019). Figure 4 shows the NSE coefficient, coefficient of determination ( 2 R ), and variability ratio (CVR) between simulated annual HP (using model variant V0) and EIA data for 1980-2016. In general, the metrics vary strongly among countries. NSE and 2 R are relatively low in Africa, with 27 out of 38 countries having negative NSE and 22 with 2 R of less than 0.5. The unsatisfactory performance in Africa is partly due to the unsatisfactory simulation of streamflow of WaterGAP in this region (Müller Schmied et al., 2021  the annual time series are dominated by a strong upward trend due to an increasing number of hydropower stations (e.g., China and India, Figure S1), not by climatic variations. Figure 5 presents a comparison of the simulated and statistical annual time series of HP (V0) for all plants within the six world regions. The statistical data are well captured by the HP simulation, except for the region East Asia and Pacific. The latter is due to the incomplete records on installation of new hydropower plant, particularly in China, which contributes most to the overall rapid increase behavior of regional HP ( Figure S1a). The observed interannual variabilities in Europe and North America are simulated well by the HP model ( Figure 5). In case of Africa, however, statistics do not support the international variations around the trend that is simulated. In the other three world regions, the annual time series are dominated by upward trends.
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12 of 25  The hydro-impact lines do not show any significant trends but large variations around the zero due to the interannual variability of streamflow, with negative values (of differences between the HP simulation with historical streamflow/storage and the simulation with long-term mean monthly streamflow/storage, see Table 2) indicating unusually dry years. For example, Africa witnessed two obvious HP depressions in 1982-1988 and 2002-2006, which coincide with the reported extreme droughts in Africa (Masih et al., 2014). Equally, the large North America droughts around 1977around , 1988around , and 2002around (Andreadis et al., 2005 are also reflected in the HP simulation. The mean values of the hydro-impact curves were calculated. It is found that only regions of East Asia and Pacific, South and Central Asia, and South America have negative values, which indicates a higher HP of V2 than of V0 in the long run. In the other three regions, the reverse is true. Theoretically, for hydropower plants without WaterGAP reservoir simulation, the mean monthly streamflow/storage variant (V2) should result in more or at least the same HP as variant V0 because of less high flow losses due to the installed capacity constraint. However, for the WaterGAP reservoir plants, the assumption in variant V2 may conversely decrease HP because of the existence of the complementary effect between release and storage, that is, per unit release becomes more productive as storage increases (Zhao et al., 2014). For instance, consider two periods, when in period 1 t both turbine release and hydraulic head equal 1, and in period 2 t equal 3, then the total HP is 10Δt according to Equation 1. Assuming mean release and storage of 2 as in the case of V2, the total HP becomes 8Δt. WAN ET AL.   . Gold lines represent the impact of hydrological variability (difference between V0 and V2, the latter assuming mean monthly streamflow and reservoir storage) on simulated HP, blue lines the impact of plant variability (difference between V0 and V1, the latter assuming that the 2016 plants existed throughout the simulation). HP, hydroelectricity production.

Performance of Streamflow Drought Simulation
Simulation of streamflow drought impact relies on a reliable simulation of streamflow and in particular streamflow drought. Performance of WaterGAP with respect to streamflow has already been extensively discussed (e.g., Müller Schmied et al., , 2021Zaherpour et al., 2018). Therefore, we tested the performance of streamflow drought simulation as indicated by standardized streamflow index (SSI3) against observations at 183 stations ( Figure S2) worldwide for which continuous time series of monthly streamflow were available during 1971-2000 (more details are provided in Section S4). The observed streamflow was provided by Global Data Runoff Centre. The agreement of NSE for SSI3 was moderate with a median of 0.5 and an interquartile range between 0.2 and 0.7 ( Figure S3). The goodness-of-fit for streamflow is very similar, albeit with slightly lower quartile of 0.14. At 25 stations (41% of assessed basin area), both NSEs exceeded 0.7. At a large number of stations (83% of assessed basin area), simulated and observed SSI3 values were classified into the same drought hazard class in 70% of the time ( Figure S4).

Monthly HP in the US
To test the capability of the HP model for simulating drought impact on HP, one would ideally compare simulation results at spatial scales below the country scale and temporal scales below the annual. However, such data are not available globally. We therefore evaluated data on monthly HP in the federal states of the US that are available from January 2001 (EIA, 2019). Figure 6   in late winter and dropping in late summer, recognizable difference between wet and dry years (Figure 6a). Both the statistical and simulated HP deficit series (see Equation 10 in Section 2.6) in the period 2001-2016 reveal three major drought events in 2001-2002, 2007-2009, and 2012-2016 (Figure 6b). The simulated mean HP deficit of 713 GWh is close to the observed value of 794 GWh. The -2009 droughts struck large parts of California. In 2016, hydropower in California represented 13.7% of the national total installed capacity, with conventional plants of 10.2 GW and pumped-storage plants of 3.9 GW in GHD; this composition has remained almost constant since 1990. The HP model overestimates seasonal variability and underestimates the seasonal low values (Figure 6c). This may be due to the artificial water transfers into California that are not taken into account by WaterGAP. The HP model reproduces the observed HP deficit (Figure 6d) much better than the HP itself. This makes sense because the HP deficits are relative values after removing seasonality. Initiation and termination of HP deficit events almost coincide with that obtained from EIA statistics. During the most recent two multiyear droughts, HP is observed substantially below average, and the cumulative HP reductions (severity as defined in Equation 11)

Analysis of HP Reduction During the 2003 Central European Drought
To reveal how streamflow drought influences HP at the country scale, we took the 2003 European drought, focusing on the Central European countries (hereinafter referred to as 2003 CEU drought, Figure 7a). The 2003 CEU drought was classified as a 30-year drought, that is, a drought with a return period of 30 years, based on temperature data (Charpentier, 2011). According to the three-dimensional drought event identification method explained in Section 2.5, the 2003 CEU drought began in early spring (February 2003) and intensified from June, then rapidly expanded to cover 75% area of Central Europe in August. The drought began to quickly recede in October and completely disappeared in March 2004 (Figure 7b). The grid-level drought duration (see Equation 8) was found the longest in Poland, where most grids were under drought for more than 8 months (Figure 7a). Central north Germany and eastern Hungary were least affected, with some grid cells without any negative streamflow anomalies.
Due to the low precipitation and extremely high temperature and thus low streamflow, the energy sector was challenged by a reduced potential of hydropower (Mukheibir, 2013). In CEU, most plants are concentrated in the south in Switzerland (CH), Austria (AT), Czech Republic (CZ), and Slovakia (SK) (Figure 7c). The time series of annual HP (V0) over CEU simulates well the strong interannual variability of HP shown by the EIA statistics, with years of high HP such as 1993 and 2013 and years of low HP such as 1996, 1997, and 2010 being reproduced (Figure 7d). However, the HP reduction in the drought year 2003 (but not in 2015) is strongly overestimated by the HP model. Compared to 1980-2016, the simulated HP reduction is 11.8%, while according to EIA it is only 4.0%. Considering the CEU drought period February 2003 to March 2004, HP was reduced by 11.4% with respect to 1980-2016. The overestimation of drought impact in CEU during 2003 as compared to EIA statistics is due to an overestimation of HP reduction for two HP producers, Switzerland and Germany (Figures 7e and S6a, compare red triangles to black circles for country-scale relative anomalies). In both countries, the HP value according to the statistics was very close to normal. The simulated HP (V0) anomalies are quite consistent with the statistics in Austria (AT), the country with the second highest installed capacity, Slovakia (SK), Czech Republic (CZ), and Hungary (HU) and relatively close in Slovenia (SL).
To isolate the drought impact on HP reduction, HP during the drought period should not be compared to the time series of actual HP within any spatial unit as this includes the impact of the number of active plants on HP. Evaluation of the V1 runs, with a constant distribution of hydropower plants, resulting in larger reductions from normal conditions during 2003 (Figures 7f and S6b). All counties, except Czech Republic, are simulated to suffer reductions of more than 15%, or around 1.0-2.0 . WAN ET AL.

HP Reduction During Large Contiguous Droughts
Globally, a total of 14,641 large contiguous drought events with a minimum extent of more than 25,000 km 2 have been identified in the period 1975-2016 using the method explained in Section 2.5. During these 42 years, several prolonged as well as widespread droughts have occurred. Table 3 summarizes the drought characteristics of the 20 most notable events in terms of severity, which are in agreement with the major drought events reported in the literature (Bonsal et al., 2011;Masih et al., 2014;Spinoni et al., 2015 & Zhou, 2015). From the listed events, areas of Northern Europe (and Russia) and North America show the highest number of drought events between the 1970s and 2010s, making up 13 of the top 20 severest events.
Among these top events, the 1976 European drought that occurred between April 1975 and August 1977 is ranked as the most severe one and lasted for 29 months. If the hydropower plants of the year 2016 existed during this drought (model variant V1), the simulated HP reduction would have been 13%. Hydropower in the drought-affected region accounted for 6% of worldwide installed hydropower capacity in 1977 and for 16% in 2016 (Table 3). Since 2000, Europe has witnessed a series of extreme dry events in combination with heatwaves, for example, 2003, 2010(Laaha et al., 2017Schewe et al., 2019). The 2003 CEU drought presented in Section 3.4.2 is part of the detected 2003 European drought, which is ranked as the twelfth strongest drought event. It occurred from February 2002 to August 2005 and reached its peak in September 2003, with a total severity of 15,719 (Table 3).
The fifth strongest drought event originated from the Northwest Territories of Canada and gradually moved south to western America in the end of 2000; the sixth severest drought also began in Canada but the region of Central Canada and invaded much of the eastern and southern regions of the United States. The two extreme droughts together led to a tremendous HP deficit in the US in June 2001 of up to 25% (6.6 TWh) less HP compared to that of the corresponding period for the year 2001-2016, as shown in Figure 6b.

Risk of HP Reduction due to Drought
Each plant, grid cell, or other spatial units is under a certain risk of HP reduction due to drought, which can be expressed as the probability that a certain reduction of normal annual HP is exceeded in each year or WAN ET AL. Note. A severity of 5,000 could be due to, for example, the existence of a drought patch with on average 1,000 cells with a 1-in-10 year drought occurrence ( , int t q = 0.5) over on average 10 months. HP reduction (V1) indicates the relative deviation from the mean monthly HP (V1, based on 2016 hydropower plants) over 1975-2016. installed N coverage refers to the installed capacity affected by the drought event in percent of the globally installed capacity in GHD in 2016. equivalently as the HP reduction that is exceeded with a certain probability or return period. Using model variant V1 considering hydropower plants existing in 2016 (Section 2.6), we computed, for 0.5° grid cells and whole countries, the HP reduction in percent of mean annual HP that is expected to be exceeded with a probability of 0.1 in any year or, equivalently, in 1 out of 10 years (Figure 8). A value of 20%, for example, means that, considering the streamflow variability during 1975-2016, there is a 10% chance in any year that this location faces a reduction of at least 20% of its mean annual HP (Equation 12). Under nonstationary conditions, which are mainly due to climate change, the values in Figure 8 are only an approximation also because historical streamflow time series can no longer be directly used to derive probabilities.
In 1 out of 10 years, 54% of all 4,082 grid cells containing power plants face an HP reduction of more than 20%. HP reduction is particularly high in semiarid areas, like the western United States and the Mediterranean region, unless hydropower plants are located on large rivers. In 7% of the cells, HP is even expected to be reduced, in 1 out of 10 years, by more than 70% as compared to mean annual HP. In contrast, there is almost no HP reduction in 18% of the cells (HP reduction  5%) when a 10-year HP deficit event occurs.
WAN ET AL.

10.1029/2020WR028087
18 of 25 At the country level, HP reduction in 1 out of 10 years is between 3% in Venezuela and 79% in Burkina Faso ( Figure 8b). China, accounting for 22% of global HP, shows a small HP reduction of only 8% even though many individual power plants are simulated to suffer from reduction of more than 10% or even 40% (Figure 8a). This is because (1) as a large country, if one region of the country suffers from a drought the other would not and vice versa, and (2) most of the large Chinese hydropower plants are subject to very low reductions of less than 5%. There are 67 out of 134 countries with relatively small HP reductions (20%), while 49 countries show moderate HP reductions between 20% and 40%, including countries in Central America and the Middle East. It appears that the majority of these moderately affected regions also have relatively low proportion of hydropower in energy (    r HP 0.3, Figure 1b). The 18 countries with high HP reductions of more than 40% are mostly found in Africa. Only two countries show more than 70% HP reduction, Burkina Faso (79%) and French Guiana (73%). In these countries, HP is not the dominant source of electricity. According to our study, total electricity production in 1 out of 10 years is only reduced by 11% and 36% in Burkina Faso and French Guiana, respectively. It is, rather, Togo whose total electricity production is calculated to be most strongly affected by streamflow drought. There is every year a 10% chance that total electricity production in Togo, which heavily relies on HP (    r HP 0.87), is reduced by 55%.

Discussion
In Section 4.1, we discuss the uncertainties of global-scale HP simulation as presented in this paper. The relation between streamflow drought and HP reduction is analyzed in Section 4.2.

Uncertainties of Global-Scale Simulation of HP
Drought adaptation strategies, for example, modification of electricity prices and the demand-load portfolio, are not taken into account in the HP model. Therefore, actual reduction of HP during periods with streamflow deficits may be overestimated by the HP model. The HP model only simulates the direct impact of changes in streamflow or outflow from reservoirs on HP during periods of drought.

Uncertainty of Simulated Streamflow
An assessment of these direct impacts requires a good quantification of changes of flow during drought. A comparison to streamflow observations at 40 globally distributed gauging stations in eight hydrobelts showed that WaterGAP simulates the streamflow that is exceeded in 95% of all months very well, while annual 3-month low flows for different return periods are overestimated (Zaherpour et al., 2018). Our analysis of model performance specifically during drought conditions, comparing SSI3 indicators based on simulated and observed streamflow at 183 gauging stations, indicates that WaterGAP simulates reduction of streamflow during drought reasonably well (median NSE equals to 0.5, Section 3.3).
Furthermore, while anthropogenic alterations of streamflow by water use and reservoir operations are modeled in WaterGAP, in particular the simulation of the effect of reservoir operation on streamflow is very uncertain. The existence of reservoir modeling mostly improves model performance, yet the discrepancies between modeled and observed outflows remain high due to a variety of reasons, including uncertainty of simulated inflow and water use as well as of the assumed reservoir operation algorithm (Döll et al., 2009). Therefore, unfortunately even for the 693 WaterGAP reservoir hydropower plants that account for 35% of the global installed capacity of convention plants, the uncertainty related to the simulated turbine release, reservoir storage (Section S6) and thus HP is high.
We believe that mainly due to the uncertainty of the climate forcing, in particular of global data sets of precipitation, a higher temporal (daily) and spatial resolution of streamflow modeling would not increase the reliability of simulated streamflow. A 36-fold higher spatial resolution of WaterGAP (5 arc-minutes, approx. 9 km × 9 km at the equator) did not lead to an improved simulation of observed streamflow as compared to the 0.5° model version applied in this study (Eisner, 2016). and that total streamflow is diverted into the power plant. In reality, hydropower plants rarely operate 24/7. The actual turbine release is not constant within a month. However, the load factor is not available for most hydropower plants. Only 36 large plants were equipped with the attribute of load factor (see Table 1) because (1) their data were relatively easily available and (2) the simulated HP of these plants was found to deviate significantly from the reported mean annual HP (i.e., attribute Gen_Gwhyr in Table S2) and thus substantially affects the country-level HP as compared to the EIA statistics due to their large installed capacities. To deal with these uncertainties, we (1) used the installed N as upper boundary of power output (see Equation 1) and (2) adopted a head reduction coefficient  (see Equation 4) for a better fit to HP statistics, which partly reflects the load factor. As only relative changes in HP are analyzed in this study, the uncertainty due to flow and head deviations is believed to be within acceptable limits, as demonstrated in the case of California in Figure 6.

Uncertainty Regarding the Category of HP and the Incomplete Representation of Reservoir-Storage Plants
For almost half of the globally installed conventional capacity, there is no information in GHD on the plant category (Section 2.1), that is, is unknown whether the plant is a run-of-river plant without any control on the amount of water flowing through the turbine or a reservoir-storage plant with controlled release. 12.4% of the installed capacity is known to be related to run-of-river reservoirs (or pondages) and 42.1% to reservoir-storage reservoirs. In the HP model, only 35% of the installed conventional capacity (693 plant records) is located at WaterGAP reservoirs and is thus simulated with a temporally varying hydraulic head (Equation 3). Three hundred and sixteen of these 693 plant records are known to relate to reservoir-storage plants and 20 to run-of-river plants.
The question is what the likely category of the hydropower plants without information on category is. We have compared the total installed capacities of run-of-river and reservoir-storage plants in some European countries to ENTSO-E (2017) data, which provide the fraction of run-of-river and reservoir-storage installed capacity per country. In case of Switzerland, the majority of installed capacity without known category belongs to reservoir-storage plants, while in Austria and Germany, the majority belongs to run-of-river plants (Figure 9). It is therefore not possible to make general assumptions about the category of plants without known category.
Anyway, run-of-river plants can have a large fall (hydraulic head) and a quite large reservoir (even though low-head plants dominate). For example, the Fatschbach power plant (15 MW) in Switzerland produces electricity over a useable gradient of 578 m (Axpo, 2020), and the Chief Joseph Dam (2620 MW) in the United States, with a dam height of 72 m, is operated in a run-of-river mode (Yildiz & Vrugt, 2019  The HP model does not distinguish simulation of run-of-river hydropower from reservoir-storage hydropower ( Figure 2) which is an appropriate approach given the large fraction of hydropower plants without known category. However, even if there were more information on plant category available, this approach could not be changed because the WaterGAP model cannot simulate the water balance of individual small reservoirs that may be located at small tributaries whose streamflow cannot be resolved at the 0.5° grid cell resolution. It is therefore necessary to assume constant hydraulic heads t H (Equation 4) for all reservoirs that are not located at large WaterGAP reservoirs that are assumed to be located at the river mainstem. WaterGAP does take into account 5000 small man-made reservoirs with a storage capacity below 0.5 km 3 (Müller Schmied et al., 2021) that are located in 32% of the cells with hydropower plants. However, these small reservoirs are aggregated with all small natural lakes within each grid cell and local runoff is routed through this aggregate water storage compartment, such that small reservoirs affect streamflow in the river mainstem, smoothing, and delaying streamflow from subscale tributaries. With an increased spatial resolution of WaterGAP, the number of reservoirs with an explicitly modeled water balance and thus the hydropower plants whose HP could be modeled as a function of reservoir storage (Equation 3) could be increased. However, given the difficulty to simulate very plant-specific operation rules by a globally applicable algorithm, it is expected to lead to very uncertain reservoir storage and thus t H simulation.  (Equation 4) was applied. The V3 simulation was run for the period 2001-2016 in the Columbia River Basin (CRB), which is located in the Pacific Northwest of North America (Figure 10). The CRB covers an area of 668,000 km 2 . Two hundred and six conventional plants amounted to 39.8 GW in 2016, and only 27 of them, with an installed capacity of 15.4 GW (39% of basin total) and producing 25% of the total basin HP, are simulated as WaterGAP reservoir plants (purple cross in Figure 10). We found that the impact of constant t H on mean and variability of HP and HP deficit strongly depends on the specific hydropower plants taken into account so that no general conclusions on the impact of this assumption on HP can be drawn. overestimate the drought impacts. However, the results in Section 3.4 reveal that this is not always the case. We assume that the deviations from the EIA statistics in the US and CEU lie in the following reasons.

Interpretation of the Simulated HP Bias in the US and CEU
(1) The lack of glacier mass balance modeling in WaterGAP. In Switzerland, summer streamflow over the last decades has increased due to the glacier mass loss (Hänggi & Weingartner, 2012). (2) The impact of electricity prices, which are known to have a significant positive effect on HP (Golombek et al., 2012;Jääskeläinen et al., 2018), is not taken into account in the simulation of reservoir release. (3) The lack of WaterGAP reservoirs (there are no WaterGAP reservoirs in Germany) such that the positive effect of reservoir management on water release during drought cannot be simulated. However, it is still surprising that there was so little HP reduction in Germany according to EIA, as both the observed and the simulated streamflow drought at two streamflow gauging stations on Danube and Rhine, which are downstream of the most important hydropower plants in Germany, are very strong ( Figure S5). (4) Simulated reservoir outflow and storage may differ strongly from observations, in particular for smaller reservoirs. For five reservoirs in the US, we compared simulated and observed time series of reservoir storage. The NSE for storage of the rather small Big Bend reservoir (494 MW) is negative and the 2 R 0.03, while in case of the larger Oahe reservoir (784 MW), a moderate NSE of 0.46 and 2 R of 0.68 are achieved ( Figure S7).

Relation Between Streamflow Drought and HP Reduction
Is it possible to estimate HP reduction in whole river basins from streamflow drought as determined from streamflow observations at gauging stations? Total HP in the CRB, for example, is found to be less strongly correlated with streamflow and streamflow deficit at the mouth of the river (cell A in Figure 10) than at the internal cell B ( Figure S8). This can be explained by the fact that B is the cell in which the hydropower plant with the largest upstream area is located, while there is no plant at the river stretch between A and B. Correlation between basin-wide HP and streamflow deficits depends largely on distribution of installed capacities of the hydropower plants.
With respect to grid-level streamflow and HP reductions that are exceeded in 1 out of 10 years, computed according to Section 2.6, a weak but significant positive correlation between the two values is observed (r = 0.43,  p 0.001, Figure 11). The reduction during a deficit period can be larger than 100% of the mean annual value of either streamflow or HP if the deficit event is a multiyear event. For the cells where WaterGAP reservoir plants are located, the Pearson correlation coefficient is even lower (r = 0.37,  p 0.001). The weak correlations indicate that HP reduction occurring with a probability of 10% in any year is very different from the severity of the streamflow drought. In case of run-of-river plants, a simulated decrease in streamflow only leads to an HP reduction if actual HP is not constrained by installed capacity (Equation 1). Typically, installed capacity puts a cap on HP during the high flow season, leading to differences in the periods of below normal streamflow and below normal HP. In case of various power plants in one grid cell, the higher the hydraulic head of the power plant, the more frequently HP is constrained by installed capacity.

Conclusions
In this study, a GHD was compiled. In comparison with EIA country statistics of installed capacity, GHD has proven to be a relatively reliable and complete representation of global hydropower plants. An HP model was developed to simulate, for the period 1975-2016, monthly HP worldwide based on the GHD as well as on outputs of the global hydrological model WaterGAP. Reliability of the monthly streamflow simulated by WaterGAP was tested by comparing simulated values of the streamflow drought indicator SSI3 to observed values at 183 streamflow gauging stations. With a median NSE of 0.5, model performance can be regarded as moderate. The country-level HP trends and interannual variabilities are captured quite WAN ET AL. well by the HP model, at least for countries with large HP. The ability to simulate HP as well as HP deficits due to drought was tested in the US using statistical data of monthly HP. The HP model can reproduce the observed HP deficit better than the HP itself, and multiyear drought periods in the US and California are clearly identified by the HP model. However, HP reduction during individual drought events can be significantly overestimated or underestimated.
We identified spatially extensive streamflow drought events between 1975 and 2016 worldwide and determined how HP was impacted during these droughts. A global drought risk analysis shows that at the scale of 0.5° grid cell, HP reduction during HP deficit events that occur with a probability of 10% in any year can range between 0% and 267% of mean annual HP, while the respective reductions at the country scale show a narrower range of 3%-79%. Eighteen out of 134 countries suffer from a reduction of more than 40%.
To improve the reliability of the simulated impact of drought on HP, more data on hydropower plants and HP should be made available openly and free of charge. Then, fewer of the hydropower plant attributes in the GHD that are required for simulation of HP would have to be estimated. Equally important, the capability of the WaterGAP model to simulate streamflow and hydraulic head at hydropower plants needs improvement. This requires in particular a better representation of reservoirs and their management, which is a very challenging task.