The WATCH Forcing Data (WFD) consist of time series of meteorological variables (e.g. rainfall, snowfall, temperature, wind speed) and are a product of the EU-FP6 project WATCH (WATer and global CHange). The WFD are derived from bias-corrected ECMWF ERA-40 reanalysis data , which have a sub-daily, 1∘ resolution. For the WFD these data have been downscaled to 0.5∘ and temperature and specific humidity were bias corrected for elevation difference between the ERA-40 grid and WFD grid . Bias corrections were applied to the daily temperature cycle and average temperature values using the CRU 2.0 data and to the number of “wet” days using the CRU data, while monthly rainfall and snowfall totals were corrected with the GPCCv4 data set . The CRU grid was used for the projection of the WFD resulting in a total of 67,420 land points at 0.5∘ × 0.5∘ resolution. The WFD for the period 1971–2000 have been used as a reference forcing data set in this study. The WFD were successfully used in multiple hydrological studies e.g.. In this study the WFD were used to identify the reference hydrological situation for every selected location, with the synthetic hydrological modelling approach.

In this study the output from three coupled atmosphere–ocean GCMs for the SRES A2 scenario has been used. The SRES A2 scenario includes extensive emission of carbon dioxide and slow adaptation by the global population, leading to severe changes in future climatology. Through the EU-WATCH project, simulation outcome from three GCMs was available on a global scale. The GCMs included are ECHAM5 , CNRM3 and IPSL . Each GCM provides meteorological forcing for the period 1960–2100. We used the period 1971–2000 as control period. The same procedure as for the WFD was applied in WATCH to downscale each GCM to the higher resolution 0.5∘ grid of the WFD. The WFD were used to determine the bias correction required for rainfall, snowfall, minimum, mean and maximum air temperature for the control period. The procedure is described in more detail by , , and . More detailed information on the GCMs can be found in Table . The data from the GCMs were used as meteorological input data for the synthetic hydrological modelling approach to produce groundwater discharge time series and associated drought characteristics for: (i) the control period (1971–2000), and (ii) the periods 2021–2050 and 2071–2100 to intercompare obtained drought characteristics against those derived from the reference model (1971–2000).

The advantages of this mini-ensemble is that the bias correction was performed by experts in the field both for the control period using the WFD data set to correct the models and for the future . This resulted in consistent downscaled and bias-corrected GCM data for 1963–2100. The period 1963–1970 was used to initialize the hydrological model and make sure that the groundwater discharge simulations were no longer influenced by the initial conditions. Although this mini-ensemble most likely under-samples the climate variability, the advantage of having a long initialization period and a validated bias correction is deemed more important.

The conceptual hydrological model is a lumped conceptual hydrological model, which consists of reservoirs for snow cover, soil moisture and groundwater (Fig. ). The model concept is a simplified representation of the natural system that simulates daily fluxes and state variables. The conceptual hydrological model generates time series of potential realizations for soil moisture storage and groundwater discharge without use of specific local catchment information apart from meteorological forcing (synthetic catchments). The simulations do not claim to provide actual site-specific soil moisture storage and groundwater discharge, but rather give a possible realization of these variables given the local meteorological data e.g.. The water balance of the modelled soil moisture is given by SS(t)=SS(t-1)+(Pra(t)+Qsn(t)-Eact(t)-Qs(t))⋅Δt, where SS is the soil moisture storage (mm), Pra the rainfall (mm d-1), Qsn the snowmelt (mm d-1), Eact the actual evapotranspiration (mm d-1), Qs(t) is groundwater recharge generated by percolation through the unsaturated zone (mm d-1) and Δt the time step of the model, which is 1 day for all simulations. The model is forced with daily temperature, precipitation and potential evapotranspiration to enable snow accumulation, soil moisture, actual evapotranspiration and discharge simulations. Estimates of daily evapotranspiration are calculated using the Penman–Monteith reference evapotranspiration . The potential evapotranspiration was calculated from daily temperature (minimum, mean, maximum), air pressure, humidity and wind speed . The daily mean temperature was also used in the snow module for snow accumulation and melt, following the widely accepted approach of the HBV model . Precipitation is simulated as snow when air temperature is below a pre-defined threshold, snowmelt only occurs above the threshold temperature and is simulated with the degree-days approach . The snow water balance of the snow module is given by

Sn(t)=Sn(t-1)+(Psn(t)-Qsn(t))⋅Δt, where Sn is the snow storage (mm) and Psn is snowfall (mm d-1). The groundwater recharge (mm d-1) is given by Rch(t)=Qs(t)+Qb(t), where Qs(t) is recharge generated by unsaturated zone (mm d-1) and Qb(t) is recharge generated by bypass in the unsaturated zone (mm d-1). The percolation through the unsaturated zone is given by Qs(t)=(SS(t)-SSFC)⋅ΔtifSS(t)≥SSFCQs(t)=SS(t)-SSCRSSFC-SSCRbkFC⋅ΔtifSSCR≤SS(t)≤SSFCQs(t)=0ifSS(t)≤SSCR, where SS(t) (mm) is the soil moisture content at time t (in d), b is a shape parameter derived from the soil retention curve (–), kFC is the unsaturated hydraulic conductivity at field capacity (mm d-1), SSCR (95.2 mm) and SSFC (168.9 mm) are the critical and field capacity soil moisture content, respectively. The bypass to the groundwater Qb(t) is 50 % of the rainfall above 2 mm, when the soil is below SSCR to simulate flow through the macropores of the unsaturated zone. A soil with an intermediate soil moisture supply capacity was selected to simulate the response of the unsaturated zone . This soil has a total supply capacity of 125.4 mm (from SSFC to wilting point, SSWP is 43.5 mm) where about 75 mm (between SSFC and SSCC) is readily available for evapotranspiration. Below SSCC the evapotranspiration is linearly reduced to 0.0 mm d-1 at SSWP. The water balance of the groundwater system is given by SG(t)=SG(t-1)+(Rch(t)-Qout(t))⋅Δt, where SG is the groundwater storage (mm) and Qout is the groundwater discharge (mm d-1). The Qout is calculated with the De Zeeuw–Hellinga approach : Qout(t)=Qout(t-1)⋅e-1j+Rch(t)⋅1-e-1j where j is the groundwater response parameter (in d), which can be derived from data on the aquifer transmissivity, storativity and the distance between rivers. The j-value in this study was fixed to 250 d, which corresponds to an intermediate-responding groundwater system. The groundwater discharge is hereafter called discharge (Q=Qout). The ability of the conceptual model to reproduce observed streamflow was demonstrated by . The conceptual model was evaluated against observed drought characteristics of four contrasting catchments in Europe. It was shown that the model is capable to correctly simulate hydrological drought characteristics. The Nash–Sutcliffe NS, for the selected catchments was between 0.35 and 0.75, with an improved performance for the low-flow conditions (NS 0.35–0.85). For a more detailed description of the conceptual hydrological modelling, sensitivity analysis or the validation results, the reader is referred to , and .

Hydrological drought characteristics (e.g. drought duration and deficit volume) were derived from simulated time series of daily groundwater discharge (Q) using the threshold level approach . In this study the Q80 (mm d-1) was derived from the flow duration curve, where the Q80 is the threshold which is equalled or exceeded for 80 % of the time. The Q80 has been used in multiple studies where drought is studied e.g.. A monthly threshold was applied, where the Q80 is derived for every month of the year in the control period. With a moving average window of 30 days the threshold was smoothed, resulting in the variable monthly threshold used for this study . The Q80 obtained from the reference period was also used for the future period to enable drought identification in the period 2000–2100, relative to 1971–2000. The drought state is given by Ds(t)=1forQ(t)<Q80(t)0forQ(t)≥Q80(t), where Ds(t) is a binary variable indicating whether a location is in drought at time t. The drought duration for each event was calculated with Duri=∑t=SiLiDs(t), where Duri is the drought duration (d) of event i, Si the first time step of an event i and Li the last time step of the event. The percentage drought per year (PDY) was used in this study as a measure of drought occurrence that enables a comparison between the simulated groundwater discharge time series of different time periods (e.g. 2021–2050 relative to 1971–2000). The PDY was calculated by PDY=∑t=1TDs(t)⋅365T, where PDY is the fraction of the total simulation period that a location is in drought (d yr-1) and T is the total number of time steps. Please note that PDY = 73 d yr-1 for the control period 1971–2000 by definition. The deficit volume was defined by Def(t)=Q80(t)-Q(t)forDs(t)=10forDs(t)=0, where Def(t) is the daily deficit volume of drought i (mm). The total drought deficit volume for each drought event was calculated with Defi=∑t=SiLiDef(t), where Defi is the total deficit volume of the drought event i (mm). The deficit volume is the cumulative deviation of the discharge from the threshold over the duration of a drought event. Furthermore, the standardized deficit volume (in d) was obtained with StDefi=DefiQ‾, where StDefi is the deficit volume of event i [d] divided by Q‾, the mean yearly discharge (mm d-1). StDefi was introduced to enable a comparison across the globe between locations with different flow magnitudes. Since the deficit volume (Defi) is highly correlated to the discharge, the obtained StDef provides the drought severity relative to the local hydrological situation. The StDef can be interpreted as the number of days that the mean yearly discharge is missing. The drought duration and standardized deficit volume are hereafter referred to as the duration and deficit volume. If the Q80 equals 0 mm d-1 for more than 20 % of the time, no drought characteristics were calculated since by definition a drought will not occur (Eq. ). These locations were excluded from the analysis, since frequent zero-discharge situations are part of the local climate (i.e. aridity) and are not a situation with below-normal water availability. When a drought is already present at the beginning of a simulation period or still present at the end no valid average characteristics could be obtained and therefore the drought event was excluded from the analysis to avoid including incomplete drought events in the statistics.

The similarity index (SI) was introduced as a measure to examine changes in drought characteristics . Bivariate probability distributions were used to find relations between drought duration (Eq. ) and deficit volume (Eq. ). The bivariate probability distributions were compared for different time periods and their joint occurrence was evaluated with the SI. The area of the 90 % of the bivariate probability distribution field was calculated and used for further evaluation. Both low and high extreme values of Duri and Defi were excluded, since the focus of this study is not on changes in the most extreme drought conditions. The SI quantifies the degree of overlap (%) between two 90 % Dur–StDef probability fields as follows: SI=R1|R2R1⋅100R1=∑x=1m∑Y=1nMR1(m,n)ifMR1(m,n)=1R1|R2=∑x=1m∑Y=1nMR1(m,n)ifMR1(m,n)=1andMR2(m,n)=1, where R1 is the 90 % Dur–StDef probability field of realization of period 1 (e.g. 1971–2000), R1 | R2 is the coinciding 90 % Dur–StDef probability fields of realizations of period 1 and 2 (e.g. 1971–2000 and 2021–2050, respectively), and m and n indicate probable realizations of Duri and Defi. MR1 and MR2 are matrices, MR1 contains the conditional probabilities of realization of period 1, and MR2 the field of realization of period 2. MR1(m,n) and MR2(m,n) are binary quantities where 1 equals a value within, and 0 a value outside the 90 % Dur–StDef probability field of realizations 1 and 2, respectively. In this study m⋅n was set at 150 ⋅ 150 and physical limits of Dur and StDef were fixed to 1296 and 256 d, respectively. By definition the SI can range between 0 % (no joint occurrence) and 100 % (complete joint occurrence). For a more detailed description of the SI the reader is referred to .

For a global evaluation of the change in drought duration and deficit volume as a result of climate change, locations (i.e. WATCH cells) were randomly selected around the world. The Köppen–Geiger climate classification was used to ensure that sufficient locations were selected in all different major climate regions. The five climate types distinguished in this study are: Equatorial (A), Arid (B), Warm temperate (C), Snow (D) and Polar climates (E). The global map with Köppen-Geiger climate classification was recalculated based on the WFD, to obtain correct positioning of climate regions (Fig. ). found that 1495 locations were sufficient to adequately include world's climates and were also used for this study (21 locations were excluded due to high number of no-flow conditions). They show that at least 30 randomly selected locations are required per major climate region to obtain reliable general drought characteristics. The selected locations were distributed over the climate types A, B, C, D and E as follows: 16, 21, 16, 34 and 13 %, reflecting differences in area of major climate regions.

To examine the impact of climate change on characteristics of groundwater discharge droughts, the synthetic hydrological modelling approach was used and forced with meteorological data from three GCMs (GCM forced) over the period 1960–2100 and the WFD over the period 1960–2000 (reference model). This period was divided into three evaluation periods, namely 1971–2000, 2021–2050, 2071–2100. An 11-year warm-up period (1960–1970) was applied for the hydrological model to remove biases resulting from the initial conditions. The monthly Q80 was derived over the period 1971–2000 for each simulation separately to determine the simulation-dependent variable threshold (Sect. ). The 1971–2000 threshold was applied to the two other future periods (for the GCM forced simulation), to enable calculation of the drought characteristics (D and StDef, Eqs.  and ), and to determine the effect of climate change relative to the period 1971–2000. The effect of climate changes on drought duration and deficit volume was studied for all different major climate regions. The groundwater discharge drought characteristics of each GCM forced hydrological model simulation over the control period (1971–2000) were compared against the characteristics derived from the model forced with the WFD reference model for the same period to explore uncertainty due to GCM forcing. Ideally, there should be only minor differences in drought characteristics between the characteristics derived from groundwater discharge simulated with the GCM forcing and the simulation with the WFD, since the control periods of each GCM are bias corrected to match the WFD . The changes in future drought characteristics were evaluated for the period 2021–2050 and 2071–2100 by comparing against the control period (1971–2000) of each GCM forced hydrological model simulation. For the evaluation the SI was calculated for all major climate types and used to determine the changes in drought duration and deficit volume as a result of a changing climate. For the seasonal analysis of changes in drought deficit volumes, the season for the location at the Southern Hemisphere has been transposed to match the Northern Hemisphere climatology.

Hydrological droughts derived from groundwater discharge time series that were simulated with the synthetic hydrological modelling approach using re-analysis data (WFD) as meteorological forcing (reference model) were the benchmark in this study. The hydrological drought characteristics were intercompared for the control period from 1971–2000 with those obtained from the same hydrological model that was forced with downscaled and bias-corrected outcome from three GCM forced models.

The bivariate density distributions obtained for the control period for all three GCM forced models show large similarity with the reference model for all climate types (Fig. ). However, some deviations occur for the polar (E) and arid (B) climate types where the GCM forced models show less spread in the drought characteristics than the reference model. In the snow-dominated (D) climate type a division between short duration and long multi-year drought events was found. This is caused by the fact that groundwater storage is not replenished in the winter season. Below-zero temperatures in the following summer prevent snowmelt and groundwater recharge and hence drought conditions will not lift. When summer temperatures are too low to generate enough snowmelt to replenish the groundwater, this drought will continue over the next winter. If the drought continues over winter this will automatically result in a multi-year drought and hence long drought durations . Overall, the GCM forced models show a large resemblance to the reference model throughout the climate regions, especially for the less extreme climate types. This is also illustrated through the SI (Eq. ), when the GCM forced models are compared against the reference model (Table ). For example, the SI for the A climate is 100 % which means that the bivariate distribution of drought duration and deficit volume for the three GCM forcing data sets is identical to the WFD forcing. The SI for the C climate is almost 100 %, and for the D climate around 90 %. For the B climate the SI is still 75 % or more, whereas for the E climate the SI is above 60 %.

The average drought duration and deficit volume for the major climates and for averaged over all climates show that the GCM forced models are in good agreement with the reference model with some mismatch in the extreme arid and polar climate types (Figs.  and ). The results from Table  support the SI findings (Fig.  and Table ) – that the GCMs are capable to produce realistic meteorological forcing for hydrological drought assessment under most climate conditions, but show difficulties in desert and polar climates. The drought duration derived from the GCM forced models for the A, C and D major climate types deviates less than 10 % from the duration obtained for the reference model (Table , IPSL for the A climate type is an exception). For the B and E climates the deviation is larger in particular for the latter (up to more than 50 %). The deficit volume shows a similar pattern but relative deviations are larger because of smaller magnitude (Table ). Uncertainties in the differences are low (Table ), increasing the confidence that bias-corrected GCM output can correctly reproduce hydrological drought characteristics for the control period.

The monthly drought deficit for the control period for all three GCM forced models shows a large similarity with the reference model derived from the WFD (Fig. ). The GCM forced simulations show identical patterns with respect to the monthly distribution of the drought deficit. An exception is found for the polar (E) climate type, where the drought deficit volume in summer is overestimated by the GCM forced simulations.

The deviations of the GCM forcing from the reference situation that are found are most likely caused by the discrepancies between the GCM forcing data and the WFD forcing. Although the bias correction removes most of these discrepancies for precipitation and temperature simulations, still differences remain. An example can be found in the co-occurrence of precipitation which is very important to lift drought conditions. When multiple drought events co-occur they are more likely to increase groundwater recharge and hence result in increased groundwater discharge. This in turn will lead to an end of a drought event, while the same precipitation volumes over a prolonged period of time would have a different effect. Since the precipitation is corrected using a fitted gamma-distribution these second-order statistics are not included in the bias correction. This could especially in dry climate have a significant impact on the drought characteristics, where a small amount of rainfall could end a drought event. In the polar climate, the interaction between precipitation amounts and temperatures is of significant importance with respect to the ending of drought events. If the forcing of the GCM were to have exactly the same higher-order statistical properties as the WFD, no differences would occur in drought characteristics. Therefore, it is concluded that the statistical properties of the precipitation and temperature are not fully matched for the polar climates and to a lesser extent for the B-climate, which significantly impacts the drought characteristics in these climates.

All GCM forced models show a decrease in the number of hydrological droughts throughout climate types (Fig. , upper row, note logarithmic scale). This decreasing number of droughts is associated with an increase in the duration by 143 to 157 % for all GCM forced models in 2071–2100 (Figs.  and , second row, Table ). The most severe droughts also show a very strong increase relative to the control period and the spread in duration between locations strongly increases (Fig. ). The overall effect of climate change on the PDY over the two future periods shows a decreasing trend (Fig. , third row). The total time a location is in drought decreases by 67 to 74 % in 2071–2100 (Table ), indicating that the locations are less in drought throughout the 30-year period (Fig. ). The deficit volume shows an overall increase of slightly over 200 % in 2071–2100 (Table , Fig. ), which indicates that although droughts are less frequent, the severity in both duration and deficit volume increases, for the remaining events. Uncertainties in the estimated relative changes are low, 2–5 % for durations and 1–5 % for the PDY (Table ), with the exception of the deficit volume (4–64 %). This indicates that it is more difficult for the ensemble of GCMs to indicate changes in deficit volumes with high certainty.

The projected changes in the median of groundwater discharge drought characteristics (duration, deficit volume and PDY) for each major climate type are included in Table . The duration increases relative to the control period in all major climate regions, where the period 2071–2100 is more affected than 2021–2050 (Table ). The strongest increase occurs for the equatorial and arid climates, where duration increases up to 181 % for IPSL (Table ). For the snow and polar climate (D, E) the increase in duration is smaller (114–138 %) and lower than for the warmer A, B and C climates.

The PDY is projected to decrease throughout the 21st century (Fig. , Table ). However, changes vary throughout climate regions. Averaged over all climates by the end of the century, median PDY will decrease to 26–33 % relative to the control period leading to an average of ≈22 d yr-1. For the equatorial climate (A) the direction of the change is not uniform. The IPSL forced model shows an increase for the equatorial climate (A) in 2071–2100 (128 %), while both ECHAM and CNRM show that the PDY will decrease throughout all climate types (74 and 44 %). For the other climate regions the direction of the change is uniform and shows a decrease in the PDY. For the snow climate, the changes are largest, the total PDY reduces to 5–8 % relative to the control period, leading to an average PDY of ≈5 d yr-1 by the end of the 21st century.

A substantial increase was found for the deficit volume for all climate regions in both future periods, where the mean deficit volume clearly increases over the century (Fig. , Table ). This increase is strongest for the A, B and C climates, where the ranges increase by 217–327 % leading to median deficit volumes between 9.24 and 21.6 d, i.e. 9.24 and 21.6 times the mean daily discharge. This is 2.5–6 % of the annual discharge for these regions.

Seasonal changes in the relative importance of the drought deficit are small, with the exception of the polar (E) and snow-dominated (D) climate types (Fig. ). In these regions a shift to more spring- and summer-dominated drought are projected. This is caused by shifts in the snowmelt season due to temperature rise (as a result of climate change), resulting in a lower water availability in late spring and summer development towards warm snow season drought,. This effect is not found in the other major climates, since the groundwater discharge seasonality in the regions is not dominated by snow accumulation and melt periods. Although locally the changes in the drought seasonality might be severe, on a global scale no changes have been found as a result of changes in climatology (e.g. shifts in precipitation patterns).

For all future GCM forced models the 90 % probability fields were calculated and the changes relative to the control period are presented using the SI (Table ). All models indicate that changes occur with a similar magnitude for all major climate types. For example, the SIs obtained with the ECHAM forced model show that 19 % of drought characteristics (duration and deficit volume) of events in 2021–2050 (averaged over all climates) did not occur in the control period. This percentage increases up to 31 % by the end of the century. The strongest decrease in SI (i.e. largest change) was found in the equatorial, arid and warm temperate climates (A, B, C) where SI values can be as low as 60 %. The same pattern was found for the snow climate (D) – however, changes in SI are smaller.