In this study, we use the outputs of the latest version of the global hydrological and water use model WaterGAP 2.2d (Müller Schmied et al., 2021). WaterGAP consists of three major components: the water use models, the linked groundwater–surface water use (GWSWUSE) model and the global hydrological model (WGHM). The water use models compute water use in the five sectors: household, manufacturing, cooling of thermal power plants, livestock and irrigation. Household and manufacturing water use is computed based on national statistics (Flörke et al., 2013). The amount of water required for cooling of thermal power plants is calculated based on the location, type and size of power plants and the annual time series of thermal electricity production (Flörke et al., 2013). Irrigation water use is computed based on information on the irrigated area and climate for each grid cell. The irrigation model first computes cell-specific cropping patterns and growing periods and then irrigation consumptive water use, distinguishing only rice and non-rice crops (Döll and Siebert, 2002). The irrigated areas change over time (Siebert et al., 2015). The globally small amount of livestock water use is the only temporally constant water use and is determined from the number of livestock and livestock-specific water use values (Alcamo et al., 2003). Water use for households, manufacturing and cooling of thermal power plants is constant throughout the year but changes from year to year.

The water use models themselves do not take into account the source of the sectoral water abstractions. This is done by GWSWUSE, which computes monthly time series of 0.5∘ grid-cell values of human water abstractions from (1) surface water bodies (river, lakes and man-made reservoirs) and (2) groundwater, for each of the five sectors, as well as the respective net abstractions from both sources (Döll et al., 2012). A comparison of simulated annual sectoral water abstractions per country to independent values from the AQUASTAT database of FAO showed a rather high similarity between the two datasets (Müller Schmied et al., 2021).

Taking into account the net abstractions, i.e., the difference between water abstractions and return flows, WGHM simulates, with a daily time step, the most relevant hydrological processes occurring on the continents and computes water flows such as actual evapotranspiration, runoff, groundwater recharge and streamflow, as well as the amount of water stored in diverse compartments such as the soil and the groundwater for all land areas, excluding Antarctica (Müller Schmied et al., 2014; Döll et al., 2003; Alcamo et al., 2003). The soil is represented as one water storage compartment that is characterized by (1) soil water capacity (Smax), which is computed as the product of land cover, specific rooting depth and soil water capacity in the upper meter, and (2) soil texture, which affects groundwater recharge (Müller Schmied et al., 2014). The temporal development of soil moisture (S) is computed from the balance of inflows (precipitation and snowmelt minus interception by the canopy) and outflows (actual evapotranspiration and total runoff from the land). Total runoff from the land fraction of the grid cell is then partitioned into the fast surface and subsurface runoff and the diffuse groundwater recharge. Both components are subject to so-called fractional routing to the various other storages within the 0.5∘ grid cell, which include the groundwater as well as lakes, wetlands, man-made reservoirs and rivers (Döll et al., 2014). Streamflow (Qant) in each grid cell depends on the runoff generated within the cell, inflow from upstream grid cells as well as human water abstractions and takes into account the impact of man-made reservoirs.

WGHM is calibrated to match long-term annual observed streamflows at the outlets of 1319 drainage basins that cover ∼54 % of the global drainage area, following the calibration principles provided by Müller Schmied et al. (2014), Hunger and Döll (2008), and Döll et al. (2003). In validation studies against time series of observed streamflows, WaterGAP has been repeatedly shown to be among the best-performing global hydrological models (Zaherpour et al., 2019, 2018; Veldkamp et al., 2018). Nevertheless, there can be significant mismatches between the observed and simulated seasonality and interannual variability.“It is found that WaterGAP can simulate the low flow percentile (Q95) very well, but it can also overestimate the return period of low streamflow” (Zaherpour et al., 2018).

This study uses 30 years (1981–2010) of monthly time series of WaterGAP gridded (0.5∘×0.5∘) outputs for 67 420 land grid cells covering all land areas of the globe except Greenland and Antarctica. These include (1) soil moisture (S) [mm]; (2) streamflow (Qant) [km3 per month]; (3) streamflow under naturalized conditions (Qnat) [km3 per month], assuming there are no human water abstractions or man-made reservoirs; and (4) total surface water abstractions [km3 per month]. In addition, the consistent dataset of soil water capacity (Smax) [mm] is utilized.

Water deficits (dsoil and dQ) and anomalies (psoil and pQ) are combined into single deficit anomaly indicators (SMDAI and QDAI) based on the desired indicator characteristics as elaborated by Cammalleri et al. (2016). The combined drought indicator should be zero if there is either no deficit- or no anomaly-based drought. It should be equal to p and d if p and d are the same, while it should have lower values if either d or p is close to zero. Thus, following Cammalleri et al. (2016) 7SMDAI=psoil⋅dsoil and accordingly 8QDAI=pQ⋅dQ.

Both SMDAI and QDAI values range from 0 to 1, where 0 corresponds to no drought hazard and 1 corresponds to extreme drought hazard. The indicator values are put into classes and coinciding drought classifications according to Table 2.

Out of the total 67 420 WaterGAP land grid cells, only 57 043 grid cells were considered in this study. Grid cells with barren or sparsely vegetated land cover, based on the MODIS-derived static land cover input map used in WGHM (Müller Schmied et al., 2014), together with grid cells in Greenland, were not considered. For each of these grid cells and each calendar month, we determined the best-fitting beta and gamma cumulative distribution functions for monthly dsoil and Qant, respectively, by utilizing a combination of functions from the R packages gamlss, gamlss.dist, extremeStat and fitdistrplus. However, as tested by the one-sample Kolmogorov–Smirnov test (KS test) at the 0.05 significance level, for 27.12 % of the grid cells in the case of dsoil and 39.94 % in the case of Qant, the fits were rejected for all 12 calendar months. Examples of an accepted grid cell and a rejected grid cell of the beta distribution function are shown in Fig. S3 in the Supplement. In the rejected grid cells, the probability of non-exceedance F is determined directly from the time series of 30 monthly values using the R function empirical cumulative distribution function (ECDF). The ECDF is a step function that increases by 1/30 at each of the 30dsoil values of SMDAI or Qant values of QDAI (Fig. S3 left). The computed F value of a specific dsoil or Qant value is the fraction of all 30dsoil or Qant values that are less than, or equal to, the specific dsoil or Qant value. Figure S4 in the Supplement shows the grid cells where ECDFs had to be used to compute F.

We compared QDAI with the well-established anomaly-based drought indicator standardized streamflow index (SSFI) introduced by Modarres (2007). SSFI is computed separately for each calendar month, similar to the standardized precipitation index (SPI) (Mckee et al., 1993), as 9SSFI=Qanti-Q‾antσ, where Qanti [km3 per month] is the streamflow value at time interval i, Q‾ant is the long-term mean of the streamflow values and σ is the standard deviation of the streamflow values.

The relations between dsoil, mean monthly (dsoil_mean), psoil and SMDAI are further clarified by the time series of these variables in Fig. 1 for two grid cells with rather different characteristics: a grid cell in Germany (42.25∘ N, -121.75∘ E, left panels in Fig. 1) and one in northeast India ( 27.25∘ N, 88.25∘ E, right panels in Fig. 1). The values of dsoil in the German grid cell show, on average over the whole reference period, high deficits in the summer months and low deficits only in one to two winter months (dashed grey line). According to the definition of psoil, an anomaly-based drought hazard, as indicated by psoil>0 (blue line), occurs only if the actual soil moisture deficit (green line) is much higher than the mean calendar month values dsoil_mean; per definition, this is the case in only 1 out of 5 years (Eq. 3 and Table 1). According to Eq. (7), SMDAI is always between psoil and dsoil. In the German cell, an anomaly-based drought occurred during the unusually dry, but still low-deficit, winter months of 2006, resulting in an SMDAI value that was much smaller than psoil. During the central European (CEU) summer drought of 2003, SMDAI was approximately equal to psoil. Thus, SMDAI appropriately indicates that anomalously low soil moisture during generally wet winter months is less of a hazard to vegetation than the same anomaly would be during generally dry summer months. The grid cell in northeast India is characterized by a low seasonality of soil moisture and a generally very high soil water content. Even for some unusually dry months (with high psoil), dsoil almost always remains below 0.25. Due to the low deficit, even in cases of high psoil, SMDAI is much smaller than psoil during all drought events indicated by psoil. When comparing temporally averaged drought hazards between the two grid cells, SMDAI would indicate a relatively higher drought hazard for the German grid cell than for the Indian grid cell, which would not be the case if a purely anomaly-based indicator, such as psoil, were used as the drought hazard indicator.

The relationship between SMDAI, psoil and dsoil can be further explored by using global indicator maps for a specific month, e.g., August 2003 (Fig. 2). WaterGAP computes soil moisture deficits of 75 % or more in most grid cells, while low deficits occur only in a few areas, where August belongs to the rainy season, e.g., the Sahel region and the monsoon areas in India (Fig. 2a). In each grid cell, psoil is, per definition, zero in 80 % of all August months. Therefore, in any month, approximately 80 % of the grid cells indicate no drought and psoil equals 0 (Fig. 2b). Only grid cells with a non-zero psoil have a non-zero SMDAI (Fig. 2c). For example, southeast India shows extremely high dsoil values, but as there is no anomalously high soil moisture deficit except for a few grid cells where psoil is mostly zero, SMDAI is also mostly zero. Thus, no soil moisture drought hazard is indicated. The difference between SMDAI and psoil is shown in Fig. 2d. In most grid cells with differences, SMDAI is higher than psoil due to high dsoil. Focusing on central Europe, SMDAI (in Fig. 2c) correctly indicates the summer drought of 2003, documented in the EM-DAT International Disaster Database (http://www.emdat.be, last access: 11 May 2020), the European Drought Reference database (http://www.geo.uio.no/edc/droughtdb, last access: 15 May 2020) and Spinoni et al. (2019). The location of grid cells from Fig. 1 is represented in Fig. 2a with blue points drawn at the center of each grid cell. During Northern Hemisphere winter months, soil moisture deficits are lower, for example, in Europe and the eastern part of North America, but high in most snow-dominated northern high-latitude regions (as no liquid water enters the soil), with corresponding effects for the relationship between psoil and SMDAI (see Fig. S5 in the Supplement showing the drought situation in December 1999). In Europe and the eastern part of North America, for example, SMDAI is smaller than psoil (Fig. S5d).

Figure 3 shows the frequency of occurrence of the four SMDAI drought classes specified in Table 2 and of the no-drought condition (SMDAI = 0) during the reference period 1981–2010. SMDAI is zero in about 80 % of the cases, following psoil as monthly soil moisture almost never reaches the maximum soil moisture capacity. Extreme soil moisture drought hazards occur with a relatively high frequency in the northwestern parts of Australia and southeastern parts of Africa. Regions with mostly low soil moisture deficits, such as central and eastern European countries and the eastern USA, show very low occurrence frequencies of extreme drought hazards and more often than other regions a moderate drought hazard (Fig. 3b). Snow-dominated regions, such as parts of Russia and Canada, show a relatively high frequency of extreme soil moisture droughts due to the high values of simulated soil moisture deficits created by the lack of liquid water to infiltrate the soil during the winter months and the temperature-driven seasonal shifts of snowmelt and, thus, infiltration of water into the soil.

QDAI indicates the drought hazard for surface water supply required for satisfying human water demand (WUsw), assuming the water suppliers also take into consideration the water demand by freshwater biota (EFR). The deficit component of QDAI (dQ) is the relative difference between the total surface water demand and streamflow, while the anomaly component (pQ) is based on the unusualness of streamflow. QDAI depends on more individual variables (i.e., WUsw, Qant and EFR) than SMDAI (i.e., S and Smax). Figure 4 shows their relation for two grid cells with different characteristics of human surface water demand compared to streamflow. In the grid cell in the western USA, where streamflow of the Klamath River is observed in Keno (42.25∘ N, -121.75∘ E, left panels of Fig. 4), water demand (mostly for irrigation, with a mean of 0.038 km3 per month) is high compared to the relatively small streamflow (0.105 km3 per month). In the grid cell in Germany, human surface water demand of 0.056 km3 per month is small compared to the rather high streamflow of 4.6 km3 per month of the Rhine at Mainz (49.75∘ N, 8.25∘ E, right panels of Fig. 4).

In the US grid cell, the difference between the mean monthly streamflow under the naturalized condition (Qnat_mean) and mean monthly simulated streamflow (Qant_mean) is high, especially in the growing period, due to large anthropogenic abstractions of streamflow water in the drainage basin of the grid cell (observed in the topmost plot). While the observed (Qant_obs) and simulated (Qant) streamflow shows a reasonable correlation, WaterGAP appears to overestimate streamflow depletion by human water use in the summers. Characterized by a high seasonality, anthropogenic surface water demand WUsw (dashed grey line in center plot) and total surface water demand (i.e., WUsw+EFR_0.8, orange line in center plot) result in very high deficits dQ (green line of the bottom plot) during almost every summer. However, there are only a few months with drought as identified by the anomaly-based drought hazard pQ exceeding zero (dark blue line). This occurs because the decade shown in Fig. 4 happens to be a very wet decade compared to the whole reference period. Another reason is that more than 20 % of the years show zero streamflow in the calendar months August and September such that pQ is zero in all 30 August and September months of the reference period; i.e., no drought is indicated even in case of zero streamflow (see left panel of Fig. S7 in the Supplement). Due to the large deficit values, pQ is almost always smaller than dQ in this US grid cell.

In the German grid cell (right panels in Fig. 4), the relatively low anthropogenic surface water abstractions result in almost identical values of Qnat_mean and Qant_mean (lines overlap in the top plot), and total surface water demand is very similar to EFR (lines overlap in the center plot). Non-zero dQ values (bottom plot) are mainly computed if Qant is lower than EFR, such as during the central European drought of 2003. It is reasonable to consider this type of situation as a drought hazard as water supply companies would have to stop any surface water abstraction if they wished to protect the river ecosystem. Different from the US grid cell, droughts are rather equally distributed over all decades of the reference period in the German grid cell but the summers of 2003 and 2005 suffer from the most severe droughts of the reference period, in line with expected drier summer due of climate change. Even if taking into account EFR as 80 % of Qnat_mean (EFR0.8), the total surface water demand is so low that in contrast to the US cell, dQ is always smaller than pQ.

Assumptions about the magnitude of EFR have a strong impact on dQ and thus QDAI of all grid cells except those with very high surface water abstractions such as the US cell. If the water demand of the ecosystem were assumed to be only 20 % of Qnat_mean(EFR_0.2) instead of 80 % of Qnat_mean, dQ decreases somewhat in the US cell but reduces to zero during the whole reference period in the German cell (Fig. S6 in the Supplement). Therefore, water suppliers in the German grid cell would not suffer from any drought hazard (as indicated by QDAI) and would not have to decrease their surface water abstractions even during a drought similar to the 2003 central European drought.

The global streamflow drought hazard maps for August 2003 (Fig. 5) help to illustrate the global variations in QDAI as a function of its components pQ and dQ, which again depends on the human surface water demand WUsw. Streamflow deficits are not restricted to areas with high mean annual WUsw during the period 1981–2010 (Fig. 5a) but can be greater than 75 % in regions such as South Africa were Qant is low (Fig. 5b). Different from soil moisture drought, pQ and dQ are strongly correlated (Fig. 5c). This is due to the fact that total surface water demand is dominated in many grid cells by EFR, which is a fraction of Qnat. In the EFR-dominated cells, the mean monthly Qant is very similar to the mean monthly Qnat, such that dQ is then approximately the difference between mean monthly Qant and Qant; this difference is also the basis for computing by pQ (Fig. 5d). QDAI is mostly less than pQ (Fig. 5e). The 2003 central European drought hazard for the surface water supply for humans (Fig. 5d) is, at least in many parts of Germany, less pronounced than the soil moisture drought hazard for vegetation (Fig. 2c). Figure 5c–e also indicate the grid cells with Qant=0. If streamflow in a grid cell is zero in 20 % or more of all August months (left panel of Fig. S7), pQ and thus QDAI are zero because the zero streamflow is not an anomaly that occurs in less than 1 out of 5 years.

In contrast to SMDAI, the frequency of occurrence of no-drought conditions according to QDAI (Fig. 6) is larger than 80 % in grid cells, particularly with large rivers and barely any human water use, such as the Amazon River in South America, the Congo River in Africa and the Ob River in Russia (Fig. 6e), where the deficit is often zero. In addition, grid cells with intermittent flows also show a high percentage of no-drought conditions, as for any calendar month with at least 6 months without streamflow pQ is always equal to zero (Fig. S7). In these grid cells, no-drought conditions occur in the case of zero streamflow. This type of intermittent grid cell, where Qant=0 for at least 20 % of the months of any calendar month is marked separately in Fig. 6c–e. Extreme streamflow drought hazard for human water supply (Fig. 6d) occurs most often in regions with high streamflow deficits (compare Fig. 5b), such as South Africa and parts of southeastern Australia, i.e., regions with low streamflow and relatively high surface water abstractions, mainly for irrigation (Fig. 5a). Regions with low water human surface water abstractions such as northern Canada and the Amazon and Congo basins show an exceptionally high occurrence of mild drought hazards (Fig. 6a).

Smax is one of the key components for computing SMDAI. WaterGAP calibration and validation studies have indicated that Smax may be underestimated in WaterGAP by a factor of 2 or more (Hosseini-Moghari et al., 2020). In order to understand the sensitivity of SMDAI to changes in Smax, we ran a version of WaterGAP in which Smax was doubled (Smax2). Figure 7 presents global maps of dsoil_Smax2 (Fig. 7a), psoil_Smax2 (Fig. 7c) and SMDAI_Smax2 (Fig. 7e) for August 2003 and the change in each parameter with respect to the standard WaterGAP output, i.e., the difference between parameters computed using Smax2 and Smax (Fig. 7b, d and f). With doubled Smax, mean monthly soil moisture increases, too. In most grid cells, the soil moisture deficit increases compared to standard Smax (Fig. 7b). Differences are mostly small except for scattered grid cells in which the soil moisture deficit decreases by more than 50 percentage points. Such cells are also found in central Europe where, under the heavy drought conditions of August 2003, computed deficits dQ are generally smaller in the case of doubled Smax; in this region, psoil increases in the case of doubled Smax (Fig. 7d). Globally, psoil increases or decreases in some grid cells by more than 50 percentage points. Equally, for SMDAI, the sensitivity to doubled Smax is low for most grid cells but can be greater for a few (Fig. 7e).

The streamflow drought hazard for water supply indicated by QDAI depends on how EFR is defined. In Fig. 8, we compare the global distribution of QDAI values among the 57 043 0.5∘ grid cells, assuming that either 80 % or 50 % of mean monthly natural streamflow is required to remain in the river for the well-being of the river ecosystem, or that there is no EFR at all that needs to be considered when the decisions about river water abstractions are made. We distinguish between humid and (semi)arid grid cells (Fig. S8 in the Supplement) and consider the two months of August and December 2003 as well as all 360 months of the reference period. The QDAI distributions are very similar for all three time periods. The boxplots show that a drought hazard in humid areas is only identified if the existence of an EFR is acknowledged. If water suppliers in humid areas assume that all water in the river can be abstracted, they will very rarely be unable to satisfy their demand. In humid grid cells, QDAI increases strongly with the selected EFR, which means that with increasing consideration of the water requirements of the river ecosystems, drought hazards to the water supply increase; i.e., there are more situations where water abstractions would have to be reduced to keep enough water in the river for the ecosystems to thrive. In (semi)arid regions, QDAI is already very high, even without acknowledging any water requirement of the river ecosystem. This is due to an often high surface water demand compared to naturalized streamflow, in particular as crop production requires irrigation. Like in humid regions, QDAI increases with increasing EFR. The slightly higher median QDAI values in August 2003 than in December 2003 reflect the larger amount of humid grid cells in the Northern Hemisphere. Figure 8 shows that water suppliers in (semi)arid and arid regions suffer much more strongly from drought hazards than water suppliers in humid areas due to the much higher ratio of water demand to streamflow.

Further differences between QDAI values computed for an alternative EFR are explored for two widely known drought events, the South Asian drought of 2009 (Neena et al., 2011) and the North American drought of 2002 (Seager, 2007). Figure 9 presents the spatial extent of both the droughts detected by QDAI at a continental scale (left panels of Fig. 9) for August 2009 and March 2002. Time series plots (right panels of Fig. 9) for an Indian grid cell (24.75∘ N, 75.75∘ E, top panel), as well as another for a US grid cell (44.25∘ N, -110.75∘ E, bottom panel), provide a better understanding of the sensitivity of QDAI to EFR. As expected, QDAI values calculated with EFR=0 (green) are lower and drought periods shorter than if it is assumed that water needs to remain in the river for the well-being of the ecosystems. Interestingly, short but severe droughts in the Indian grid cell in 2002, 2006 and 2010 have almost equal QDAI values for all three EFR alternatives.

Like pQ, SSFI (see Sect. 2.6) assumes biota and humans are accustomed to the seasonal and interannual variability of the streamflow. In order to quantify the added value of QDAI, we compared QDAI values to SSFI values computed with a 1-month timescale. The anomaly of streamflow in SSFI was computed in the same manner as for pQ, by fitting the gamma cumulative distribution function for monthly Qant. It was then transformed into a Gaussian distribution by calculating the mean and standard deviation, as well as using the approximate conversion provided by Abramowitz and Stegun (1965); this is also used by Kumar et al. (2009). Figure 10 shows three grid cells characterized by rather different values of the ratio R of long-term average annual WUsw to long-term average annual Qant: high (Vietnam, 10.75∘ N, 107.25∘ E in Fig. 10a), moderate (southeast USA, 31.75∘ N, -84.75∘ E in Fig. 10b) and low (Russia, 63.75∘ N, 136.75∘ E in Fig. 10c).

As expected, pQ and SSFI show an equivalent behavior in all grid cells as they are based on the same streamflow data, do not use any additional information and can be mathematically transformed from one to the other (Table 1). In contrast, QDAI is based additionally on estimates of the grid cell's specific human surface water demand and assumptions on EFR. A comparison of SSFI and QDAI is, therefore, essentially a comparison of pQ and QDAI. If R is very small, such as in the case of the Russian grid cell, with R=3.5×10-6 (Fig. 10c), QDAI is very similar to pQ, while dQ is very similar to EFR, being 80 % of the mean monthly Qnat (see explanation in Sect. 3.2). For the Vietnamese grid cell with a high R value of 0.143, QDAI does not interpret the anomalously low streamflow values in December 2003 and December 2005 as a drought hazard due to the low human water demand for surface water in December. Globally averaged, the fraction of months under drought during 1981–2010 is 16.0 % according to QDAI and 19.1 % according to SSFI. This reflects that QDAI only identifies a drought condition if there is, in addition to the anomalously low flow, a water deficit.