Soil moisture and streamflow deficit anomaly index: An approach to quantify drought hazards by combining deficit and anomaly

Drought is understood as both a lack of water (i.e., a deficit as compared to some requirement) and an anomaly in the condition of one or more components of the hydrological cycle. Most drought indices, however, only consider the anomaly aspect, i.e., how unusual the condition is. In this paper, we present two drought hazard indices that reflect both the 10 deficit and anomaly aspects. The soil moisture deficit anomaly index, SMDAI, is based on the drought severity index, DSI, but is computed in a more straightforward way that does not require the definition of a mapping function. We propose a new indicator of drought hazard for water supply from rivers, the streamflow deficit anomaly index, QDAI, which takes into account the surface water demand of humans and freshwater biota. Both indices are computed and analyzed at the global scale, with a spatial resolution of roughly 50 km, for the period 1981-2010, using monthly time series of variables computed 15 by the global water resources and the model WaterGAP2.2d. We found that the SMDAI and QDAI values are broadly similar to values of purely anomaly-based indices. However, the deficit anomaly indices provide more differentiated, spatial and temporal patterns that help to distinguish the degree of the actual drought hazard to vegetation health or the water supply. QDAI can be made relevant for stakeholders with different perceptions about the importance of ecosystem protection, by adapting the approach for computing the amount of water that is required to remain in the river for the well20 being of the river ecosystem. Both deficit anomaly indices are well suited for inclusion in local or global drought risk studies.

which can occur in different components of the hydrological cycle" (Van Loon et al., 2016, p.3633). Assuming that humans and other biota are accustomed to seasonal variations of water availability in the form of precipitation, soil moisture, 30 streamflow or groundwater storage, droughts are mostly defined by the deviation of a water quantity at a specific point in time (e.g., precipitation in May 2005) from its long-term mean or median (e.g., of all May precipitation values during the reference period 1981-2010). It is further assumed for most drought hazard indicators that humans and other biota are used to interannual variability. Therefore, drought is not defined by a percentage deviation but rather by using percentiles (e.g., precipitation in May 2005 is less than the 10 th percentile of all May precipitation values during the reference period) or by 35 standardized drought indicators where the anomaly is divided by the standard deviation. Anomaly-based drought indicators include the Standardized Precipitation Index (SPI) (Mckee et al., 1993), the Standardized Precipitation Evapotranspiration Index (SPEI) (Vicente-Serrano et al., 2010;Bergez et al., 2013), the China Z index (CZI) (Wu et al., 2001) and, for streamflow drought, the Standardized Streamflow Index (SSFI) (Modarres, 2007) and the percentile-based low-flow index by Cammalleri et al. (2017) can be used. 40 Some researchers have quantified drought by only considering the deficit aspect of drought, i.e., by computing the difference between an optimal water quantity and the actual quantity. Examples of deficit-based indicators include the Soil Moisture Deficit Index (SMDI) as well as the Evapotranspiration Deficit Index (ETDI) from Narasimhan and Srinivasan (2005) and the Soil Water Storage (SWS) from British Columbia Ministry of Agriculture (2015). A drawback of deficitbased drought hazard indicators is that they indicate strong drought events in arid and (semi)arid regions, even though the 45 vegetation in these regions is adapted to generally lower soil moisture (Cammalleri et al., 2016). To the best of our knowledge, streamflow drought has not, as yet, been characterized by a deficit-based drought indicator.
Two notable attempts in identifying and bringing together both the anomaly and deficit aspects are the Palmer Drought Severity Index (PDSI) (Palmer, 1965) and the Drought Severity Index (DSI) (Cammalleri et al., 2016). PDSI is a standardized index developed to quantify the cumulative deficit of moisture supply in the form of precipitation as compared 50 to demand in the form of potential evapotranspiration; it indicates meteorological drought, has been extensively used in the USA (Heim, 2002) and its strengths and weaknesses have been investigated (Dai et al., 2004). DSI indicates soil moisture drought by combining the soil moisture deficit (as compared to the situation in which plant evapotranspiration is not constrained by soil moisture availability) and the anomaly of the deficit, thus indicating rare events in which plants suffer from water stress. An anomaly-based soil moisture drought may, however, be unsuitable for indicating a drought hazard for 55 vegetation as, in areas with high soil moisture in most years, the low interannual variability and, thus, the standard deviation, would indicate a strong drought hazard in years with unusually low soil moisture values that are, nevertheless, still close to the optimal values and do not cause any water stress for the plants (Cammalleri et al., 2016).
Similar to the demand for soil water by plants, humans have a demand for water from rivers in situations where they rely on river water for their water supply. About 75% of global water withdrawals for irrigation, cooling of thermal power 60 plants, manufacturing and domestic use, totaling about 3700 km 3 /a in the first decade of this century, are sourced from surface water . Globally, irrigation is the largest water demand sector, accounting for 60% of total surface https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License.
water withdrawals . To date, however, streamflow drought indicators only describe the anomaly of streamflow but do not indicate whether there is enough water in the river to meet water demand. Thus, to assess the risk of drought for human water supply from rivers, an indicator that combines the anomaly of streamflow conditions with a deficit, 65 with respect to water demand, is desirable. In this way, the locations and times where human water supply is at risk can be identified.
Differing from anomaly-based streamflow drought indicators, a combined analysis of streamflow anomaly and deficit requires time series information of both streamflow and water demand. This information is available from global water resources and uses models such as WaterGAP with a spatial resolution of 0.5° (55 km by 55 km at the equator) and a 70 monthly temporal resolution (Alcamo et al., 2003;Müller Schmied et al., 2020). Up to the present time, macro-scale drought risk assessments have included the demand for water as vulnerability indicators by using a country's averagewater withdrawal to water availability ratio (e.g., Meza et al., 2020).
In this study, we introduce two drought hazard indicators that combine both the deficit and anomaly aspects: one for soil moisture drought and the other for streamflow drought. In the soil moisture deficit anomaly index (SMDAI), the deficit is 75 calculated as the difference between the soil moisture at field capacity (that which should allow optimal, non-water-limited plant growth) and the actual soil moisture. The SMDAI slightly modifies and simplifies the DSI introduced by Cammalleri et al. (2016). Another difference from Cammalleri et al. (2016), is that the SMDAI is computed globally using the output of WaterGAP, rather than just for Europe. The streamflow deficit anomaly index QDAI is, to our knowledge, the first-ever streamflow drought indicator that combines both the anomaly and deficit aspects of streamflow drought. In the case of 80 QDAI, the deficit is computed by comparing actual streamflow to the combined human and environmental surface water demand per grid cell. QDAI focuses on determining the drought hazard for the water supply for humans, including domestic, industrial and irrigation water demand. QDAI is constructed similarly to SMDAI and computed globally using WaterGAP.
Whether QDAI should be called a drought hazard indicator, or a combined drought hazard and vulnerability indicator, is up for discussion. However, for global-scale drought risk assessments, gridded QDAI values can be meaningfully combined 85 with country-scale vulnerability indicators of, for example, coping capacity.
In Section 2, we describe (a) the methods for calculating SMDAI and QDAI and (b) how streamflow, surface water use and soil moisture are computed by WaterGAP 2.2d (Müller Schmied et al., 2020). In section 3, spatial and temporal patterns of SMDAI and QDAI are presented. In Section 4, we analyze the components of SMDAI and QDAI, compare SMDAI to DSI, compare QDAI to a standardized streamflow indicator (SSFI) and discuss the limitations of the study. 90 Finally, we draw conclusions in Section 5.

Methods and data
2.1 Global-scale simulation of soil moisture, soil water capacity, streamflow and human water withdrawal In this study, we use the output of the latest version of the global hydrological and water use model WaterGAP 2.2d (Müller Schmied et al., 2020). WaterGAP consists of two major modules: the water use models for five different sectors and 95 the global hydrological model (WGHM). The submodel GWSWUSE distinguishes water use from groundwater and surface water sources and computes human water abstractions from surface water and groundwater as well as the respective net abstractions from both sources (Döll et al., 2012). Taking into account the net abstractions, WGHM simulates, with a spatial resolution of 0.5° by 0.5° (55 km by 55 km at the equator) and 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 100 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 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 . The temporal development of soil moisture (S) is 105 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 . Streamflow (Q ant ) in each grid cell depends on the runoff 110 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 115 has been repeatedly shown to be among the best-performing global hydrological models (Zaherpour et al., 2018(Zaherpour et al., , 2019Veldkamp et al., 2018). Nevertheless, there can be significant mismatches between the observed and simulated seasonality and interannual variability.

Deficit 125
Soil moisture deficit (d soil ) refers to the lack of water in the root zone for plants as compared to optimal growing conditions assumed to occur at soil water capacity. d soil is calculated as where Smax [mm] is the amount of water stored in the soil between field capacity and wilting point within the plant's root zone, S [mm] is the actual amount of soil water. d soil ranges from 0 (no deficit/stress) to 1 (extreme deficit/stress). 130

Anomaly
Interannual variability of both monthly soil moisture and monthly soil moisture deficit can be used to examine the occurrence frequency of soil moisture droughts and identify the normal state of the system. The unusualness of drought, compared to the normal state for a specific site and calendar month, is commonly quantified using the standard z-score. In general, the z-score is computed separately for each calendar month (here using, for example, 30 monthly soil moisture 135 deficits in the 30 January months during the period 1981-2010), by standardizing the variable using the calendar month mean and standard deviation after translating the cumulative distribution function that optimally fits the distribution of monthly values to a normal distribution (McKee et al., 1993). Sheffield et al. (2004) found that long-term soil moisture data is best represented by the beta distribution function. The probability density function f and cumulative density function F of the beta distribution function can be expressed as 140 where a, b ≥ 0 are the shape parameters, B(a, b) is the beta function and B(d soil ; a, b) is the incomplete beta function. In this form, the b supports the range of d soil ∈ [0, 1]. 145 In this study, we could confirm the assumption made by Cammalleri et al. (2016) that the beta distribution function represents satisfactorily the distribution of d soil , which is the same as that of the soil moisture itself. The beta cumulative distribution function was fitted to d soil values for each calendar month and grid cell (i.e., for each grid cell, twelve beta functions are fitted corresponding to the twelve calendar months).
Following Cammalleri et al., the next step was to derive from F a drought probability index (p soil ) that translates the 150 probability that a certain soil water deficit status is drier than usual into the range [0,1]. As suggested by Agnew (2000), a z-https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License. score of -0.84, which corresponds to a return period of 5 years, was assumed to be the threshold for drought (Table 1), for which p soil = 0. Then, the drought probability index is calculated as where F(d soil ) is the beta cumulative distribution function fitted to d soil . If the beta cumulative distribution function is fitted to S, then (1-F(S)) should be used instead of F(d soil ). Cammalleri et al. (2016) calculated p soil using the mode instead of median as the reference for the normal status of 160 d soil . The computation of p soil from F(d soil ) was carried out done in two steps. First, for d soil values that are greater than or equal to the mode, a new standardized cumulative distribution function F*(d soil ) is computed (Eq. 3 in Cammalleri et al., 2016). Subsequently, F*(d soil ) values ranging from 0.6 to 1 are mapped onto the p soil range of [0, 1] by an exponential function that was fitted to subjectively defined pairs of F*(d soil ) and p soil (Eq. 4 in Cammalleri et al., 2016). In this study, we have simplified the unnecessarily complex approach of Cammalleri et al. (2016) by relying directly on F(d soil ) for 165 mapping F(d soil ) to p soil according to Eq. 4 ( Figure S1). In our opinion, there is no added value in defining an arbitrary exponential mapping function for deriving an indicator for the probability of a drought occurrence (p soil ). Furthermore, like most other drought researchers, we prefer the median to the mode, as among 30 deficit values, which are rational numbers, there is no true mode, i.e., no value that occurs most often. Table 1 shows the relationship of the anomaly component (p) of SMDAI (i.e., p soil ) to the non-exceedance probability of the soil moisture deficit (F(d soil )) and the pertaining return periods, 170 z-scores and class names, according to Agnew (2000) as well as the p-values by Cammalleri et al. (2016) (p_DSI). Figure S2 shows, for the example of August 2003, that there are only slight differences between the values of p_DSI and p and of DSI and SMDAI, if they are all computed using WaterGAP output. 175 180 https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License. Table 1. Relationship of the anomaly component p of SMDAI and QDAI to the non-exceedance probability of the soil 185 moisture deficit (F(d soil )) or of streamflow (F(Q)), the pertaining return periods, z-scores and class names according to Agnew (2000) as well as the p-values by Cammalleri et al. (2016) to compute DSI. The class name refers to the drought conditions with z-score values that are larger than those listed in the z-score column. The equiprobability transformation technique, first suggested by Abramowitz and Stegun (1965) and utilized in Kumar et al. (2015)  assuming that 80% of the natural mean monthly streamflow that would have occurred in the river without human water use and man-made reservoirs needs to remain in the river for the well-being of the river ecosystem. Differing from Smax, which represents the vegetation demand for soil water, the streamflow demand is temporally variable. d Q is, like d soil , in the range 205 of 0 (no deficit/stress) to 1 (extreme deficit/stress); if WU sw equals 0, then d Q is set to 0. To explore how assumptions about EFR and, thus, total surface water demand affect QDAI, we set EFR to be alternatively equal to half of Q nat , or zero (Section 3.2 and Section 4.1.2). These alternatives represent situations in which humans wish to protect freshwater biota less, or not at all, so the total surface water demands and, thus, streamflow deficits are lower.

Anomaly 210
The quantification of the streamflow anomaly (p Q ) is computed with interannual variability of monthly aggregated streamflow (Q ant )[ km 3 month -1 ] values. The unusualness of a streamflow drought is better captured by a standard cumulative distribution function that can reproduce the statistical structure of streamflow (Q ant ) compared to a standard distribution function reproducing the statistical structure of streamflow deficit ( d Q ). Furthermore, the methodological consistency between the calculation of p Q and p soil is maintained, as the anomaly of soil moisture deficit (d soil ) is equal to 215 the anomaly of soil moisture (S) [mm]. In some regional streamflow drought studies (Langat et where a, b ≥ 0 are the shape parameters, G(a) is the gamma function and g(Q ant ; a, b) is the incomplete gamma function; in this form the gamma distribution supports d > 0. Taking into account that streamflow drought occurs when a 225 certain streamflow value is not exceeded, while in the case of p soil a soil moisture drought occurs when a certain soil moisture deficit is exceeded, the drought probability index for streamflow drought p Q is computed as

Combining deficit and anomaly to compute SMDAI and QDAI
Water deficits (d soil and d Q ) and anomalies (p soil and p Q ) are combined into single deficit anomaly indicators 230 (SMDAI and QDAI) based on the desired indicator characteristics as elaborated by Cammalleri et al. (2016). The combined https://doi.org/10.5194/nhess-2020-265 Preprint.

Fitting standard cumulative functions
Out of the total 67420 WaterGAP land grid cells, only 57043 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 , 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 250 d soil and Q ant , 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 d soil and 39.94% in the case of Q ant , the fits were rejected for all 12 calendar months.
An example of an accepted grid cell and a rejected grid cell of the beta distribution function are shown in Figure S3. In these cells, the probability of non-exceedance F is determined directly from the time series of 30 monthly values using the R 255 function empirical cumulative distribution function (ECDF). The ECDF is a step function that increases by 1/30 at each of https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License. the 30 d soil values of SMDAI or Q ant values of QDAI. The computed F value of a specific d soil or Q ant value is the fraction of all 30 d soil or Q ant values that are less than, or equal to, the specific d soil or Q ant value.

SMDAI 260
To clarify the interplay of d soil , the anomaly of d soil as compared to the mean monthly d soil_mean (which is indicated by p soil , and SMDAI), the respective time series of these variables are shown in Figure 1 for two grid cells with rather different characteristics: a grid cell in Germany (42.25N, -121.75 E, left panels in Figure 1) and one in northeast India (88.25 E,27.25 N, right panels in Figure 1). The values of d soil in the German grid cell shows, on average over the whole reference period, a high deficit in the summer months and low deficits only in 1-2 winter months (dashed grey line). 265 According to the definition of p soil , an anomaly-based drought hazard, as indicated by p soil > 0 (blue line), occurs only if the actual soil moisture deficit (green line) is much higher than the mean seasonal values; this is so high that this deficit is exceeded in only 1 out of 5 years (Eq. 4 and Table 1). According to Eq. 10, SMDAI is always between p soil and d soil . 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 p soil . During the Central European (CEU) summer drought of 270 2003, SMDAI was approximately equal to p soil . 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 moisture saturation. Even for some unusually dry months (with high p soil ), d soil remains almost always below 0.25. Due to the low deficit, even in cases of high p, SMDAI is much smaller than p during all drought events indicated by p. 275 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 p, were used as the drought hazard indicator.  The relationship between SMDAI, p soil , and d soil can be explored further by using global indicator maps for a specific month, e.g., August 2003 ( Figure 2); WaterGAP computes soil moisture deficits of 75% or more in most grid cells, 285 while only in a few areas where August belongs to the rainy season, e.g., the Sahel region and the monsoon areas in India, do low deficits occur (Figure 2a). In each grid cell, p soil is zero in 80% of all August months. Therefore, in any month, approximately 80% of the grid cells indicate no drought and psoil equals 0 (Figure 2b). Only grid cells with a non-zero p soil have a non-zero SMDAI ( Figure 2c); for example, southeast India shows extremely high d soil values, but as there is no anomalously high soil moisture deficit except for in a few grid cells where p soil is mostly zero, SMDAI is also mostly zero 290 and, thus, no soil moisture drought hazard is detected. The difference between SMDAI and p soil is shown in Figure 2d; in most grid cells with differences, SMDAI is higher than p soil due to high d soil . Focusing on central Europe, SMDAI (in relationship between psoil and SMDAI (see Figure S4 showing the drought situation in December 1999); in Europe and the eastern part of North America, for example, SMDAI is smaller than psoil ( Figure S4d).   Table 2 and of the nodrought condition (SMDAI = 0) during the reference period 1981-2010. SMDAI is zero in more than 80% of the months as 305 p soil should be zero in 80% of the months ( Figure. 3e) and if d soil were often zero, SMDAI would be zero more often than p soil . However, Figure 3 shows larger values in the dry regions and, thus, we believe that the higher frequency of no-drought conditions and constant low occurrences of drought hazards in areas with high soil moisture deficits, such as the Sahel region, are due to the imperfect fits of the applied CDFs. Extreme soil moisture drought hazards (Figure 3d)  extreme drought hazards and more often than other regions a moderate drought hazard (Figure 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 snow melts and, thus, infiltration of water into the soil. 315  (Table 2).

QDAI 320
The QDAI indicates the drought hazard to the surface water supply required for satisfying human water demand (WU sw ), assuming the water suppliers also take into consideration the water demand by freshwater biota (EFR). The deficit component of QDAI (d Q ) is the relative difference between the total surface water demand and streamflow, while the anomaly component (p Q ) is based on the unusualness of streamflow. QDAI depends on more individual variables than https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License. SMDAI; Figure 4 shows their interplay for two grid cells with different characteristics of human surface water demand as 325 compared to streamflow. In the grid cell in the western USA, where streamflow of the Klamath River is observed in Keno   (42.25N, -121.75 E, left panels of Figure 4), water demand is mostly for irrigation (i.e., 0.038 km 3 month -1 temporal mean) is high compared to the relatively small streamflow (i.e., 0.105 km 3 month -1 temporal mean). In the grid cell in Germany, human surface water demand (i.e., 0.056 km 3 month -1 temporal mean) is small as compared to the rather high streamflow of the Rhine (i.e., 4.6 km 3 month -1 temporal mean), where the streamflow is measured in Mainz (49.75 N,8.25 E right panels 330 of Figure 4).
In the USA grid cell, the difference between the mean monthly streamflow under the naturalized condition (Q nat_mean ) and mean monthly simulated streamflow (Q ant_mean ) is high, especially in the growing period, due to the high anthropogenic extraction of streamflow water (observed in the topmost plot). While the observed (Q ant_obs ) and simulated (Q ant ) streamflow show a reasonable correlation; WaterGAP appears to overestimate streamflow depletion by human water 335 use in the summers. Characterized by a high seasonality of anthropogenic surface water demand, WU sw (dashed grey line in center plot) and generally unfulfilled surface water demand (i.e., WU sw + EFR_0.8, orange line in center plot) result in frequent high summer d Q (green line of bottom plot). In addition, an anomaly-based drought hazard indicated by p Q > 0 (dark blue line) indicates high summer values occurring as Q ant , which are much lower than the mean seasonal value (Q ant_mean ). Hence, QDAI, which is always between p Q and d Q (Eq. 12), detects extreme streamflow droughts incurred by 340 high water extractions for irrigation during the summer months.
If water suppliers do not take into account when extracting water, the water that needs to remain in the river for the river ecosystem (EFR is assumed to be zero), the streamflow deficit (i.e., WU sw + EFR_0.2, orange line in the center plot of In the German grid cell (the right panels in Figure 4), the relatively low anthropogenic surface water demand results in almost identical values of Q nat_mean and Q ant_mean (lines overlap in the top plot), as well as the total surface water demand and EFR (lines overlap in the center plot). Non-zero d Q values (bottom plot) are mainly computed if Q ant is lower than EFR, such as during the central European drought of 2003. It is sensible to consider this type of situation as a drought hazard as 350 water supply companies would have to stop any surface water abstraction if they wished to protect the river ecosystem. If the water supply companies do not stop any surface water abstraction (EFR_0.2), then they would not suffer from any hazard, even during a drought similar to the 2003 central European drought (right panels Figure S5). Differing from a purely anomaly-based drought hazard indicator, the QDAI indicates much stronger droughts in the USA grid cell when compared to the German cell, as it indicates a drought hazard only if surface water demand, the sum of human and the ecosystem water 355 demand, is higher than the streamflow.  Streamflow deficits are not restricted to areas with high mean annual WU sw during the period 1981-2010 (Figure 5a), but can be greater than 75% in regions such as South Africa were Q ant is low (Figure 5b). Unlike factors of soil moisture drought, p Q and d Q are strongly correlated (Figure 5c). This is due to the fact that total surface water demand is dominated in 365 many grid cells by EFR, which is a fraction of Q nat . In the EFR-dominated cells, the mean monthly Q ant is very similar to the mean monthly , such that d Q is then approximately the difference between mean monthly Q ant and Q ant , ; this is represented by p Q .QDAI ( Figure 5d) and is found to be, mostly, less than p Q (Figure 5e). The 2003 central European drought hazard for the surface water supply for humans ( Figure 5d) is, at least in many parts of Germany, less pronounced than the soil moisture drought hazard for vegetation.  Differing from SMDAI (Figure 3), the no-drought conditions, as identified using QDAI, occur more often than 80% 375 of the time as d Q is often zero, in particular, in very large rivers with scarcely any human water use such as the Amazon river in South America, the Congo river in Africa and the Ob river in Russia; these are clearly visible in Figure 6e (Table 2).

Sensitivity of SMDAI to the Smax values assumed in WaterGAP
S max is one of the key components for computing SMDAI. WaterGAP calibration and validation studies have 390 indicated that Smax may be underestimated in WaterGAP by a factor of two or more (Hosseini-Moghari et al., 2020). In order to understand the sensitivity of SMDAI to changes in S max , we ran a version of WaterGAP in which S max was doubled https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License.
(S max2 ). Figure 7 presents global maps of d soil_Smax2 (Figure 7a), p soil_Smax2 (Figure 7c), and SMDAI _smax2 (Figure 7e)for the August, 2003, and the change in each parameter with respect to the standard WaterGAP output i.e., difference between parameter computed using Smax2 and Smax (Figure 7b, 7d and 7f).With Smax2, more amount of soil moisture is kept in the soil 395 and soil deficits, expressed relative to Smax, can be observed to increase or decrease with doubled Smax (Figure 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 d Q are generally smaller in the case of doubled Smax; in this region, psoil increases in the case of doubled Smax (Figure 7d). Globally, psoil increases or decreases in some grid cells by more than 50 percentage points. Equally, for 400 SMDAI, the sensitivity to doubled Smax is low for most grid cells but can be greater for a few (Figure 7e).

Sensitivity of QDAI to different assumptions about EFR
The streamflow drought hazard for water supply indicated by QDAI depends on how EFR is computed, i.e., given that the protection of river ecosystem as one of the important conditions is included. In Figure 8, we compare the global distribution of QDAI values among the 57043 0.5° grid cells that are computed for alternative EFR, 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, 410 or that there is no EFR at all that needs to be considered when the decisions about river water abstractions for water supply are made. We consider the two months of August and December 2003 and distinguish between humid and (semi)arid grid cells (Fig. S6). 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 415 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. As in humid regions, QDAI increases with increasing EFR. As can be expected, QDAI, for example, as shown by the median, is overall somewhat higher in the northern hemisphere summer month of August 2003 than in 420 December 2003, but the impact of alternative EFR assumptions is similar. Figure 8 also clearly shows that water suppliers in (semi)arid and arid regions suffer from drought hazards much more strongly than water suppliers in humid areas due to the much higher ratio of water demand to streamflow.
where Q anti [km 3 month -1 ] is the streamflow value at time interval , is the long-term mean of the streamflow values and is the standard deviation of the streamflow values used in calculating the long-term mean. SSFI assumes biota 435 and humans are accustomedto 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 p Q , by fitting the gamma cumulative distribution function for monthly Q ant , which is then transformed into Gaussian distribution by calculating the mean, standard deviation, as well as using the approximate conversion provided by Abramowitz and Stegun (1965); this is also used by Kumar et al. (2015). Figure 9  440 shows three grid cells characterized with rather different values of the ratio R of long-term average annual WU sw to longterm average annual Q ant : high (Vietnam, 10.75N, 107.25E in Figure 9a), moderate (south-east USA 31.75N, -84.75E in Figure 9b) and low (Russia,63.75 N,136.75E in Figure 9c).
As would be expected, p Q 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  445 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 p Q and QDAI. If R is very small, such as in the case of the Russian grid cell, with R = 3.5 x 10 −6 (Figure 9c), p Q and QDAI are very similar to p Q , while d Q are very similar to EFR, being 80% of the mean monthly Q nat (see explanation in Section 3.2). For the Vietnamese grid cell with a high R value of 0.143, QDAI does not interpret the anomalous streamflow values in late 2003 and 2005 as a 450 drought hazard due to the low human water demand for surface water.

Conclusion
In this paper, we presented two drought hazard indices that combine the drought deficit and anomaly characteristics: one for soil moisture drought (SMDAI) and the other for streamflow drought (QDAI). With SMDAI, which describes the drought hazard for vegetation, we achieved the simplification of the deficit-anomaly based Drought Severity Index 460 introduced by Cammalleri et al. (2016). We transferred the DSI concept to streamflow drought, creating an indicator that specifically quantifies the hazard that drought poses for the water supply from rivers. To our knowledge, QDAI is the firstever streamflow drought indicator that combines the anomaly and deficit aspects of streamflow drought.
The concept of SMDAI and QDAI was tested at the global scale by using simulated data from the latest version of the global water resources and using the model WaterGAP. Whereas the reliability of the computed SMDAI and QDAI 465 values strongly depends on the quality of the model output, the indicators themselves have been proven to provide meaningful quantitative estimates of drought hazard that depend not only on the unusualness of the situation but also the concurrent deficit of available water as compared to demand. We found that the values of the combined deficit-anomaly drought indices are often broadly similar to purely anomaly-based indices, however, they do provide more differentiated spatial and temporal patterns that help to distinguish the degree of the drought hazard. QDAI can be made useful as a tool for 470 enlightening relevant for stakeholders, who holddifferent perceptions on the importance of ecosystem protection, by adapting the approach for computing EFR, the amount of water that is required to remain in the river for the well-being of the river ecosystem.
The term "drought hazard" can be defined as the source of a potential adverse effect of an unusual lack of water on humans or ecosystems. In this sense, SMDAI and QDAI are drought hazard indicators, even if they include some elements 475 of vulnerability to drought. Both SMDAI and QDAI are well applicable in drought risk studies. In local drought risk studies, additional indicators of ecological or societal vulnerability should be added. In regional or global drought risk studies, the inclusion of grid-scale values of QDAI and SMDAI would be beneficial as both indices contain spatially, highly resolved information on vulnerability, while most other vulnerability indicators represent spatial averages of much larger spatial units such as countries. 480 485 https://doi.org/10.5194/nhess-2020-265 Preprint. Discussion started: 19 August 2020 c Author(s) 2020. CC BY 4.0 License.