3.1.1 Computation of cropping patterns and growing periods of rice and non-rice crops

The cropping pattern for each cell with irrigated cropland describes whether only rice, non-rice crops or both are irrigated during either one or two growing seasons. The growing period for both crop types is assumed to be 150 d. A total of 17 cropping patterns are possible including simple variants (e.g., one cropping season with non-rice on the total irrigated area) and complex variants (non-rice after rice on one part of the total irrigated area and non-rice after non-rice on the other). The following data are used to model the cropping pattern: total irrigated area, long-term average temperature and soil suitability for paddy rice in each cell, harvested area of irrigated rice in each country, and cropping intensity in each of 19 world regions. In a second step, the optimal start date of each growing season is computed for each crop. To this end, each 150 d period within a year is ranked based on criteria of long-term average temperature, precipitation and potential evapotranspiration provided in Döll and Siebert (2002). The most highly ranked 150 d period(s) is (are) defined as growing season(s).

3.1.2 Computation of consumptive water use due to irrigation

GIM implements the Food and Agriculture Organization of the United Nations (FAO) CROPWAT approach of Smith (1992) to compute crop-specific ICU per unit irrigated area (mm d⁻¹) during the growing season as the difference between crop-specific optimal evapotranspiration $E_{{\mathrm{pot}}_{\mathrm{c}}}$ and effective precipitation P_irri,eff if the latter is smaller than the former, with

where $E_{{\mathrm{pot}}_{\mathrm{c}}}$ is the product of potential evapotranspiration E_pot and the dimensionless crop coefficient k_c which depends on the crop and the crop development stage (Döll and Siebert, 2002). As a standard, E_pot is calculated according to Eq. (7). P_irri,eff is the fraction of the total precipitation P (including rainfall and snowmelt) that is available to plants and is computed as a simple empirical function of precipitation. Equation (1) is implemented with a daily time step, but to take into account the storage capacity of the soil and to remain consistent with the CROPWAT approach, daily precipitation values are averaged over 10 d, except for rice-growing areas in Asia, where the averaging period is only 3 d to represent the limited soil water storage capacity in the case of paddy rice (Döll and Siebert, 2002).

3.1.3 Irrigated area

In the standard version of WaterGAP 2.2d, irrigated area per grid cell used in GIM is based on the HID (Siebert et al., 2015), which provides area equipped for irrigation (AEI) in 5 arcmin grid cells for 14 time slices between 1900 and 2005. HID data are aggregated to 0.5^∘ × 0.5^∘ and temporally interpolated to obtain an annual time series of AEI. Cropping patterns and growing periods are generated for every year, with an individual combination of year-specific AEI and harvested area of rice and the respective 30-year climate averages, which are then used to calculate ICU for every day of the same year (Sect. 3.1.1). Harvested area of rice per country from the MIRCA2000 dataset, representative for the year 2000 (Portmann et al., 2010), is scaled according to annual AEI country totals, ensuring consistency to AEI.

To take into account that not the whole AEI is actually used for irrigation in any year, country-specific values of the ratio of area actually irrigated (AAI) to AEI are used to estimate AAI in each grid cell. AAI is then applied for calculating the consumptive irrigation water use in volume per time. AAI $/$ AEI ratios were derived from the Global Map of Irrigation Area (GMIA) for 2005 (Siebert et al., 2013). To set AAI from 2006 to 2016, we found country-specific AAI for 2006–2008 from the AQUASTAT database of the FAO, other international organizations, and national statistical services (e.g., EUROSTAT and USDA) for 61 countries. For these countries, the AAI values for 2009–2016 were set to the 2008 values, while for the rest of the countries, AAI was set to the 2005 values for the whole period 2006–2016.

Alternatively, as in previous WaterGAP versions, GIM in WaterGAP 2.2d can be executed based on a temporally constant dataset of AEI per grid cell, e.g., the GMIA for 2005 (Siebert et al., 2013). Cropping patterns and growing periods are then computed for AEI and harvested area of rice in a reference year and the pertaining 30-year average climate. For more details and application examples, we refer to Portmann (2017) and Döll and Siebert (2002).

3.2.1 Livestock

Withdrawal water uses for livestock are computed annually by multiplying the number of animals per grid cell by the livestock-specific water use intensity (Alcamo et al., 2003). The number of livestock are taken from FAOSTAT (2014). It is assumed that the withdrawal water uses for livestock are equal to their consumptive water use.

3.2.2 Domestic

Domestic water use comprises withdrawal water uses and consumptive water uses of households and small businesses and is estimated on a national level. The main concept is to first compute the domestic water use intensity (m³ per capita per year) and then to multiply this by the population of water users in a country. The domestic water use intensity is expressed by a sigmoid curve which indicates how water use intensity (per capita water use) changes with income (gross domestic product per capita) and is derived from historical data on a national or regional level (Flörke et al., 2013). Besides changes driven by income and population, technological changes are considered to reflect improvement in water-use efficiency. Continuous improvements in technology make appliances more water efficient and, hence, contribute to reductions in water use. Detailed data on domestic consumptive water uses do not exist from statistics, but a simple balancing equation has been used in WaterGAP since the year 2000 to simulate consumptive water uses as the difference between withdrawal water use and wastewater volume (i.e., return flow) as the latter information is available from statistics. The calculation of consumptive water use before the year 2000 is based on the application of consumptive water use coefficients (Shiklomanov, 2000) that accounts for the proportion of the withdrawal water use that is consumed. In order to allow for a spatially explicit analysis, country values of domestic water uses are allocated to grid cells (0.5^∘ ×  0.5^∘) within the country based on the geo-referenced historical population density maps from HYDE version 3.1 (Goldewijk et al., 2010). Additionally, population numbers beyond 2005 as well as information on the ratio of rural to urban population of each grid cell come from UNEP (2015).

3.2.3 Manufacturing

The manufacturing sector is rather diverse in terms of water use and varies between countries and subsectors, for example highly water-intensive production processes in the chemical industry compared to the processes in the glass industry that use less water. In WaterGAP, the manufacturing water use model simulates the annual withdrawal water use and consumptive water use of water that is used for production and cooling processes, whereas the water used for power generation is modeled separately. A manufacturing structural water intensity that describes the ratio of water abstracted over the manufacturing gross value added (GVA) is derived per country for the base year 2005 (in m³ USD (constant for the year 2000)⁻¹) based on national statistics (Flörke et al., 2013). GVA is found to be positively correlated with the sector's withdrawal water uses (Dziegielewski et al., 2002) and is used as the driving force to reflect the time variant system. In addition, technological improvements are considered through a technological change factor.

The consumptive water use for this sector is obtained by using the same approach as described for the domestic sector, i.e., the calculation of the difference between the withdrawal water use and the return flows (starting in the year 2000) and the application of a consumption factor before the year 2000. Contrary to the domestic sector, return flows from the manufacturing sector are further subdivided into cooling water and wastewater. For countries where no data are available, the fraction of consumptive water use is derived from neighboring or economically comparable countries. Less information is available on the location of manufacturing industries; therefore country-level manufacturing water use is downscaled to grid cells proportional to its urban population (Flörke et al., 2013).

3.2.4 Thermal power

Water is abstracted and consumed for the production of thermal electricity, particularly for cooling purposes where water is used to condense steam from the turbine exhaust. The volume of cooling withdrawal water use and consumptive water use is modeled on a grid-cell level based on input data on the location, type and size of power stations from the World Electric Power Plant Database (UDI, 2004). Here, the annual cooling water requirements in each grid cell are calculated by multiplying the annual thermal electricity production with the respective water-use intensity of each power station (Flörke et al., 2013). A key driver is the annual thermal electricity production (MWh yr⁻¹) on a country basis, which is downscaled to the level of thermal power plants according to their capacities. Time series on thermal electricity production per country until 2010 are available online from the Energy Information Administration (EIA, 2012). Cooling water intensities in terms of withdrawal water use and consumptive water use vary between plant types and cooling systems. Therefore, the model distinguishes between four plant types (biomass and waste, nuclear, natural gas and oil, coal, and petroleum) and three cooling systems (tower cooling, once-through cooling, ponds) (Flörke et al., 2012). The approach is complemented by considering technological change leading to reduced intensities.

In general, water abstractions of once-through flow systems are considerably higher compared to the withdrawal intensities of pond cooling or tower cooling systems. In contrast, consumptive water use of tower cooling systems is much higher than water consumed by once-through cooling systems. In ordering plant-type-specific water intensities, i.e., water abstraction per unit electricity production, it becomes obvious that intensities are highest for nuclear power plants, followed by fossil, biomass, and waste-fuelled steam plants, while natural gas and oil combined-cycle plants have the lowest intensities, respectively. The model has been validated for the year 2005 by comparing modeled values with published thermoelectric withdrawal water uses (Flörke et al., 2013).

4.2.1 Water balance

The canopy storage S_c (mm) is calculated as

where P is precipitation (mm d⁻¹); P_t is throughfall, the fraction of P that reaches the soil (mm d⁻¹); and E_c is evaporation from the canopy (mm d⁻¹).

4.2.2 Inflows

Daily precipitation P is read in from the selected climate forcing (see Sect. 7.1).

4.2.3 Outflows

Throughfall P_t is calculated as

where S_c,max is maximum canopy storage calculated as

where m_c is 0.3 mm (Deardorff, 1978), and L (−) is the one-side leaf area index. L is a function of daily temperature and P and limited to minimum or maximum values. Maximum L values per land cover class (Table C1) are based on Schulze et al. (1994) and Scurlock et al. (2001), whereas minimum L values are calculated as

where f_d,lc is the fraction of deciduous plants and c_e,lc is the reduction factor for evergreen plants per land cover type (Table C1).

The growing season starts when daily temperature is above 8 ^∘C for a land-cover-specific number of days (Table C1) and cumulative precipitation from the day where growing season starts reaches at least 40 mm. In the beginning of the growing season, L increases linearly for 30 d until it reaches L_max. For (semi)arid cells, at least 0.5 mm of daily P is required to keep the growing season on-going. When growing season conditions are not fulfilled anymore, a senescence phase is initiated and L linearly decreases to L_min within the next 30 d (Kaspar, 2004). It is noteworthy that in WaterGAP L only affects the calculation of the canopy water balance. L is not taken into account in computing consumptive water use for irrigated crops (Sect. 3.1) and evapotranspiration from land (Sect. 4.4).

Following Deardorff (1978), E_c is calculated as

where E_pot is the potential evapotranspiration (mm d⁻¹) calculated with the Priestley–Taylor equation according to Shuttleworth (1993) as

where, following Shuttleworth (1993), α is set to 1.26 in humid and to 1.74 in (semi)arid cells (Appendix B). R is net radiation (mm d⁻¹) that depends on land cover (Table C2) (for details on the calculation of net radiation, the reader is referred to Müller Schmied et al., 2016b), and s_a is the slope of the saturation vapor pressure–temperature relationship ($\mathrm{kPa}{}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$) defined as

where T (^∘C) is the daily air temperature and g is the psychrometric constant ($\mathrm{k}\mathrm{Pa}{}^{\circ }{\mathrm{C}}^{-\mathrm{1}}$). The latter is defined as

where p_a is atmospheric pressure of the standard atmosphere (101.3 kPa), and l_h is latent heat (MJ kg⁻¹). Latent heat is calculated as

4.3.1 Water balance

Snow storage accumulates below snow freeze temperature and decreases by snow melt and sublimation. Snow storage S_sn (mm) is calculated as

where P_sn is the part of P_t that falls as snow (mm d⁻¹), M is snowmelt (mm d⁻¹) and E_sn is sublimation (mm d⁻¹).

4.3.2 Inflows

Snowfall P_sn (mm d⁻¹) is calculated as

where T is daily air temperature (^∘C), and T_f is snow freeze temperature, set to 0 ^∘C. In order to prevent excessive snow accumulation, when snow storage S_sn reaches 1000 mm in a subcell, the temperature in this subcell is increased to the temperature in the highest subcell with a temperature above T_f (Schulze and Döll, 2004).

4.3.3 Outflows

Snow melt M is calculated with a land-cover-specific degree-day factor D_F ($\mathrm{mm}{\mathrm{d}}^{-\mathrm{1}}{}^{\circ }\mathrm{C}$) (Table C2) when the temperature T in a subgrid surpasses melting temperature T_m (^∘C), set to 0 ^∘C, as

Sublimation E_sn is calculated as the fraction of E_pot that remains available after E_c. For calculating E_pot according to Eq. (7), land-cover-specific albedo values are used if S_sn surpasses 3 mm in the 0.5^∘ × 0.5^∘ cell (Table C2).

4.4.1 Water balance

The change of soil water storage S_s (mm) over time (d) is calculated as

where P_eff is effective precipitation (mm d⁻¹), R_l is runoff from land (mm d⁻¹) and E_s is actual evapotranspiration from the soil (mm d⁻¹). Once the water balance is computed, R_l is partitioned into (1) fast surface and subsurface runoff R_s, representing direct surface runoff and interflow, and (2) groundwater recharge R_g (Fig. 2) according to a heuristic scheme (Döll and Fiedler, 2008).

4.4.2 Inflows

P_eff is computed as

where P_t is throughfall (mm d⁻¹; see Eq. 3), P_sn is snowfall (mm d⁻¹; see Eq. 12) and M is snowmelt (mm d⁻¹; see Eq. 13).

4.4.3 Outflows

E_s is calculated as

where E_pot is potential evapotranspiration (mm d⁻¹), E_c is canopy evaporation (mm d⁻¹; Eq. 6) and S_s,max is the maximum soil water content (mm) derived as a product of total available water capacity in the upper meter of the soil (Batjes, 2012) and land-cover-specific rooting depth (Table C2) (Müller Schmied, 2017). E_pot,max is set to 15 mm d⁻¹ globally. Following Bergström (1995), runoff from land R_l is calculated as

where γ is the runoff coefficient (–). This parameter, which varies between 0.1 and 5.0, is used for calibration (Sect. 4.9). Together with soil saturation, it determines the fraction of P_eff that becomes R_l (Fig. 3). If the sum of P_eff and S_s of the previous day exceed S_s,max, the exceeding fraction of P_eff is added to R_l. In urban areas (defined from MODIS data, Sect. C), 50 % of P_eff is directly turned into R_l.

Figure 3Relation between runoff from land R_l as a fraction of effective precipitation P_eff and soil saturation $S_{\mathrm{s}}/S_{\mathrm{s},\max }$ for different values of the runoff coefficient γ in WaterGAP.

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R_l is partitioned into fast surface and subsurface runoff R_s and diffuse groundwater recharge R_g calculated as

where $R_{{\mathrm{g}}_{\max }}$ is soil-texture-specific maximum groundwater recharge with values of 7, 4.5 and 2.5 mm d⁻¹ for sandy, loamy and clayey soils, respectively, and f_g is the groundwater recharge factor ranging between 0 and 1. f_g is determined based on relief, soil texture, aquifer type, and the existence of permafrost or glaciers (Döll and Fiedler, 2008). If a grid cell is defined as (semi)arid and has coarse (sandy) soil, groundwater recharge will only occur if precipitation exceeds a critical value of 12.5 mm d⁻¹, otherwise the water remains in the soil. The fraction of R_l that does not recharge the groundwater becomes R_s, which recharges surface water bodies and the river compartment.

4.5.1 Water balance

The temporal development of groundwater storage S_g (m³) is calculated as

where R_g is diffuse groundwater recharge from soil (m³ d⁻¹, Eq. 19), $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ is point groundwater recharge from surface water bodies (lakes, reservoirs and wetlands) in (semi)arid areas (m³ d⁻¹, Eq. 26), Q_g is groundwater discharge (m³ d⁻¹) and NA_g is net abstraction from groundwater (m³ d⁻¹).

4.5.2 Inflows

R_g is the main inflow in most grid cells, except in (semi)arid grid cells with significant surface water bodies where $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ may be dominant. $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ varies temporally with the area of the surface water body, which depends on the respective water storage (Sect. 4.6). In many cells with significant irrigation with surface water, NA_g is negative, and irrigation causes a net inflow into the groundwater due to high return flows (Sect. 3.3).

4.5.3 Outflows

Q_g quantifies the discharge from groundwater storage to surface water storage, with

where k_g=0.01 d⁻¹ is the globally constant groundwater discharge coefficient (Döll et al., 2014). The second outflow component NA_g is described in Sect. 3.3.

4.6.1 Water balance

The water balance for the five types of LResW compartments is calculated as

where $S_{\mathrm{l},\mathrm{res},\mathrm{w}}$ is volume of water stored in the water body (m³), Q_in is inflow into the water body from upstream (m³ d⁻¹), A is global (or local) water body surface area (m²) in the grid cell at time t, P is precipitation (m³ d⁻¹), E_pot is potential evapotranspiration (m³ d⁻¹, Eq. 7), $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ is groundwater recharge from the water body (only in arid/semiarid regions) (m³ d⁻¹, Eq. 26), NA_l,res is the net abstraction from the lakes and reservoirs (m³ d⁻¹) (Fig. 2 and Sect. 4.8), and Q_out is outflow from the water body to other surface water bodies including river storage (m³ d⁻¹) (Fig. 2).

The temporally varying surface area A of the water body is computed in each daily time step using the following equation:

where r is reduction factor (–), and A_max is maximum extent of the water body (m²) from GRanD or GLWD databases. In the case of local and global lakes

where S_l is the volume of the water (m³) stored in the lake at time t (d), S_l,max is the maximum storage of the lake (m³), S_l,max is computed based on A_max and a maximum storage depth of 5 m, and p is the reduction exponent (–), set to 3.32. According to the above equation, the area is reduced by 1 % if S_l=50 % of S_l,max, by 10 % if S_l=0 and by 100 % if $S_{\mathrm{l}}=-S_{\mathrm{l},\max }$ (Hunger and Döll, 2008). In the case of global reservoirs/regulated lakes and local and global wetlands

where S_res,w is the volume of the water (m³) stored in the reservoir/regulated lake or wetland, and p is 2.814 and 3.32 for reservoirs/regulated lakes and wetlands, respectively. In the case of wetlands, $S_{\mathrm{res},\mathrm{w},\max }$ (m³) is computed based on A_max and a maximum storage depth of 2 m. Wetland area is reduced by 10 % if S_w=50 % of $S_{\mathrm{res},\mathrm{w},\max }$ and by 70 % if S_w is only 10 % of $S_{\mathrm{res},\mathrm{w},\max }$. In the case of reservoirs/regulated lakes, storage capacity $S_{\mathrm{res},\mathrm{w},\max }$ is taken from the database. Reservoir area is reduced by 15 % if S_res is 50 % of $S_{\mathrm{res},\mathrm{w},\max }$ and by 75 % if S_res is only 10 % of $S_{\mathrm{res},\mathrm{w},\max }$. For regulated lakes without available maximum storage capacity, $S_{\mathrm{res},\mathrm{w},\max }$ is computed as in the case of global lakes.

While storage in reservoirs/regulated lakes and wetlands cannot drop below zero due to high outflows, high evaporation or NA_s, storage in lakes can become negative. This represents the situation where there is no more outflow from the lake to a downstream water body (Q_out=0). There, like groundwater storage, storage of local and global lakes is a relative and not an absolute water storage. Reservoir/regulated lake storage is not allowed to fall below 10 % of storage capacity.

With changing A of the surface water compartments local wetland, global wetlands and local lakes, the land area fraction is adjusted accordingly. However, in the case of global lakes and reservoirs/regulated lakes, which may cover more than one 0.5^∘ × 0.5^∘ cell, such an adjustment is not made as it is not known in which grid cells the area reduction occurs. Therefore, land area fraction is not adjusted with changing r and precipitation is assumed to fall on a surface water body with an area of A_max instead of A.

4.6.2 Inflows

Calculation of Q_in differs between local and global water bodies. In the case of local lakes and local wetlands, they are recharged only by local runoff generated within the same grid cell. A fraction f_swb of the fast surface and subsurface runoff generated within the grid cell R_s (m³ d⁻¹) and, only in the case of humid grid cells, a fraction f_swb of the base flow from groundwater Q_g (m³ d⁻¹) become inflow to local water bodies (Fig. 2, Sect. 4.4.3, 4.5.2). In the case where one grid cell contains both local lake and wetland, then the outflow of the local lake will be the inflow to the local wetland according to Fig. 2. Global lakes, global wetlands, and global reservoirs/regulated lakes receive, in addition to local runoff, inflow from streamflow of the upstream grid cells as river inflow (Fig. 2). In many cells with significant groundwater abstraction, NA_s is negative, and return flow leads to a net inflow into surface water bodies (Sect. 3.3).

4.6.3 Outflows

LResWs lose water by evaporation E_pot, which is assumed to be equal to the potential evapotranspiration computed using the Priestley–Taylor equation with an albedo of 0.08 according to Eq. (7). In semiarid and arid grid cells (Appendix B), LResWs are assumed to recharge the groundwater with a focused groundwater recharge, $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ with

where $K_{{\mathrm{gw}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ is the groundwater recharge constant below LResWs (=0.01 m d⁻¹). This process is applied only in the arid and semiarid grid cells, as in humid areas groundwater mostly recharges the surface water bodies as explained in Sect. 4.6.2 (Döll et al., 2014).

It is assumed that water can be abstracted from lakes and reservoirs but not from wetlands. An amount of NA_l,res (m³ d⁻¹) is the net abstractions from lakes and reservoirs, which depends on the total unsatisfied water use Rem_use and the water storage in the surface water compartment. In the case of a global lake and a reservoir within the same cell, NA_l,res is distributed equally. In a reservoir, abstraction is only allowed until water storage reaches 10 % of storage capacity (after fulfilling E and $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res}}}$ ). Outflow from LResWs to downstream water bodies including river storage (Fig. 2) is calculated as a function of LResW water storage. The principal effect of a lake or wetland is to reduce the variability of streamflow, which can be simulated by computing outflow Q_out as

where S_ll,wl is the local lake or local wetland storage (m³), and k is the surface water outflow coefficient (=0.01 d⁻¹). $S_{\mathrm{ll},\mathrm{wl},\max }$ (m³) is computed based on A_max and a maximum storage depth of 2 m for local lakes and 5 m for local wetlands. The exponent a is set to 1.5 in the case of local lakes, based on the theoretical value of outflow over a rectangular weir, while the exponent of 2.5 used for local wetlands leads to a slower outflow (Döll et al., 2003). The outflow of global lakes and global wetlands is computed as

Different from the commissioning year of a reservoir, which is the year the dam was finalized (Appendix D), the operational year of each reservoir is the 12-month period for which reservoir management is defined. It starts with the first month with a naturalized mean monthly streamflow that is lower than the annual mean. To compute daily outflow, e.g., release, from global reservoirs/regulated lakes, the total annual outflow during the reservoir-specific operational year is determined first as a function of reservoir storage at the beginning of the operational year. Total annual outflow during the operational year is assumed to be equal to the product of mean annual outflow and a reservoir release factor k_rele that is computed each year on the first day of the operational year as

where S_res is the reservoir/regulated lake storage (m³), and S_res,max is the storage capacity (m³). Thus, total release in an operational year with low reservoir storage at the beginning of the operational year will be smaller than in a year with high reservoir storage.

During the first filling phase of a reservoir after dam construction, k_rele = 0.1 until S_res exceeds 10 % of S_res,max. If the storage capacity to mean total annual outflow ratio is larger than 0.5, then the outflow from the reservoir is independent of the actual inflow and temporally constant in the case of a non-irrigation reservoir. In the case of an irrigation reservoir, outflow is driven by monthly NA_s in the next five downstream cells or down to the next reservoir (Döll et al., 2009; Hanasaki et al., 2006). For reservoirs with a smaller ratio, the release additionally depends on daily inflow and is higher on days with high inflow (Hanasaki et al., 2006). If reservoir storage drops below 10 % of S_res,max, release is reduced to 10 % of the normal release to satisfy a minimum environmental flow requirement for ecosystems. Daily outflow may also include overflow, which occurs if reservoir storage capacity is exceeded due to high inflow into the reservoir.

4.7.1 Water balance

The dynamic water balance of the river water storage in a cell is computed as

where S_r is the volume of water stored in the river (m³), Q_r,in is inflow into the river compartment (m³ d⁻¹), Q_r,out is the streamflow (m³ d⁻¹) and NA_s,r is the net abstraction of surface water from the river (m³ d⁻¹).

4.7.2 Inflows

If there are no surface water bodies in a grid cell, Q_r,in is the sum of R_s, Q_g and streamflow from existing upstream cell(s). Otherwise, part of R_s, and in the case of humid cells also part of Q_g, is routed through the surface water bodies (Fig. 2). The outflow from the surface water body preceding the river compartment then becomes part of Q_r,in. In addition, negative NA_s values due to high return flows from irrigation with groundwater lead to a net increase in storage. Thus, if no surface water bodies exist in the cell, negative NA_s is added to Q_r,in (Sect. 3.3 and Fig. 2).

4.7.3 Outflows

Q_r,out is defined as the streamflow that leaves the cell and is transferred to the downstream cell.

It is calculated as

where v (m d⁻¹) is river flow velocity, and l is the river length (m). l is calculated as the product of the cell's river segment length, derived from the HydroSHEDS drainage direction map (Lehner et al., 2008), and a meandering ratio specific to that cell (method described in Verzano et al., 2012). v is calculated according to the Manning–Strickler equation as

where n is river bed roughness (–), R_h is the hydraulic radius of the river channel (m) and s is river bed slope (m m⁻¹). Calculation of s is based on high-resolution elevation data (SRTM30), the HydroSHEDS drainage direction map and an individual meandering ratio. The predefined minimum s is 0.0001 m m⁻¹.

To compute the daily varying R_h, a trapezoidal river cross section with a slope of 0.5 is assumed such that it can be calculated as a function of daily varying river depth D_r and temporally constant bottom width W_r,bottom (Verzano et al., 2012). Allen et al. (1994) empirically derived equations relating river depth, river top width and streamflow for bankfull conditions. In former model versions, these equations were also applied at each time step, even if streamflow was not bankfull, to determine river width and depth required to compute R_h and thus v. As usage of these functions for any streamflow below bankfull is not backed by the data and method of Allen et al. (1994), WaterGAP 2.2d implements a consistent method for determining daily width and depth as a function of river water storage.

As bankfull conditions are assumed to occur at the initial time step, the initial volume of water stored in the river is computed as

where S_r,max is the maximum volume of water that can be stored in the river at bankfull depth (m³), D_r,bf (m) and W_r,bf (m) are river depth and top width at bankfull conditions, respectively, and W_r,bottom is river bottom width (m). River water depth D_r (m) is simulated to change at each time step with actual S_r as

Using the equation for a trapezoid with a slope of 0.5, R_h is then calculated from W_r,bottom and D_r. Bankfull flow is assumed to correspond to the maximum annual daily flow with a return period of 1.5 years (Schneider et al., 2011) and is derived from daily streamflow time series.

The roughness coefficient n of each grid cell is calculated according to Verzano et al. (2012), who modeled n as a function of various spatial characteristics (e.g., urban or rural area, vegetation in river bed, obstructions) and a river sinuosity factor to achieve an optimal fit to streamflow observations. Because of the implementation of a new algorithm to calculate D_r, we had to adjust their gridded n values to avoid excessively high river velocities (Schulze et al., 2005). By trial and error, we determined optimal n-multipliers at the scale of 13 large river basins that lead to a good fit to monthly streamflow time series at the most downstream stations and basin-average total water storage anomalies from GRACE. We found that in 9 out of 13 basins, multiplying n by 3 resulted in the best fit between observed and modeled data. We therefore set the multiplier to 3 globally, except for the remaining four basins, where other values proved to be more adequate; this concerns the Lena basin, where n is multiplied by 2; the Amazon basin, where n is multiplied by 10; and the Huang He and Yangtze basins, where n is kept at its original value (Fig. S1).

Net cell runoff R_nc (mm d⁻¹), the part of the cell precipitation that has neither been evapotranspirated nor stored with a time step, is calculated as

where A_cont is the continental area (0.5^∘ × 0.5^∘ grid cell area minus ocean area) of the grid cell (m²). Renewable water resources are calculated as long-term mean annual R_nc computed under naturalized conditions (Sect. 4.1). Renewable water resources can be negative if evapotranspiration in a grid cell is higher than precipitation due to evapotranspiration from global lakes, reservoirs or wetlands that receive water from upstream cells.

4.9.1 Calibration approach

The main purpose of WaterGAP is to quantify water resources and water stress for both historical time periods and scenarios of the future. Not only due to very uncertain global climate input data, uncalibrated global hydrological models may compute very biased runoff and streamflow values (e.g., Haddeland et al., 2011). To reduce the bias and simulate at least mean streamflow and thus renewable water resources with a reasonable reliability, WGHM has been calibrated to match observed long-term average annual streamflow at gauging stations on all continents (Döll et al., 2003; Kaspar, 2004). Calibration is required due to uncertain model parameters, input data (e.g., deviations of precipitation from meteorological forcings to observation networks; Wang et al., 2018) and model structure including the spatial resolution. The rationale behind the approach can be summed up by the phrase “if the model is not able to properly capture the average observed hydrological conditions, how well founded are future projections?” (see also the discussion in Krysanova et al., 2018, 2020). In order to minimize the problem of equifinality, WGHM is calibrated in a very simple basin-specific manner to match long-term mean annual observed streamflow (Q_obs) at the outlet of 1319 drainage basins that cover ∼ 54 % of the global drainage area (except Antarctica and Greenland) (Fig. 4). The runoff coefficient γ (Eq. 18) and up to two additional correction factors (the areal correction factor, CFA, and the station correction factor, CFS; for a brief description the reader is referred to the calibration status CS3 and CS4 below or to Hunger and Döll, 2008), if needed, are adjusted homogeneously for all grid cells within the drainage basin. Calibration starts in upstream basins and proceeds to downstream basins, with the streamflow from the already calibrated upstream basin as inflow.

While the calibration approach in WaterGAP 2.2d is generally the same as in previous model versions (Döll et al., 2003; Hunger and Döll, 2008; Müller Schmied et al., 2014), it was modified (Müller Schmied, 2017, Appendix A3) to allow for a ±10 % gauging station observation uncertainty (following Coxon et al., 2015; Pascolini-Campbell et al., 2020) instead of ±1 % in previous model versions. It is noteworthy that the discharge uncertainty (approximated here with ±10 %) is unlikely to be stationary in space and time (Coxon et al., 2015), but there are no further data available to better constrain the specific uncertainty of each gauging station. The source of streamflow data and selection criteria for stations is the same as in Müller Schmied et al. (2014) (their Appendix B2), but the 30-year period was shifted (if available) from 1971–2000 to 1980–2009 to capture a more recent time period.

Calibration follows a four-step scheme with specific calibration status (CS):

1. CS1. Adjust the basin-wide uniform parameter γ (Eq. 18) in the range of [0.1–5.0] to match Q_obs within ±1 %.

2. CS2. Adjust γ as for CS1, but within 10 % uncertainty range (90 %–110 % of observations).

3. CS3. As CS2 but apply the areal correction factor CFA (adjusts runoff and, to conserve the mass balance, actual evapotranspiration as counterpart of each grid cell within the range of [0.5–1.5]) to match Q_obs with 10 % uncertainty.

4. CS4. As CS3 but apply the station correction factor CFS (multiplies streamflow in the cell where the gauging station is located by an unconstrained factor) to match Q_obs with 10 % uncertainty to avoid error propagation to the downstream basin. Note that with CFS, actual evapotranspiration of this grid cell is not adapted accordingly to avoid unphysical values. Hence, mass is not conserved in the case of CS4 for the grid cell where CFS is applied in the upstream basin. For global water balance assessment, the mass balance is kept by adjusting the actual evapotranspiration component by the amount CFS modified streamflow.

For each basin, calibration steps 2–4 are only performed if the previous step was not successful.

4.9.2 Regionalization approach

The calibrated γ values are regionalized to river basins without sufficient streamflow observations using a multiple linear regression approach that relates the natural logarithm of γ to basin descriptors (mean annual temperature, mean available soil water capacity, fraction of local and global lakes and wetlands, mean basin land surface slope, fraction of permanent snow and ice, aquifer-related groundwater recharge factor). Just like the calibrated γ values, the regionalized values are limited between 0.1 and 5.0; CFA and CFS are set to 1.0 in uncalibrated basins. A manual modification of the regionalized γ value to 0.1 was done (from values of 3–5) for basins covering the North China Plain in northeastern China as groundwater depletion was overestimated by a factor of 4 in this region (Döll et al., 2014); a lower γ allows higher runoff generation that translates into higher groundwater recharge and thus a weaker overestimation.

4.9.3 Calibration and regionalization results

Calibration of WaterGAP 2.2d driven by the standard climate forcing (Sect. 7.1) results in 485 basins with calibration status CS1, 185 basins with calibration status CS2, 277 basins with calibration status CS3 and 372 basins with calibration status CS4. This means that in 72 % of the calibration basins, the usage of the station correction factor CFS is not required to match the simulated long-term annual streamflow to observations. The spatial distribution of the calibration parameters and status is shown in Fig. 4.

Figure 4Results of the calibration of WaterGAP 2.2d to the standard climate forcing with (a) the calibration status (see Sect. 4.9.1) of each calibration basin, (b) calibration parameter γ, (c) areal correction factor CFA and (d) station correction factor CFS. Grey areas in (d) indicate regions with regionalized calibration parameter γ and for (a)–(d) dark green outlines indicate the boundaries of the calibration basins.

6.2.1 AQUASTAT withdrawal water use data

AQUASTAT is the Food and Agriculture Organization of the United Nations Global Information System on Water and Agriculture (FAO, 2019). It contains information on country-level withdrawal water uses for different sectors. These data represent estimates mainly provided by the individual countries. In particular irrigation withdrawal water uses are, for most countries, not based on observations. Six different withdrawal water use variables (Table 3) were available for comparison to WaterGAP 2.2d. For the evaluation, all database entries available on FAO (2019) were used; hence it contains yearly values per country as data units. The evaluation metrics (Sect. 6.3.1) are calculated using each single data point of AQUASTAT without any temporal aggregation by country.

Table 3AQUASTAT variables used for evaluating WaterGAP 2.2d potential withdrawal water use WU, including variable ID reference of AQUASTAT.

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6.2.2 GRDC streamflow data

Monthly streamflow time series from 1319 calibration stations from the Global Runoff Data Centre (GRDC) were used for evaluating the performance of WaterGAP 2.2d and 2.2. As the GRDC archive has certain gaps in some regions and times and the calibration objective is to benefit from a maximum of observation data, the typical split-sampling calibration/validation is not appropriate. Even though the same observation data are used for calibration and validation, the validation against monthly time series is meaningful as only long-term mean annual streamflow values have been used for calibration.

6.2.3 GRACE total water storage anomalies

Three mascon solutions of monthly time series of TWSAs from the Gravity Recovery And Climate Experiment (GRACE) satellite mission are considered. The Jet Propulsion Laboratory (JPL) mascon dataset (Watkins et al., 2015; Wiese et al., 2018, 2016) from the GRACE Tellus Website (JPL, 2020) is based on the Level-1 product processed at JPL. A geocenter correction is applied to the degree-1 coefficients following the method from Swenson et al. (2008), the c₂₀ coefficient is replaced with the solutions from satellite laser ranging (SLR; Cheng et al., 2011) and a glacial isostatic adjustment (GIA) correction is applied based on the ICE6G-D model published in Richard Peltier et al. (2018). The Center of Space Research (CSR) RL05 GRACE mascon solution (Save et al., 2016) from the University of Texas website (CSR, 2019) performs the same degree-1 and c₂₀ replacements (but following Cheng et al., 2013) and removes the GIA signal based on the model from Geruo et al. (2012). Last, the Goddard Space Flight Center (GSFC) GRACE mascon solutions (Luthcke et al., 2013) from the Geodesy and Geophysics Science Research Portal (NASA, 2020) applies trend corrections for the c₂₁ and s₂₁ coefficients following Wahr et al. (2015) in addition to the degree-1, c₂₀ and GIA corrections described for CSR.

Monthly TWSA values are provided on 0.5^∘ × 0.5^∘ grid cells for JPL and CSR, while GSFC provides equal area grids with a spatial resolution of around 1${}^{\circ }\times \mathrm{1}{}^{\circ }$ at the Equator. In this study, the grid values are spatially averaged over 143 river basins with a total area of more than 200 000 km² each, out of the 1319 basins used for calibration. The considered time span for this study is 2003–2015 (full years of data), limited by available monthly solutions from GSFC between January 2003 and July 2016.

6.3.1 Nash–Sutcliffe efficiency

The Nash–Sutcliffe efficiency metric (NSE) (–) (Nash and Sutcliffe, 1970) is a traditional metric in hydrological modeling. It provides an integrated measure of modeling performance with respect to mean values and variability and is calculated as follows:

where O_i is the observed value (e.g., monthly streamflow), S_i is the simulated value and $\stackrel{\mathrm{‾}}{O}$ is the mean observed value. The optimal value of NSE is 1. Values below 0 indicate that the mean value of observations is better than the simulation (Nash and Sutcliffe, 1970). For assessing the performance of low values of water abstraction (Sect. 6.4.1), a logarithmic NSE was calculated in addition by applying logarithmic transformation before calculation of the performance indicator.

6.3.2 Kling–Gupta efficiency

The Kling–Gupta efficiency metric (KGE) (Kling et al., 2012; Gupta et al., 2009) transparently combines the evaluation of bias, variability and timing and is calculated (in its 2012 version) as follows:

where KGE_r is the correlation coefficient between simulated and observed values (–), an indicator for the timing; KGE_b is the ratio of mean values (Eq. 38) (–), an indicator of biases regarding mean values; and KGE_g is the ratio of variability (Eq. 39) (–), an indicator for the variability of simulated (S) and observed (O) values.

where μ is mean value, σ is standard deviation and CV is coefficient of variation. The optimal value of KGE is 1.

6.3.3 TWSA-related metrics

For the evaluation of total water storage anomaly performance, the following metrics were used: R² (coefficient of determination) as the strength of the linear relationship between simulated and observed variables, and the amplitude ratio as the indicator for variability and trends of both GRACE and WaterGAP data. Amplitude and trends were determined by a linear regression for estimating the most dominant temporal components of the GRACE time series. The time series of monthly TWSAs was approximated by a constant a, a linear trend b, and an annual and a semiannual sinusoidal curve as follows:

where r denotes the residuals. The parameters a to f were estimated via least-squares adjustment. The annual amplitude can be computed by $A=\mathrm{sqrt}(c^{\mathrm{2}}+d^{\mathrm{2}})$, and thus the annual ratio was calculated by $A_{\mathrm{WGHM}}/A_{\mathrm{GRACE}}$.

6.4.1 Water withdrawals

The performance of WaterGAP potential withdrawal water uses is generally of reasonable quality (Fig. 5, for a non-logarithmic graph see Fig. S6). The highest agreement in terms of performance indicator is shown for the total withdrawal water uses with both efficiency metrics close to the optimum value. Slightly less agreement is visible for the separation into groundwater withdrawals (underestimation by WaterGAP) and surface water withdrawals (overestimation by WaterGAP). The domestic sectoral withdrawal water uses are best simulated with WaterGAP, followed by the industrial sector. Here, large differences between NSE and logarithmic NSE are visible, indicating that WaterGAP has specific problems in representing the small values and tending to a general overestimation of industrial withdrawal water uses. Comparing simulated industrial water uses from WaterGAP with data of the FAO AQUASTAT database reveals inconsistencies due to overestimation (i.e., for values > 200 km³ yr⁻¹) as well as underestimation (i.e., for small values) (Fig. 5 and Fig. S6). In terms of overestimated values, values for India and Germany dominate the differences in the time intervals 2008–2012 and 2013–2016, respectively. Water withdrawals of 56 km³ yr⁻¹ for the industry sector (including thermoelectric) were assessed by India's National Commission on Integrated Water Resources Development for 2010 (Bhat, 2014). Here AQUASTAT reports 17 km³ yr⁻¹ and WaterGAP simulates 72 km³ yr⁻¹. In the case of Germany, AQUASTATs reports only the water use of the manufacturing sector but omits the water abstractions of cooling water for thermal electricity production that is included in the WaterGAP results. The underestimation of industrial water uses > 200 km³ yr⁻¹ (Fig. S6) is particularly biased by the reported numbers from the US statistics. While AQUASTAT data include both freshwater and saline water abstractions from manufacturing, thermoelectric abstractions and mining, WaterGAP only accounts for the freshwater part of the manufacturing and thermoelectric abstractions.

WaterGAP performs reasonably well in the irrigation sector with a slightly better logarithmic NSE metric but with the overall lowest sectoral performance in terms of NSE (no visible direction in under- or overestimation).

Figure 5Comparison of potential withdrawal water uses from WaterGAP 2.2d with AQUASTAT (FAO, 2019). Each data point represents one yearly value (if present in the database) per country for the time span 1962–2016.

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6.4.2 Streamflow

The performance of WaterGAP 2.2d in terms of monthly streamflow time series at 1319 gauging stations (Fig. 6) reaches a median NSE (KGE) of 0.52 (0.61). However, NSE values below 0 for 259 stations show that WaterGAP 2.2d cannot reproduce monthly and annual streamflow dynamics in one-fifth of the evaluated basins, although the simulated mean annual streamflow fits to the observations due to the calibration. The median for KGE_r of 0.79 indicates a relatively satisfactory simulation of the timing of monthly streamflows both seasonally and interannually. As the model is calibrated to match long-term annual river discharge (Sect. 4.9), the median of the bias measure KGE_b is, with a value of 1.01, close to the optimum value. In rare cases, values outside the range of 0.9–1.1 occur as for calibration the individual basins were run for the calibration time period (plus 5 initialization years) while the evaluation run was a global run from 1901 to 2016. In the normal global runs, water demand can be fulfilled from neighboring grid cells while this is not possible in the calibration runs. This partially explains the larger biases also seen in Fig. 8. Streamflow variability is mostly underestimated by WaterGAP 2.2d, and median KGE_g is 0.85 (Fig. 6).

When analyzing the spatial distribution of streamflow performance indicators, note that a highly seasonal streamflow regime tends to lead to high NSE and KGE_g not due to the quality of the evaluated hydrological model but due to the highly seasonal precipitation input. The global distribution of NSE classes shows a diverse pattern (Fig. 7). Whereas large parts of central Europe, Asia and southern America are simulated reasonably well, the performance in northern America and large parts of Africa is in many cases below a value of 0.5. Based on NSE alone it remains unclear why WaterGAP consistently fails to satisfactorily simulate large parts of the well observed northern American region. Further insights can be gained by assessing the spatial distribution of KGE and its components (Fig. 8). The broad picture of overall KGE (Fig. 8a) is similar to the NSE spatial distribution (Fig. 7). In a large fraction of river basins with low NSE and KGE, the timing is off, with KGE_r<0.5. One reason could be the inappropriate modeling of the dynamics of lakes and wetland (mainly in Canada) and of reservoir regulations. As most snow-dominated basins in Alaska, Europe and Asia show a reasonably high KGE_r of >0.8, it is not likely that snow dynamics are the dominant cause for low correlations between observed and simulated streamflow. For many other regions (e.g., central Asia and the Nile Basin), streamflow regulations due to reservoirs as well as the timing of water abstractions are most likely to cause low performance in timing. The indicator of variability KGE_g shows a medium to strong underestimation of streamflow variability in most of the northern snow-dominated basins. Underestimation in the Amazon basin is caused by the inability of WaterGAP to simulate wetland dynamics there. There are also many gauging stations for which WaterGAP overestimates seasonality, even by more than 50 %. Further research and development is needed for improving the GHMs in this respect (Veldkamp et al., 2018).

Figure 6Efficiency metrics for monthly streamflow of WaterGAP 2.2d at the 1319 GRDC stations with NSE, KGE and its components. Outliers (outside 1.5× inter-quartile range) are excluded but the number of stations that are defined as outliers are indicated after the metric.

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Figure 7Classified NSE efficiency metric for the 1319 river basins in WaterGAP 2.2d.

Figure 8Classified KGE efficiency metric and its components for the 1319 river basins in WaterGAP 2.2d.

6.4.3 TWSA

WaterGAP 2.2d underestimates the mean annual TWSA amplitude in 54 % of the 143 investigated river basins by more than 10 % (Fig. 9). Most of these basins are located in Africa, in the northern and monsoon regions of Asia, in Brazil, and in western North America. In contrast, the mean annual amplitude is overestimated in western Russia as well as in eastern and central North America. The correlation coefficient exceeds 0.7 in almost 75 % of the river basins and 0.9 in 22 %. Only 8 % of the basins show a correlation coefficient below 0.5.

The comparison of the TWSA trends shows that GRACE and WaterGAP 2.2d agree in the sign of the trend for 63 % of the 143 basins, for example most European basins; nearly the entire South American continent; and several basins in North America, Asia and Australia, but trends are often underestimated, e.g., in the Amazon and western Russia. Basins with different signs of the trend are scattered around the globe. GRACE suggests strong decreases in water storage in Alaskan basins, which is likely due to glacier mass loss, while WaterGAP determines a small mass increase, likely because WaterGAP does not simulate glaciers. Comparing the spatial pattern of Figs. 9 and 8, no obvious interrelation can be derived between the performances of streamflow and TWSAs.

Figure 9Comparison of basin-average TWSAs of WaterGAP 2.2d and the average values of three GRACE mascon products for 143 basins larger than 200 000 km², with (a) ratio of amplitude (reddish colors indicate underestimated amplitude of WaterGAP, vice versa for bluish), (b) correlation coefficient, (c) trend of GRACE and (d) trend of WaterGAP 2.2d. All values based on the time series January 2003–December 2015.

7.2.1 Renewable water resources

The quantification of (total) renewable water resources is one of the key elements of WaterGAP model application. They are defined as the long-term annual difference between precipitation and actual evapotranspiration of a spatial unit, or long-term annual net cell runoff. As runoff and evapotranspiration are influenced by human interference, renewable water resources are calculated based on the naturalized model variant, by averaging R_nc (Sect. 4.7.3) over e.g., a 30-yr time period, resulting in $R_{\mathrm{nc},\mathrm{lta},\mathrm{nat}}$. On around 42.6 % of the global land area (excluding Greenland and Antarctica), total water resources are calculated to be < 100 mm yr⁻¹ during the period 1981–2010, whereas on 19.8 % values are > 500 mm yr⁻¹ (Fig. 11a). Globally averaged renewable water resources are computed to be 307 mm yr⁻¹ or 40 678 km³ yr⁻¹. The global map of inter-annual variability of runoff production (Fig. 11b), here defined as the ratio of runoff in a 1-in-10 dry year to total renewable water resources, shows regions with relatively constant and relatively variable annual runoff generation, in bluish and reddish colors, respectively. High variability is linked with low renewable water resources.

Total renewable water resources include renewable groundwater resources which are the sum of long-term average diffuse groundwater recharge R_g (Fig. 11c) and long-term average point (or focused) groundwater recharge from surface water bodies $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ (Fig. 11d). While focused recharge is the major type of groundwater recharge in some (semi)arid grid cells, its quantification is highly uncertain, and diffuse groundwater recharge dominates in most cells. For 1981–2010, global mean diffuse groundwater recharge is calculated as 111.0 mm yr⁻¹, and global mean focused recharge as 12.8 mm yr⁻¹. Note that as R_g is calculated on (time-variable) land area (continental area minus fraction of lakes, reservoirs, wetlands) but is related to continental area in the standard output (Sect. 5.2), grid cells with large gaining surface water bodies, e.g., wetlands along the Amazon river, show significant lower R_g values than surrounding grid cells.

The sum of diffuse and focused renewable groundwater resources amounts to 40 % of total renewable water resources, highlighting the important contribution of groundwater resources. There have been a number of studies on the potential impact of climate change on renewable groundwater resources (either including or excluding focused recharge), in which WaterGAP was applied as the impact model (Portmann et al., 2013; Döll, 2009; Döll et al., 2018; Herbert and Döll, 2019).

Figure 11Water resources assessment 1981-2010 using WaterGAP 2.2d, with (a) total renewable water resources defined as long-term annual net cell runoff $R_{\mathrm{nc},\mathrm{lta},\mathrm{nat}}$ [mm yr⁻¹], (b) 1-in-10 dry-year runoff generation in percent of total renewable water resources [%], (c) long-term annual diffuse groundwater recharge R_g [mm yr⁻¹], (d) long-term annual focused groundwater recharge $R_{{\mathrm{g}}_{\mathrm{l},\mathrm{res},\mathrm{w}}}$ [mm yr⁻¹]. Results are based on naturalized model runs. In (a) note that negative values for total water resources are possible (Sect.  4.7.3). In (b) areas where the denominator is $<{\mathrm{10}}^{-\mathrm{5}}$ are labeled as not defined.

Figure 12Streamflow indicators of WaterGAP 2.2d for 1981–2010 with (a) long-term average annual streamflow $Q_{\mathrm{r},\mathrm{out},\mathrm{lta}}$ (km³ yr⁻¹); (b) indication of streamflow alteration due to human water use and man-made reservoirs, where a reddish color indicates less streamflow for ant conditions, blue the opposite; (c) statistical monthly low flow $Q_{\mathrm{r},\mathrm{out},\mathrm{90}}$ in percent of $Q_{\mathrm{r},\mathrm{out},\mathrm{lta}}$; (d) differences of long-term average statistical monthly low flows as indication of low flow alteration due to human water use and man-made reservoirs. Not defined are areas where the denominator is smaller than 10⁻⁵ km³ yr⁻¹.

7.2.2 Streamflow

Streamflow (or river discharge) Q_r,out is the model output that integrates all model components and human intervention, routing runoff along the river network. The global map of long-term average annual streamflow under anthropogenic conditions distinctly shows the very high spatial variability of streamflow and very distinctly the large river systems of the Earth (Fig. 12a). Temporal variability of monthly streamflow is much higher in the (semi)arid areas than in humid areas, increasing the spatial discrepancy of streamflow; this can be seen in Fig. 12c, which presents the ratio of the statistical low flow Q₉₀ (the streamflow that is exceeded in 9 out of 10 months) to long-term average annual streamflow. The regions with a ratio of less than 5 % of low flow contribution on average streamflow (the hydrologically highly variable regions) follow in general the definition of (semi)arid grid cells (Fig. B1) with some exceptions such as northern Asia. Different from the spatial pattern of interannual variability of long-term average net cell runoff (Fig. 11b), the spatial pattern of streamflow is characterized by low temporal variability in cells with large rivers, due to the integration of runoff from diverse grid cells as well as large water storage capacities in lakes, reservoirs or wetlands.

The impact of human interventions (human water use and man-made reservoirs) on streamflow is assessed in Fig. 12b for long-term averages and Fig. 12d for the statistical low flow indicator Q₉₀ (please note the different legend for both subfigures). In general, human interventions reduce long-term average streamflow by at least 10 % (50 %) in 11.3 % (1.8 %) of the global land area, mainly due to reduced groundwater discharge to lakes, reservoirs, wetlands and rivers as a consequence of groundwater abstractions, in particular groundwater depletion (compare the red pattern with net abstraction from groundwater in Fig. 15a). There is only a minor share (0.7 %) of global land area, where long-term annual streamflow has been increased by more than 10 % due to human interventions (mainly return flow from groundwater abstractions). The impact of human interventions on Q₉₀ is more pronounced (Fig. 12d). Large reddish patterns (consistent to net abstraction from groundwater in Fig. 15a) indicate the reduction of low flows by at least 10 % (90 %) on 29.7 % (14.4 %) of the global land area. However, there are also bluish river systems visible which represent a global land area of 5.3 % with increase in low flows of more than 10 %. Those areas are located downstream of large reservoirs that due to their storage capacity attenuate the flow regime towards a temporally less variable streamflow. As WaterGAP 2.2d considers only the largest reservoirs with reservoir management algorithm and handles the remaining ∼6000 reservoirs of GRanD as unmanaged water bodies, the impact of streamflow regulation is most likely underestimated.

7.2.3 Water stress

A major motivation for the initial WaterGAP development was to consistently assess water stress on all land areas of the globe (Döll et al., 2003; Alcamo et al., 1998). A common water stress indicator (WSI) is calculated as the ratio of long-term average annual withdrawal water uses (or water abstractions of withdrawal water use) (Sect. 3) and total renewable water resources for different spatial units (e.g., river basins). Renewable water resources in a basin are equal to long-term average naturalized annual streamflow at the outlet of the basin. WSI of 0.2–0.4 is generally assumed to indicate mild water stress and WSI > 0.4 severe water stress (e.g., Greve et al., 2018), while WSI > 1.0 represents a situation where withdrawal water uses are larger than renewable water resources, indicating extreme water scarcity (e.g., Veldkamp et al., 2017). For this example, zero-order river basins (basins that drain to the oceans or inland sinks) were chosen as spatial units (Fig. 13). River basins covering 73.6 % of global land area have a WSI < 0.2 and thus are calculated to have none to only minor water stress. Mild (severe, but below extreme) water stress is represented in river basins that cover 9.7 % (6.9 %) of global land area. Extreme water stress (WSI > 1.0) is simulated in river basins that cover 9.9 % of global land area (red colors in Fig. 13). The spatial pattern of river basins with water stress is similar to the pattern of modification of statistically low flow alteration due to human interventions (Fig. 12d).

Figure 13Water stress in zero-order river basins for 1981–2010, computed as the ratio of the basin sum of long-term average annual potential total withdrawal water uses (Sect. 3) to long-term average annual streamflow $Q_{\mathrm{r},\mathrm{out},\mathrm{lta},\mathrm{nat}}$ of the basin (i.e., at its outflow cell to the ocean or at its inland sink).

Output of global models is usually shown in the form of two-dimensional planar global maps, which are necessarily distorted. While the Robinson projection that we normally use when presenting WaterGAP results is pleasing to the eye, it does not preserve the actual area of the land surface, and areas closer to Equator are shown relatively smaller than the areas closer to the poles. Using an equal-area projection as in Fig. 14b, Africa is shown larger than in the traditional Robinson maps. For Africa, large blue areas indicate high total renewable water resources per capita. However, very few people live in these large areas. For representing water resources for people instead of on areas, cartograms with population numbers as a distorter can be used (Fig. 14b). In cartograms, map polygons representing spatial units on the Earth's surface are distorted in a way that the units' polygon areas on the map are proportional to a quantitative attribute of the spatial unit (Döll, 2017), here the population in 0.5^∘ × 0.5^∘ grid cells in 2010. The latter was derived by aggregating 2010 GPWv3 gridded population estimate for the year 2010 (CIESIN, 2016) from its original resolution of 2.5 arcmin. Clearly, with a higher share of red areas, the cartogram indicates a world with less water availability than the “normal” map, and it leads the eye to regions where humans are affected by water scarcity.

Figure 14Water availability indicator per capita renewable water resources $Q_{\mathrm{r},\mathrm{out},\mathrm{lta},\mathrm{nat}}$ (${\mathrm{m}}^{\mathrm{3}}{\mathrm{cap}}^{-\mathrm{1}}{\mathrm{yr}}^{-\mathrm{1}}$) for 1981–2010 visualized in (a) an equal area projection and (b) as a cartogram with population in 2010 as distorter. In the cartogram each half-degree grid cell is distorted such that its area is proportional to the population of the grid cell.

Figure 15Long-term (1981–2010) annual net abstractions: potential net water abstractions from surface water bodies (a), potential net water abstractions from groundwater (b), ratio of actual net water abstractions from surface water bodies to its potential value (c) and ratio of actual net water abstractions from ground water to its potential value. In (a) and (b) negative values indicate a net recharge of surface water and groundwater, respectively, due to return flows caused by human water use, while positive values indicate a net removal of water from the sources. In (c) and (d), cells with potential net water abstractions smaller than $\left|\mathrm{1}\right|$ mm yr⁻¹ are greyed out. Furthermore, grid cells where the sign of water abstractions changes between potential and actual net abstractions are displayed in red.

7.2.4 Water abstractions

With human water use being essential for the estimation of water stress, quantification of sectoral water uses was a focus already in the initial stages of WaterGAP development (Alcamo et al., 1998). However, a distinction of the sources of water abstractions and the sinks of return flows (groundwater or surface water) was only implemented later, such that potential net abstractions from groundwater and from surface water could be computed (Döll et al., 2012, 2014). Model refinements (see Appendix A2) have lead to a more consistent computation of actual net abstractions from both sources. The general patterns of potential net abstractions (Fig. 15a and b) are consistent with the earlier assessment of Döll et al. (2012). Positive values of NA_s and NA_g indicate that human water use results in a net subtraction of water from surface water bodies and groundwater, while negative values indicate a man-made addition of water to these water storage compartments. As noted in Sect. 4.8, the actual net abstractions can differ from their potential values. The ratio of actual to potential net surface water abstractions NA_s (Fig. 15c) shows a heterogeneous pattern, with adjacent grid cells with values below 0.9 and above 1.1. This is explained by the option to satisfy water demand from a neighboring grid cell. In the case of negative NA_s, potential and actual values are always the same, as it is assumed in the model that NA_g can always be fulfilled so that return flows to surface water are not changed. There are only a few longer river stretches where actual NA_s is smaller than the potential value.

Actual NA_g is equal to potential NA_pot,g except in a few grid cells where potential NA_pot,s cannot be fulfilled and there is irrigation with surface water (Fig. 15d). In these cells, return flows to groundwater decrease and actual values of NA_g increase compared to their potential values. For example, in the case of a positive (negative) potential NA_g, a ratio of 1.1 (0.9) means that the difference between actual and potential NA_g is 10 % of the absolute value of potential NA_g. In most grid cells, actual NA_g is equal to the potential value.

Table 6Global-scale (excluding Antarctica and Greenland) water balance components for different time spans as simulated with WaterGAP 2.2d. All units in km³ yr⁻¹. Long-term average volume balance error is calculated as the difference of component 1 and the sum of components 2, 3 and 7.

¹ Including actual consumptive water use. ² Sum of rows 5 and 6.

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Table 7Globally aggregated (excluding Antarctica and Greenland) water storage component changes during different time periods as simulated by WaterGAP 2.2d. All units in km³ yr⁻¹.

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Table 8Globally aggregated (excluding Antarctica and Greenland) sectoral potential withdrawal water use WU and consumptive water use CU (km³ yr⁻¹) as well as use fractions from groundwater (%) as simulated by GWSWUSE of WaterGAP 2.2d for the time period 1991–2016. These values represent demands for water that cannot be completely satisfied in WGHM due to lack of surface water resources (row 5 in Table 6).

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7.3.1 Major water balance components

Estimation of globally aggregated components of the land water balance components is an intrinsic application field of GHMs. Independent of the time span assessed in Table 6, streamflow into oceans and inland sinks, equivalent to global renewable water resources, amounts to around 40 000 km³ yr⁻¹ (with a range of around 1000 km³ yr⁻¹). Actual evapotranspiration is estimated to be around 71 000 km³ yr⁻¹ (with a range of 1200 km³ yr⁻¹). Renewable water resources estimates are in the range of the estimates of previous WaterGAP model versions and of other global assessments (compare Müller Schmied et al., 2014, their Table 3). Temporal trends of precipitation, actual evapotranspiration and streamflow may not be reliable due to uncertainty of the climate forcing and WaterGAP 2.2d. With less than 10⁻¹ km³ yr⁻¹, the water balance error is negligible (Table 6), which is an improvement compared to earlier model versions (see Müller Schmied et al., 2014, their Table 2).

7.3.2 Water storage components

Total actual consumptive water use has increased over time and reaches the maximum in the most recent time period 2001–2016. The negative value of actual net abstraction from groundwater in Table 6 indicates that, globally aggregated, the groundwater compartment is recharged by return flows from irrigation with surface water (addition of the positive and negative values of NA_g in Fig. 15b). A globally averaged anthropogenic increase in groundwater recharge is consistent with a decrease in groundwater storage that is mainly caused by the net groundwater abstractions. The global groundwater storage, however, has decreased (Table 7), mainly due to groundwater depletion in those grid cells where (positive) NA_g is higher than groundwater recharge (Döll et al., 2014). The anthropogenic net recharge of groundwater in the grid cells with negative NA_g in Fig. 15b does not lead to a substantial increase in groundwater storage but mainly increases groundwater discharge to surface water bodies. The decreasing trend of total water storage is dominated by increasing water storage losses that were balanced in earlier periods by increased water storage in newly constructed reservoirs while dam construction became less during the last three decades (Table 7, Cáceres et al., 2020). However, WaterGAP 2.2d underestimates water storage increases because only the largest reservoirs are simulated as reservoirs including their commissioning year and because the GRanD v1.1 database used in WaterGAP 2.2d does not include some of the major reservoirs that were put into operation after 2000 (Cáceres et al., 2020). Soil water storage also contributes significantly to total water storage changes, showing increases since 1981. Different from what may be expected due to global warming, simulated global snow storage does not decrease over time (Table 7).

7.3.3 Water use components

For the time period 1991–2016, Table 8 presents global sums of annual sectoral potential withdrawal water uses and consumptive water uses as well as the respective fractions that are taken from groundwater (Sect. 3.3). Potential net abstractions from surface water (groundwater) are calculated by GWSWUSE to be 1406 (−153) km³ yr⁻¹ (Sect. 3.3). Actual net abstractions from surface water (groundwater) are computed by WGHM to be 1304 (−66) km³ yr⁻¹ due to restricted surface water availability and consequently less return flows to groundwater from irrigation with surface water. It is thus estimated that 98.8 % of potential consumptive water use of 1253 km³ yr⁻¹ could be fulfilled during 1991–2016, albeit causing groundwater depletion.