CWatM is able to use different datasets of meteorological forcing for the current climate – e.g., MSWEP (Beck et al., 2017), WFDEI (Weedon et al., 2014), PGMFD (Sheffield et al., 2006), GSWP3 (Kim et al., 2012), or EWEMBI (Lange, 2018) – or future climate projections from different general circulation models (GCMs) (e.g., data from ISIMIP project, Frieler et al., 2016). CWatM can use the netCDF4 repositories of original meteorological forcing without reformatting. As long as the forcing data are using the CF 1.6 Convention, CWatM takes care of the different names of the input variables and divides the dataset for the catchment or global scale, depending on a mask map or predefined rectangular selection. The forcing data are automatically regridded to the model grid (e.g., 30′′ or 5′) using the delta change method (Moreno and Hasenauer, 2016; Mosier et al., 2018) based on high-resolution monthly data from WorldClim version2 (Fick and Hijmans, 2017).

Depending on the method used for calculating potential evaporation, e.g., Penman–Monteith method (Allen et al., 1998), Hargreaves method (Hargreaves and Samani, 1958), or Hamon method (Hamon, 1963), different climate data are needed. As a default, the Penman–Monteith needs as inputs precipitation; humidity; long- and short-wave downward surface radiation fluxes; maximum, minimum, and average 2 m temperature; 10 m wind speed; and surface pressure. Temperature data are additionally needed to distinguish between snow and rain.

Potential reference crop evaporation rate (ET0) is calculated from a hypothetical reference vegetation with specific characteristics and unlimited availability of water (Allen et al., 1998). In the same way, the potential evaporation of an open water surface (EW0) is calculated. ET0 and EW0 are treated as pure climatic variables, because for calculation purpose they are not influenced by land cover or soil properties. In reality, the potential evapotranspiration might be different to ET0 due to differences in vegetation characteristics, aerodynamic resistance, or surface reflectivity (albedo). To account for the variability of vegetation, ET0 is multiplied by an empirical “crop coefficient” (kcrop) that lumps these differences into one factor, yielding a potential crop evapotranspiration rate (ETcrop). The method used here is based on work described in Allen et al. (1998) and Supit and van der Goot (2003).

Precipitation is split into rainfall and snow, depending on the temperature. If the average temperature is below 1 ∘C (default, but can be changed), all precipitation is assumed to be snow. For large grid cells, e.g., 0.5∘ or 5′ resolution, there is a considerable subgrid heterogeneity in elevation and therefore in temperature and snow accumulation and melt (Anderson, 2006). Because of this, snow accumulation and melt are modeled in up to 10 separated elevation zones on the subgrid level using different elevation zones and a fixed, defined moist adiabatic lapse rate.

Snow accumulates until it melts or evaporates. The rate of snowmelt is estimated using a degree-day factor method, which take into account the fact that snowmelt increases when it is raining (Speers and Versteeg, 1979): 1M=Cm⋅CSeasonal(1+0.01⋅RΔt)(Tavg-Tm)⋅Δt, where M is snowmelt per time step (mm), R is rainfall intensity (mm d-1), Δt is time interval (d), Tm is equal to 0 ∘C, Cm is the degree-day factor (mm ∘C-1 d-1), and CSeasonal is the seasonal variable melt factor.

CSeasonal is a factor depending on the day of the year, which varies the snow melt rate. A similar factor is used in several other models (e.g., Anderson, 2006; and Viviroli et al., 2009). At high altitudes the model tends to accumulate snow without any melting loss, because temperature never exceeds 1 ∘C. In these altitudes snow is accumulated and is converted into firn, which is then converted into ice as glaciers move to lower regions over decades or even centuries. In the ablation area, the ice is again melted. In CWatM this process can be optionally simulated by melting the snow at higher altitudes on an annual basis over summer using a higher degree-day factor and temperature from a lower subgrid zone. Hydrological processes occurring near the soil surface are affected and halted if the soil surface is frozen. To estimate whether the soil surface is frozen, a frost index F is calculated to estimate whether the soil surface is frozen based on Molnau and Bissell (1983). The frost index changes by day at a rate given by 2dFdt=-(1-Af)F-Tav⋅e-0.04⋅K⋅ds/wes, where dF/dt is given (∘C d-1), Af is the decay coefficient (here 0.97 d-1), K is snow depth reduction coefficient (here 0.57 cm-1), ds is grid average of depth of the snow cover (mm equivalent water depth), and wes is snow water equivalent.

For each time step, the value of F (∘C d-1) is updated as 3F(t)=F(t-1)+dFdtΔt. The soil is considered frozen when the frost index is above a critical threshold of 56; then, every soil process in the first two layers will be stopped. Precipitation bypasses soil and is transformed into surface runoff until the frost index is again lower than 56.

The calculation for interception and evaporation is based on Allen et al. (1998). For each land cover class, a maximum interception storage is defined. Interception storage can be filled by rainfall and depleted by evaporation using potential evaporation from open water. The leftover interception storage is added to the water available for infiltration in the other time step. Evaporation from soil is calculated using the potential reference evapotranspiration rate multiplied by a soil crop factor (default: 0.2). Evaporation from sealed area or open water is calculated using the potential evapotranspiration for the open water rate multiplied by a factor (defaults: 0.2 for sealed, 1.0 for water).

Potential transpiration from plants is calculated using the potential reference evapotranspiration multiplied by a crop-specific factor available as a spatially distributed dataset for each land cover type for every 10 d over a year. The crop coefficient is aggregated from MIRCA2000: a global dataset of monthly irrigated and rainfed crop areas (Portmann et al., 2010). The actual transpiration rate depends on the available water and on the ability of the crop type to deal with water stress. The energy already used up for the evaporation of intercepted water is subtracted here in order to respect the overall energy balance. The actual transpiration rate is reduced by a water stress factor which takes into account the ability of the crop to deal with water stress and an index of water stress of the soil: 4rws=(w1-wwp1)(wcrit1-wwp1), where rws is the reduction factor because of water stress, w1 is soil moisture in the two upper soil layers (mm), wwp1 is soil moisture at wilting point (soil moisture potential pF 4.2), and wcrit1 is soil moisture below which water uptake is reduced and plants start closing their stomata.

The critical amount of soil moisture is calculated as 5wcrit1=(1-p)⋅(wfc1-wwp1)+wwp1p=1/0.76+1.5⋅Tmax⁡-0.1⋅(5⋅Cropgroupnumber), where p is soil depletion fraction; wfc1 is soil moisture at field capacity; and Cropgroupnumber is the crop group number, which is an indicator of adaptation to dry climate (e.g., olive groves are adapted to dry climate and can therefore extract more water from soil that is drying out than rice can).

The actual transpiration Ta is calculated as 6Tact=rWS⋅Tpot. The procedure for estimating p and Rws is described in detail in Supit and van der Goot (2003).

To estimate the infiltration capacity of the soil, the approach of Xinanjiang (also known as VIC/ARNO model) (Zhao and Liu, 1995 and Todini, 1996) is used. The saturated fraction of a grid cell that contributes to surface runoff is related to the overall soil moisture of a grid cell through a nonlinear distribution function. The saturated fraction As is approximated by the following distribution function: 7As=1-1-w1ws1b, where ws1 and w1 are the maximum and actual soil moisture in the upper two soil layers and b is an empirical shape parameter. 8INFpot=ws1b+1-ws1b+11-(1-As)b+1b To simulate the preferential bypass flow of the soil, a fraction of the water available for infiltration is passed directly to the groundwater zone. The fraction is calculated as a function of the relative saturation of the first two soil layers. 9Dpref,gw=Wavw1ws1cpref, where Dpref,gw is preferential flow per time step, Wav is available water for infiltration, and cpref is empirical shape parameter.

A preferential flow component that lets more water bypass the soil as the soil gets wetter is calculated.

The actual infiltration INFact is calculated as 10INFact=min⁡INFpotWav-Dpref,gw.

Unsaturated flow and transport processes can be described with the 1D Richard equation, which requires a high spatiotemporal distribution of the soil's hydraulic properties and a numerical solver. 11ΔθΔt=ΔΔzKθΔhθΔz-1-Sθ(1D Richard equation), where θ is soil volumetric moisture content [L3L-3], t is time [T], h is soil water pressure head [L], K(θ) is unsaturated hydraulic conductivity [LT-1], z is vertical coordinate, and S is the source–sink term [T-1]

In order to apply an analytical and faster solution, Van Genuchten (1980) hydraulic functions based on the model of Mualem (1976) were adopted. It assumes a matric potential gradient of zero, which implies a flow that is that is always in a downward direction at a rate equal to the conductivity of the soil, and free drainage as the lower boundary condition in the lowest soil layer. The relationship between hydraulic conductivity and soil moisture status is described by the Van Genuchten (1980) equation. 12Kθ=Ksθ-θrθs-θr0.51-1-θ-θrθs-θr1/mm2(Van Genuchten equation), where Ks is saturated conductivity of the soil (m d-1); K(θ) is unsaturated conductivity; Θ, θs, and θr are the actual, maximum, and residual amounts of moisture in the soil (m); and m is calculated from the pore-size index (λ): m=λλ+1.

The soil hydraulic parameters Θ, θs, θr, λ, and Ks are needed to simulate soil water transport for the Van Genuchten model and are derived via a pedotransfer function (e.g., model Rosetta of Zhang and Schaap, 2017) from standard soil properties (soil texture, porosity, organic matter, and bulk density).

Once the unsaturated conductivity for each soil zone is determined, the water flux to the next zone can be estimated. At a time step of 1 d and high K(θ), the vertical flux can exceed the available soil moisture: 13Kθ>θ-θr. Therefore, the soil moisture equation has to be solved iteratively on a subdaily time step.

Capillary rise occurs only when the groundwater level is close to the surface. CWatM estimates the total fraction of the area with groundwater level of between 0 and 5 m from the surface in discrete steps and calculates the flux from groundwater to the soil layer based on unsaturated conductivity and field capacity (Wada et al., 2014).

Groundwater storage and baseflow are modeled using a linear reservoir approach as in LISFLOOD (De Roo et al., 2000; Udias et al., 2016). The groundwater zone is filled by the water percolating from the lower soil zone and the preferential flow and is emptied by capillary rise and baseflow. The outflow from the groundwater zone is given by 14Qbase=1TbaseStorage=RcoeffStorage, where Qbase is baseflow or outflow from the groundwater zone, Tbase is a groundwater reservoir constant in days, Storage is water stored in the groundwater zone, and Rcoeff is a recession coefficient of the groundwater zone.

For considering lateral fluxes among grid cells and the explicit computation of groundwater levels over finer spatial domains, CWatM has an option to couple with MODFLOW (McDonald and Harbaugh, 1988, Harbaugh, 2005) using the FloPy Python package (Bakker et al., 2016) in a similar way to PCR-GLOBWB (Sutanudjaja et al., 2014). The 5′ resolution version of CWatM is coupled with a one-layer MODFLOW model at a finer MODFLOW resolution (from 4 km to 400 m) with the aim of integrating the small-scale topographic control. The coupling is made on a daily to weekly base water balance.

CWatM simulates the vertical soil water flow in three soil layers, while MODFLOW simulates lateral groundwater flows. CWatM-MODFLOW is technically coupled (using the Drain package) via capillary rise from groundwater to the soil zones, groundwater recharge from the soil zones, and baseflow outflow from groundwater to the river network system. As the MODFLOW resolution can be smaller than the CWatM resolution, the CWatM mesh is subdivided into two parts: one part where groundwater recharge occurs and one part where capillary rise from groundwater occurs. The area of each part is determined by the percentage of MODFLOW cell, where the water level reaches the lower soil layer inside a CWatM mesh. To distinguish whether the groundwater flow to the surface will be attributed to capillary rise or baseflow, a percentage of rivers is attributed to each MODFLOW cells and calculated based on a 200 m resolution topographic map. Aquifer properties, like transmissivity or aquifer thickness, are estimated using the approach of de Graaf et al. (2015) and Gleeson et al. (2011). The results presented in Sect. 5 of this work are calculated using the simplified linear reservoir approach.

The process between runoff generation and river routing for each grid cell is called runoff concentration. The runoff generated from each cell is routed to the corner of each cell. Depending on land cover class, slope, and runoff group (surface, interflow, or baseflow), a concentration time (peak time) is determined. The total runoff for a grid cell is then calculated using a triangular weighting function. 15Qt=∑landcover∑runoff∑imax⁡ciQrunofft-i+1, where Q(t) is the total runoff of a grid cell of a time step, runoff is the runoff component (surface, interflow, baseflow), Qrunoff is the runoff of land cover class of a runoff component, t is time (1 d), and c(i) is a triangular function: 16ci=∫i-1i2max⁡-u-max⁡2⋅4max⁡2du.

Flow through the river network is simulated using kinematic wave equations. The basic equations used are the equations of continuity and momentum. The continuity equation is 17ΔQΔx+ΔAΔt=q, where Q is channel discharge (m3 s-1), A is cross-sectional area of the flow (m2), and q is the amount of lateral inflow per unit flow length (m2 s-1).

The momentum equation can also be expressed as in Chow et al. (1998): 18A=α⋅Qβ. The coefficients α and β are calculated by putting in Manning's equation. This leads to a nonlinear implicit finite-difference solution of the kinematic wave if you transform the right side: 19ΔtΔxQi+1j+1+αQi+1j+1β=ΔtΔxQij+1+αQi+1jβ+Δtqi+1j+1+qi+1j2, where J is time index, I is the space index, and α and β are coefficients.

With the coefficients α and β, the nonlinear equation can be solved for each grid cell and for each time step using an iterative approach given in Chow et al. (1998). The coefficients can be calculated using Manning's equation. 20A=n⋅P2/3S03/5Q3/5, where n is Manning's roughness coefficient, P is wetted perimeter of a cross section of the surface flow (m), and S0 is the topographical gradient.

Solving this for α and β gives 21α=nP2/3S0βandβ=0.6, where P is the wetted perimeter approximated in CWatM: P equals channel width plus 2 times the channel bankfull depth, n is Manning's coefficient, and S0 is gradient (slope) of the water surface: S0 equals the change in elevation divided by the channel length.

To calculate α, CWatM uses a fixed network depending on the spatial resolution, and, for each grid cell, the channel width, depth, length, gradient, and Manning's roughness have to be known. As water can travel a distance greater than a cell size in 1 d, river routing and the lake and reservoir routines are performed on a subdaily time step, based on the chosen spatial resolution.

Reservoirs and lakes (RL), based on the HydroLakes database (Messager et al., 2016; Lehner et al., 2011), are simulated as part of the channel network. Using the approach of Hanasaki et al. (2018) and Wisser et al. (2010), we distinguish between global RL and local RL. Global RL are located in the main channel of a grid cell with a catchment upstream of this grid cell. Local RL are more or less situated inside one grid cell at the tributaries of the main channel and not attached to the main river. Local RL are defined in CWatM depending on the spatial resolution. All RL with an RL area of less than 200 km2 at 0.5∘ (5 km2 for 5′) or with a watershed of less than 5000 km2 at 0.5∘ (200 km2 for 5′) are defined as “global” RL. The approach for calculating water storage and outflow of RL is the same for local and global RL, but the retention effect of local RL will be calculated during the runoff concentration process within a grid cell, while the effect of global RL will be calculated during the river routing process and includes the whole river network of a catchment.

The method of simulating reservoir operations is taken from LISFLOOD (Burek et al., 2013). A total storage capacity S is assigned to each reservoir, and the fraction of filling of a reservoir is calculated. Three filling levels are defined. (a) The “conservative storage limit” fraction because a reservoir should never be completely empty (default set to 10 % of the total storage). For prevention of damage in case of flooding, a reservoir should not be filled to the full storage capacity. (b) The “flood storage limit” (Lf) represents this maximum allowed storage fraction (default set to 90 % of the total storage); (c) the “normal storage limit” (Ln) defines the buffering capacity and the available storage of a reservoir between Ln and Lf.

Another three parameters define how the outflow of a reservoir is regulated. (a) Each reservoir has a “minimum outflow” Omin. The default is set to 20 % of the average discharge, e.g., for ecological reasons. (b) A maximum possible outflow or the “non-damaging outflow”, Ond, is defined which causes no problems downstream in case of flood. The default for this outflow is set to 400 % of the average discharge. (c) Between the state of flood and normal storage limit, a reservoir is managed as much as possible to deliver a constant outflow so that there is also a constant energy output from hydropower generation. “Normal outflow”, Onorm, is set as a default value to average discharge.

The outflow Ores, is calculated depending on the fraction of the filling of the reservoir as 22Ores=min⁡Omin,1ΔtF⋅SF≤2Lc;23Ores=Omin+Onorm-OminF-2LcLn-2LcLn≥F>2Lc;24Ores=Onorm+F-LnLf-Ln⋅max⁡Ires-Onorm,Ond-OnormLf≥F>Ln;25Ores=max⁡F-LfΔtSOndF>Lf; where S is reservoir storage capacity (m3), F is reservoir fill fraction (1 at total storage capacity) (–), Lc is conservative storage limit (–), Ln is normal storage limit (–), Lf is flood storage limit (–), Omin⁡ is minimum outflow (m3 s-1), Onorm is normal outflow (m3 s-1), Ond is non-damaging outflow (m3 s-1), and Ires is reservoir inflow (m3 s-1).

Lakes are simulated using the modified Puls approach (Chow et al., 1998, Maniak, 1997) similar to the approach as in LISFLOOD (Burek et al., 2013). As lake inflow, the channel flow upstream of the lake location is used. As lake evaporation, the potential evaporation rate of an open water surface is taken. The modified Puls approach assumes that lake retention is a special case of flood retention with horizontal water level and the equations of river channel routing (see Sect. 2.3.10, “River routing”) can be written as 26QIn1+QIn22-QOut1+QOut22=S2+S1Δt, where QIn1 is inflow to lake at time 1 (t), QIn2 is inflow to lake at time 2 (t+Δt), QOut2 is outflow from lake at time 1 (t), QIn2 is outflow from lake at time 2 (t+Δt), S1 is lake storage at time 1 (t), and S2 is lake storage at time 2 (t+Δt).

The change in storage is inflow minus outflow and open water evaporation. The equation is solved by calculating the lake storage curve as a function of sea level, S=f(h), and the rating curve as a function of sea level, Q=f(h). Lake storage and discharge are linked by the water level.

The assumptions made here to simplify the equation are the following.

A modification of the weir equation by Poleni from Bollrich and Preißler (1992) is assumed:27Q=μcb2g⋅H3/2=α⋅H3/2.

Irrigation is by far the biggest consumer of water at around 70 % of global gross water demand (Döll et al., 2009). Irrigation water demand is calculated by following the method developed in PCR-GLOBWB (Wada et al., 2011, 2014) using the MIRCA2000 crop calendar of Portmann et al. (2010) and irrigated areas from Siebert et al. (2005) to account for seasonal variability, different crops, and different climatic conditions. MIRCA2000 explicitly considers multiple cropping. The associated crop- and stage-specific crop coefficients are derived from the Global Crop Water Model (Siebert et al., 2010). The crops are then aggregated into paddy and non-paddy and the crop coefficients are similarly aggregated by weighing the area of each crop class. Then, the cell-specific crop coefficient as it changes in time is related to the crops growing in this cell, inclusive of multiple cropping considered in the MIRCA2000 dataset. We refer to Wada et al. (2014) for the detailed descriptions. In brief, irrigation and water withdrawal and consumption are calculated separately for paddy (rice) irrigation and irrigation of other crops. To represent flooding irrigation of paddy fields, a 50 mm surface water depth is maintained until a few weeks before the harvest. Paddy irrigation demand is a function of the storage change of the surface water layer, net precipitation, infiltration to lower soil layers, and open water evaporation from the surface water layer. For non-paddy irrigation, the irrigation demand is calculated using the difference between total and available water in the first two soil layers where total water is equal to the amount of water between field capacity and wilting point and available water is equal to the amount of water between current status and wilting point. Water withdrawal is calculated using the water efficiency rate of FAO (2012) and Frenken and Gillet (2012).

Livestock water demand is assumed to be the same as livestock water consumption and is calculated by the number of livestock in a grid cell with the daily drinking water requirement per individual livestock type (six livestock types in total) and per air temperature for seasonal change in drinking water requirement. The approach is taken from Wada et al. (2011).

Calculation of industrial water demand also follows the method of Shen et al. (2008) and Wada et al. (2011) using the gridded industrial water demand data for 2000 from Shiklomanov (1997) and multiplying it by water use intensity. Water use intensity is a function of gross domestic product (GDP), electricity production, energy consumption, household consumption, and a technological development rate per country. Domestic water demand is calculated by multiplying the population in a grid cell by a country-specific per capita domestic water withdrawal rate taken from FAO (2007) and Gleick et al. (2009). Adjustments for air temperature and for country-based economic and technological development are carried out based on the approach of Wada et al. (2011).

The approach for calculating water withdrawal from different sources, water consumption, and return flows is based on the work of de Graaf et al. (2014), Wada et al. (2014), Sutanudjaja et al. (2018), and Hanasaki et al. (2018). Water demand can be fulfilled by surface water and groundwater. Based on the work of Siebert et al. (2010), groundwater for irrigation can be only used in areas that are equipped for irrigation. Groundwater is, at first, only abstracted from the renewable groundwater storage. Water demand that cannot be fulfilled purely from groundwater uses surface water from rivers, reservoirs, and lakes. An environmental flow cap can be set in order to sustain environmental needs for rivers, reservoirs, and lakes. If water demand still cannot be fulfilled, additional water is taken from nonrenewable groundwater. At 5′ resolution, water demand cannot always be covered by surface or groundwater resources in the same grid cell; therefore, CWatM uses the approach of LISFLOOD (Burek et al., 2013) and takes water from up to five grid cells downstream moving along the local drainage direction.

Return flow and associated losses (i.e., conveyance, application) are calculated using the approaches of LPJmL (Rost et al., 2008) and H08 (Hanasaki et al., 2018). Return flow is the flow which is withdrawn from surface water or groundwater but is not consumed. For the return flow rate, we follow the approach of Hanasaki et al. (2018). For irrigation, the return flow is calculated using the irrigation efficiency by Döll and Siebert (2002). For domestic and industrial use, the return rate is based on Shiklomanov (2000) (i.e., 90 % for the industrial sector and 85 % for the domestic sector). Fifty percent of return water from irrigation is lost to evaporation and 50 % is returned to the channel network. This assumption is taken from Hanasaki et al. (2018). Domestic and industrial return flow 100 % is returned to the river channel network.

The essential component of the Water Futures and Solution Initiative of IIASA (Burek et al., 2016; Wada et al., 2016) is the assessment of the balance of water supply and demand for the present and into the future. With the support of the Government of Austria through the Austrian Development Agency (ADA), we aim to provide a deeper understanding of critical parameters for achieving water security in East Africa. This is in the context of competing demands for basic water supply, sanitation, food security, economic development, and the environment. UN-Water (2013, p. 1) defines water security as the following:

The capacity of a population to safeguard sustainable access to adequate quantities of and acceptable quality water for sustaining livelihoods, human well-being, and socio-economic development, for ensuring protection against waterborne pollution and water-related disasters, and for preserving ecosystems in a climate of peace and political stability.

Water security is also a key ambition expressed in the “Vision 2050” of the East African Community (EAC, 2016) as rapid growth of the economy and population and a high rate of urbanization are expected for the region and will lead to increased water demand in all sectors as well as further pressure on the water quality status.

The examples of operational areas for CWatM in this paper are not presented with specific results in mind, nor do they reflect results from the project's intensive stakeholder processes. They are there to demonstrate the value of a global hydrological model used in a regional case study that combines the spatiotemporal scale dependencies of water systems produced through a scenario analysis designed to include both the regional and global scales. An “East Africa Regional Vision Scenario” (EA-RVS) was developed (Tramberend et al., 2019, 2020), based on regional visions, and we used available regional scenarios and data that were developed in the context of global studies. As well as regional visions, the study also integrates into the widely applied global scenario development process of the Intergovernmental Panel on Climate Change (IPCC). It is characterized by a Scenario Matrix Architecture (van Vuuren et al., 2014) including the community-developed Shared Socioeconomic Pathways (SSPs) (Jiang and O'Neill, 2017) and the Representative Concentration Pathways (RCPs) (van Vuuren et al., 2011) for the characterization of climate change.

The study area, the extended Lake Victoria basin (eLVB), is a transboundary basin in the tropics. It comprises the headwaters of the Nile and includes an area of over 460 000 km2. The Equator crosses the region approximately in the middle of the eLVB just south of Kampala. The eLVB includes the source of the Nile and major lakes in East Africa, foremost Lake Victoria, Lake Albert, Lake Edward, and Lake Kyoga. The eLVB has been subdivided into interconnected subbasins. According to the water flow regime, we have aggregated the 61 basins into eight major basins (see Fig. 6). The CWatM model setup uses the default global dataset at 5 arcmin. Discharge data for calibrating river discharge were made available courtesy of the Ministry of Water and Environment, Uganda. Calibration is performed for three stations. The calibration parameters are valid for the subbasin up to the gauging station. The upstream station is calibrated using the best fit of the downstream calibrated subbasins. The 10 years of available observed data are used for the calibration period. Therefore, no other time period is available for a validation period.

For assessing climate change impact, RCP6.0 was chosen as the most plausible future for East Africa by the “EAC Vision 2050” (EAC, 2016) even though it represents a rather pessimistic outlook of global temperature increases despite being published after the Paris Climate Agreement of 2015. We have chosen the two general circulation models (GCMs) of HadGEM2-ES and MIROC5 out of the four GCMs (see Table 8) used in ISIMIP 2b (Frieler et al., 2016) as being the most feasible for eLVB as the discharge results that were run with CWatM for the historical runs of the GCMs GFDL-ESM2M and IPSL-CM5A-LR showed a large discrepancy from historical results.

Discharge is the variable which incorporates all the meteorological and hydrological processes into a basin and encompasses all the storage components in a basin (i.e., soil, groundwater, lakes, and reservoirs) Especially with the large lakes in the basin, discharge in eLVB has a long memory of past conditions.

The seasonal pattern of discharge in Fig. 7 shows more discharge for 2040 (10-year period 2036–2045) and 2050 (10-year period 2046–2055) in the river system from Lake Victoria, especially for the 2040 period. This is due to a wetter period of weather in the two GCMs from 2038 to 2049 and the strong memory effect of groundwater and the lakes. It also shows the big influence of interannual variability in the eLVB. Even if a general trend of less runoff in the 2050 period can be detected, long-lasting periods of wetter conditions can nevertheless be superimposed over this trend. Because of the strong interannual variability in the lower latitudes, it is difficult to assess the effect of a general climate change impact towards a wetter or drier climate. But under climate change, southwestern Uganda will show generally drier conditions than the western part of the eLVB.

Available water resources per capita, the Water Crowding Index (WCI) (also called the Falkenmark indicator), is one of the most widely used measures of water stress (Falkenmark et al., 1989). Based on per capita water availability, the water conditions in an area can be categorized into different categories of stress expressed as cubic meters (m3) of water available per capita and per year. Another indicator is the Water Resources Vulnerability Index (Raskin et al., 1997) that is also known as Water Exploitation Index (WEI) (EEA, 2005), defined as the ratio of total annual withdrawals for human use to total available renewable surface water resources. Regions are considered water scarce if annual withdrawals exceed the percentage of annual supply (Alcamo et al., 2003). The thresholds for both indicators are shown in Table 9.

The WCI and WEI are mainly shown as annual indicators, but in regions with high intra-annual variability the rainy seasons show a different picture from that of the dry season. An example in Fig. 8 shows the WCI and WEI for the dry season and the most water-scarce month, July, for 61 subbasins of the extended Lake Victoria basin by comparing the situations of 2010 and 2050. The figure shows that there is a clear increase in the WCI. While in the current situation (2010) about half of the subbasins are exposed to some level of water scarcity with some subbasins indicating absolute water scarcity, in 2050 almost all subbasins that are neither directly crossed by the river Nile nor adjacent to a lake experience stress or scarcity and many of them absolute water stress. The water resource availability for the WEI is also based on the RCP6.0 climate scenario and includes the effect of human consumption and effects of land use change up to 2050. Looking at this index for the month of July only, it shows that 9 out of 61 subbasins are likely to experience water scarcity and even severely water-scarce situations by 2050. Such subbasins are mainly located at the south and southeastern shores of Lake Victoria and in densely populated areas of Rwanda and Burundi.

Interestingly, the WEI shows a much lower signal of water scarcity compared to the WCI. The WCI assumes that, regardless of the socioeconomic conditions, every person on the globe has the same “water demand entitlement”. The Water Exploitation Index is based on the in situ situation and on balancing changing water availability and water demand. The fact that both indices show a rather different picture might be interpreted as an indication of economic water scarcity. The situation of low economic development for the extended Lake Victoria basin may still prevail in 2050 (at least compared to the global average). This is the main reason for the relatively low actual water demand compared to global averages and therefore relatively low water scarcity signal for the WEI compared to the WCI.

The hydrological model CWatM is intended to be scalable and can be applied over finer spatial scales (e.g., the basin). CWatM has been calibrated for the Zambezi, using six subcatchments and measured discharge provided by the Global Runoff Data Centre (2007). Figure 9 shows two time series of measured vs. simulated river discharge, and the comparison shows good agreement of the modeled discharge with the measured data. The station Matundo-Cais is downstream of the two big reservoirs Kariba Dam and Cahora Bassa, which are included in the model. The reservoir operations are calculated with the approach in Sect. 2.3.11.

By comparing the outputs of the hydrological model ensemble, we see that, especially for sub-Saharan Africa, there is a strong overestimation of river discharge, which indicates an erroneous picture if compared, for example, to water demands for calculating water scarcity. Figure 10 shows a comparison of discharge for the Lukulu in the Zambezi basin of different hydrological models as a violin plot which shows the probability density of the data. While a box plot shows some statistics like mean and quartiles a violin plot shows the full distribution of the data.

The GHMs in Fig. 10 use the WFDEI (Weedon et al., 2014) as forcing meteorological data from 1981 to 2004. Apart from WaterGAP and CWatM (both calibrated), one can see a strong overestimation of discharge for all other models compared to the observed discharge and some models also show a different shape than the observed data.

Average discharge is overestimated for the noncalibrated models from 2 up to 3 times and maximum discharge up to 7 times. This shows the need to put efforts into calibration of the hydrological model for regional applications to be in line with measured water resources and to minimize the uncertainty from hydrological modeling. Setting up model calibration has been time-consuming but inevitable for the Zambezi case study.

Calibration for the Zambezi basin is performed for six stations (Lukulu, Kongola, Katima, Kafue Hook, Luangwa Road Bridge, Tete – see Fig. 6). The calibration parameters are valid for the subbasin up to the gauging station. The upstream station is calibrated using the best fit of the downstream calibrated subbasins. The parameter set is valid for the subbasin except for the downstream subbasins which have their own parameter sets.

In a second phase, the CWatM calibrated model is used to assess water scarcity until 2050 in the Zambezi basin. Water resources at each grid cell are dependent on climate; water management (e.g., reservoirs); and water use for irrigation, livestock, domestic, or industry. For each cell (at 5′) (see Fig. 11) and for aggregated regions, water resources can be related to water demand from different sectors. Results from the distributed hydrological model CWatM are aggregated into 21 subbasins (see Fig. 12) based on a regional distribution shared by the Zambezi Water Commission (http://zamwis.wris.info, last access: 27 June 2020). In addition, the regions of Kariba, Kafue, and Tete are split into, respectively, four, two, and four subbasins to look specifically into the more densely populated areas.

Projection of future water resources builds on quantifications of climate scenarios CMIP5 (Distributed by the Coupled Model Intercomparison Project (CMIP); see https://pcmdi.llnl.gov/index.html, last access: 27 June 2020) based on the RCPs from the Inter-Sectoral Impact Model Intercomparison Project (ISI-MIP) (Frieler et al., 2016). We applied climate change projections from four GCMs (see Table 8) for a first setting of RCP6.0. Land use data projection is used from the GLOBIOM model (Havlík et al., 2013). Nineteen different crop types with different classes of farming intensity and eight land use classes (e.g., forest, build up classes) of GLOBIOM output, for different RCPs and SSPs, are transformed to fit into the arrangement of six land use classes of CWatM.

Water demand for agriculture is taken from calculations within CWatM. Water demand for domestic, livestock, and industry is calculated within CWatM using the approach of Wada et al. (2011). The socioeconomic background needed for this approach uses data and methods for spatial disaggregation for the SSP2 scenario from Jones and O'Neill (2016), Gao (2017), Klein Goldewijk et al. (2017), Kummu et al. (2018), and Gidden et al. (2018).

The WEI is defined in Falkenmark et al. (1989), Falkenmark (1997), and Wada et al. (2011) as comparing blue water availability with net total water demand. A region is considered “severely water stressed” if the WEI exceeds 40 % (Alcamo et al., 2003). The yearly WEI in Fig. 12 shows no water stress for the whole basin in 2010, but water stress will intensify up to 2050 for the business-as-usual (BAU) scenario (composed of the SSP2 and RCP6.0 scenarios), mainly due to agricultural and domestic water demand increasing by a factor of 5; as annual mean river discharge is only increasing by 6 %. August is chosen for monthly comparison as this is the month with the highest rate of water withdrawal (WW) and a mean monthly discharge (MMD) that is only slightly higher than in November. The eastern part of the Zambezi basin, except for the main course of the Zambezi river, was already showing severe water stress in 2010. This will increase in 2050, but the western part is still not suffering from water stress.