Spatial and Temporal Variability in Hydrological Responses of the Upper Blue Nile basin, Ethiopia

To assess the spatial and temporal availability of blue and green water for upand downstream stakeholders, the hydrological responses of the upper Blue Nile basin in the Ethiopian Highlands was modelled and analysed with newly generated input data, such as soil and land use maps. To consider variations in the seasonal climate, topography, soil, land use, and land management, the upper Blue Nile basin was modelled in seven major sub-basins. The modelling showed significant spatial and temporal differences in the hydrological responses of different sub-basins and years. The long-term mean annual drainage ratios of the watersheds range from <0.1 to >0.65, and the annual drainage ratio of one sub-basin can vary from 0.22 to 0.49. Steep slopes, shallow soils, and cultivated areas increase the drainage ratios due to high surface runoff, low soil moisture content, and a smaller share of evapotranspiration. Various climate change scenarios predict more precipitation, and land use change scenarios foresee a higher share of cultivated areas due to population growth. In view of these trends, results from our study suggest that drainage ratios will increase and more available blue water can be expected for downstream stakeholders.


Introduction
Most of the water used in the lowlands between Ethiopia and the Mediterranean Sea originates in the Ethiopian Highlands.The Blue Nile basin alone contributes 60%-70% of the water in the River Nile flowing through Sudan and Egypt [1,2].In Sudan and Egypt, up to 95% of the water used is blue water from the Nile [3].By contrast, in the headwaters, until recently, more than 95% of the agricultural area was rained, thus using almost exclusively green water [4,5].Driving forces, such as economic development and population growth, are increasing the demand for water along the entire length of the Nile for food and energy production, and domestic and industrial use.New dams and intensification of agriculture are changing the temporal and spatial use of blue and green water along the Nile, affecting drainage ratios and water availability.Knowledge about the characteristics of different catchments and each catchment's hydrological response is essential to predict the influences of, for example, land use-, irrigation-, and climate change on future spatial and temporal water availability for up-and downstream stakeholders.
In the last few years, various studies were conducted on discharge and precipitation along the upper Blue Nile (Abay) basin.These studies investigated different discharge and precipitation trends [6,7] or modelled climate change scenarios [8,9], analysed different models with different discharge data from the upper Blue Nile [10][11][12][13][14][15][16], and calibrated discharge to model sediment losses along the upper Blue Nile basin [14,17].Other studies looked at evaporation [18] or different satellite-estimated or measured rainfall data and precipitation distribution in the Blue Nile basin [2,[19][20][21].However, owing to the scarcity of data and the large size of the upper Blue Nile basin, these studies used a digital elevation model (DEM) with a resolution of 90 m or a higher pixel size and a very general soil and land use map.In addition, most studies incorporated the data of only a few weather stations for a few years in their model and calibrated and validated it with data from one or two gauging stations along the upper Blue Nile Basin.More detailed discharge modelling was conducted by many studies at the catchment level in different watersheds in the upper Blue Nile basin [22][23][24][25][26][27][28][29].Lemann et al. [30] showed the different hydrological responses to different rainfall patterns and different meteorological conditions in the upper Blue Nile basin, but only at the sub-basin level.Prior to this study, there was no detailed analysis of hydrological responses and discharge simulations over a longer time period at the national basin level, with a soil and land use map of a high spatial resolution and DEM.The heterogeneity of the seasonal climate, topography, soil and land cover, and land management cause big differences in discharge ratios in the Ethiopian Highlands and show the importance of studies with a higher temporal and spatial resolution [30].
The objectives of this study are therefore to generate a detailed overview of the temporal and spatial variations in the drainage ratios over the whole upper Blue Nile basin in the Ethiopian Highlands at the watershed level (mean size 500 km 2 ), and to analyse the influences of different parameters, such as soil cover, land use, and amount and intensity of rainfall.Other than the above mentioned studies, we used a DEM with a 30 m resolution, a newly compiled map with a soil-topography relationship, and a newly developed land use map served as a spatial basis for modelling discharge.To overcome the problem of incomplete and fragmentary temporal and spatial resolution of available weather data, we used data series from three climatic stations and from Climate Forecast System Reanalysis (CFSR), which were statistically tested with available measured data and excluded if the goodness of fit was unsatisfactory.This enabled a continuous modelling from 1982 to 2010.After new hydropower infrastructure was built, such as the Tana-Beles hydroelectric power plant in 2010, discharge was artificially controlled and could no longer be reasonably modelled.
To consider the different hydro-climatic conditions in the Ethiopian Highlands, the whole upper Blue Nile basin was split into eight sub-basins (>3500 km 2 ).Such a splitting is assumed to help with locating inconsistencies or uncertainties during calibration of the sub-basins and to enable further analysis and follow-up modelling on the sub-basin level.Furthermore, no high computing power is needed for the modelling and calibration of smaller sub-basins, and processes can be distributed to different computers to save time.Discharge was modelled with the Soil and Water Assessment Tool (SWAT) [31], and calibrated and validated with available measured discharge data from the outlets of seven sub-basins using the Sequential Uncertainty Fitting (SUFI-2) programme [32,33].With the parameters giving the best objective function in the calibration process, discharge was simulated for the entire modelling period at the watershed level, and drainage ratios were calculated with precipitation data from the weather station closest to the centre of every watershed.
The simulations of the drainage ratio with a high spatial and temporal resolution allows detailed analyses of the impact of different parameters (e.g., precipitation, soil type, land use, and slope) on runoff generation.These model possibilities and knowledge gained will further help to assess and improve cultivation strategies in terms of blue and green water use for the long-term planning of local, national, and international water, energy, and food security.

Study Area
The upper Blue Nile basin originates in Lake Tana and has its outlet at the border to Sudan.The basin covers a large part of the Ethiopian Highlands (175,000 km 2 ), from an altitude of less than 500 meter above sea level at the Sudanese border to more than 4200 meter above sea level in the centre and the eastern escarpment of the Ethiopian Highlands (see Figure 1).The climate is dominated by the movement of air masses associated with the Inter-Tropical Convergence Zone (ITCZ).During the dry season from November to March, the highlands are affected by a dry north-eastern continental air mass.From March to May, the ITCZ brings a small rainy season (Belg) to the north-eastern part of the basin.Later in the year, the south-western airstream extends over the entire basin and causes the major rainy season (Kremt) from May to October [34].The Kremt accounts for a large proportion of the mean annual rainfall and this proportion generally increases with altitude [15].The movement of air masses and the different altitudes are the reason for the different rainfall patterns within the study area.While the northern, western, and southern parts of the study area have one prolonged rainy season from May to September, the eastern part is characterized by a bimodal rainfall regime.To capture these temporal and spatial differences of seasonal climate, the upper Blue Nile basin was split into eight sub-basins of major tributaries with available discharge data, where seven sub-basins where modelled, calibrated, and validated.The upper Blue Nile basin originates in Lake Tana and has its outlet at the border to Sudan.The basin covers a large part of the Ethiopian Highlands (175,000 km 2 ), from an altitude of less than 500 meter above sea level at the Sudanese border to more than 4200 meter above sea level in the centre and the eastern escarpment of the Ethiopian Highlands (see Figure 1).The climate is dominated by the movement of air masses associated with the Inter-Tropical Convergence Zone (ITCZ).During the dry season from November to March, the highlands are affected by a dry north-eastern continental air mass.From March to May, the ITCZ brings a small rainy season (Belg) to the north-eastern part of the basin.Later in the year, the south-western airstream extends over the entire basin and causes the major rainy season (Kremt) from May to October [34].The Kremt accounts for a large proportion of the mean annual rainfall and this proportion generally increases with altitude [15].The movement of air masses and the different altitudes are the reason for the different rainfall patterns within the study area.While the northern, western, and southern parts of the study area have one prolonged rainy season from May to September, the eastern part is characterized by a bimodal rainfall regime.To capture these temporal and spatial differences of seasonal climate, the upper Blue Nile basin was split into eight sub-basins of major tributaries with available discharge data, where seven sub-basins where modelled, calibrated, and validated.

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Lake Tana sub-basin The source of the Blue Nile, the Lake Tana sub-basin, is dominated by a large shallow lake and its surrounding floodplains.These wetlands and several water resource projects, such as hydropower schemes and dams for irrigation and flood control purposes [35], make modelling difficult, because only little data are available on these natural and human influences.We therefore did not model the Lake Tana sub-basin, but used discharge data from the outflow of Lake Tana from 1982-2010 as inflow to the Upper Abay sub-basin.Since the inauguration of the Tana-Beles hydropower scheme in 2010, the river regime has changed [36].However, as no data were available after this change, we were unable to reasonably model more recent runoff.

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Upper Abay sub-basin • Lake Tana sub-basin The source of the Blue Nile, the Lake Tana sub-basin, is dominated by a large shallow lake and its surrounding floodplains.These wetlands and several water resource projects, such as hydropower schemes and dams for irrigation and flood control purposes [35], make modelling difficult, because only little data are available on these natural and human influences.We therefore did not model the Lake Tana sub-basin, but used discharge data from the outflow of Lake Tana from 1982-2010 as inflow to the Upper Abay sub-basin.Since the inauguration of the Tana-Beles hydropower scheme in 2010, the river regime has changed [36].However, as no data were available after this change, we were unable to reasonably model more recent runoff.

• Upper Abay sub-basin
The Upper Abay sub-basin is not a tributary, but contains the upstream part of the upper Blue Nile basin between Lake Tana and the Dessie Bridge.Further upstream, no discharge data from the upper Blue Nile River or major tributaries were available.The outlet of Lake Tana was used as inlet discharge for the Upper Abay Sub-basin.The eastern part of the basin is dominated by two rainfall patterns, while the western part has a unimodal rainfall regime.These differences have an impact on plantation activities, and the cropping calendar varies greatly within the sub-basin.For this reason, the cropping calendar of all the watersheds east of the upper Blue Nile and the Beshilo River contains a second crop.In addition to selected CFSR climatic data, we used precipitation data from two observatories of the Water and Land Resource Centre (WLRC) at the eastern borders of the upper Blue Nile basin where data was available for more than 30 years.Average annual precipitation ranges from 500 mm in the northeast to 1750 mm in the northwest.
• Muger sub-basin More than 75% of the Muger sub-basin is cultivated, mainly with barley and teff.Annual precipitation of only 1200 mm is distributed over two rainy seasons, so we used the cropping calendar from the eastern part of the Blue Nile basin.Recent studies showed that the aquifer system of the Muger sub-basin has a hydraulic connection with the aquifer system of the Upper Awash basin, a basin which does not drain into the Blue Nile [37,38].

• Temcha sub-basin
The Temcha sub-basin is located in the southern Gojam region.More than 70% of the whole sub-basin is cultivated or used for pasture.At 1680 mm, the Temcha sub-basin has the highest average annual precipitation of the whole upper Blue Nile basin.However, the highest measured discharge peaks during the rainy season could still not be simulated with the available precipitation data.Rainfall data originates not only from CFSR, but also from the WLRC observatory at Anjeni [39].

• Didesa sub-basin
The Didesa River originates in the Mt.Vennio and Mt.Wache ranges, and is, together with the Anger River, the largest tributary of the upper Blue Nile basin in terms of the volume of water.In the highlands, long-term mean annual precipitation reaches up to 2000 mm, while the lower area receives on average less than 800 mm precipitation per year.

• Dabus sub-basin
The Dabus sub-basin drains the southwestern part of the Blue Nile basin.In its headwater is an area of wetlands of approximately 900 km 2 [16].The whole sub-basin has a size of 14,700 km 2 , over 40% of which is cultivated.

• Beles sub-basin
The Beles sub-basin, located in the western part of the upper Blue Nile basin, abuts the Tana basin and is today linked with the Tana Beles hydropower scheme.With the inauguration of this scheme in 2010, the drainage behaviour of Lake Tana changed and it was no longer possible to model the discharge of the whole upper Blue Nile basin, due to missing data from the outlets of Lake Tana.The size of the sub-basins was reduced to only 3500 km 2 and delimited by the Upper Main Beles gauging station, because of inconsistent available discharge data from the main outlet of the Beles River.The small sub-basin has on average 1570 mm precipitation per year, and is dominated by shrubland, grassland, and pasture (70%).

• Lower Abay sub-basin
The lower Abay sub-basin contains the area along the upper Blue Nile basin below the Didesa Bridge, which could not be modelled with larger tributaries.The Upper Abay and all the five modelled tributaries flow into this sub-basin and were included as basin inlets.

Hydrological Model
For this study, we used SWAT to simulate the discharge of the sub-basins in the upper Blue Nile basin.Other modelled physical processes, such as potential evapotranspiration and base flow [40], were calculated with the Hargreaves Method [41] and an automated base flow separation and recession analysis technique [42], respectively, and used to control the plausibility of the shares of these processes.However, due to a lack of measured data, they could not be calibrated and validated.The model requires input parameters, such as soils, land use, land management, topography, or climate data [43].It is designed to calculate runoff and sediments for individual drainage units, called hydrologic response units (HRUs), in generated sub-catchments.It also routes modelled discharge and sediment load towards the outlet of the basin [44].A more detailed description of the model can be found in many reviews of its performance and parameterization in Ethiopia and other regions [9,14,[45][46][47][48][49][50]].

Topographical and Land Use Data
For the topographic map this study used the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) Global Digital Elevation Model Version 2 (GDEM V2) from the Ministry of Economy, Trade, and Industry (METI) of Japan and the United States National Aeronautics and Space Administration (NASA) of a 30 m resolution [51] (see Appendix C).
Regarding land use and land cover (LULC) information, most available data sets were found to be outdated and produced with a spatial resolution insufficient to represent the heterogeneity of the study area, which was the main focus of this study.The data sets in question are the Global Land Cover Characterization (GLCC) database of the United States Geological Survey (USGS) with a spatial resolution of 1 km [17], the map from the Eastern Nile Technical Regional Office (ENTRO) with five dominant LULC categories [10], or the data from BCEOM [52] with seven dominant land cover categories [53,54].Other high resolution land use maps are only available for small watersheds, such as the land use maps from the Water and Land Resource Centre (WLRC) [55].Kassawmar et al. [56] produced a land cover dataset for the Ethiopian Highlands with a resolution of 30 m. Due to cloud and haze cover, it was not possible to use images from only one specific year.The applicability of such data sets for a similar purpose was explained in the Economics of Land Degradation (ELD) Ethiopia Case Study [57].For the present study, we needed additional land use classes that could explain the very heterogeneous land use, management, and practices.The required information was missing in the data set produced by Kassawmar et al. [56].For that reason, we added new classes, based on the 35 land cover classes used in the ELD Ethiopia Case Study.We identified the new classes by integrating different auxiliary data sets, such as farming, cropping system, and livelihood zone maps of the Food and Agriculture Organization (FAO) [58], agro-ecological zone maps [59], and local knowledge.All the different crops growing in the highlands of Ethiopia could not be distinguished at the pixel level with a 30 m × 30 m pixel resolution.Moreover, due to crop rotation practices, it was not reasonable to assign one land use category to a certain area.For these categories, e.g., BWTF (barley, wheat, and teff), the most prevalent crop types were selected and for the different crop parameters in SWAT, the average value of the three crop types was used (Figure 2 Appendix B).More than 20% of the whole upper Blue Nile basin is categorized as shrub/bushland (SHRB).This is because especially along the gorges and in the western part of the basin, towards the outlet, many areas are covered in different kinds of shrubs.Teff is the staple crop of Ethiopia and covers more than 13% of the study area (see Appendix D).It grows at a wider altitude range and exists in combination with other crops.Thus, the land use is characterized by a combination of teff with other land use categories, which include more than one crop type; BWTF (barley, wheat, and teff), COTF (corn and teff), BATF (barley and teff), and SGTF (sorghum and teff).The planting dates of the different crops were adapted according to the rainfall pattern.In the eastern part, where two rainy seasons allow the farmers to plant two crops on the same field in one year, the cropping calendar of Loetscher [60] was used.For the other part of the basin, with only one prolonged rainy season, the planting dates were adapted to the cropping calendar by Ludi [61].The growing duration of the different crop types was scheduled by pre-defined heat units and the auto-fertilization and autoirrigation option of SWAT were used to simulate crop growth.Tillage was adapted to the use of the traditional Ethiopian maresha plough with a random roughness (RRNS) of 25 mm, a depth of mixing (DEPTIL) of 150 mm, and a mixing efficiency of 0.3 (EFTMIX) [62,63].

Soil Data
The most detailed available soil information in Ethiopia at the basin level are from the Harmonized World Soil Database (HWSD) [64].However, because these soil data are not related to topography, Brunner [65] generated a soil map for Ethiopia with a soil-topography relationship, but with only the superordinate soil categories (see Appendix A).
To obtain a soil map with the soil-topography relationship from Brunner [65] and the specific soil categories of HWSD, we reclassified the map of Brunner with the soil categories of HWSD (see Figure 3).For the reclassification, we considered the spatial and geomorphological appearance of the different soil types.The 19 soil types (+water) of the new soil map of the upper Blue Nile basin were linked with the soil parameters of the SWAT database to run the model and to simulate discharge.More than 20% of the whole upper Blue Nile basin is categorized as shrub/bushland (SHRB).This is because especially along the gorges and in the western part of the basin, towards the outlet, many areas are covered in different kinds of shrubs.Teff is the staple crop of Ethiopia and covers more than 13% of the study area (see Appendix D).It grows at a wider altitude range and exists in combination with other crops.Thus, the land use is characterized by a combination of teff with other land use categories, which include more than one crop type; BWTF (barley, wheat, and teff), COTF (corn and teff), BATF (barley and teff), and SGTF (sorghum and teff).The planting dates of the different crops were adapted according to the rainfall pattern.In the eastern part, where two rainy seasons allow the farmers to plant two crops on the same field in one year, the cropping calendar of Loetscher [60] was used.For the other part of the basin, with only one prolonged rainy season, the planting dates were adapted to the cropping calendar by Ludi [61].The growing duration of the different crop types was scheduled by pre-defined heat units and the auto-fertilization and auto-irrigation option of SWAT were used to simulate crop growth.Tillage was adapted to the use of the traditional Ethiopian maresha plough with a random roughness (RRNS) of 25 mm, a depth of mixing (DEPTIL) of 150 mm, and a mixing efficiency of 0.3 (EFTMIX) [62,63].

Soil Data
The most detailed available soil information in Ethiopia at the basin level are from the Harmonized World Soil Database (HWSD) [64].However, because these soil data are not related to topography, Brunner [65] generated a soil map for Ethiopia with a soil-topography relationship, but with only the superordinate soil categories (see Appendix A).
To obtain a soil map with the soil-topography relationship from Brunner [65] and the specific soil categories of HWSD, we reclassified the map of Brunner with the soil categories of HWSD (see Figure 3).For the reclassification, we considered the spatial and geomorphological appearance of the different soil types.The 19 soil types (+water) of the new soil map of the upper Blue Nile basin were linked with the soil parameters of the SWAT database to run the model and to simulate discharge.

Climate and Hydrological Data
The density of available measured discharge and temperature data in the Ethiopian Highlands is low: Most of the time series are error-prone and have a lot of missing data.Therefore, the only available measured complete data set from three observatories from the Water and Land Resources Information System [39] have been complemented with generated data from the National Centers for Environmental Prediction (NCEP).This Climate Forecast System Reanalysis (CFSR) precipitation and climate data (minimum and maximum temperature, solar radiation, wind speed) are available from the Texas A&M University (TAMU) spatial science website (www.globalweather.tamu.edu,accessed May 2017) for the entire upper Blue Nile basin (bounding box: Latitude 8.60-12.27N and longitude 33.94-40.40E).Previous studies showed that these data are unsuitable for small-scale catchments in the upper Blue Nile basin [66], but according to Dile and Srinivasan [62], CFSR weather is a viable option for hydrologic modelling in data-scare regions on a larger scale, like the Ethiopian Highlands.For this reason, we compared CFSR rainfall data with available, but incomplete, precipitation data from 35 meteorological stations of the National Meteorological Agency of Ethiopia (NMA) with a statistical goodness of fit of time series (NSE, R 2 , mean error, PBIAS) and excluded unrealistic CFSR weather points.Finally, 43 CFSR climate and precipitation point stations were used as well as three local weather stations from WLRC to simulate the discharge of the whole upper Blue Nile basin and to calculate the drainage ratio for the delineated watersheds.Potential evapotranspiration was simulated with the Hargreaves method [41].For discharge calibration, we used measured data from the NMA for the outlets of eight sub-basins.Due to the incomplete time series, the calibration and validation period of the sub-basins contain different years (see Table 1).

Climate and Hydrological Data
The density of available measured discharge and temperature data in the Ethiopian Highlands is low: Most of the time series are error-prone and have a lot of missing data.Therefore, the only available measured complete data set from three observatories from the Water and Land Resources Information System [39] have been complemented with generated data from the National Centers for Environmental Prediction (NCEP).This Climate Forecast System Reanalysis (CFSR) precipitation and climate data (minimum and maximum temperature, solar radiation, wind speed) are available from the Texas A&M University (TAMU) spatial science website (www.globalweather.tamu.edu,accessed May 2017) for the entire upper Blue Nile basin (bounding box: Latitude 8.60-12.27N and longitude 33.94-40.40E).Previous studies showed that these data are unsuitable for small-scale catchments in the upper Blue Nile basin [66], but according to Dile and Srinivasan [62], CFSR weather is a viable option for hydrologic modelling in data-scare regions on a larger scale, like the Ethiopian Highlands.For this reason, we compared CFSR rainfall data with available, but incomplete, precipitation data from 35 meteorological stations of the National Meteorological Agency of Ethiopia (NMA) with a statistical goodness of fit of time series (NSE, R 2 , mean error, PBIAS) and excluded unrealistic CFSR weather points.Finally, 43 CFSR climate and precipitation point stations were used as well as three local weather stations from WLRC to simulate the discharge of the whole upper Blue Nile basin and to calculate the drainage ratio for the delineated watersheds.Potential evapotranspiration was simulated with the Hargreaves method [41].For discharge calibration, we used measured data from the NMA for the outlets of eight sub-basins.Due to the incomplete time series, the calibration and validation period of the sub-basins contain different years (see Table 1).1983-2004 1982-1992 1982-1992 1982-1992 1986-2010 1984-2002 1982-2010 Calibration period (year) Not modelled 1996-20041987-19921987-19921987-19921987-19921995-20021988-1995 Validation period (year) Validation period (year) Not modelled 1988-1995 1982-1986 1983-1986 1982-1986 1982-1986 1989-1994 1996-2004 * According to the National Meteorological Agency of Ethiopia (NMA).

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The upper Blue Nile basin was divided into eight sub-basins where sufficient discharge data were available (see Figure 1).Seven sub-basins were simulated individually with SWAT [31,40] and also individually calibrated and validated with the SUFI-2 programme [32,33,67].The topmost sub-basin with the outlet of Lake Tana was not modelled, due to human activities for which no data were available, such as irrigation and damming up the lake.Instead of simulated data, we used available discharge data from the outlet of Lake Tana (1985-2010) from the NMA as an inlet of the subsequent Upper Abay sub-basin.Other water infrastructure was not incorporated into the model, because there was no data available or the influence on the total discharge was negligible; • with the parameters giving the best objective function in the calibration process, discharge was simulated for the whole time period (1982-2010) of the sub-basins starting with the upstream sub-basins; • the newly simulated discharge of each sub-basin was used as the inlet discharge for the next lower sub-basin; • the total discharge of the upper Blue Nile basin was finally calibrated and validated at the outlet of the Lower Abay sub-basin, which is the border of Sudan and today the outlet of the Grand Ethiopian Renaissance Dam; and • with this complete discharge data set comprising modelled data for all delineated watersheds, the percentage of precipitation leaving the watersheds through the river (drainage ratio) could be calculated on a monthly resolution with precipitation data from the next available weather station.
In total, the whole modelled upper Blue Nile basin was divided into seven sub-basins, 323 watersheds, and 60,634 hydrological response units (HRU).In SWAT, the delineated watersheds are defined as sub-basins of the defined sub-basins of the upper Blue Nile basin.For every sub-basin, a three-year warm-up period was selected, which allowed the model to initialize and stabilize starting values for the modelled parameters [55].

Sensitivity Analysis and Calibration Setup
The calibration and validation period was chosen based on the discharge data available for the different sub-basins (Table 1).For all sub-basins, 13 sensitive discharge parameters were chosen according to the literature [66,[68][69][70].After an individual sensitivity analysis with the same parameter ranges for all sub-basins, insensitive parameters where excluded for the final calibration and validation process (see Appendix F).Finally, three to five calibration iterations (500 simulations each) were carried out for every sub-basin [33].
The goodness-of-fit of the calibration and validation was quantified with hydrographic observations and five model evaluation statistics, such as the widely used coefficient of determination (R 2 ) and Nash-Sutcliff efficiency (NSE) [23,71,72], the P-factor and R-factor, and the objective function, bR 2 .The P-factor is the percentage of observed values inside the 95% prediction uncertainty band (95PPU) and ranges between 0 and 1.The R-factor is the thickness of the average 95PPU band divided by the standard deviation of the observed data.A P-factor of 1 and R-factor of 0 is a simulation that exactly corresponds to the measured data [67].The percentage of measurement error in SUFI-2 was set to 0. In order to compare the measured and simulated discharge, this study used bR 2 as an objective function [33], which is a slightly modified version of the efficiency criterion defined by Krause et al. [73]: where b is the slope of the regression line between the observed and simulated runoff and R 2 is the coefficient of determination to represent the discharge dynamics.The minimum value of the objective function threshold was set to 0.6; according to Faramarzi et al. [74] and Schuol, Abbaspour, Yang, et al. [75], bR 2 should be ≥0.6 to be sufficient.So far no absolute criteria for judging model performance have been firmly established in the literature [43].Acceptable statistical measures are always project specific [76].However, Moriasi et al. [71] and Andersen et al. [77] have proposed to judge a calibration and validation result as "very good" if NSE > 0.75 and R 2 > 0.95, "good" if 0.65 < NSE ≤ 0.75 and 0.85 < R 2 ≤ 95, and "satisfactory" if NSE > 0.5 and R 2 > 0.7.Satisfactory P-and R-factors depend on the quality of the measured data.If the measured data are of high quality, then the P-factor should be > 0.8 and R-factor < 1 [33].However, according to Schuol et al. [75], a P-factor > 0.5 and R-factor < 1.3 are still sufficient under less stringent model quality requirements.

Calibration-Uncertainty Analysis
Discharge was calibrated for seven sub-basins within the upper Blue Nile basin.Different periods were selected according to the measured data available.Sensitivity analysis with SUFI-2 was carried out by keeping the chosen parameters constant, while varying one parameter in a realistic range [33].The sensitivity of the parameter varied in the different sub-basins, but the most sensitive were GW_DELAY (groundwater delay), RCHRG_DP (deep aquifer percolation fraction), and CN2 (runoff curve number).For calibration and validation, we selected 11 to 13 parameters for their individual sensitivity (see Appendix F).
Calibration and validation were first conducted in the sub-basins with no inlet from other sub-basins, except for the Upper Abay sub-basin, where the outlet from Lake Tana (in Bahir Dar) was used as the inlet.Due to different available discharge data, the length of time varied in the different sub-basins for calibration and validation (see Figure 4).
The overall goodness-of-fit for the different discharge calibration and validation varies from "satisfactory" to "very good", except for the Muger and Dabus sub-basins, where the NSE is slightly unsatisfactory for the validation period (see Table 2).In the Muger sub-basin, this results from a very low measured base flow during the dry season, which could not be simulated properly.An explanation for this discrepancy is the aquifer system of the Muger sub-basin, which has a connection with the aquifer system of the Upper Awash basin [37,38].These water losses were not included in the model setup.In the Dabus basin, a discharge shift is the cause of unsatisfactory modelling results.One reason is the presence of wetlands in the Dabus headwater [16], where water can be stored and lead to delayed discharge, which was not modelled properly.Like the Muger sub-basin, the Temcha sub-basin also shows an unsatisfactory P-factor: This is the result of very high measured discharge peaks during the rainy season, which could not be simulated with available precipitation data.In the Lower Abay sub-basin, the low P-factor and R-factor can be explained by the high share of the streamflow coming from the upstream sub-basins; only roughly 25% of the streamflow is generated within the catchment.Therefore, realistic parameter ranges have only a small impact on total discharge and the thickness of the average 95PPU band does not become wide enough to cover a higher percentage of measured discharge.However, the overall goodness-of-fit for the final outlet of the upper Blue Nile basin can be judged as "satisfactory"-and for the calibration period, when most upstream sub-basins have been calibrated, even as "good" to "very good".
Lower Abay sub-basin, the low P-factor and R-factor can be explained by the high share of the streamflow coming from the upstream sub-basins; only roughly 25% of the streamflow is generated within the catchment.Therefore, realistic parameter ranges have only a small impact on total discharge and the thickness of the average 95PPU band does not become wide enough to cover a higher percentage of measured discharge.However, the overall goodness-of-fit for the final outlet of the upper Blue Nile basin can be judged as "satisfactory"-and for the calibration period, when most upstream sub-basins have been calibrated, even as "good" to "very good".

Modelling Approach Discussion
Unlike previous studies (see introduction), this study did not model the whole upper Blue Nile basin in one run.The upper Blue Nile basin was divided into seven sub-basins, each of which was modelled separately.Due to incomplete time series and gaps in the measured data, the measured outflow was only used for calibration and validation, and a complete time series of the modelled outflow was used as an inlet for the subsequent sub-basin.Sensitivity analysis of the calibrated parameters was very different for each sub-basin, and the final parameter ranges also differed for every sub-basin (see Appendix F).This indicates that every sub-basin has its own characteristics due to differences in e.g., topography, land management practices, or rainfall patterns.If using only one model for the whole upper Blue Nile basin, it is difficult to locate inconsistencies or uncertainties during calibration at the basin or watershed level.In addition, the data on the seven sub-basins can be used for further analysis, and follow-up modelling (in sediment, land use/land cover change, or climate change) can be conducted on the sub-basin level.
A further advantage of the divided basin is of a technical nature: When modelling the whole upper Blue Nile basin using the given spatial resolution, high computing power is required for modelling and calibration.By splitting up the upper Blue Nile basins into different sub-basins, modelling, calibration, and validation can be carried out on a usual desktop computer, and the processes can be distributed to different computers to save time.This issue is crucial if the model is being used by different research teams.

Spatial Variabilities in Drainage Ratio
The highest average annual drainage ratios can occur in the southwestern, northern, and eastern part of the upper Blue Nile basin (>0.6).Low drainage ratios can be observed along the valley of the upper Blue Nile River, in the Didesa sub-basin, and in the north-eastern part of the upper Blue Nile basin (less than <0.1) (see Figure 5 and Figure S1).These spatial variations in drainage ratio are the results of different rainfall patterns and amounts of annual rainfall (compare Figure 5, Figure 6 and Figure S1).The most important observation is that drainage ratios increase with higher amounts of precipitation.The correlation (r = 0.54) is shown in Figure 6 (left), with the mean annual precipitation and drainage ratio data from the 323 watersheds in the upper Blue Nile basin.This correlation was already observed by Lemann et al. [30] in a comparison of the different hydrological responses of three small-scale catchments in the upper Blue Nile basin; after a predefined amount of precipitation, additional rainfall apparently increases the share of blue water leaving a catchment.Liu et al. [78] and Steenhuis et al. [79] discussed an effective precipitation threshold (precipitation minus potential evaporation) of 500 mm, where hydrological response can be predicted by its linear relationship to precipitation.Sub-basins with high amounts of rainfall have a higher drainage ratio and therefore a disproportional increase in blue water, compared to dryer sub-basins.
Nevertheless, the drainage behaviour of every sub-basin is different, not only because of different precipitation rates, but also because of different characteristics and individual calibration.For example, the Didesa sub-basin has an average drainage ratio of 0.21, while in Dabus, the average drainage ratio is as high as 0.52 (see Table 3), with almost the same long-term mean annual precipitation (1424 mm and 1418 mm).One reason for these differences can be found in the slope and different land use cover of the two sub-basins: The Dabus sub-basin has an average slope of 14% and land use is dominated by cultivated areas (>40%) and shrubland (20%), while Didesa has an average slope of 12% and the most common land use types are forest and shrubland (22% and 19%).This is also one explanation for the differences between the Temcha and the Beles sub-basins, which have almost the same annual precipitation, but different average drainage ratios (0.55 and 0.37).The Temcha watershed is intensively cultivated (>70% crop and pasture), while shrub and grassland (>50%) dominate in the small Beles watershed.Other studies support the modelling results: e.g., Hurni et al. [80] found at the plot level, 5-40 times more runoff from degraded and cultivated lands than from forest lands.A higher share of forest means among other parameter changes, a lower curve number and higher leaf area index, both of which result in lower surface runoff [81,82] and a higher evapotranspiration rate.Higher evapotranspiration rates, e.g., in the Didesa and Beles sub-basins, were also shown by Allam et al. [18].
Land use change dynamics, with an increase in farmland and settlement and a decrease in forest and shrubland, will therefore lead to a higher share of blue water, but a lower level of green water in soil and vegetation.Various studies reported a change in land use and land cover where cultivated areas have increased within the last 40 years [24,29,83,84].Land use/land cover changes could not be shown within this study, as no older land use maps with a comparable resolution were available.Nevertheless, this study shows that an expansion in cultivated area increases surface runoff and thus also the drainage ratio.This effect can be partly reduced with integrated watershed conservation measures, which are also important to reduce sediment yield generation [81].
Another reason for the different shares of blue and green water availability can be found in the different dominating soil types.In the north-western part of the Lower Abay sub-basin, where 24 watersheds receive the same temporal distribution and amount of precipitation, drainage ratios range from 0.44 to 0.56.While the share of forest/shrub and cropland is similar in most watersheds, different soil types can be observed there.Watersheds with high drainage ratios are dominated by Leptosols, and watersheds with a lower share of discharge are covered by Alisols and Nitisols.In the model, the very shallow Leptosols have a defined soil depth of only 25 cm, while Alisols and Nitisols have 1 m and more.Even if Leptosols are moist (to arid), they are only wet for short periods [85] and store less precipitation than Alisols and Nitisols.This results in a higher share of blue water and a higher drainage ratio.

Temporal Differences in Drainage Ratio
Drainage ratios of the single sub-basins vary not only within-but also between-years. Figure 6 shows that years with higher precipitation rates generate a higher drainage ratio than dry years, when significantly less water leaves the sub-basins throughout the river.However, rainfall properties, such as duration, intensity, and inter-event duration, also vary in the upper Blue Nile basin [86] and influence the drainage behaviours in dry and wet years differently in every sub-basin.High annual precipitation rates do not necessarily lead to high drainage ratios if rainfall is distributed over several months.In the upper Abay sub-basin, for example, the highest amount of annual rainfall was calculated for 1986 (1493 mm).However, because rainfall was distributed over several months and only 49% of annual rainfall occurred in July and August, less than 40% of rainfall left the subbasin through the river.This was not the case in 1994, when the drainage ratio reached 0.49: 70% of the annual precipitation occurred in July and August, the two months with the highest share of rainfall (Figure 7) and when, accordingly, most discharge is generated.The lowest drainage ratio (0.22) was calculated in 2002, when the lowest amount of annual precipitation-658 mm-was measured.In 2008 and 2009, annual precipitation was almost the same (835 mm and 834 mm), but the drainage ratio was 0.27 and 0.30, respectively.These differences can again be explained by the distribution and intensity of annual rainfall.In 2009, 77% of the annual precipitation occurred during July (48%) and August (29%), while in 2008, these two months only received a total of 59% (33% in July and 26% in August) and the annual precipitation was distributed more equally over the whole rainy season.These correlations between intensity and temporal distribution of precipitation and drainage ratios can also be observed in the other sub-basins (see Appendix D).Monthly drainage ratios can only be considered in months with a certain amount of rainfall.In a dry month, when discharge is baseflow-dominated, high drainage ratios are not relevant for the total annual drainage ratio, as discharge in these months is very low.

Temporal Differences in Drainage Ratio
Drainage ratios of the single sub-basins vary not only within-but also between-years. Figure 6 shows that years with higher precipitation rates generate a higher drainage ratio than dry years, when significantly less water leaves the sub-basins throughout the river.However, rainfall properties, such as duration, intensity, and inter-event duration, also vary in the upper Blue Nile basin [86] and influence the drainage behaviours in dry and wet years differently in every sub-basin.High annual precipitation rates do not necessarily lead to high drainage ratios if rainfall is distributed over several months.In the upper Abay sub-basin, for example, the highest amount of annual rainfall was calculated for 1986 (1493 mm).However, because rainfall was distributed over several months and only 49% of annual rainfall occurred in July and August, less than 40% of rainfall left the sub-basin through the river.This was not the case in 1994, when the drainage ratio reached 0.49: 70% of the annual precipitation occurred in July and August, the two months with the highest share of rainfall (Figure 7 Appendix E) and when, accordingly, most discharge is generated.The lowest drainage ratio (0.22) was calculated in 2002, when the lowest amount of annual precipitation-658 mm-was measured.In 2008 and 2009, annual precipitation was almost the same (835 mm and 834 mm), but the drainage ratio was 0.27 and 0.30, respectively.These differences can again be explained by the distribution and intensity of annual rainfall.In 2009, 77% of the annual precipitation occurred during July (48%) and August (29%), while in 2008, these two months only received a total of 59% (33% in July and 26% in August) and the annual precipitation was distributed more equally over the whole rainy season.These correlations between intensity and temporal distribution of precipitation and drainage ratios can also be observed in the other sub-basins (see Appendix D).Monthly drainage ratios can only be considered in months with a certain amount of rainfall.In a dry month, when discharge is baseflow-dominated, high drainage ratios are not relevant for the total annual drainage ratio, as discharge in these months is very low.Most climate change scenario models predict more annual rainfall for the near future; however, variations between models are high [87], as are seasonal variations [88][89][90][91].Higher precipitation would lead to a higher drainage ratio, meaning that the amount of blue water leaving the Ethiopian Highlands would increase disproportionately to precipitation.However, in all cited literature, the scenario models also projected an increase in the annual mean temperature, and as a result, a part of the blue water would convert to evapotranspiration and decrease the drainage ratio and the water for downstream stakeholders [30].The mutual interaction of precipitation and temperature, and the influence on discharge, are highly dependent on the magnitude of local changes.With the available time series, the effect of changing temperatures could not be shown in this study as there were no significant changes in the amplitude of temperature during the model period.However, using the prepared model as well as the newly available maps and data sets as a basis, further analysis can be performed and different climate scenarios can be modelled at the catchment level.

Conclusions
The present study simulated and calculated the long-term drainage ratios of the upper Blue Nile basin in the Ethiopian Highlands.To represent the heterogeneity of the study area, we developed a new soil and land use map to model seven sub-basins of the upper Blue Nile basin with a 30 m digital elevation model, or DEM.With the best parameter range from the calibration and validation process, discharge was modelled for years and areas where no data was available.This allowed us to calculate and analyse temporal and spatial drainage ratios of 343 watersheds in the upper Blue Nile basin for 26 years (1985-2010).Most climate change scenario models predict more annual rainfall for the near future; however, variations between models are high [87], as are seasonal variations [88][89][90][91].Higher precipitation would lead to a higher drainage ratio, meaning that the amount of blue water leaving the Ethiopian Highlands would increase disproportionately to precipitation.However, in all cited literature, the scenario models also projected an increase in the annual mean temperature, and as a result, a part of the blue water would convert to evapotranspiration and decrease the drainage ratio and the water for downstream stakeholders [30].The mutual interaction of precipitation and temperature, and the influence on discharge, are highly dependent on the magnitude of local changes.With the available time series, the effect of changing temperatures could not be shown in this study as there were no significant changes in the amplitude of temperature during the model period.However, using the prepared model as well as the newly available maps and data sets as a basis, further analysis can be performed and different climate scenarios can be modelled at the catchment level.

Conclusions
The present study simulated and calculated the long-term drainage ratios of the upper Blue Nile basin in the Ethiopian Highlands.To represent the heterogeneity of the study area, we developed a new soil and land use map to model seven sub-basins of the upper Blue Nile basin with a 30 m digital elevation model, or DEM.With the best parameter range from the calibration and validation process, discharge was modelled for years and areas where no data was available.This allowed us to calculate and analyse temporal and spatial drainage ratios of 343 watersheds in the upper Blue Nile basin for 26 years (1985-2010).
Our results indicate that in the upper Blue Nile basin, precipitation and drainage ratios vary greatly over the basin and over time.In regions with high annual precipitation levels, drainage ratios are much higher than in dryer areas.In years in which annual precipitation is distributed over the whole rainy season, the percentage of rainfall leaving the watersheds through the river is lower than in years in which most annual precipitation is concentrated over a period of two months.Higher drainage ratios due to different amounts and intensity of rainfall can be explained through higher surface runoff, which is, inter alia, the result of saturation-excess processes.Other influencing parameters are the land use, where cultivated land generated a higher share of runoff than a forest-dominated watershed due to less surface runoff and higher evapotranspiration rates.However, soil type is also crucial: Deep Alisols or Nitisols generate lower drainage ratios than, for example, shallow Leptosols.
Looking at different forecasts up to the year, 2100, for changes in climate and land use (the latter due to population growth), we found that several changing parameters cause higher runoff.Areas with a greater level of cultivation and rainfall will have higher drainage ratios and higher amounts of blue water for downstream stakeholders.Only a predicted rise in temperature may partly cushion these effects, due to higher evapotranspiration rates.Nevertheless, the higher amount of available blue water is linked with increasing surface runoff and erosivity.Therefore, the predicted changes in land use and climate are likely to lead to higher erosion rates in the upstream area and increasing sediment loads in the Blue Nile.This is not only a threat to the upstream, mainly rainfed area, where fertile topsoil is being eroded, but also for downstream stakeholders, where high sediment rates are reducing the lifespan of water infrastructure.Only sustainable and integrated watershed conservation measures in areas with high rainfall can cushion these climate and land use change dynamics and reduce soil erosion and sediment loads in the river.Even if such conservation measures can somewhat reduce the drainage ratio over time (by resulting in deeper soil, reduced slopes, changed land use), downstream stakeholders will not receive less water, due to predicted changes in the amount of rainfall and calculated shares of available blue water.
This study contributes to the understanding of hydrological processes and availability of blue and green water in the upper Blue Nile basin.This knowledge is crucial for analysing future changes and improving sustainable and integrated watershed management from which up-and downstream stakeholders will benefit.

Appendix B
Land use classes in the upper Blue Nile basin (map see Figure 2).

Figure 1 .
Figure 1.Overview of the upper Blue Nile basin and its sub-basins.

Figure 1 .
Figure 1.Overview of the upper Blue Nile basin and its sub-basins.

Figure 2 .
Figure 2. Newly developed land use map.

Figure 2 .
Figure 2. Newly developed land use map.

Figure 4 .
Figure 4. Hydrographic model calibration and validation results: Observed discharge and discharge simulated with the parameters giving the best objective function in the calibration process at the seven outlets of the sub-basins.

Figure 4 .
Figure 4. Hydrographic model calibration and validation results: Observed discharge and discharge simulated with the parameters giving the best objective function in the calibration process at the seven outlets of the sub-basins.

Figure 5 .
Figure 5.Long-term mean annual drainage ratio and precipitation at the watershed level.Drainage ratios have not been modelled for the Lake Tana sub-basin.

Figure 5 .
Figure 5.Long-term mean annual drainage ratio and precipitation at the watershed level.Drainage ratios have not been modelled for the Lake Tana sub-basin.

Figure 6 .
Figure 6.Correlation of drainage ratio and rainfall with a regression line for all data.Left: Mean annual correlation for all 323 watersheds.Right: Annual correlation for every year from 1985 to 2010 for all seven sub-basins.

Figure 6 .
Figure 6.Correlation of drainage ratio and rainfall with a regression line for all data.Left: Mean annual correlation for all 323 watersheds.Right: Annual correlation for every year from 1985 to 2010 for all seven sub-basins.

Figure 7 .
Figure 7. Monthly and annual distribution of precipitation (PCP) and drainage ratios (DR) for the Upper Abay sub-basin.Data for the other six sub-basins can be found in Appendix D.

Figure 7 .
Figure 7. Monthly and annual distribution of precipitation (PCP) and drainage ratios (DR) for the Upper Abay sub-basin.Data for the other six sub-basins can be found in Appendix D.

Table 1 .
Information on the sub-basins.

Table 2 .
Final calibration and validation statistics for the seven sub-basins in the upper Blue Nile basin.

Table 2 .
Final calibration and validation statistics for the seven sub-basins in the upper Blue Nile basin.

Table 3 .
Rainfall distribution and modelling results of drainage ratios for the seven sub-basins.
* Without water areas.
In the parameter names, A__ means the given value is added to the existing parameter value; r__ means the existing parameter value is multiplied by (1 + a given value); v__ means the existing parameter value is to be replaced by the given value[67].*After sensitivity analysis, these insensitive parameters where excluded for the final calibration.