UBN water budget is estimated using the JGrass-NewAge hydrological system, which is, in turn, based on the Object Modelling System framework . It is a set of modeling components, reported in Table , that can be connected at runtime to create various modeling solutions. Each component is presented in detail and tested against measured data in the corresponding papers cited in the Table . A similar study using the JGrass-NewAge system, but utilizing mostly in situ observations, has been conducted in Posina River basin in northeastern Italy . A brief description of the components used in this study are provided in the following sections. In this study, the shortwave solar radiation budget component (Sect. ), the evapotranspiration component (Priestley and Taylor, Sect. ), the Adige rainfall–runoff model (Sect. ), and all the components illustrated in Fig.  are used to estimate the various hydrological flows.

A necessary step for spatial hydrological modeling is the partitioning of the topographic information into an appropriate spatial scale. The SRTM 90 m × 90 m elevation data are used to generate the basin Geographic Information System (GIS) representation. The basin topographic representation in GIS, as detailed in  and , is based on the Pfafstetter enumeration. The basin is subdivided in hydrologic response units (HRUs), where the model inputs (i.e., meteorological forcing data), and hydrological processes and outputs (i.e., evapotranspiration, discharge, shortwave solar radiation) are averaged . A routing scheme, which is applied to move the discharges from HRUs to the basin outlet through the channel network, is included in the Adige component.

In this study, the UBN basin is divided into 402 subbasins (HRUs of mean area of 430 ± 339 km2) and channel links, as shown in Fig. b. This spatial partitioning may not be the finest scale possible, but it is consistent with input data resolution, including satellite products, meaning that a finer subdivision would imply uniform inputs for adjacent HRUs, and a coarser one would average out input variability. In this paper, the term HRU actually refers to the different subbasins.

The spatiotemporal precipitation input term of Eq. (), J(t), is quantified with RS-based approaches. Currently, there are several satellite rainfall estimates (SREs) available for free, and   compared five of them with high spatial and temporal resolutions over the same basin. It was shown that SM2R-CCI  is one of the best products, particularly in capturing the total rainfall volume. With regard to the quality of SM2RAIN-based products, recent studies positively assessed their accuracy on a regional  and a global  scale. A comparative analysis of the effects of different SREs on basin water-budget components is an interesting area of research; however, here SM2R-CCI is only used for obtaining the precipitation input. The systematic error (bias) of SM2R-CCI is removed according to the “ecdf” matching techniques by  and specialized for UBN by  by using in situ observations. The subbasin mean precipitation is estimated by averaging all the pixels of RS-corrected data within each subbasin. In accordance with the basin partition described in Sect. , the 1994–2009 daily precipitation set is generated for each of the 402 subbasins.

Evapotranspiration estimation is crucial for agricultural and water resource management as it is an important flux within a basin. The lack of in situ data relating to ET impedes modeling efforts and makes it probably the most difficult task in water-budget assessment. Here, ET is estimated according to the NewAge specific component. It provides estimates at any temporal and spatial resolution required by using the Priestley and Taylor (PT) formula , which is one of the more common models used. PT is mainly based on net radiation estimation, Rn, grouping all the unknowns into the αPT coefficient, as shown in Eq. (): PET=αPTΔΔ+γRn, where PET is Priestley–Taylor potential evapotranspiration, Δ is the slope of the Clausius–Clapeyron relation and γ is the psychometric constant . In this study, however, we need an estimate of the actual evapotranspiration, which is constrained not only by the atmospheric demands as in Eq. (), but it uses storage information which can be obtained from the ADIGE rainfall–runoff component of JGrass-NewAge. Hence, the ET equation is modified as follows : ET(t)=αPTS(t)SmaxΔΔ+γRn, where S(t) is the subsurface storage, and Smax is the maximum storage capacity for each HRU. The important unknown coefficient αPT and the Smax are calibrated within the rainfall–runoff model component, as explained below. The ratio S(t)/Smax represents a stress coefficient which became very popular since the work of .

In our procedure, given that S(t) is not measured, the assumption that there is null water storage difference after a long time, named Budyko's time, TB, , is required. So, here, what is searched is a time duration (TB) such that the water storage again assumes its initial value . Once TB is fixed, the tools for automatic calibration, provided by the Object Modelling System, produce the set of parameters in Table , including αPT and Smax, for which discharge is well reproduced and is also S(TB)=S(0). In this study, TB=6 years.

In Eq. (), Rn is the main input modulating the atmospheric demand component of ET. To this scope, the NewAge shortwave radiation budget component SWRB; is used to return a value for each subbasin in clear sky conditions. Irradiance in clear sky conditions, however, is unsuitable for all sky conditions since surface shortwave radiation is strongly affected by cloud cover and cloud type . Therefore, the clear sky SWRB estimated using NewAge-SWRB is modified by using the cloud fractional cover (CFC) satellite data set  , processed and provided by the EUMETSAT Climate Monitoring Satellite Application Facility (CM SAF) project . In this case, net radiation is generated only from the shortwave radiation and the cloud cover data, as in the following formulation : Rn=(1-CFC)RS, where RS is the net shortwave radiation and Rn is the net radiation. The daily CFC data originates from polar orbiting satellites, version CDRV001, using a daily temporal resolution and a 0.25∘ spatial resolution, from 1994 to 2009 (16 years). Satellite data are processed  to obtain the mean daily CFC for each subbasin. In comparison to CFC, the effects of surface albedo on Rn is minimal, particularly in highland areas with vegetation and no snow cover, such as the UBN basin.

Once ET is estimated according to the methods described, it is useful to compare it with independently obtained ET estimates or data. In situ ET observations are not present for this basin, as is the case for most regions. Estimates of ET based on RS have been made available by different algorithms . In this study, the Global Land Evaporation Amsterdam Methodology  GLEAM, version_v3_BETA;, a global, satellite-based, ET data set is used. GLEAM, as well NewAge, uses the PT scheme for estimating ET. However, all inputs of the formula, in GLEAM and NewAge, are evaluated according to different strategies and RS tools. GLEAM sets αPT=0.98 while in NewAge it has been calibrated. In GLEAM PET is additively increased by intercepted rainfall estimated according to a version of the Gash model , and multiplicatively decreased by a stress coefficient depending on five soil cover types (bare soil, snow, tall vegetation, two levels of low vegetation) and has a different expression for any one of the storages. Moreover, depending on the case, the stress coefficient is evaluated through various RS products, according to procedures which are described in the paper by . In contrast to the NewAge approach, GLEAM also considers dynamic vegetation information to estimate the stress factor .

GLEAM is available at 0.25∘ spatial resolution (28 km laterally or 800 square kilometers of area) and daily temporal resolution, and is assessed positively in different studies . The most recent version of GLEAM was validated globally over 64 Fluxnet sites  with consistent results, letting us assume that it behaves properly also in Ethiopia. The differences between NewAGE estimation and GLEAM's one allow us to assume that the our results and their results can be seen as largely independent. For comparison with NewAge ET, we averaged GLEAM ET for each HRU polygon. Comparison of the NewAge ET with MODIS-standard ET product is also available in the Supplement of the paper.

For discharge estimation, the ADIGE rainfall–runoff component is used. It is based on the well-known HYMOD model  as a runoff production component which also include a routing component and artificial inflow–outflow management. Detailed descriptions of HYMOD implementations in the NewAge model system are given in  and and summarized in Appendix . The main inputs for the ADIGE model are J(t) and PET(t), as estimated in the previous sections. The NewAge Hymod component is applied to each HRU, in which the basin is subdivided and the total watershed discharge is the sum of the contribution of each of the 402 HRUs routed to the outlet. The ADIGE rainfall–runoff has five calibration parameters (Cmax, Bexp, αHymod, Rs, and Rq; see the details in Appendix ), and the calibration is performed using the particle swarm (PS) optimization method. PS is a population-based stochastic optimization technique . The objective function used to estimate the optimal value of the parameter is the Kling–Gupta efficiency (KGE, ). The KGE is preferred to the commonly used Nash–Sutcliffe efficiency (NSE, ) because the NSE has been criticized for its overestimation of model skill for highly seasonal variables by underestimating flow variability . For evaluation of the model performances, in addition to the KGE, the two other goodness-of-fit methods (percentage bias (PBIAS) and correlation coefficient) used in this study are described in Appendix .

The ds / dt in Eq. () is the water contained in the ground, soil, snow and ice, lakes and rivers, and biomass. It is the total water storage (TWS) change, calculated as the residuals of the water-budget fluxes for each control volume. In this paper, the ds / dt estimation at daily time steps is based on the interplay of all the other components, as presented in Eq. (). There is no way to estimate areal TWS from in situ observations. The new GRACE data  have a potential to estimate this component, but at very low spatial and temporal resolutions. On a large scale, however, it can still be used for constraining and validating data of the modeling solutions. Here, the performance of our modeling approach to close the water budget is assessed using the GRACE estimation on the basin scale. Monthly GRACE data are obtained from NASA's Jet Propulsion Laboratory (JPL) ftp://podaac-ftp.jpl.nasa.gov/allData/tellus/L3/landmass/RL05. The leakage errors and scaling factor  that are provided with the product are applied to improve the data before the comparison is made. The total error of GRACE estimation is a combination of GRACE measurement and leakage errors . Based on the data of these two error types, the mean monthly error of GRACE in estimating total water storage change (TWSC) in the basin is about 8.2 mm. Since the other fluxes, for instance Q and ET, are modeled as functions of basin water storage, the good estimation of water storage by a model affects the goodness of fit of all the other fluxes as well .

The satellite precipitation data set (SM2R-CCI) is error corrected based on in situ observations. At the basin outlet (Ethiopia–Sudan border), the ADIGE rainfall–runoff component (i.e., HYMOD model) is calibrated to fit the observed discharge during the 6 years of the calibration period (1994–1999) at daily time steps. Based on the approach described in Sect. 3.2, αPT is calibrated by imposing that S(0)=S(TB) after TB=6 years. The value of 6 years is arbitrary but it was found to give good agreement with GRACE data (see below), so no other values were used. The simulation for each hydrological component is then verified using available in situ or remote sensing data (Table ), and three goodness-of-fit methods (KGE, PBIAS, r) are used as comparative indices (for detailed information please see Appendix ), as follows:

Discharge validation: discharge simulation is validated at the outlet close to the Ethiopian-Sudan border, where the model is calibrated. In addition, the simulation of NewAge at the internal links is validated at 15 discharge measurement stations, where in situ data are available. The evaluations of discharges at the internal links provide an assessment of model estimation capacity at ungauged locations.

The spatial distribution of mean, long-term, annual precipitation is presented in Fig. a. Generally, precipitation increases from the east (about 1000 mm yr-1) to the south and southwest (1800 mm yr-1). This spatial pattern is consistent with the results of  and . SM2R-CCI shows that the southern and southwestern parts of the basin receive higher precipitation than the eastern and northeastern parts of the highlands. The rainiest subbasins are in the southern part of the basin. For this location, the precipitation data used correspond to a mean annual rainfall of about 1900 mm yr-1, while the mean annual precipitation reported for this region by  is about 2049 mm yr-1. The latter estimation, however, is from point gauge data, while this study is based on areal data. To understand the spatial distribution of the seasonal cycle, the quarterly percentage of total annual precipitation, calculated from 1994 to 2009 in daily estimations, is presented in Fig. b. During the summer season (June, July, and August), while the subbasins in the north and northeast receive about 65 % of the annual precipitation (Fig. b), the subbasins in the south receive about 40 % of total precipitation.

ET is estimated for each subbasin at daily time steps. In this section we mainly provide discussion about the comparison of NewAge ET and RS estimates, but further comments on ET can be found in Sect. 4.5, which show that ET is more water-limited than energy-limited. Figure a shows the comparisons of the ET time series from 1994 to 2002 (aggregated at daily, weekly, and monthly intervals, from top to bottom) between NewAge and GLEAM. The figure specifically refers to three selected subbasins representing different ranges of elevations and spatial locations. NewAge estimates have higher temporal variability in comparison to GLEAM. In the represented locations, GLEAM therefore accumulates a systematic growing difference in water-volume evapotranspiration, which could be not consistent with the estimated storage (see below).

The agreement or disagreement between the two ET estimations vary from subbasin to subbasin (Fig. ). The spatial distribution correlation and PBIAS between the NewAge and GLEAM ET is presented in Fig. b. Spatially, the correlation between JGrass-NewAGE and GLEAM is higher in the eastern and central parts of the basin, while it tends to decrease systematically towards the west (i.e., to the lowlands, see Fig. b). The correlation between the two ET estimations increases when passing from daily to monthly time steps. The PBIAS between the two estimates ranges from -10 to 10 %, with large numbers of subbasin being from -3 to 3 %. Spatially, the comparison shows that GLEAM overestimates ET in the western parts of the basin (border to the Sudan) and underestimates ET in the northern parts of the basin (Fig. b). The overall basin correlation is 0.34 ± 0.07 (daily time step), 0.51 ± 0.08 (weekly time step), and 0.57 ± 0.10 (monthly time steps). Generally, except at daily time steps, the two estimates have acceptable agreements (very low bias and acceptable correlation). In comparison with the correlation (0.48 ± 0.15) and PBIAS (14.5 ± 18.9 %) obtained between NewAge ET and MODIS ET Product (MOD16), as shown in the Supplement, the correlation and PBIAS between NewAge ET and GLEAM ET is much better.

The optimized parameters of the Adige model, obtained using automatic calibration procedure of NewAge, are given at Table . At the basin outlet, the automatic calibration of the NewAge components provided very good values of the goodness-of-fit indices (KGE = 0.93, PBIAS = 2.2, r= 0.94). The performances at the outlet also remain high during the validation period, having KGE = 0.92, PBIAS = 2.4, and r= 0.93. Model performances are also evaluated within the basin at the internal-catchment outlets (Table ) where stage measurements are available. Figure  shows simulated hydrographs along with the observed discharges for some locations. The results show that the performances of the NewAge simulation are a little better than the performances reported by , with slightly lower PBIAS value (PBIAS = 8.2, r= 0.95). Generally, the model predicts both the high flows and low flows well, with slight underestimation of peak flows (Fig. a). This is likely due to the underestimation of SM2R-CCI precipitation data for high rainfall intensities . An additional source of error can also be caused by model inconsistency due to averaging out input data over large areas or from some inadequacy in stage–discharge curves used to obtain discharges from water levels. The slight underestimation of runoff could result from the overestimation of evapotranspiration. However, in this case, GLEAM (or MODIS) would cause larger discrepancies.

Regarding the internal-site discharge simulation, we highlight some representative results. The hydrograph comparison between the NewAge simulated discharge and the observed one of the Gelgel Beles River, enclosed at the bridge near to Mandura with an area of 675 km2, is shown in Fig. b. The performance of the uncalibrated NewAge at Gelegel Beles has a correlation coefficient of 0.70, PBIAS is 11.40 % and the KGE value of 0.68 (Table ).

Simulation performances for the medium size basins, such as the Ribb River, enclosed at Addis Zemen (area = 1592 km2, KGE = 0.81, PBIAS = 12 %, and r= 0.82; Fig. c), and Gilgel Abay River, enclosed at Merawi (area = 1664 km2, KGE = 0.81, PBIAS = 12 %, r= 0.93), are very good. For the Ribb River, the NewAge simulation performance can be compared with SWAT Model performances by  (r= 0.74–0.76). Even with SWAT model calibration for this specific subbasin, the results of our study are much better. Similarly, without calibration for the Gilgel Abay River, the NewAge simulation performance is better than the results of Wase-Tana (, PBIAS = 34) and FlexB (, PBIAS = 77.6) or comparable to SWAT (PBIAS = 5).

To analyze the simulation capacity of NewAge for the larger-size basins, the performances at Angar River (area 4674 km2), Lake Tana (area 15 321 km2), and Dedisa River basin (9981 km2) are reported. The simulation analyses at the Angar River enclosed near Nekemt (KGE = 0.72, PBIAS = -14.10 %, and r = 0.82), Lake Tana (KGE = 0.26, PBIAS = 5.10, and r = 0.60), and Dedisa (KGE = 0.55, PBIAS = 19.60, and r = 0.81) indicate that the performances are acceptable. The comparison of simulated and observed discharges, as well as the locations of the Angar (basin brief description; ) and Dedisa rivers are shown in Fig. h and g, respectively.

For most subbasins, because of the good model performances (i.e., KGE is higher than 0.5 and PBIAS is within 20 %), the estimated discharges are deemed adequate for estimating water resource at locations where gauges are unavailable. The model is also able to reproduce discharge across the range of scales. For instance, the model performances at the Ethiopia–Sudan border (175 315 km2), Dedisa near Arjo (9981 km2), main Beles (3431 km2), and Temcha near Dembecha (406 km2) are also acceptable. An exception is Lake Tana, where the discharge is regulated (Fig.  and Table ). Model performance varies with basins and a consistent behavior with respect to basin size, climate, vegetation density and topographic complexity is not found. Indeed, there are many factors that affect the model performance, including uncertainties in input observations. Sample simulations at all the channel links of the study basin at daily time steps are provided in the Supplement ().

NewAge-simulated ds / dt for 16 years for each subbasin is calculated as a residual of the flux terms. The simulated ds / dt is represented and compared with the GRACE-based TWSC in Fig. . The storage change shows high seasonality over the basin, with positive change in summer and negative change in winter. The change varies from -100 to +120 mm month-1. The model ds / dt, aggregated at monthly timescales and for the whole basin, is in accordance with the GRACE TWSC both in temporal pattern and amplitude. The good correlation coefficient of 0.84 and the general good performances of the ds / dt component is certainly caused also by the ability of NewAge to reproduce the other water fluxes well. Due to the possible high leakage error introduced in GRACE TWSC at high spatial resolutions , statistical comparison at subbasin level is not performed. However, the spatial distribution of NewAge and GRACE ds / dt estimates can be found in the Supplement.

The water-budget components (J, ET, Q, and ds / dt) of 402 subbasins of the UBN are simulated for the period 1994–2009 at daily time steps. Figure  shows the long-term, monthly-mean, water-budget closure derived from 1994 to 2009. The 4 months (January, April, July, and October) are selected to show the four seasons (winter, spring, summer, and autumn). For all components, the mean seasonal variability is very high. Generally, the seasonal patterns of Q and ds / dt follow the J, showing the highest values in summer (i.e., July) and the lowest in winter (i.e., January). However, simulated ET shows distinct seasonal patterns with respect to the other components, the highest being during autumn (October), followed by winter (January). During the summer it is low, most likely due to high cloud cover.

The variability between the subbasins is also appreciable. Generally, all water-budget components tend to increase from the east to the southwestern part of the basin, except for the summer season (July). During summer, however, the eastern part of the basin receives its highest rainfall, stores more water, and generates high runoff as well. In general the dominant budget component varies with months. For instance, in January ET is dominant while in June and July ds / dt is more dominant. After the summer season, Q and ET are the dominant fluxes. A regression analysis based on the results for all subbasins and all years shows that, on short timescales (e.g., daily or monthly), the variability in ET is not due to variability in J (R2= 0.01). Conversely, on the yearly timescale, 78 % of ET variance is explained by variability in J.

The spatial variability of the long-term mean annual water-budget closure is shown in Fig. . The spatial variability for J and Q is higher than ds / dt and ET. The higher Q and ET in the southern and southwestern part of the basin are due to higher J. Similarly, Q is lower in the eastern and northeastern part of the basin. In terms of the percentage share of the output term (Q, ET, ds / dt) of total J (Fig. c), ET dominates the water budget, followed by Q. It is noteworthy that the eastern subbasins with low ET still have percentage share of ET due to the low amount of J received.

The long-term basin-average water-budget components show 1360 ± 230 mm of J, followed by 740 ± 87 mm of ET, 454 ± 160 mm of Q and -4 ± 63 mm of ds / dt. While the spatial variability of the water budget is high, the annual variability is rather limited. Higher annual variability is observed for J, followed by Q. 2001 and 2006 are wet years, characterized by high J and Q. Conversely, 2002 and 2009 are dry years with 1167 mm and 1215  mm per year of precipitation. Details on the two dry years (2002, 2009) of the region can be read in .

Figure  provides long-term monthly-mean estimates of water-budget fluxes and storage. The average basin-scale budget is highly variable. The highest variability is mainly in J and ds / dt. During summer months, J, Q, and ds / dt show high magnitude. ET is not high in June, July, and August, but it is in October and December. The S(t) accumulated in the summer season feeds high ET in autumn, and causes very high drops in ds / dt (Fig. ). The seasonal trend between J and ET is slightly out of phase, i.e., the highest energy to evaporate water occurs during low precipitation months (March, April, and May). Due to this slight out-of-phase trend, ET is minimal and Q and ds / dt are enhanced during wet months (Fig. ), thus revealing that ET is water-limited more than energy-limited. The same Figure also shows the complex interplay between discharges, (variation of) storages, and evapotranspiration. A first look at Figs. 4 and 5 could lead to the conclusion that overestimation of ET brings in underestimation of Q. However, Fig. 10 shows that the role of ds / dt is not negligible at all.