As one of the longest rivers in the world, River Nile that traverses 11 countries of Africa goes through a restively long journey of 6695 km from its furthest source (Ruvyironza in Kagera Basin) to the Nile Delta in Egypt. The drainage area of the River Nile with the coverage from 31∘ N to 4∘ S (in north–south direction) and 24 to 40∘ E (in west–east direction) is about 3 400 000 km2 (Fig. 1). The lakes within the River Nile Basin include the Victoria, Edward, Kyoga, Albert, No, Tana, and Nasser. There are two main sources of the River Nile including the White Nile (from the equatorial region), and the Blue Nile (from the Ethiopian highlands). The Nile Basin covers parts of several countries (Food and Agriculture Organization FAO, 1997): Uganda (98.1 %), Kenya (8.0 %), Tanzania (8.9 %), Rwanda (75.5 %), Burundi (47.6 %), Democratic Republic of Congo (0.9 %), Sudan and South Sudan (79.0 %), Ethiopia (33.2 %), Eritrea (20.4 %), and Egypt (32.6 %). The River Nile receives little or negligible runoff from about 40 % of its drainage (basin) area which comprises dry lands of either arid or hyper-arid condition. Moreover, the River Nile loses about 50 % by evaporation in the Sudd region of South Sudan. These altogether make the Nile River to have its runoff coefficients rather lower in comparison with what would be expected from its vast drainage area.

Monthly river flow data recorded at 18 locations (Table 1) in the Nile Basin were obtained from three sources. Flow data for 12 stations were obtained from the Global Runoff Data Centre (GRDC), Koblenz, Germany. For 2 stations, data were obtained at KU Leuven from the database of the River Nile basin Flow Regimes from International, Experimental and Network Data (FRIEND/Nile) project (http://www.unesco.org/new/en/cairo/natural-sciences/hydrology-programme/friendnile/, last access: 10 September 2014). Some flow data were obtained from the report by Kennedy & Donkin Power Ltd (1997). The long-term average monthly flow in the last column of Table 1 is noted to range from 20 m3s-1 (station 5) up to 2699 m3s-1 (station 18).

A number of rainfall stations were used in this study. The daily rainfall data at 5 locations over the Blue Nile were those used in a study by Taye and Willems (2013). Data for daily (monthly) rainfall at 4 (6) locations in or around Kagera (Atbara) catchment were obtained from the FRIEND/Nile project. Furthermore, daily rainfall data from 4 stations in the Kyoga Basin were obtained from the Ministry of Water and Environment, Uganda. Especially for the last two data sources, missing rainfall data records were filled-in (using the inverse distance weighted interpolation technique) in a similar way as done for a number of meteorological stations of the Nile Basin in previous studies by Onyutha and Willems (2015a, b).

Table 2 shows location and ID of the selected stations as well as the data period and long-term statistical metrics coefficient of variation (Cv), skewness (Cs) and actual excess kurtosis (Ck) for the monthly rainfall. Values of Cs and Ck greater than zero indicate that the distribution of the data deviate from the Gaussian type. The values of Cv in Kyoga and Kagera were lower than those of Atbara and Blue Nile. The highest values of Cv, Cs and Ks were obtained for stations in the Atbara catchment. This is because the catchment is located in an arid climate region and thus the data are characterized by large extent of ties caused by the existence of zeros. Moreover, the data from Atbara have larger differences between the minimum and maximum monthly rainfall totals than for other selected catchments. More monthly rainfall data series as shown in Table 3 were adopted from Onyutha and Willems (2015a).

Similarity in flow variation patterns was studied and used in a clustering procedure to group the hydrological stations. On assumption that the flow variation can be primarily explained by that in rainfall, the grouping of the stations was done based on both the seasonal and annual time scales. It is known that the rainfall in the equatorial region exhibit bimodal pattern (Nicholson, 1996). The “long-rains” and “short-rains” occur over the months of March–May (MAM) and October–December (OND) respectively. The June–September (JJAS) and January–February (JF) are dry periods. However, the rainfall in the middle section (Sudan and Ethiopia) of the River Nile Basin exhibit a unimodal pattern (Camberlin, 2009; Onyutha and Willems, 2015a) with the JJAS (MAM) as the main (slight) rainy season. The dry season is experienced over the October–February (ONDJF) period. The validity and/or consistency of the obtained groups of hydrological stations (especially with respect to regional coverage) was checked based on those formed from meteorological stations by Onyutha and Willems (2015a).

The steps taken to group the discharge stations were as follows: i.

form a common pool by putting together all the discharge stations under consideration;

In each group of the hydrological stations formed, the variation of flow was compared with that of the rainfall at both seasonal and annual time scales. This was done on a regional basis as well as at a catchment scale. For the regional basis: (1) the rainfall variation patterns at the different stations within a group (or region) were compared, (2) the variation of the region-wide rainfall average was compared with that of the region-wide mean river flow. To check on the co-variation of rainfall and flow at a catchment scale, representative catchments each with a number of meteorological stations were selected from each hydrological group formed. For each selected catchment, comparison was made between the patterns of the variation of flow at the outlet of the catchment and: (1) rainfall at each meteorological station, and (2) catchment-wide average rainfall. The idea was to assess how well, at both catchment level and regional scale, the variation in flow could be explained by that in rainfall.

Three rainfall–runoff models including NAM, VHM and HBV were applied under the same meteorological conditions in simulating daily flows at the outlet of each selected catchment. The rainfall–runoff modeling was used to assess any possible empirical evidence for the change in catchment characteristics in the form of temporal change in catchment runoff response to rainfall, hence between observed and simulated flow. Explanation on this idea will be given in Sect. 3.4. The selected conceptual catchment runoff models make use of the catchment-wide averaged rainfall and evaporation as their inputs to simulate the rainfall–runoff at the lumped catchment scale. To get the details on these models including the description of their model structure, variables and parameters, the reader is referred to Danish Hydraulic Institute DHI (2007), Madsen (2000) and Nielsen and Hansen (1973) (for NAM), Willems (2014), and Willems et al. (2014) (for VHM), and AghaKouchak and Habib (2010), AghaKouchak et al. (2013), and Bergström (1976) (for HBV).

For each selected catchment, the potential evaporation was computed using the FAO Penman–Monteith method (Allen et al., 1998) considering minimum and maximum temperature. The catchment-wide mean areal rainfall was calculated using the Thiessen polygon method. The calibration (validation) period of the models for each selected catchment was ensured to be at least 25 (12) years. Some of the model calibration strategies and uncertainty estimation techniques include the Generalized Likelihood Uncertainty Estimation (GLUE) (Beven and Binley, 1992), and Uncertainty Estimation based on Local Error and Clustering (UNEEC) (Solomatine and Shrestha, 2009). The UNEEC method by considering the model residuals to be indicative of the model uncertainty quantifies the uncertainty in three steps including: clustering, model error probability distribution estimation, and building model uncertainty based on the error probability distribution (Solomatine and Shrestha, 2009). As a Bayesian approach, GLUE procedure uses parameters' sets randomized from the prior distribution to infer the output (posterior) distribution based on the simulations. Because the HBV version used in this study employs the GLUE technique, GLUE was also adopted for NAM and VHM. This was for the uniformity of calibration scheme to obtain an ensemble of simulated flows from each of the models. The optimal set of parameters was considered as that with the highest Nash–Sutcliffe Efficiency (ENS) (Nash and Sutcliffe, 1970). The model performance was evaluated both statistically and graphically. Statistically, the “goodness-of-fit” was evaluated in terms of the ENS and the coefficient of determination (R2). Graphically, the plots of Box–Cox (BC) transformed observed vs. simulated series were made for the maximum as well as minimum flow in each year. The BC (Box and Cox, 1964) transformation (Eq. 1) with the parameter (λ) set to 0.25 was applied to give similar weights to the maximum and minimum flows (f) so as to obtain homoscedastic model residuals. Comparison of the simulated and observed cumulative flow was also made. BC(f)=fλ-1λ

The change in catchment behavior due to the anthropogenic influence would lead to temporal change in the difference between the observed and modeled runoff flows and sub-flows. Anthropogenic influences such as deforestation, overgrazing, significant expansion of urbanized areas etc over a given catchment would: (1) affect the amount of infiltration into the soil, (2) alter the amount and velocity of the overland flow, (3) modify the rate and amount of evaporation, etc. Hence, these would alter the catchment response to the rainfall input. This difference in response should be visible through the changes in runoff volumes, sub-flow volumes, ratio between sub-flow volumes, model parameters describing the sub-flow response to such times such as the recession constant.

Because of the importance to study the runoff sub-flows and more specifically the overland flow separately, a numerical digital filter was applied to split the flow into the various sub-components. This discharge splitting was done based on the sub-flow recession constants as applied in the tool provided by Willems (2009). The temporal change in the overland flow was analyzed using two approaches including the Cumulative Rank Difference (CRD) (Onyutha, 2015) technique and the Quantile Perturbation Method (QPM) (Ntegeka and Willems, 2008; Willems, 2013). The two methods were applied to the annual maxima, annual minima and annual mean flow. Each of the two methods CRD and QPM analyzes the given data in a different way. Whereas the CRD focuses on the cumulative effects of the variation, the QPM considers quantile changes.

The concept behind the CRD is not new as it is related to a Brownian bridge which employs the standard Brownian motion. As stated in Benson et al. (2013), a Brownian motion describes a limit Markov or memory-less process of finite-variance random walks with short-range correlation (Bhattacharya and Gupta, 1983). According to the central limit theorem, a finite-variance motion converges toward the Gaussian limit distribution (Benson et al., 2013) and this property makes the application of the Brownian motion so attractive in hydrology. The concept of the Brownian bridge in hydrology is applied in the Pettitt test (Pettitt, 1979), distribution free CUSUM test (Pages, 1954), etc, which are all important for change-point detection. However, as opposed to focusing on the change-point detection, the CRD method accumulates the difference between the exceedance and non-exceedance counts of the data points in a sample to establish periods over which the cumulative effect of the variation in the series is positive or negative. This is vital to graphically reveal hidden (short-durational) increase or decrease in the variable over unknown time periods. Such an approach falls in line with the need for graphical exploration of changes in series as opposed to the purely statistical results which might be meaningless sometimes (Kundzewicz and Robson, 2000) to an environmental practitioner. In this study, the CRD capability was deemed important to expose any persistent mismatches between the observed and modeled flow. Moreover, being rank-based, the CRD is not affected by non-normally distributed data which frequently occur in hydro-meteorology.

To apply the CRD method for sub-trend analysis, the following steps were taken: i.

rescaling of the given series in a nonparametric way using Eq. (2) to obtain the difference (D) between the exceedance and non-exceedance counts of the data points;D(i)=2Ra(i)-(n-w(i))for1≤i≤nwhere Ra is the number of times a data point is exceeded, and w the number of times a data point appears within the given sample. To determine Ra or w, each data point is counted as if it was not considered before.

Unlike the CRD method which relies on rescaled series, the QPM uses the given series directly (i.e. without rescaling) to obtain quantile anomalies. This allows the QPM outputs to be importantly applicable, for instance, in revising design quantiles to account for the decadal or multi-decadal oscillations or variability in the hydro-meteorological variable. To apply the QPM, two series are derived from the same data set. One series (call it y) is the full series, and the other (denoted by x) is a sub-set extracted as a sub-period from the full series. The sub-series are contained in a moving window of a specified block length (taken as 15 years in this study). The moving window is first put at the beginning of the full time series and afterwards moved by 1 year at a time. For each moving window, quantile perturbation factors are computed as the quantiles above a selected exceedance probability threshold selected from x and divided by their corresponding counterparts from y. The ultimate anomaly for the window under consideration is determined as the average of the perturbation factors for all empirical quantiles above a given threshold. The ultimate anomalies from the different moving window positions are considered to characterize the variability of the extreme quantiles in the series. An elaborate and systematic description of the QPM can be obtained from Ntegeka and Willems (2008) and Willems (2013).

Two homogenous groups of the DMS were obtained based on the clustering approach. The stations numbered 1 to 9 in Table 1 (hereinafter referred to as “group 1”) are in the equatorial region and South Sudan (or more generally along the White Nile). This group comprises various main rivers and sub-basins including the Victoria Nile, Kyoga Nile, Albert Nile, Bahr El Jebel and the White Nile between Malakal and Khartoum. The flow stations in Sudan, Ethiopia and Egypt, i.e. at the outlets of the Blue Nile and Atbara, and those along the main Nile formed “group 2” (stations numbered 10 to 18 in Table 1). Positive significant cross-correlation between the flow from the stations of each group can be seen in Tables 4 and 5 for seasonal and annual flow respectively. The correlation between the flow from a group 2 station and that from another station in group 1 was generally negative. This is illustrated using the radar plots in Fig. 2 based on annual flow. It is shown in Fig. 2a–d and e–h based on selected group 1 and 2 stations that the correlation between the annual flow of the two groups is statistically insignificant at 5 % significance level. These two DMS groups are consistent with the two homogenous regions formed by Conway and Hulme (1993) based on the inter-basin correlations of 40 year (1945–1984) precipitation and runoff data. They are the White Nile (Lake Victoria and Equatorial Lakes), and that of the Ethiopian highlands (Blue Nile and Atbara).

In another study by Nyeko-Ogiramoi et al. (2012), agglomerative hierarchical cluster algorithms to identify homogenous regions of the Nile Basin based on a combination of physiographic characteristics and hydrological properties. The authors identified 30 regions based on only catchment characteristics, and 15 considering a combination of both catchment characteristics and hydrological properties. Importantly, Nyeko-Ogiramoi et al. (2012) remarked in their conclusion that the homogenous regions were not convincing because some sub-regions were highly influenced by others especially those upstream the river based on the dependency of the flow data. This dependency of the homogenous regions on the flow data is linked to the two sources of the Nile River, which corresponds to the two groups of hydrological stations found in this study. Based on the research findings by Sestini (1993), we anticipate that the two DMS groups formed in this study follow a different spatio-temporal influence. The precipitation over the group 1 region is controlled by the changes in the equatorial circulation compared with that for group 2 which might be under the influence of the North African monsoon (Sestini, 1993).

It is important to note that the outcomes of regionalization of catchments depend on the criteria used in the grouping procedure and the intended means and purpose of the application. For a more detailed study at sub-basin level, for instance, further sub-delineation may be useful. For the Lake Victoria sub-basin, Nyeko-Ogiramoi et al. (2012) identified 5 regions to estimate flood frequency distributions from catchment characteristics. In a follow up study by Onyutha and Willems (2015c) a peak flow quantile estimation regional model was developed in a way that accounts for the spatial differences in both the physiographic characteristics and hydro-climatic properties across the sub-basin. The DMS grouping in this study was to assess the regional difference in the main flow variation attribute in the Nile Basin. Eventually, the driving forces of the rainfall variability provided also on regional basis, e.g. by Onyutha and Willems (2015a), can be linked to the DMS grouping in this study for an insight into the regional flow-rainfall co-variation.

Figure 3 shows the temporal variations in the rescaled annual river flow. Rescaling in which each data point was divided by the sample mean was done to have comparable orders of magnitude for the flows at the different stations. The long-term mean of the rescaled flow (taken as the reference) thus has a value of one. Further confirmation of the validity of “group 1” is shown in Fig. 4 based on the co-occurrence of the long-term variation of the outflows from three lakes in the Great Lakes region (Ministry of Water, Lands and Environment MWLE, 2004). The flow of “group 1” (Fig. 3a) was above (below) the long-term reference over the period 1915–1920, mid 1960s–early 1980s (mid 1920s–late 1950s). There was a step jump in the flow mean around 1960. However, slowly over time, the equatorial region went through a recovery process to even out the effect of this step jump so as to bring the long-term mean of the Nile River flow back to its value before 1960. This recovery process was evidently still on-going even up to late 1990s (where the data used in this study ended). Figure 3b shows that the flow from “group 2” was also above the reference over the period from mid 1910s to early 1920s. The coincidence of the rainfall total being above the reference for both groups by around 1920s could be because of the high rainfall extremes that occurred across the entire study area. For instance, on the 31 July 1920, Khartoum received daily rainfall of 88 mm which was the highest since late 1890s (Hulme and Trilsbach, 1989). However, after 1920, the flow in “group 2” was characterized by its fluctuation about the reference up to the late 1950s. From 1960 to the late 1980s, the flow was below the reference. This decrease was because of a remarkable decline in rainfall over the region. Over the Sahel region, the decline in annual rainfall was as low as 30 % over the 1970s and 1980s (Hulme, 1992).

The flows from “group 1” are noticeably different from those of “group 2” (especially after the year 1920). This is consistent with the correlation analyses given in Sect. 4.1. Related to this difference, Sestini (1993) also found that the flow from the Blue Nile is uncorrelated with that of the White Nile. However, the author found that the runoff from the Blue Nile has a moderately good correlation with the rainfall from the Sahel region. This correlation might be an indication of the close agreement between the variability patterns for the rainfall over central Ethiopia and that in central Sudan as shown by Onyutha and Willems (2015a).

Recently, Onyutha and Willems (2015a) grouped meteorological stations across the study area into two and three based on the patterns of QPM anomalies and Long-Term Monthly Mean (LTMM) of rainfall respectively. Based on the QPM anomalies, the two groups included those; in the equatorial region (group A), and Ethiopia and Sudan (group B). The same groups were realized for the LTMM with the third one (group C) for the rainfall stations in Egypt. Therefore, the regional coverage of group 1 in this study is consistent with that of group A for the rainfall stations in the study by Onyutha and Willems (2015a). Moreover, the rainfall variation in group B of the cited reference was found to be in a close agreement with that of the flow for this study's group 2. The LTMM of the rainfall in Egypt is far lower (and with unclear variation patterns) than those in groups A and B. This suggests that the influence of the rainfall over Egypt on the Nile flow is minimal.

Figure 5 shows the correlation as well as the variation of rescaled annual rainfall at selected locations within the two hydrological groups. The rainfall rescaling was done in the same way as for the flow. Figure 5a and b show close agreement between the variation of rainfall at one selected station and that of another i.e. A and B of group 1, and K and AA for group 2. Within each group, when a station was selected and the correlation between its rainfall and those at other stations computed, generally positive correlation coefficients are obtained as illustrated in Fig. 5c and d. Moreover, for the selected stations, the correlation values are statistically significant at 5 % significance level. Considering all the selected stations, the cross-correlation coefficients between the annual rainfall from one station and series of other stations are shown in Table 6 (for group 1) and Table 7 (for group 2). The close agreement between the rainfall at these various stations from each group in terms of the correlation of their QPM quantile anomalies was also demonstrated by Onyutha and Willems (2015a). However, in some few cases negative correlation was obtained between the rainfall of one station and that of another, even within the same group. This may be due to the high noise to signal ratio or spatial dissimilarity in microclimate (micro-scale features). To even out such spatial dissimilarity, the short-term fluctuations can be smoothened by averaging the temporal variation patterns of the rainfall at the various meteorological stations of each group. This was deemed vital and performed for assessing the co-variation of flow and rainfall of each group as presented next.

The consideration of both the regional scale and catchment level is important to provide a better understanding on the flow-rainfall co-variation. Averaging of the flow and rainfall over the entire region of each group can be considered as a means of spatial filtering of the local influences from the various stations. However, for the catchment-scale flow-rainfall co-variation, consideration was given to the flow at the catchment outlet and catchment-wide weighted average rainfall upstream of the catchment outlet. A zoomed-in analysis such as that for the catchment-scale is important to obtain an insight into how strongly the micro-climate (micro-scale features) influence the flow-rainfall co-variation.

The main catchment within the geographical coverage of each group formed in Sect. 4.1 was selected. These are the Kagera catchment at Kyaka Ferry (60 000 km2) and the Blue Nile catchment at Khartoum (325 000 km2) for group 1 and 2 respectively. The three models including NAM, VHM and HBV were applied to each catchment. The calibration (validation) period of the models was 1 January 1965–31 December 1989 (1 January 1990–31 December 2002) for the Blue Nile catchment and 1 January 1950–31 December 1974 (1 January 1975–31 December 1986) for the Kagera catchment.

Figure 8 shows the time series of the observed and simulated Blue Nile and Kagera flows. The model parameters following the GLUE technique are listed in Appendix Table A1. Based on a visual judgment considering each model, better modeled results were obtained for the Blue Nile (Fig. 8a) than for the Kagera (Fig. 8b) catchment. This is because of the larger catchment size and stronger seasonal differences for the Blue Nile which leads to smoother catchment response to rainfall than that for the Kagera Basin.

Table 9 shows the statistical assessment of the models' performance. The value of both, the ENS and R2 for calibration were acceptably high. Consistent with the visual judgment from Fig. 8, the model performance (though reasonably good) in the validation was better for the Blue Nile than the Kagera catchment. For the Kagera catchment, in reference to the model calibration results, the validation ENS for NAM, VHM and HBV exhibited a drop of 27, 30 and 26 % respectively. In order to check whether this drop in the ENS is explained by model over-calibration, the validation input series were considered as independent model inputs and when calibration based on the GLUE scheme was repeated for this new input, there was no significant increase in the ENS values compared to those for the validation shown in Table 9. One reason for the ENS drop could be the lower data quality taking into account that some measurement stations tend to be irregularly operational due to poor maintenance. Another potential reason might be the difficulty in the models to capture the dynamics of runoff generation at the catchment level as explained next. The validation period for Kagera Basin (i.e. 1975–1986) had its beginning not far from around 1960 during which the equatorial region experienced a step jump in the flow mean. It could be possible that all the models failed to adequately capture the catchment behavior in its recovery from the effect of the step jump (as seen from Figs. 3 and 4). However, because the ENS values for all the models are higher than 0.5 for all the validation runs, the modeled flow was deemed adequate for the empirical investigation of the possible change in catchment rainfall–runoff response.

Figure 9 shows the graphical assessment of the goodness-of-fit between the Box–Cox transformed observed and modeled flow. Good model performance was obtained for both the annual maximum (Fig. 9d) and minimum (Fig. 9e) flows of the Kagera. For the Blue Nile, though the performance of all the models were good for the annual maxima (Fig. 9a), the HBV model tends to overestimate most of the annual minima (Fig. 9b). With respect to the cumulative flow volumes (Fig. 9c and f), the models show slight over-estimations. For Kagera catchment, the slight overestimations are due to the lower performance of the simulation results from the validation period. Note that because the Blue Nile flow has stronger seasonal variations, the flow scatter is more wide-spread for the Blue Nile (Fig. 9a and b) than for the Kagera (Fig. 9c and d). Based on these performance evaluation results, it can be generally concluded that the three models jointly allow an assessment to be made of potential temporal changes in the catchment rainfall–runoff responses.

Figure 10 shows results of sub-trends in the observed and modeled overland flow. In Fig. 10a and c, it is perceptible that about half the CRD curve fell below (above) the reference over the period 1965–1983 (1984–2000). This showed that there were both negative and positive sub-trends in the annual mean and maximum overland flows. However, the annual minimum overland flows were mainly characterized by a decrease since almost its entire CRD curve fell below the reference (Fig. 10b). The presence of a step jump in the mean flow around 1960 is evident for the Kagera (Fig. 10d–f). In the 1990s, some deviations between the modeled and observed overland annual maximum flow sub-trends (Fig. 10a) for the Blue Nile is visible for the outputs from all the models.

Figure 11 shows changes in observed and simulated overland flow in terms of the QPM quantile anomalies. For the annual maximum and mean overland flows at the Blue Nile (Fig. 11a and c), there were oscillation highs (OHs) in the mid 1960s to late 1970s, and in the 1990s. There was an oscillation low (OL) from the late 1970s to around 1990. Taye and Willems (2013) found similar results especially for the annual maximum flows in the upper Blue Nile Basin. However, for the annual minimum flows (Fig. 11b), the period from the mid 1960s to late 1970s (early 1980s to late 1990s) was characterized by an OH (OL). For Kagera, the period 1950–1959 (1960–1986) was characterized by an OL (OH) (Fig. 11d–f). Based on the QPM results, the peak of the OH was around 1965.

Consistent with the CRD sub-trend results, again some slight over- or underestimation of the observed changes was also demonstrated in the QPM anomalies. These minor discrepancies between the observed and modeled flow as demonstrated in both the CRD and QPM change detection techniques could be indicative of some possible slight changes in the catchment behavior, which may be attributed to an anthropogenic influence. A number of previous studies also ascribed hydrological changes in the different parts of the Nile Basin to anthropogenic factors. Using rainfall–runoff modelling, Legesse et al. (2004) noted a remarkable mismatch between the observed and modeled lake levels over the period 1984–1996 compared with that in 1968–1983. This discrepancy was attributable to human influence on the lake in terms of abstractions from the influent rivers (Legesse et al., 2004). According to Bewket and Sterk (2005), for the period between 1960 and 1999 there was a decrease of 0.6 mmyr-1 in the Chemoga catchment flow during the dry season (October to May) probably due to an increase in cultivation area in the catchment. According to Rientjes et al. (2011), forest cover decreased from 50 to 16 % in the Gilgel Abay catchment over the period 1973–2001. They claimed this was probably due to deforestation for agriculture. Using satellite data, Elmqvist (2005) noted that the cropland area per household reduced from 0.4 to 0.1 km2 over the period 1969–2002 in Sararya Makawi, Sudan. This decrease was probably due to an increase in the population and intensification of agriculture (Elmqvist, 2005). Based on the land-use scenario investigation using a semi-distributed hydrological model, Mango et al. (2011) concluded that the magnitude of the extreme low (high) flows would reduce (increase) if the conversion of forests to agriculture and grassland in the headwaters of the Mara catchment would continue. In the equatorial region, Olang and Fürst (2011) used rainfall–runoff modeling for 14 sub-catchments to investigate the effect of the land-use changes on the hydrology of the Nyando watershed over the period between 1973 and 2000. Although the authors found an average increase of 16 % in the peak discharges over the entire period considered, they obtained larger changes in the sub-catchments with higher deforestation rates than others.

These findings on significant catchment changes and their effects on catchment runoff flows would not be confirmed in this study. Despite the slight over- or underestimation of the observed changes for both selected catchments, the outputs from all the models indeed exhibited close agreement in capturing the flow variability or quantile changes (by the QPM) (Fig. 11) and the cumulative effect of the flow variations or sub-trends (by the CRD approach) (Fig. 10). This generally indicates that changes in the catchment behavior in transforming the rainfall input into runoff is minimal. In related studies, similar conclusions were also made by e.g. Taye and Willems (2013) and Gebrehiwot et al. (2013), all done for the period 1960–2004. Gebrehiwot et al. (2013) applied the HBV model to the Birr, Upper-Didesa, Gilgel Abbay, and Koga catchments of the Blue Nile Basin and found that although some model parameters changed over some selected periods, the integrated functioning of the catchments showed minimal changes. Using NAM and VHM models, Taye and Willems (2013) also concluded that there are no discernible changes noted for the Blue Nile catchment response. Therefore as shown in this study, the temporal flow variations in the Nile Basin may be attributed mainly to the rainfall variations.