Sensitivity of Streamflow to Changing Rainfall and Evapotranspiration in Catchments Across the Nile Basin

Abstract

This research focuses on the complex dynamics governing the sensitivity of streamflow to variations in rainfall and potential evapotranspiration (PET) within the Nile basin. By employing a hydrological model, our study examines the interrelationships between meteorological variables and hydrological responses across six catchments (Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb) and explores the intricate balance between rainfall, PET, and streamflow. Nash Sutcliffe Efficiency (NSE) for calibration of the hydrological model ranged from 0.636 (Ribb) to 0.831 (El Diem). For validation, NSE ranged from 0.608 (Ribb) to 0.811 (Blue Nile). With rainfall kept constant while PET was increased by 5%, the streamflows of the Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb decreased by 7.00, 5.08, 2.49, 4.10, 1.84, and 7.67%, respectively. With the original PET data unchanged, increasing rainfall of the Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb by 5% led to an increase in streamflow by 9.02, 9.87, 5.38, 4.34, 6.58, and 8.32%, respectively. The research reveals that the rate at which a catchment losing water to the atmosphere (determined by PET) substantially influences its drying rate. Utilizing linear models, we demonstrate that the surplus rainfall available for increasing streamflow (represented by model intercepts) amplifies with higher rainfall intensities. This highlights the pivotal role of rainfall in shaping catchment water balance dynamics. Moreover, our study stresses the varied sensitivities of catchments within the basin to changes in PET and rainfall. Catchments with lower PET exhibit heightened responsiveness to increasing rainfall, accentuating the influence of evaporative demand on streamflow patterns. Conversely, regions with higher PET rates necessitate refined management strategies due to their increased sensitivity to changes in evaporative demand. Understanding the intricate interplay between rainfall, PET, and streamflow is paramount for developing adaptive strategies amidst climate variability. By examining these relationships, our research contributes essential knowledge for sustainable water resource management practices at both the catchment and regional scales, especially in regions susceptible to varying sensitivities of catchments to climatic conditions.

1. Introduction

Rainfall and potential evapotranspiration (PET) are the two most important meteorological variables regulating the delicate equilibrium of water balance [1]. Under a changing climate, these two variables are expected to be affected, thus, impacting water resources. Several studies have documented the impacts of climate variability on rainfall and PET within the diverse catchments of the Nile basin [2,3,4]. Despite the existing body of knowledge, e.g., [5,6,7], a comprehensive understanding of the intricate interplay between rainfall and PET, and their consequent effects on streamflow remains a critical research gap. A systematic investigation, meticulously examining the response and sensitivity of a streamflow to the shifting patterns of increasing/decreasing rainfall and PET across the varied catchments of the Nile basin remains crucial. Shedding light on these complex dynamics advances the scientific understanding of hydrological processes. Moreover, the insights obtained hold paramount importance for policymakers and water resource managers, facilitating the formulation of evidence-based strategies to sustainably manage the vital water resources of the region.

A deeper understanding of the hydrological responses within a catchment necessitates a meticulous exploration of its sensitivity to rainfall inputs, particularly in the context of anthropogenic influences [8,9]. To accomplish this, the employment of fully distributed physical hydrological models (FDHMs) emerges as an indispensable tool. These models offer the capability to incorporate spatial variability of rainfall and the heterogeneous nature of land use and land cover (LULC) types as the integral determinants of PET variability across the entire catchment area. The application of FDHMs in the context of the Nile basin catchments remains notably absent from the existing body of literature, and this can be attributed to the requisite high-resolution topographic data, including digital elevation models, soil maps, and detailed LULC information, which are challenging to acquire [10,11]. Moreover, the structural complexity of FDHMs, characterized by a large number of parameters, often complicates the process of model optimization, further limiting their widespread utilization. Consequently, alternative hydrological modeling approaches, such as lumped conceptual hydrological models, have gained traction. These models, characterized by their simplicity and ease of calibration due to a reduced parameter set, offer a pragmatic solution in situations where comprehensive data or resources are limited.

Previous research endeavors in the Nile basin have predominantly focused on understanding the impact of LULC changes [12] on streamflows ([13,14,15]). However, these studies have primarily focused on individual catchments, failing to provide a holistic perspective on the diverse hydrological responses across the entire Nile basin. Notably, a significant research gap exists in the understanding of hydrological responses due to climate variability within distinct catchments of the Nile basin, an aspect that has been identified to surpass human-induced influence, including alterations to LULC [16,17]. This study applies to a lumped conceptual model to investigate the hydrological responses of several catchments across the Nile basin. The primary objective of this study is to investigate the intricate hydrological dynamics inherent to Nile basin catchments under diverse scenarios involving rainfall and PET. Specifically, the scenarios were conducted; (1) under increasing rainfall but constant PET; (2) under increasing PET but constant rainfall; (3) under simultaneous increase in rainfall and PET. Through these systematic analyses, this research aims to explore the interrelationships between rainfall and PET and hydrological responses in the region. The outcomes of this study are of paramount significance to provide indispensable insights to inform regional planning initiatives, enabling proactive and predictive adaptations in anticipation of the effects of climate variability on extreme streamflows. This study focuses on a detailed analysis of six distinct catchments within the Nile basin—Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb—each of which exhibits unique hydrological responses due to varying climatic and environmental conditions. By examining the behavior of each catchment under different rainfall and PET scenarios, we aim to provide basin-specific insights that are essential for tailored water resource management strategies in the Nile basin.

2. Materials and Methods

2.1. Study Area

This study selects six (6) catchments across the Nile basin (Figure 1). These selected catchments, including the Blue Nile, El Diem, Kabalega (also known as the Wambabya River catchment), Malaba, Mpanga, and Ribb, were purposely identified based on the availability of modeling data from prior investigations e.g., [3,18]. The Nile River, renowned for its historical significance, draws its waters from two principal sources: the White Nile region and the central region drained by the Blue Nile. Consequently, the catchments selected in the central region include the Blue Nile, El Diem, and Ribb, while those in the White Nile region consist of Malaba, Mpanga, and Kabalega.

The Blue Nile basin stretches from Ethiopia to Sudan, covering an area of nearly 309,700 km². It has a total length of about 1460 km, emanating from the Ethiopian Highlands and extending up to Tuti Island located between Omdurman and Khartoum North. The length of the Blue Nile from Lake Tana to El Diem at the Ethiopian–Sudanese border is nearly 940 km. The drainage area of the Blue Nile from the source up to El Diem is about 175,064 km². Ribb River emanates from the Guma Mountains, and it is located within the upper Blue Nile sub-basin. It has a drainage area of about 1485 km². Wambabya River in Uganda contains the Kabalega Reservoir and has a catchment area of about 790 km². The two main contributing tributaries of Wambabya River include Rwamutonga River (originating from the areas of Hoima) and Nyamanga River emanating from Kiziranfumbi. Malaba River originates from the slopes of Mount Elgon and drains into Lake Kyoga in Uganda. It has a drainage area of about 2234 km². Mpanga River originates from the foothills of Mount Rwenzori and flows through the southwest region of Uganda. It has a drainage area of about 4734 km². The meticulous selection of these catchments provides a robust foundation for the comprehensive hydrological analysis conducted in this study.

2.2. Selected Hydrological Models

A lumped conceptual model referred to as a hydrological model focusing on sub-flow variations (HMSVs) [19] was selected and applied in this study. This model is freely available online. HMSV is specifically designed to reproduce extreme hydrological events and simulate rainfall–runoff processes in a lumped, instead of distributed, way. This structure enables HMSV to effectively capture rainfall–runoff dynamics while maintaining simplicity, making it well suited for this study’s focus on streamflow sensitivity to rainfall and PET variations across the Nile basin. Furthermore, earlier studies demonstrated the robustness of HMSV in simulating the hydrology of some catchments in the Nile basin [3,19].

The HMSV makes use of lumped daily rainfall and PET as model inputs. Following the model’s structure, lumped daily rainfall and PET are required by one main soil moisture store. Any excess runoff after the rainfall has fulfilled the evaporation demand and replenished the soil moisture is separated into overland runoff, interflow, and base flow. Each of these sub-flows is routed separately and later combined to become the total streamflow. The structure of the HMSV can be found in Appendix A Figure A1.

2.3. Model Data, Model Build Up, Calibration, and Validation

Quality controlled daily streamflow, rainfall, and PET data were adopted from various sources (Table 1). For each catchment, rainfall and PET were in the form of catchment-wide averaged daily series. There were no missing values in each series.

Calibration of HMSV was based on the generalized likelihood uncertainty estimation (GLUE) strategy [20]. The calibration period for both Ribb and El Diem was 1980–1991. The calibration periods for Blue Nile, Kabalega, Mpanga, and Malaba were 1965–1984, 1990–2005, 1990–2001, and 1999–2008, respectively. The validation period for both Ribb and El Diem was 1991–2000. The validation periods for Blue Nile, Kabalega, Mpanga, and Malaba were 1985–2000, 2006–2019, 2002–2009, and 2009–2016, respectively.

Table 1. Modeling data adopted for this study.

SNo	Catchment	Data Period	Data Source
1	Blue Nile	1965–2000	Onyutha [21]
2	El Diem	1980–2000	Onyutha [21]
3	Ribb	1980–2000	Onyutha [21]
4	Mpanga	1999–2009	Onyutha et al. [22]
5	Kabalega	1990–2019	Chelangat and Abebe [18]
6	Malaba	1999–2016	Mubialiwo et al. [3]

Note that the data adopted at each station included daily streamflow, rainfall intensity, and PET.

Table 1. Modeling data adopted for this study.

SNo	Catchment	Data Period	Data Source
1	Blue Nile	1965–2000	Onyutha [21]
2	El Diem	1980–2000	Onyutha [21]
3	Ribb	1980–2000	Onyutha [21]
4	Mpanga	1999–2009	Onyutha et al. [22]
5	Kabalega	1990–2019	Chelangat and Abebe [18]
6	Malaba	1999–2016	Mubialiwo et al. [3]

Note that the data adopted at each station included daily streamflow, rainfall intensity, and PET.

Figure 2 shows differences between catchments in the White Nile and Blue Nile regions in terms of the long-term mean of monthly flow and rainfall. Due to differences in the magnitudes, the datasets for Ribb (Figure 2a), as well as those for Mpanga and Kabalega (Figure 2b), were plotted on a secondary y-axis for comparability. The Blue Nile region is characterized by a unimodal pattern of rainfall and flow, with the June–September (JJAS) months comprising the main wet season (Figure 2a,c). The Nile region has a bimodal pattern of rainfall and flow characterized by the March–May (MAM) and October–December (OND) rainy seasons (Figure 2b,d). These patterns are the same as those obtained in a previous study [22].

2.4. Model Evaluation

The model performance in terms of the extent of the mismatch between observed and modeled flow was quantified using Nash Sutcliffe Efficiency (NSE) [23]. Consider that ${\mathit{Q}}_{\mathit{x}}$ and ${\mathit{Q}}_{\mathit{m}}$ denote observed and modeled series, respectively. The metric NSE was computed using

$$\mathit{N}\mathit{S}\mathit{E}=\mathbf{1}-{\displaystyle \frac{{\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{n}}{\left({\mathit{Q}}_{\mathit{m},\mathit{i}}-{\mathit{Q}}_{\mathit{x},\mathit{i}}\right)}^{\mathbf{2}}}{{\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{n}}{\left({\mathit{Q}}_{\mathit{x},\mathit{i}}-{\bar{\mathit{Q}}}_{\mathit{x}}\right)}^{\mathbf{2}}}}$$

(1)

where $\mathit{n}$ is the sample size.

The model performance was also graphically conducted through comparison of ${\mathit{Q}}_{\mathit{x}}$ and ${\mathit{Q}}_{\mathit{m}}.$ The idea was to assess the extent to which the model overestimated or underestimated the observed streamflows.

2.5. Trends and Variability in the Model Data

2.5.1. Trends

The trend test was applied to the annual means of rainfall, PET, and flow for the various catchments. The trend test involved computing the trend slope and testing the significance of the monotonic increase or decrease in the data. This was done using a MATLAB-based tool CSD-VAT_v.2 that can be downloaded via http://dx.doi.org/10.13140/RG.2.2.25896.38401 (accessed: 23 November 2024).

The slope (m) of the trend was computed using [24,25].

$$\mathit{m}=\mathit{m}\mathit{e}\mathit{d}\mathit{i}\mathit{a}\mathit{n}\left({\displaystyle \frac{{\mathit{x}}_{\mathit{j}}-{\mathit{x}}_{\mathit{i}}}{\mathit{j}-\mathit{i}}}\right),\forall \mathit{i}<\mathit{j}$$

(2)

The null hypothesis H₀ (no trend) was tested using the method of [26]. For a given variable Y of sample size n, we can rescale Y into series d_y in terms of

$${\mathit{d}}_{\mathit{y},\mathit{i}}=\mathit{n}-{\mathit{w}}_{\mathit{y},\mathit{i}}-2{\mathit{t}}_{\mathit{y},\mathit{i}}\mathrm{for}1\le i\le n$$

(3)

where t_y,i is the number of times the ith observation exceeds other data points in Y. Furthermore, ${\mathit{w}}_{\mathit{y},\mathit{i}}$ denotes the number of times the ith data point appears within Y. The trend statistic T is given by

$$\mathit{T}={\sum }_{\mathit{j}=\mathbf{1}}^{\mathit{n}}{\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{j}}{\mathit{e}}_{\mathit{y},\mathit{i}}$$

(4)

where

$${\mathit{e}}_{\mathit{y},\mathit{i}}={\mathit{d}}_{\mathit{y},\mathit{i}}\times \sqrt{{\displaystyle \frac{\left(\mathit{n}-\mathbf{1}\right)}{{\sum }_{\mathit{i}=\mathbf{1}}^{\mathit{n}}{\left({\mathit{d}}_{\mathit{y},\mathit{i}}\right)}^{\mathbf{2}}}}}\mathrm{for}1\le i\le n.$$

(5)

The mean of T is zero, and for large n, the distribution of T is approximately normal with the variance of T or given by [26].

$$\mathit{V}\left(\mathit{T}\right)={\displaystyle \frac{\mathit{n}\left({\mathit{n}}^{\mathbf{2}}-\mathbf{1}\right)}{\mathbf{12}}}.$$

(6)

Consider ${\mathit{V}}^{\mathit{q}}\left(\mathit{T}\right)$ as the variance of the trend statistic after the correction of $\mathit{V}\left(\mathit{T}\right)$ from the influence of persistence on the trend results using the method in [26]. The standardized test statistic Z, which follows the standard normal distribution with a mean (variance) of zero (one), is given by

$$\mathit{Z}={\displaystyle \frac{\mathit{T}}{\sqrt{{\mathit{V}}^{\mathit{q}}\left(\mathit{T}\right)}}}$$

(7)

Consider Z_α/2 as the standard normal variate at the selected α. The H₀ (no trend) is rejected $\left|\mathit{Z}\right|>\left|{\mathit{Z}}_{\mathit{\alpha }/\mathbf{2}}\right|$, Otherwise, the H₀ is not rejected at α. In this study, α was taken as 0.05, and this corresponded to a Z value of 1.96.

2.5.2. Variability Analysis

Variability was analyzed in the annual mean of rainfall, PET, and flow for the various catchments. Variability was analyzed by testing the H₀ (natural randomness) in terms of the fluctuations of sub-trends in the data. This was done using the CSD-VAT_v.2. The first step involved the choice of a time slice $\mathit{t}$ with the time unit of the series. Based on the selected $\mathit{t},$ we obtain $\mathit{\lambda }=\mathbf{0.5}\times (\mathit{t}+\mathbf{1})$ and $\mathit{\lambda }=\mathbf{0.5}\times \mathit{t}$ when $\mathit{t}$ is odd and even, respectively. A window of length $\mathit{t}$ covering the $\mathit{u}\mathit{t}\mathit{h}$ to $\mathit{v}\mathit{t}\mathit{h}$ data points of a variable—say X—is moved in an overlapping manner from the beginning to the end of the series. For every time slice, a sub-trend in the sub-series is computed in terms of the standardized trend statistic Z (Equation (7)). The sub-trends for all the time slices in the series can be computed using

$${\mathit{Z}}_{\mathit{i}}^{\left(\mathit{t}\right)}=\mathit{f}\left(\mathit{x}\subset \mathit{X}|{\mathit{x}}_{\mathit{u}}\le \mathit{x}\le {\mathit{x}}_{\mathit{v}}\right)\mathbf{for}\mathit{i}=\mathbf{1},\mathbf{2},\dots ,\mathit{n}$$

(8)

where Z_i is the ith value of Z, and the terms u and v are all based on i and can be given by:

$$\left.\begin{array}{l}\mathit{if} \mathit{i}<\mathit{\lambda }, \mathit{u}=\mathbf{1}, \mathit{v}=\mathit{t}+\mathit{i}-\mathit{\lambda }-\mathbf{1}\\ \mathit{if} \mathit{i}\ge \mathit{\lambda }\mathbf{and} \mathit{i}\le \left(\mathit{n}-\mathit{\lambda }\right), \mathit{u}=\mathit{i}-\mathit{\lambda }+\mathbf{1}, \mathit{v}=\mathit{i}+\mathit{\lambda }\\ \mathit{if} \mathit{i}>\left(\mathit{n}-\mathit{\lambda }\right)\mathbf{and} \mathit{i}\le \mathit{n}, \mathit{u}=\mathit{i}-\mathit{\lambda }+\mathbf{1}, \mathit{v}=\mathit{n}\end{array}\right\}$$

(9)

The values of Z_i are plotted against the corresponding data year, and the confidence interval limits (CILs) on every sub-trend are taken as the ${\mp \mathit{Z}}_{\mathit{\alpha }/\mathbf{2}}$. If the sub-trend statistic values do not go beyond the CILs, it means that the H₀ (natural randomness) is not rejected. Otherwise, the H₀ is rejected at a given α. The $\mathit{Z}=\mathbf{0}$ is taken as the reference. Fluctuations of the values of $\mathit{Z}$ about the reference characterize the variability in the data.

2.6. Model Experiments

In the simulation experiment, the original rainfall series was increased by 0.0, 2.5, 5, 7.5, 10, 15, 12.5, 17.5, and 20%, and let these series be denoted by ${\mathit{u}}_{\mathbf{1}},$ ${\mathit{u}}_{\mathbf{2}},$ ${\mathit{u}}_{\mathbf{3}},$ ${\mathit{u}}_{\mathbf{4}},$ ${\mathit{u}}_{\mathbf{5}},$ ${\mathit{u}}_{\mathbf{6}},$ ${\mathit{u}}_{\mathbf{7}},$ ${\mathit{u}}_{\mathbf{8}},$ and ${\mathit{u}}_{\mathbf{9}},$ respectively. Similarly, the original PET series was increased by 0.0, 2.5, 5, 7.5, 10, 15, 12.5, 17.5, and 20%. Again, let these new PET series be denoted by ${\mathit{v}}_{\mathbf{1}},$ ${\mathit{v}}_{\mathbf{2}},$ ${\mathit{v}}_{\mathbf{3}},$ ${\mathit{v}}_{\mathbf{4}},$ ${\mathit{v}}_{\mathbf{5}},$ ${\mathit{v}}_{\mathbf{6}},$ ${\mathit{v}}_{\mathbf{7}},$ ${\mathit{v}}_{\mathbf{8}},$ and ${\mathit{v}}_{\mathbf{9}},$ respectively. The model inputs ${\mathit{u}}_{\mathit{i}}$ and ${\mathit{v}}_{\mathit{j}}$ were obtained as combinations ${\mathit{c}}_{\mathit{i},\mathit{j}},$ such that ${\mathit{c}}_{\mathit{i},\mathit{j}}=[{\mathit{u}}_{\mathit{i}},{\mathit{v}}_{\mathit{j}}]$ for $\mathbf{1}\le \mathit{i}\le \mathbf{9}$ and $\mathbf{1}\le \mathit{j}\le \mathbf{9}.$ Thus, there were a total of 81 (or 9 × 9) sets of model inputs. In other words, the hydrological model was run 81 times while keeping the parameters at their optimal values.

2.7. Correlation Between Hydro-Climatic Variables and Climate Indices

Correlation between each of the hydro-climatic variables, including rainfall, PET, and streamflow, and selected climatic indices were analyzed. The selected climate indices included Niño3 and the Indian Ocean Dipole (IOD). Analysis was conducted in two ways. First, the original monthly series of both climate indices and hydro-climatic variables were used. In the second method, seasonal components of each series were removed before the correlation analysis. Monthly data for the IOD index were obtained in form of Dipole Mode Index (DMI) via https://psl.noaa.gov/ (accessed: 3 November 2024). Monthly series of Niño3 was obtained via https://psl.noaa.gov/data/timeseries/month/Nino3/ (accessed: 3 November 2024).

3. Results

3.1. Trends

Table 2. Statistical results of the trends.

Catchment	Flow			Rainfall			PET
	m	Z	p-Value	m	Z	p-Value	m	Z	p-Value
Kabalega	−0.310	−0.015	0.988	0.16	0.006	0.995	17.95	0.140	0.889
Malaba	0.370	0.164	0.869	3.65	0.148	0.882	−50.51	−0.141	0.888
Mpanga	2.294	0.196	0.845	5.13	0.144	0.885	−16.45	−0.166	0.868
Blue Nile	0.005	0.070	0.944	6.47	0.082	0.935	0.730	0.005	0.996
El Diem	0.008	0.086	0.932	−1.97	−0.023	0.982	−2.45	−0.026	0.979
Ribb	0.506	0.089	0.929	−2.39	−0.026	0.979	−4.076	−0.040	0.968

shows statistical results of the trend analysis. The annual flows of all the catchments except Kabalega exhibited an increasing trend. The slope of the trend varied from −0.310 to 2.294 m³/d/year. These changes in the annual mean flow were not significant (p > 0.05). Trends in rainfall were positive in four out of the six catchments. On the other hand, trends in PET were negative in four out of the six catchments. The trends in the annual rainfall and PET of all the catchments were also not significant (p > 0.05).

3.2. Variability

Figure 3 shows the results of variability in the mean annual hydroclimate of the selected catchments. Both streamflow and rainfall of the Kabalega catchment (Figure 3a) exhibited negative sub-trends from the late 1990s to the mid-2000s. However, the sub-trends became positive from the mid-2000s to the mid-2010s. The sub-trends in the PET were positive over the entire study period (Figure 3a). The H₀ (natural randomness) was not rejected (p > 0.05) for any of the hydro-climatic variables.

In the Malaba catchment, the sub-trends in PET were mainly positive and negative over the periods 1999–2005 and 2006–2016, respectively (Figure 3b). However, both rainfall and streamflow exhibited positive sub-trends from about 2000 until the mid-2010s. The variability in the hydroclimate of the Malaba catchment was not significant (p > 0.05).

The variability in the annual streamflow and rainfall of Mpanga was mainly in terms of positive sub-trends almost over the entire study period (Figure 3c). However, the sub-trends in the annual PET were mainly negative over almost the entire study period. The variability in both annual streamflow and PET were significant (p < 0.05) (Figure 3c).

The sub-trends in streamflow and rainfall for Blue Nile were mainly positive from the mid-1980s until mid-1990s (Figure 3d). The sub-trends in annual PET were negative and positive over 1980–1990 and 1991–1998, respectively. The sub-trends in rainfall and streamflow were not significant (p > 0.05). However, the variability in PET was rejected (p < 0.05) for the positive sub-trends (Figure 3d).

For the El Diem catchment (Figure 3e), the sub-trends of annual rainfall fluctuated about the reference or the Z = 0 horizontal line. The annual streamflow exhibited mainly positive sub-trends from the mid-1980 until late 1990s. Sub-trends in annual PET were noticeably positive in the 1990s. The variability in the hydroclimate of the El Diem catchment was not significant (p > 0.05) (Figure 3e).

Like for El Diem, the sub-trends of annual rainfall of Ribb catchment fluctuated about the reference or the Z = 0 horizontal line (Figure 3f). The variability in annual streamflow was mainly in terms of positive sub-trends from the mid-1980s until early 1990s. The sub-trends in annual rainfall, streamflow, and PET were not significant (p > 0.05).

3.3. Model Performance

Figure 4 shows the performance of the hydrological model. The model parameters can be found in Appendix A 

Table A1. Model parameters.

Parameter	Malaba	Kabalega	Mpanga	Blue Nile	El Diem	Ribb
Sini	92	198	2000	88.000	2.000	500.00
Smax	178.8	115.7	22.800	82.500	207.500	120.00
a1	15.91	21.301	15.510	1.500	0.013	0.93
tb1	200	2.8	12.550	1.500	0.255	0.01
a2	6.38	190.04	8.800	0.380	0.240	2.54
tb2	28	200	8.200	0.195	0.199	0.20
a3	6.1331	7.46	20.130	2.913	0.031	0.03
c3	3.8	2.802	3.780	2.150	0.013	1.00
tb3	3	50	25.000	3.500	3.340	3.25
tb4	22.99	3	34.990	30.500	4.000	10.50

The catchment areas of Malaba, Kabalega, Mpanga, Blue Nile, El Diem, and Ribb as shown in Figure 1, 2234, 789, 4733, 309,700, 175,063, 1485 km², respectively.

. The model adequately captured the temporal variability in the observations. For Blue Nile (Figure 4a,b) and Malaba (Figure 4k,l), the extreme high flows were slightly underestimated. To check overestimation and underestimation, the scatter plots (Figure 4b,d,f,h,j,l) correspond to the time series plots (Figure 4a,c,e,g,i,k). The diagonal line (or solid line or the bisector) in each of the scatter plots (Figure 4b,d,f,h,j,l) is where all the scatter points would fall if the model was perfect. The scatter points above and below the bisector were nearly balanced for each catchment. The dotted line or trendline in each of the plots (Figure 4b,d,f,h,j,l) was the basis of the obtained coefficient of determination (R²) indicating the measure of co-variability of model outputs with observations.

Table 3. Statistical model performance evaluation.

Period	Blue Nile	El Diem	Ribb	Kabalega	Mpanga	Malaba
Calibration	0.801	0.831	0.636	0.697	0.679	0.785
Validation	0.811	0.771	0.608	0.654	0.652	0.792
Full-time	0.806	0.800	0.615	0.675	0.661	0.776

shows the statistical metric NSE to indicate model performance. NSE values vary from negative infinity to one. The best model performance is when NSE is equal to one. The NSE values for calibration were all above 0.6, indicating satisfactory performance of the model [27]. Even for validation, the NSE values were still above 0.6, thereby indicating the satisfactory transferability of the model for climatic conditions of each catchment outside the calibration sub-period. The performance of the hydrological model applied to each catchment was better for calibration than validation period. However, the difference between the NSE values for calibration and validation was minimal for each catchment. Using the entire full-time series, the NSE values were still above 0.6. This indicated the acceptability of the model for application to conduct a scenario analysis.

3.4. Simulation Experiment

Figure 5 shows the impact of changes in rainfall and PET on streamflow. The plots in Figure 5a–d are illustrations using the case of the means of the modeled series using data from the Blue Nile. When the original rainfall series was gradually increased while keeping the PET unchanged (Figure 5a), the results of the model simulation showed an increase in the streamflow. Increasing rainfall intensity implies an increased amount of water that substantially surpasses the evaporative demand of the atmosphere. This leads to increased volume of generated rainfall–runoff and streamflow. The variation of the resultant streamflow with the amount (%) by which the rainfall was increased was found to be in a linear way with a positive slope. Compilations of simulations obtained by varying rainfall while keeping the PET constant at a stipulated percentage of the original PET further reveals the linear relationship between streamflow and the amount of change in rainfall (Figure 5b). The lower the PET rates, the higher the line characterizing the impact of increasing the rainfall intensity on the streamflow. In other words, the larger the PET rates, the lower the position of the line showing an increase in streamflow due to increasing rainfall. This can be explained by the fact that large PET rates are indicative of increased evaporative demand, a phenomenon that reduces the amount of excess rainfall.

By keeping the original series of rainfall intensity unchanged, the streamflow is noted to decrease with the increasing PET rates (Figure 5c). Again, the variation of the streamflow with the increasing PET rates is linear. However, the slope of the linear relationship is negative. This corroborates the fact that an increased evaporative demand at a given rainfall intensity negatively affects the streamflow. If the PET rates are greater than the rainfall intensity, it means there is no excess rainfall to generate rainfall–runoff, and in this case, water is instead lost to the atmosphere by a combination of evaporation from the soil and transpiration of plants. However, the lower the rainfall intensity, the lower the line characterizing the impact of PET on streamflow (Figure 5d). The excess rainfall to generate rainfall–runoff volume to increase streamflow is a function of the PET rates across the catchment.

For a given PET rate, the amounts by which streamflow decreased in Kabalega, Malaba, and MPanga (catchments in the White Nile region) were less negative than those from the central area of the Nile basin, including the Blue Nile, El Diem, and Ribb (Figure 5e). This suggested that the catchments in the central region were more sensitive to the changes in PET rates than those from the White Nile region. When the original PET data were kept unchanged while the initial rainfall series was increased by 2.5, 5.0, 7.5, 10.0, 12.5, 15, 17.5, and 20%, the daily Blue Nile streamflow increased by 7.8, 12.6, 14.1, 19.0, 23.9, 28.9, 34.0, and 39.1%, respectively. When rainfall was kept constant while PET was increased by 5%, the streamflows of the Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb decreased by 7.00, 5.08, 2.49, 4.10, 1.84, and 7.67%, respectively (Figure 5e). By keeping the original rainfall data unchanged while increasing the initial PET series by 2.5, 5.0, 7.5, 10.0, 12.5, 15, 17.5, and 20%, the daily streamflow of the Blue Nile decreased by 3.6, 7.0, 10.3, 13.4, 16.5, 19.3, 22.1, and 24.8%, respectively. Under constant PET, increasing rainfall of the Blue Nile, El Diem, Kabalega, Malaba, Mpanga, and Ribb by 5% led to an increase in streamflow by 9.02, 9.87, 5.38, 4.34, 6.58, and 8.32%, respectively (Figure 5f). Notably, increasing the rainfall intensity under constant PET rate, the catchments in the White Nile basin yielded response lines that were below those for the catchments in the central area of the Nile basin. Again, this shows that the sensitivity of the catchments in the Blue Nile area to increasing rainfall intensity was, for the selected period, higher than that for the White Nile region.

Table 4. Parameters of a linear model for increasing rainfall under constant stipulated PET.

Stipulated Change (%) in PET	Blue Nile	El Diem	Ribb	Kabalega	Mpanga	Malaba
	Slope (m3/s/ϕ) where ϕ is increase (%) in PET rates
0.0	63.888	59.936	0.535	0.107	0.144	0.696
2.5	62.932	57.399	0.515	0.104	0.143	0.672
5.0	61.352	55.544	0.496	0.103	0.141	0.655
7.5	59.821	53.756	0.477	0.100	0.140	0.639
10.0	58.338	52.032	0.459	0.099	0.139	0.623
12.5	56.905	50.367	0.443	0.098	0.137	0.611
15.0	55.504	48.758	0.427	0.097	0.136	0.595
17.5	54.129	46.335	0.411	0.097	0.134	0.583
20.0	52.788	43.134	0.373	0.096	0.132	0.567
	Intercept (m3/s)
0.0	1268.30	1256.00	11.726	3.646	5.163	28.558
2.5	1205.00	1157.50	10.823	3.527	5.073	27.333
5.0	1161.40	1117.00	10.401	3.483	5.045	26.777
7.5	1119.60	1078.60	9.998	3.440	4.982	26.250
10.0	1079.50	1042.10	9.613	3.400	4.938	25.847
12.5	1041.10	1007.40	9.246	3.361	4.903	25.412
15.0	1004.20	974.40	8.895	3.323	4.854	24.811
17.5	968.93	942.11	8.559	3.286	4.813	24.374
20.0	935.05	935.53	8.395	3.251	4.763	23.954

shows compilations of slopes and intercepts as parameters of linear models describing variations in streamflow with increasing change (%) in rainfall intensities for a stipulated percentage increase in PET rate. To obtain Table 4, the slope and intercept of each line, as in Figure 5b, were recorded for each of the catchments. This procedure was repeated using linear variation of the streamflow with increasing change (%) in PET rates for the stipulated percentage increase in rainfall intensity, as shown in Figure 5d, and the resulting compilations are summarized in

Table 5. Parameters of a linear model for increasing PET under constant stipulated rainfall.

Stipulated Change (%) in Rainfall	Blue Nile	El Diem	Ribb	Kabalega	Mpanga	Malaba
	Slope (m3/s/β) where β is the increase (%) in rainfall intensity
0.0	−39.954	−36.556	−0.387	−0.040	−0.044	−0.497
2.5	−42.321	−39.209	−0.413	−0.042	−0.044	−0.525
5.0	−43.801	−40.895	−0.429	−0.043	−0.046	−0.540
7.5	−45.267	−42.588	−0.446	−0.045	−0.047	−0.555
10.0	−46.289	−45.987	−0.463	−0.045	−0.049	−0.571
12.5	−48.192	−47.698	−0.481	−0.046	−0.050	−0.586
15.0	−49.662	−49.416	−0.498	−0.047	−0.051	−0.601
17.5	−51.129	−51.134	−0.516	−0.047	−0.052	−0.616
20.0	−52.590	−52.434	−0.534	−0.048	−0.053	−0.631
	Intercept (m3/s)
0.0	1306.30	1250.60	11.724	3.664	5.257	28.434
2.5	1414.70	1350.00	12.674	3.813	5.444	29.703
5.0	1478.20	1407.60	13.187	3.916	5.590	30.395
7.5	1542.60	1466.50	13.769	4.029	5.733	31.092
10.0	1585.00	1588.10	14.256	4.124	5.877	31.792
12.5	1674.30	1650.70	14.811	4.228	6.021	32.496
15.0	1741.50	1714.50	15.381	4.332	6.166	33.203
17.5	1809.60	1779.40	15.963	4.436	6.311	33.983
20.0	1878.60	1804.60	16.557	4.540	6.457	34.625

. For a given percentage increase in PET rate, both slopes and intercepts of the linear models describing the increase in streamflow due to increasing rainfall intensities were positive (Table 4). However, the slopes were reduced with the increase in PET rates. Also, the intercept was reduced with an increase in the stipulated increase (%) in PET rates. In Table 5, the slopes were all negative. As the stipulated change (%) in rainfall intensity got higher, the slopes became more negative. These results show that the drying rate of a catchment can be determined by the rate at which it loses water to the atmosphere. This underscores the importance of PET in determining the water balance of a catchment. In Table 5, the intercepts of the lines are all positive. Furthermore, the intercepts of the lines increased with the increasing intensity of rainfall. The higher the rainfall intensity, the larger the excess rainfall to increase the streamflow. Rainfall is the most important variable in determining the drying and wetting or water balance of a catchment.

Table 6. Correlation between hydroclimatic variables and climate indices.

Catchment	Climate Index	Original Series			De-Seasonalized Series
		Rainfall	PET	Flow	Rainfall	PET	Flow
Blue Nile	DMI	−0.07	0.06	−0.17	−0.02	0.07	−0.11
	Niño3	−0.19	0.01	−0.45	−0.10	0.06	−0.26
El Diem	DMI	−0.04	0.05	−0.10	−0.02	0.04	−0.09
	Niño3	−0.09	0.29	−0.48	−0.02	0.10	−0.27
Kabalega	DMI	−0.02	0.26	−0.04	−0.03	0.28	−0.05
	Niño3	−0.17	0.42	−0.23	−0.07	0.52	−0.06
Malaba	DMI	0.15	−0.04	0.19	0.24	−0.11	0.27
	Niño3	0.14	−0.29	0.05	0.19	−0.34	0.22
Mpanga	DMI	0.15	−0.15	0.20	0.15	−0.15	0.25
	Niño3	−0.01	0.02	−0.04	0.06	−0.22	0.23
Ribb	DMI	−0.05	0.03	−0.07	−0.06	0.02	−0.05
	Niño3	−0.12	0.39	−0.37	−0.01	0.10	−0.17

shows the results of the correlation analysis. Niño3 and streamflow are negatively correlated for Blue Nile, El Diem, Kabalega, and Ribb. For these same catchments, DMI and rainfall are also negatively correlated. A positive correlation between Niño3 and streamflow (as well as Niño3 and rainfall) was obtained for Malaba and Mpanga. The correlation coefficients obtained using rainfall were opposite in sign compared to those based on PET. However, the signs of correlation coefficients based on rainfall are the same as those for streamflow. The highest positive correlation (0.52) was obtained between Niño3 and PET of Kabalega. The most negative correlation coefficient (−0.48) was obtained between Niño3 and streamflow of El Diem. The highest correlation coefficient between rainfall and DMI was for Malaba. It is noticeable that de-seasonalization slightly affected that magnitude but not signs of the correlation coefficients.

4. Discussion

Our results indicate that the changes in rainfall intensities and PET rates have direct linkages with the changes in streamflow. Evidence of the changes in rainfall across East Africa can be found in the results from several studies. For instance, numerous studies [28,29,30] have documented a decline in March–May (MAM), also known as “long rains” season, which lasts for about three months [2,31,32]. This is mainly due to the seasonal migration of Inter-Tropical Convergence Zone (ITCZ) [33] that brings a westerly moist convergence. However, since 1992, numerous studies have reported a change in trend, with abrupt declining tendencies [28,30,31,34]. The change in the trends has been attributed to the net impact of El- Niño on the MAM season that tends to be insignificant due to anomalies switching signs in the middle of season, from positive in March of the post-El-Niño year to a negative shift during May and close to zero in April [35]. Moreover, other studies—for instance, [29,36,37]—reported that the abrupt change in MAM rainfall could be attributed to a weak El-Niño Southern Oscillation (ENSO) signal. They demonstrated that La Nina could either amplify the increase or decrease in MAM rainfall over the study region, depending on the features of the episode. More details on the characteristics of the ENSO signal can be obtained from an extensive review literature of East African rainfall variability by [33]. However, while a notable decline in MAM season has been observed over many parts of East Africa, over Western Uganda, a recent study [38] reported an increase in MAM duration by about 1 month, which, in turn, increased the total rainfall by approximately 70%. The prolonged rains over the Western Uganda region could be attributed to the middle-troposphere specific humidity and vertical ascent that supported the wetting trends over the region. Meanwhile, the opposite patterns (increasing trends) in the October to December (OND) season, also referred to as “short rains”, have been observed over the region, leading to more rainfall in the catchment areas [2,31,32]. This could be linked to the recent changes in SST of the Indian and Pacific because of Walker circulation cells over the Indian Ocean [39,40,41]. The variability of Walker circulation is strongly connected to the Indian Ocean dipole, which is associated with pronounced rainfall events over the last few years over the region. In addition to the sea surface temperature (SST) condition of the Indian Ocean that strongly modulates the OND rainfall, it should be noted that changes in trends for SST over the Pacific and Atlantic also contributes to the increased rainfall during OND, evidenced by a positive increase in the water level in most of the catchment areas [22,42,43]. Overall, the regions where positive/negative trends are detected should be paid close attention due to the sensitivity of the catchments like the Blue Nile area compared to that for the White Nile region.

Contributions of human factors such as land use and land cover (LULC) alteration on the changing river flows have also been notable in the riparian countries of the Nile River [15,16,44,45,46]. Human factors such as rapid urbanization, bush burning, overgrazing, and deforestation can alter the rate of infiltration; affect the speed at which the generated runoff flows over land; and change the rate of evaporation. Thus, these factors would affect the hydrological sensitivity of a catchment in responding to the rainfall input. In other words, the difference between the response of a catchment that is purely in its natural state and that when the catchment is significantly impacted by anthropogenic factors would be noticed in terms of the runoff sub-flow volumes.

The results of the percentage changes in streamflow due to the increase in rainfall and PET were distinctively grouped according to the catchments from the two sources of the Nile. Differences in the catchments from the two sources of the Nile basin were found in a previous study [22]. The first difference is in terms of the monthly pattern of rainfall. In the White Nile region or the equatorial area of the Nile basin, rainfall is of a bimodal pattern with the main and short rainy seasons occurring over March–May and October–December, respectively [47]. For the Blue Nile region, especially in Sudan and Ethiopia, the main wet season occurs in June–September and, in these months, correspond to the long dry season for the equatorial region [22]. Secondly, there is a difference in terms of rainfall variability. For instance, quantile anomalies of rainfall from the 1960s to 1980s over the White Nile were above the long-term mean or reference [22]. However, during the same period, quantile rainfall anomalies were conversely below the reference. In other words, during the given period 1960–1980, when rainfall was increasing across the White Nile, it was decreasing in the Blue Nile area [22].

Ideally, trends in streamflow and rainfall are expected to be of the same trend direction. However, contrasts in rainfall and streamflow trends were exhibited in Kabalega, El Diem, and Ribb. The rainfall datasets considered were the catchment-wide average obtained using the Thiessen Polygon method. The averaging of rainfall intensities over a catchment leads to loss of spatial variation of trends in rainfall intensities from the various parts of the catchment. For a catchment with large drainage area, rainfall intensities can have a negative trend in one part, but other areas could have positive trends. When rainfall from the various parts of the catchment is averaged, the spatial variation in the trend directions is lost. This can lead to a disparity in trend directions in streamflow and rainfall. Furthermore, if rainfall from a few weather stations is used to obtain a catchment-wide average, the overall trend in the resulting series may not be representative of the ideal trend direction to rhyme with that in the streamflow. For some areas, a decrease in rainfall can be accompanied by an increase in PET. In other locations, an increase in rainfall can be accompanied by a decrease in PET. In fact, PET depends on many factors such as humidity, windspeed, topography, soil moisture, and vegetation type, and this makes determination of the direct linkage of its trend to that of rainfall or streamflow difficult. Disparities in trend directions and magnitudes among catchments depict the hydrological differences among catchments. Any two catchments cannot be the same with respect to size, geology, soil, weather conditions, and climate variability.

The uncertainties in the hydrological model that was not given focus, for brevity, included the influence of the choice of the hydrological models and objective functions [48,49]. Other uncertainties were due to the choice of the schemes for the sampling parameters of the models [50]. For a future study on the sensitivity analysis of the catchment response to rainfall and PET inputs, many hydrological models should be applied. Each model should be calibrated using many objective functions. Many sampling schemes should be used in generating the parameters of each hydrological model. What remains also a limitation is the lack of incorporation of spatial influence of human factors such as changes in LULC types on the changes in the streamflow. This could necessitate the application of semi-distributed hydrological models for a detailed scenario analysis, in which catchment responses would be investigated under changing climatic conditions alongside the influence of human factors. Furthermore, comparing the results of a sensitivity analysis as done in this study with those when hydrological models are driven by climate change scenarios from general circulation models would lead to tailored information for the development of catchment-specific adaptation measures in the context of a changing climate.

5. Conclusions

This study investigates the response of the hydrological processes and sensitivity of streamflow to variations in rainfall and PET over diverse catchments of the Nile basin. The unique responses observed among the catchments emphasize the importance of understanding region-specific hydrological behaviors. These findings highlight the need for tailored water management and adaptation strategies that consider the distinct characteristics and climatic sensitivities of each basin. The key conclusions and findings of intricate relationships governing streamflow responses to rainfall and PET variations within the Nile basin can be summarized as follows.

The hydrological model used in the study demonstrated satisfactory performance in replicating observed streamflow temporal variability patterns within the catchments, as evidenced by the scatter plots and NSE values. This robustness allowed for confident application in scenario analyses.

For the constant PET and varying rainfall case, increasing the rainfall intensities led to a proportional rise in streamflow across catchments. The linear relationship between rainfall and streamflow was notably influenced by the balance between rainfall and PET. Catchments with lower PET exhibited a more pronounced impact of increasing the rainfall on streamflow, highlighting the significance of evapotranspiration in modulating streamflow responses.

On the other hand, or for the constant rainfall and varying PET scenario, increasing PET resulted in a linear decrease in streamflow. Catchments in the central region of the Nile basin displayed higher sensitivity to changes in PET compared to those in the White Nile region. This disparity emphasized the distinct hydrological responses within the Nile basin due to differences in climatic conditions.

According to the linear models, how fast a catchment loses water to the atmosphere, influenced by PET, impacts its drying rate. In these models, the intercepts represent the surplus rainfall accessible for increasing the streamflow. Notably, these intercepts increased with elevated rainfall amounts, emphasizing the crucial role of rainfall in regulating the water balance within a catchment.

The study’s findings have significant implications for water resource management and regional planning. Understanding the intricate interplay between rainfall, PET, and streamflow is crucial for developing adaptive strategies in the face of climate variability. Catchments with higher PET rates require nuanced management approaches, considering their heightened sensitivity to changes in evaporative demand. These insights not only enhance our understanding of hydrological processes but also provide valuable guidance for sustainable water resource management in the region.

One weakness of this study is that the periods for hydrological analysis were not the same for all the catchments. Furthermore, recent variability in the hydro-climatic conditions was not considered in the analysis due to the lack of up-to-date data. The number of catchments considered in this study were few. It is envisaged that including many more catchments across the study area would lead to results that are vital to revealing important information regarding the regional hydrological differences. What this study did not do but deemed important is incorporating socioeconomic data for further analysis, since that could help in understanding the implications of hydrological changes on local communities. Furthermore, this would be particularly crucial for developing adaptive strategies that are both environmentally sound and socially equitable. Finally, an uncertainty analysis was not given focus in this study. These limitations should be considered in any similar future studies.