Rwanda is a country in East Africa that is surrounded by land on all sides situated on the eastern side of Africa's Kivu-Tanganyika rift. It spans an area of 26,338 km2 and is confined by the D.R.Congo, Uganda, Burundi, and Tanzania (Karamage et al., 2016; Nsengiyumva and Valentino, 2020). The basin of the Nyabarongo River has its location in Rwanda and is known as the source of the Nile River. This basin comprises of three sub-basins, namely the Mukungwa sub-basin in the northern region, the Nyabarongo upstream sub-basin in the southern region, and the Nyabarongo downstream sub-basin in the eastern region. Together, these sub-basins play a significant role in Rwanda's drainage system. With an area of 8441.21 km², In Rwanda, the Nyabarongo River stands as the country's largest river. It stretches ~300 km to Lakeside Rweru from its origins in the west near the boundary with Burundi in southeastern Rwanda. The river's main channel is formed by the Akanyaru River, The Nyabarongo River originates from the elevated landscapes of the Nyungwe National Park, located on the border between the Congo and Nile regions. As it advances east, the river passes through lowland basins and small lakes in the Bugesera-Gisaka swamps in southern Rwanda. Its course is influenced by various smaller rivers, such as the Marenge and Rusine rivers, as well as urbanized areas in Kigali, including Mpazi, Rwanzekuma, Ruganwa, and Yanze rivers, which all contribute to its volume (Nsengiyumva and Valentino, 2020; Omara et al., 2020) (Figure 2).

The SWAT is a hydrological simulation designed by the US Department of Agriculture's Agricultural Research Service (ARS). This model is designed to model the manners of water resources using a daily time step. It is based on physical principles and incorporates dynamic elements to accurately represent the behavior of these resources (Neitsch et al., 2011). According to Neitsch et al. (2011), SWAT proves to be highly beneficial when it comes to examining agricultural regions and extensive basins that exhibit diverse soil types, land cover, and management approaches. Its successful adoption can be attributed to the availability of detailed documentation, including theoretical manuals and online tutorials (Heuvelmans et al., 2005; Neitsch et al., 2011; Arnold et al., 2012) as well as additional publications, GIS plug-ins, and support from the development team (Figure 3).

The hydrological cycle of a sub-basin is simulated in SWAT using the water balance equation below.

where TW_t is the final soil water content; TW_o is the initial soil water content (mm); t is time; R_day is the total quantity of precipitation; M_surf is the total quantity of surface runoff; E_a is the total quantity of evapotranspiration; W_seep is the total quantity of percolation flow exiting the soil, and M_gw is the amount of return flow.

SWAT simulates the hydrological cycle of a sub-basin using a water balance equation. The model presents two options for calculating surface runoff: the SCS curve number method (Boughton, 1989) and an additional method (Ogden and Saghafian, 1997). In this research, we utilized SWAT 2012 for hydrological modeling and employed ArcGIS 10.8 software with the Arc SWAT extension. Using the river basin's distinct soil properties, LULC, and elevation, sub-basins were split into Hydrologic Response Units. The HRU serves as the unit for determining hydrologic characteristics, with the water budget driving the simulation. The modeling process incorporates two phases: an in-stream phase, where the model calculates basin loadings from each sub-basin along the stream network, and a land phase, where SWAT simulates the flow, sediment, and nutrient contributions from each HRU, which are then aggregated at the sub-basin level (Shivhare et al., 2018).

SUFI-2 is a probabilistic algorithmic approach commonly used by scientists to assess uncertainty (Kumar et al., 2017). It evaluates both efficiency and parameter uncertainty. The measure of uncertainty in efficiency is determined in accordance with the 95PPU (95 percent accuracy of predictions band), which is calculated in accordance with the cumulative distribution of output variables in SUFI-2 at the 2.5 percent and 97.5 percent thresholds. Parameter uncertainty is captured by utilizing a parametric basis function within a parameter hypercube (Wu et al., 2019). To establish the calibration efficiency, we employ the R-factor, which is determined by scaling the measured data's standard deviation by the 95PPU band's average width. The P-factor represents the percentage of simulations that accurately match the observed data, ranging from 0 to 100 percent, while the R-factor can range from 0 to infinity. When a simulation yields a P-factor of 1 and an R-factor of 0, it signifies a complete alignment with the observed data. SUFI-2, akin to GLUE (Generalized Likelihood Uncertainty Estimation), encompasses all forms of uncertainty by considering parameter uncertainty within the hydrological model. In this research, we employed SWAT-CUP to combine the simulated values from SWAT 2012 with observed data for uncertainty analysis and calibration using the SUFI-2 algorithm (Wu and Chen, 2015). The SUFI-2 technique is as follows:

In the first phase, the goal function (gi) is considered. Next, the minimum and maximum absolute ranges (θ_j) of the physically significant parameters being optimized are defined.

In the second phase, the preliminary uncertainty estimates are restricted to the parameters for the first round of Latin hypercube testing after a sensitivity assessment for each of the parameters is performed.

In the third phase, Latin hypercube testing is performed, and the equivalent objective functions are assessed. The sensitivity matrix J_ij and the following formulas are used to calculate the correlation grid C parameter:

where C_m is the total count of rows in the sensitivity matrix, and p is the total count of parameters to be estimated?

where sg2 is the variance of the coefficients of the desired functional resulting from the m model runs?

In the fourth step, the 95PPU is identified. The p-factor (the percent of observations bracketed by the 95PPU) and the r-factor, respectively, are then evaluated:

where yti,97,5%M and yti,2,5%M indicate the 95PPU's upper and lower boundaries, and threatens to indicate the observed data's standard deviation.

ParaSol is a revised sort of the UA-SCE global optimization method that aims to incorporate estimate uncertainty during a mechanism of analysis through simulations. ParaSol utilizes the comprehensive exploring space for attributes of UA-SCE, focusing on layouts that are close to optimal (Kan et al., 2017). ParaSol follows the following procedure:

GLUE is employed to address non-uniqueness of parameter sets across model parameters and scenarios (Zhao et al., 2018). This approach acknowledges that no specific parameter arrangement substantially enhances the goodness-of-fit criterion for over-parameterized models. GLUE consideration throughout potential parameter uncertainty. The estimation of probabilities linked to a parameter set consideration throughout potential sources of error and the influences of parameter covariation on the performance of the model (Zhang et al., 2016). An analysis using the GLUE methodology consists of three primary stages:

In this context, n corresponds to the total count of recorded data points and the variables y_ti and ytiM(∅) symbolize the observed data and the model's simulated output using parameters ∅ at a time t_i, respectively, and y denotes the mean value of the annotations.

For more information on the SWAT-CUP, ParaSol, SUFI-2 and GLUE model components, you can look up the SWATCUP instruction request by Abbaspour (2014) or the SWAT model utilization, validation, and calibration document by Tejaswini and Sathian (2018).

As mentioned earlier, the calibration method involves modifying the parameters that impact the SWAT model's results, such as observed values and estimated values of runoff, evapotranspiration, and other outputs (Mapes and Pricope, 2020). Validation, on the other hand, involves comparing the SWAT model's results with observed data without making any changes to the factors that influence the model's outcomes (Devia et al., 2015; Mapes and Pricope, 2020). Calibration is a crucial step in ensuring the accuracy of hydrologic models (Beven and Smith, 2015). The calibration parameters for soil erosion and runoff utilized in this investigation are shown in Table 3, along with the related lowest and highest relative SWAT outcomes. To be able to analyze uncertainty, calibrate, and validate the hydrological modeling outcomes, we employed SWAT-CUP as a bridge between SWAT and the calibration algorithms. The TxtInOut directory of the SWAT model was imported into the SWAT-CUP tool for input drives. These figures were employed for comparisons and system calibration. The necessary modifications were made to the input files of the SWAT-CUP model. Figure 4 depicts the flowchart of the following section. We compared the capabilities of ParaSol, SUFI2, and GLUE in capturing the optimal parameter sets (in terms of the evaluation criteria) during both the calibration and validation periods in the basin. A 3-year (2011–2013) record of monthly streamflow at the basin outlet was used for calibration and another 2-year (2014–2015) dataset was used for validation. The three sets of the calibrated parameter values derived from the methods were listed in Table 4 and the graphical comparisons (scatterplots) between the observed streamflow and the best simulation were shown in Figure 4. It can be seen from Table 3 and Figure 4 that the calibrated parameter sets of the three methods were not completely in accordance with each other, implying that the three algorithms could recognize the different parameter sets that were able to produce similarly good performance.

As can be seen from Table 3, in calibration, the p-factor and r-factor yielded by ParaSol (0.39 and 0.19) were less than those generated by SUFI2 and GLUE (0.67 and 0.75 for SUFI2 and GLUE, respectively). Also, the NSE and R² in ParaSol (0.93 and 0.96) were higher than those yielded by SUFI2 (0.83 and 0.86) and GLUE (0.82 and 0.76), suggesting that ParaSol had its advantage on accurately seeking the optimized parameter set compared to SUFI2 and GLUE. In addition, based on the evaluation criteria (Table 3) and according to Moriasi et al. (2007), the overall model performance can be rated as “good” in both the calibration and validation periods.

In the SWAT model, the target watershed is divided into sub-basins linked by the channel network, each sub-basin is further subdivided into several hydrological response units (HRUs) of homogeneous land-use, slope, and soil characteristics. Hydrological components, nutrients, and sediment yield are simulated at the HRU level and then aggregated for each sub-basin. The detailed model description is found in Neitsch et al. (2011). The suitability of the SWAT model to estimate hydrologic processes to land-use change in Gumara watershed was assessed by Teklay et al. (2021). In this study, the SWAT model set-up followed a similar setting in Teklay et al. (2021). Therefore, this study presented only a sum- many of the model set-up and evaluation results. The watershed area was discretized into 22 sub-basins. These sub- basins were further discretized into HRUs by setting a zero percent threshold level for land-use, slope, and soil. The Penman-Monteith method was chosen to calculate reference evapotranspiration (Gebre et al., 2015). The Soil Conservation Service Curve Number and the variable storage method were used to calculate surface runoff and flow routing, respectively. Based on the previous studies in the region and literature survey (Setegn et al., 2008; Gebremicael et al., 2013; Dile et al., 2016), ten SWAT model parameters were considered in this research. The ranges of model parameters and fitted values are shown in Table 4. The model parameters were calibrated and validated using the Sequential Uncertainty Fitting version 2 (SUFI-2) in the SWAT-Calibration and Uncertainty Procedure (SWAT-CUP) pack- age (Arnold et al., 2012), the model was calibrated using monthly streamflow data for a period of 15 years from 1990 to 2004. The calibration was performed through a “trial and error” process by manually adjusting the parameter ranges based on published literature (Arnold et al., 2012; Dile et al., 2016; Fentaw et al., 2018). After calibration, the model was validated using streamflow data from 2005 to 2015.

When examining calibration methods for water and soil modeling, numerous difficulties emerge. We emphasized addressing the more important concerns, which include:

Moreover, we acknowledged that the outcomes of the comparison are inherently influenced by the specific applications. To resolve this concern, we separated the specific results of each algorithm application from the general ones, ensuring a more accurate evaluation.

The five important criteria were used to compare the three calibration algorithms (GLUE, ParaSol, and SUFI-2): Numerous parameters were incorporated into the calibration procedures.

Every technique produces unique estimations and levels of uncertainty for these parameters. Therefore, the initial comparison centers around the optimal estimate, minimum and maximum uncertainty ranges, and parameter correlation for each algorithm (Jahani et al., 2019). As different algorithms utilize various objective functions, the second evaluation is based on metrics such as NSE (Nash-Sutcliffe Efficiency), R², and other objective functions. The third requires consideration of the R-factor, which represents the standard deviation of the band's mean width derived from the corresponding measured variable, and the P-factor, which indicates the percentage of data contained within the 95PPU (95% Prediction Performance Uncertainty) band of each algorithm. The fourth assessment was made as a result of theoretical principles, readability, and statistical criteria being met. The final assessment was made as a result of implementation difficulties (Figure 5).

The basin area and drainage channel are both included in the basin, creating a morphometric division. It's a basin unit with naturally occurring boundaries that are characterized by similar physical characteristics, topographic patterns on the land, and climatic circumstances (Adnan et al., 2019). Basin delineation involves marking the margins of a basin on a map, typically using data from a DEM or contour maps. In SWAT modeling, the process begins with defining the basins, where the DEM serves as the input. Streams and outlet points are produced by considering the basin's slope (Sisay et al., 2017). The researcher identifies the basin's outlet locations. Additional input, such as reservoir data and designated streams, can be provided by the user. In this particular study, the area of the basin was separated into 25 smaller basins.

In Figure 6, the depicted image showcases the specified research region's allocated basin, streams, and observation locations. The subsequent step involves analyzing HRUs. The area of basin was separated into units by the HRU analysis that has topographic features, soil types, and similar land types. In this particular research, the area of basin was split into 30,70 HRUs using the soil map, and user soil data, The research area was analyzed using a map of LULC and a slope map (Figure 1). Afterward, the model was enhanced by integrating the climate database. In the final stages, the evapotranspiration, runoff, and particle outputs for each sub-basin and HRU during 35 years were calculated using the SWAT model.

In this particular research, the Nile Nyabarongo River basin was assessed by using the SWAT model. The basin was divided into 25 sub-basins and 3,070 hydrologic HRUs to ensure accurate and efficient modeling. The annual average amount of rainfall in the basin was measured at 798.4 mm, with no snowfall or snowmelt. The surface runoff (Q) amounted to 81.46 mm, while the lateral discharge was measured at 105.32 mm. The deep and shallow reservoirs contributed 53 mm and 8.53 mm of groundwater discharge, correspondingly. The typical recharge for aquifers, water yield, and evapotranspiration were determined as 71.79 mm, 243.18 mm, and 559.5 mm respectively. Figure 7 presents a visual illustration of the SWAT model's productivity, focusing on runoff and evapotranspiration. The particular outcomes indicate that more than 50% of the whole precipitation is lost through evapotranspiration and runoff. Table 4 displays the average monthly values of various characteristics in the basin, such as precipitation, snowstorm, surface runoff, lateral runoff, water yield, and evapotranspiration.

The landcover land use classification in the basin consisted of five categories (illustrated in Figure 1). The majority of the basin was identified as cropland. The mean yearly rates for parameters unique to each land use type are shown in Table 5. The findings demonstrate that excessive surface runoff may occur in forestland, wetland, and agricultural land, while in the case of cropland, it remains below 15% of the water yield for the base flow. Considering that more than half of the precipitation is lost to drainage, the sediment production is similarly fairly large.

The loss of sediment from the landscape depends on various factors. In SWAT, overestimation of sediment often occurs due to insufficient biomass production, which is particularly common in certain land use practices. Unfortunately, there is usually no measurable data can be obtained to differentiate between sediment from upland areas and sediment in streams. Streams can either contribute sediment to the overall system or act as sinks for sediment (Figure 6). The alteration of sediment within streams is influenced by physical characteristics such as channel slope, width, depth, cover, and substrate, as well as the total quantity of sediment and flow coming from upstream. Due to the evaluation of at least one HRU, the maximum sediment yield was discovered to exceed 85 thm-2 (Table 6). The collective sediment load of the entire basin was estimated to be 16.43 t-hm. Figure 8 provides a visual depiction of the sediment provides results obtained from SWAT. The highest sediment yield from upland areas is 245.02 Mg/ha, while the average yield is 16.48 Mg/ha, as indicated by the research findings.

Table 7 presents a summary of the calibration algorithms and their comparison. The analysis was conducted across five categories, and the outcomes are as follows:

After analyzing and comparing the findings in Section 5.3, it might be described that the outcomes SUFI-2 and GLUE have a lot in prevalent. Nevertheless, when examining the 95PPU plot (Figure 9), it becomes evident that SUFI-2 outperforms GLUE in terms of accuracy and handling uncertainty. SUFI-2 also demonstrates efficiency by utilizing lowered quantities of variables compared to GLUE, which relies on a large number of simulations. GLUE's existence of the fundamental criticism calculation due to its random sampling approach. Consequently, for this research, SUFI-2 was selected as the superior algorithm, and only SUFI-2 was employed for further validation and calibration of sediment yield.

These differences in parameters can be justified by the changing land surface characteristics and the topographic features of the basin. The justification for differences in parameter values can be based on several aspects noting that each basin has its unique characteristics, such as time stability, topography, soil types, land cover, and climate, which result in variations in parameter values (Kelleher et al., 2015). Furthermore, considering experience and similar work in a basin, model is calibrated for different periods and the optimal model parameter values vary over these periods, this can have several causes (Merz et al., 2011; Westra et al., 2014). Changes in the catchment may have occurred that are not incorporated in the model. Processes like climate change (Peel and Blöschl, 2011) land use change (Nanda et al., 2016) and the construction of hydrological structures like dikes (Weigel et al., 2014) can affect the hydrological system and, therefore, affect the optimal model parameter values in different calibration periods if these processes are not incorporated in the model (Merz et al., 2011) determined the time stability of optimal parameter values for six 5-year periods between 1976 and 2006 in 273 Austrian catchments and found considerable variation in optimal snow and soil moisture parameter values. However, it's important to note that regional variations may exist due to differences in climate, geology, and hydrological processes.

To estimate the amount of flow from the catchment, sensitivity analysis was done to identify the parameters most relevant in affecting the streamflow simulation (Mind'je et al., 2021). Table 4 shows the detected parameters to be important in regulating the streamflow generation for all the simulations. In the study area, number 1 was “very sensitive,” from number 2 to 5 “sensitive” while number 6 to 10 was slightly sensitive. From the SWAT initial estimations, these parameters were related to runoff and adjusted to suit the model simulations with the observed flow data. In SWAT, these parameters are usually used to calibrate the base flow, which was confirmed by Harka et al. (2020). The entire simulation was performed daily from 2005 to 2007 was a warm-up period. Data from the period 2011–2013 was used for calibration, and the data period 2014–2015 was used for validation. Generally, as confirmed by the previous literature related to model validations (Chaibou Begou et al., 2016), there are no rules of thumb for selecting the proportion of calibration and validation datasets depending on the available amount of data. Due to limited observed data similar to this study, Mourad et al. (2005) suggested using the larger portion of the data for calibration and the smaller portion of the data for validation. Chaibou Begou et al. (2016) also recommended using the split-sample approach, by splitting the discharge measurement data into two datasets: two-thirds for calibration and the other one for validation. Therefore, the available observed data in the study area were split from the period 2011–2013 was used for calibration, and the data period 2014–2015 was used for validation (Figure 10). The statistical performance of the model was considered satisfactory (Moriasi et al., 2007) with 0.87 R² and 0.87 of the NSE for calibration, and 0.80 of R² and 0.87 of NSE for validation.

Throughout this evaluation, we calibrated the model using specific parameters listed in Table 3. We identified four factors that have a substantial influence on modeling the current basin in accordance with the assessment measures of the implemented model. These factors are recommended for a month-to-month time cycle. They include the effective channel hydraulic conductivity (CH K2), Manning's n value for the main channel (CH N2), surface runoff lag time (SURLAG), and the universal soil-loss equation (USLE) with a particular focus on the support parameter (USLE P).

To carry out the validation and calibration, we divided the data into different periods. The period from 2005 to 2007 served as a warm-up period. We used data from 2007 to 2011 for calibration and data from 2011 to 2015 for validation (Figure 11). The outcomes of the validation and calibration procedures are illustrated in Figure 10, respectively.

Figure 7 depicts a graph depicting the expected and measured discharge values, while Figure 8 shows a graph depicting the estimated and measured sediment data values after calibration. The measured outputs in sub-basin 19 were evaluated at the same outlet location.

Table 7 provides the values of the coefficients of appraisal for different objective functions in the research basin, specifically for the monthly yield of sediment simulation. The table presents the assessment coefficients for various objective functions and their corresponding month-to-month sediment yield simulations. The P-factor, indicating the proportion of observations within the 95% prediction uncertainty (95PPU), is 0.77, while the R-factor stands at 0.81. These results suggest that SUFI-2 produced a smaller percentage of the observed sediment yield. Moreover, moderate indicators such as R² = 0.87, NSE = 0.83, PBIAS = 1.4 × 102 (representing percent bias), and RSR = 0.41 (the ratio of observation standard deviation) indicate a satisfactory level of fit for the model, falling within acceptable assessment ranges (Table 8). The findings demonstrate the model of SWAT effectively replicates the hydrological landscapes of the Nile Nyabarongo basin, making it an important tool for next hydrological studies around the basin.