Development and application of a hybrid artificial neural network model for simulating future stream flows in catchments with limited in situ observed data

AI

artificial intelligence

ANN

artificial neural network

CMIP6

Coupled Model Intercomparison Project Phase 6

DEM

digital elevation model

EO

evolutionary optimisation

FFNN

feed-forward neural network

FL

fuzzy logic

GRNN

generalised regression neural network

HEC-HMS

Hydrologic Engineering Centre Hydrological Modelling System

LS

linear scaling

LSTM

long short-term memory

MAE

mean absolute error

ML

machine learning

NAM

Nedbor-Afstromnings model

NSE

Nash–Sutcliffe efficiency index

OAT

one-factor-at-a-time

RBFNN

radial basis function neural network

RMSE

root mean square error

SHAP

SHapley additive explanations

SMA

soil moisture accounting

SOM

self-organising map

SSP

shared socioeconomic pathways

SVM

support vector machine

SWAT

soil and water assessment tool

WEAP

water evaluation and planning system

Globally, emerging threats such as climate change, rapid population growth, and urbanisation have been projected to increase the frequency and magnitude of extreme events that will expose larger populations to more severe flooding, drought, and reduction of available water resources (Eccles et al. 2019; UNDRR 2020; Papa et al. 2023). In East Africa, global climate and hydrological model predictions suggest increases in annual rainfall, river flows, fluctuations in lake levels, and increased frequency and intensity of floods and droughts (Olaka et al. 2019; Trisos et al. 2022; Gebrechorkos et al. 2023; Mugume et al. 2024; Sempewo et al. 2024). In addition, most conventional physically based or conceptual hydrologic models often lead to inaccurate estimation of stream flows in catchments in sub-humid tropical regions that are characterised by highly varying topography, daily and seasonal rainfall, and runoff patterns (Jimeno-Sáez et al. 2018; Tibangayuka et al. 2022). This has been attributed to insufficient in situ observed hydrometeorological data specifically in many data-scarce regions in Sub-Saharan Africa, inherent hydrological model uncertainties, insufficient understanding of underlying hydrological processes, and uncertainties in the projection of future climate change impacts (Dile et al. 2020; Sempewo et al. 2022).

In recent research, many studies have assessed the performance of existing physically based or conceptual hydrological models such as the Hydrologic Engineering Centre Hydrological Modelling System (HEC-HMS), MIKE HYDRO, soil and water assessment tool (SWAT), Hydrologiska Byråns Cattenbalansavdelning (HBV), and Water Evaluation and Planning System (WEAP) with a view of evaluating location-specific model performance (Vo et al. 2018; Chathuranika et al. 2022; Ghosh et al. 2022; Sempewo et al. 2022). However, in most studies, the performance of these models in simulating the peak flows has been constrained by insufficient catchment (topography, soil, vegetation, and geological) in situ observed rainfall and stream flow data for model calibration and validation, inherent uncertainties in the model structures and a strong requirement for the modellers' a priori understanding of inherent physical processes in the hydrological system being studied (Mount et al. 2016; Dile et al. 2020; Reddy & Pramada 2022; Pareta 2023). Therefore, it is vital to develop new, computationally efficient and less data-intensive models to facilitate more accurate prediction of stream flows in natural rivers including their low and peak flows. Accurate estimation of stream flows is vital for reliable and robust design, retrofit and operational control of engineered systems such as water treatment plants, irrigation schemes, dams, hydropower plants, spillways, weirs, and other flood control structures (Jimeno-Sáez et al. 2018; Kurian et al. 2020; Ghimire et al. 2021).

In recent years, the need to develop computationally efficient data-driven artificial intelligence (AI) models for simulating stream flows in remote data-scarce regions has been underscored (Kim et al. 2021; Rahimzad et al. 2021; Chebii et al. 2022; Rahman et al. 2022; Tibangayuka et al. 2022). Well-trained AI models provide a more computationally efficient and accurate approach for simulating stream flows in complex non-linear hydrological systems without the need for detailed knowledge of the underlying hydrological processes and where the available data may be insufficient to set up more conventional physically based or conceptual models (Javan et al. 2015; Mount et al. 2016). In addition, AI models can adequately represent noise complexity in observed data and have an inherent ability to simultaneously discover the ‘model structure’ and to optimise its parameters (Yaseen et al. 2015; Mount et al. 2016; Young et al. 2017). Furthermore, after calibration, validation, and testing, such models can be used to simulate stream flows in adjacent ungauged hydrologically similar catchments, given the increased access to open-source reanalysis climate datasets (Nakkazi et al. 2022).

The most commonly applied AI methods can be broadly categorised as artificial neural network (ANN), support vector machine (SVM), fuzzy logic, evolutionally optimisation, and wavelet conjunction models (Tiwari & Chatterjee 2011; Huang et al. 2014; Yaseen et al. 2015; Sahoo et al. 2018, 2023). ANN models are further classified into supervised (back propagation multi-layer perceptron feed-forward neural network (FFNN), radial basis function, and generalised regression neural network (GRNN)) models and unsupervised models such as the self-organising map (Yaseen et al. 2015). ANN models, which are inspired by the functionality of the human nervous system, with a network of interconnected neurons created to process information (Chen et al. 2013; Nourani et al. 2019), have been widely applied for the prediction of stream flows due to their computational efficiency and cost-effectiveness (Ali & Shahbaz 2020). A review summary of recent studies that have developed and applied ANN models is presented in Supplementary Table S1.

In more recent studies, deep learning techniques such as long short-term memory (LSTM) models have been developed for the prediction of stream flows and sediments in natural rivers (Hu et al. 2018; Ghimire et al. 2021; Sahoo et al. 2023). Ghorbani et al. (2016) compared the performance of the multi-layer perceptron FFNN, radial basis function neural network (RBFNN), and SVM models in simulating stream flows for the Zarrinehrud River located in North-Western Iran. The study results suggested that both the FFNN and RBFNN models performed better than the SVM model in simulating monthly stream flows. However, the study results suggested that the uncertainty in the SVM model was less than the corresponding values in the RBFNN and FFNN models. Koycegiz & Buyukyildiz (2022) also investigated the performance of FFNN and RBNN models in estimating monthly stream flows in the Seyhan Basin in the south of Turkey. The study results suggested that the FFNN model resulted in more superior performance when compared with the RBNN model. In addition, Awchi (2014) compared the performance of an FFNN, GRNN, and the RBFNN model in simulating stream flows in the upper and lower Zab River, which is a tributary of the Tigris River in northern Iraq. The study results indicated that their performance varied with different cases involved in the study; however, the FFNN model resulted in better performance when compared with the other neural networks utilised in the study. However, most of these ANN-based modelling studies have been undertaken considering current climate conditions. In addition, there are very few studies that have investigated the performance of ANN-based models in simulating stream flows considering the projected impacts of future climate change (Aryal et al. 2019), despite the well-understood view that hydrological model uncertainty is comparatively higher than climate model uncertainty (Karlsson et al. 2016).

Furthermore, the use of hybrid modelling approaches that combine ANN models and physically based models have been a subject of current research (Young et al. 2017; Reddy & Pramada 2022). Hybrid models have been preferred because they are less data-intensive, facilitate the representation of different aspects of the input data, which leads to more superior estimation of stream flows when compared with individual HEC-HMS, MIKE HYDRO, or ANN models (Young & Liu 2015; Young et al. 2017). The developed hybrid model overcomes the challenges of inaccurate estimation of peak flows that have been observed in studies utilising individual physically based or conceptual models. Furthermore, within the hybrid HEC-HMS-ANN modelling approach, the stream flows generated using HEC-HMS serve as a predictor for the hybrid HEC-HMS-ANN model, which facilitates the elimination of unwanted accumulated errors in the hybrid model outputs (Young et al. 2017).

Humphrey et al. (2016) compared the performance of a hybrid GR4J conceptual rainfall-runoff model and a Bayesian ANN in simulating stream flows at three key locations in the southeast of South Australia. The study results suggest that the hybrid model outperformed the individual models in simulating high flows. Young & Liu (2015) compared the performance of a hybrid HEC-HMS and ANN model for simulating peak flows in the Sandimen basin in southern Taiwan. The study results suggested that the hybrid model performance was superior when compared with the individual HEC-HMS, SWAT, and ANN models. In a recent study, Kurian et al. (2020) showed that two hybrid models, that is, HEC-HMS-ANN and SWAT-ANN, were more superior in flood forecasting when compared with individual models. Furthermore, Reddy & Pramada (2022) compared the performance of a hybrid HEC-HMS-ANN model for simulating daily stream flow for the Kallada River catchment in India. The study results suggested that the hybrid model performed better than the individual models and resulted in reduced simulation errors of 66 and 26.5% when compared with the individual HEC-HMS and ANN models.

In this study, a hybrid model that combines the physically based HEC-HMS and the multi-layer perceptron feed-forward ANN model was developed and applied to simulate current and future stream flows and water availability for the River Mayanja catchment. The performance of the developed hybrid model was compared with corresponding results obtained using individual physically based HEC-HMS, conceptual MIKE HYDRO, and ANN models considering both current and future climate change conditions. In addition, a water availability assessment was undertaken considering current and projected future water demand in the case study catchment. The study findings will inform water resource modellers, managers, and decision-makers in the choice of suitable hydrological models and approaches for undertaking climate change impact assessments and evaluation of potential mitigation and adaptation strategies when faced with limited in situ observed hydrometeorological datasets.

In this research, a new hybrid model that combines the physically based HEC-HMS and the multi-layer perceptron feed-forward ANN model developed in the Python programming language was applied to the study. The hybrid HEC-HMS-ANN model utilises two input datasets that include the daily rainfall and stream flow data.

In this study, the feed-forward ANN model was chosen for utilisation in the hybrid model as opposed to the more recent deep learning approaches such as the LSTM approaches, which require more time and resource-consuming hyperparameter tuning methods for model training (Ghimire et al. 2021) and input datasets with shorter lead times e.g. 1 h which would necessitate coupling of LSTM models with other data-driven models such as wavelet transform to decompose time series into simpler sub-timeseries components (Hu et al. 2018; Ni et al. 2020). Furthermore, the ANN-based models have a simple and straightforward architecture that requires less computational power, have fewer hyperparameters that can be optimised, and are less prone to overfitting problems when compared with LSTM models (Ghimire et al. 2021).

The conceptual and lumped MIKE HYDRO model, developed by the Danish Hydraulic Institute is an integrated rainfall-runoff and hydrodynamic model that utilises the Nedbor-Afstromnings model (NAM) to simulate rainfall-runoff (surface), subsurface, and baseflows and to undertake hydrodynamic modelling in river reaches (Ghosh et al. 2022; Pareta 2023). The model comprises a series of mathematical statements that describe the characteristics of the land area of the hydrological cycle in a simplified quantitative form (Pareta 2023).

In this study, an ANN model utilising the back propagation multi-layer perceptron feed-forward (FFNN) algorithm was developed in the Python programming language version 3.11 and applied to model the rainfall–stream flow relationship for current and projected future stream flows. This type of neural network is one of the most widely used ANN in hydrological modelling and has shown promising results when compared with other types of ANN models (Ali & Shahbaz 2020). The FFNN algorithm has a non-recurrent architecture and provides a superior model for non-linear hydrological processes including stream flow (Rahman et al. 2022).

The architecture of the FFNN model used comprises an input layer, a hidden layer, and an output layer (Tibangayuka et al. 2022). The process of determining the ANN model architecture includes specifying the number of network layers, neurons in the layers and iterations, the learning rate, the activation function, the momentum of the coefficient, and determination of the normalisation method (Koycegiz & Buyukyildiz 2022). A model with one hidden layer was utilised because various studies have determined that having more than one hidden layer yields no significant improvement in performance (Turhan 2021) rather these increase the complexity of the model and can lead to overfitting (Tanteliniaina et al. 2021).

In undertaking data normalisation, large variations that exist within the input data can slow down or even prevent the training of the network (Pramanik et al. 2011).

In order to improve the accuracy and reliability of future stream flow projections, previous studies have recommended the development of hybrid models (multi-model combinations) so as to improve overall model predictive performance (Mount et al. 2016).

Hybrid models are combined hydrologic models in which physically based or conceptual modelling is fused with data-driven modelling. The physically based or conceptual models are based on a simplified watershed system and mathematical equations that describe the physical processes involved in the movement and storage of water (Young et al. 2017). Conversely, the data-driven models establish a direct relationship between hydrologic variables that are extracted from observed (measured) data using algorithms developed in the fields of statistics, computational intelligence, machine learning, and data mining (Young et al. 2017). Data-driven models are used to model the elements of the system where there is insufficient a priori knowledge to support physically based or conceptual modelling (Mount et al. 2016).

Hybrid models can result in improved predictions of system responses because they circumvent the challenge of having to derive predictions of a system's response from models that are inadequate or incomplete conceptualizations of it (Mount et al. 2016). Furthermore, hybrid modelling approaches can exploit the strengths and minimise the weaknesses of either modelling approach, as opposed to the isolated use of individual modelling techniques (Humphrey et al. 2016; Mount et al. 2016).

In this study, a hybrid ANN model based on the multi-layer perceptron FFNN, which utilises two input variables, i.e. observed daily rainfall and stream flows was developed in the Python programming language. It is hypothesised that the hybrid model takes advantage of the complementary strengths of both physically based semi-distributed models and ANN models to provide more accurate and reliable stream flow forecasts for case study catchment (e.g. Humphrey et al. 2016). The adopted network structure for the hybrid ANN model structure is presented in Table 1.

Table 2 presents the various datasets that were used in the study and includes the observed daily rainfall recorded at Makerere University meteorological station, observed daily stream flow recorded at the Kapeeka gauging station along River Mayanja, remote sensed topographical, land use and land cover, soil, historical rainfall, and projected future climate change anomalies.

Data cleaning and filling of missing observed rainfall, temperature, and stream flow data were undertaken prior to its use in hydrological modelling. Specifically, the observed rainfall data was checked for inconsistencies, duplicates, outliers, repeated dates, and missing data. The missing data in this dataset was filled using bias-corrected NASA Power remote sensed rainfall data (Tan et al. 2023). The NASA Power rainfall data was corrected for magnitude bias using the linear scaling (LS) bias correction method to match the monthly mean of the corrected dataset as close as possible to that of the observed dataset. The bias correction factor was computed as the quotient of the observed monthly mean and the remote sensed rainfall data (Girma 2021). Furthermore, the linear interpolation method was used to fill in the missing stream flow values.

In addition, the cleaned data used in the ANN model underwent another preprocessing step to ensure accurate predictions. This data was normalised using the statistical normalisation, which rescales the features to have a mean of zero and a variance of one (Priddy & Keller 2005). Data normalisation ensures that large variations that exist within the input data do not slow down or prevent the training process from going ahead (Pramanik et al. 2011).

In addition, the raw digital elevation model (DEM) obtained was pre-processed through the removal of errors and artificial sinks so as to ensure accurate mapping of streams (Lidberg et al. 2017). In this study, raw DEM preprocessing entailed a series of steps that included: (a) filling of artificial sinks and generation of flow direction and accumulation grids (Troolin & Clancy 2016), (b) extraction of channel networks from the grid, stream segmentation, and catchment grid delineation. The generated catchment grid was then converted to vector format using the catchment polygon processing tool. Finally, the obtained stream network was also converted to vector format using a drainage line processing tool (based on a segmented grid and flow direction grid as inputs) (Akram et al. 2012; Venkatesh 2012).

Model sensitivity analysis is applied to assess how variables impact the model inputs on the model outputs (Tang et al. 2007). Identifying and estimating the most sensitive parameters (those that can cause significant changes in the simulated stream flow) is vital for enhancing model prediction accuracy. In this study, one-factor-at-a-time local sensitivity analysis was applied to identify key parameters and the parameter precision required for calibration. This was implemented by changing parameter values by up to ±50% using intervals of 10% (Tang et al. 2007; Sweetapple et al. 2014). Sensitivity analysis is preceded by running the model using initial estimates of model parameters. Thereafter, one parameter is varied at a time and analysed from −50 to 50% with increments of 10% while keeping the rest of the parameters constant. This process is repeated for all other parameters and the output values are compared with the initial estimates to determine the variation. The greater the percentage change in simulated stream flow indicates the greater sensitivity of that specific model parameter.

Based on the results of the sensitivity analysis, manual calibration was carried out for the HEC-HMS model. No autocalibration was done in this study as it was considered ineffective during the calibration process (Dariane et al. 2016). On the other hand, autocalibration was undertaken for the MIKE HYDRO model. The models were calibrated for the period between 2011 and 2014 and the obtained parameters and initial conditions were validated for the period between 2015 and 2017.

The ANN model was trained, validated, and tested using observed daily rainfall for Makerere University rain gauge station and observed daily stream flow for Kapeeka stream flow gauging stations (Table 2). In the study, seven training, validation, and testing data split percentage ratios, that is 50:25:25; 60:20:20; 60:10:30; 60:30:10; 70:10:20; 70:20:10; and 80:10:10, were investigated (Table 3). The performance of each data split ratio was evaluated using Nash–Sutcliffe efficiency (NSE), R², and RMSE measures of goodness of fit. The 70% (training):10% (validation):20% (testing) data split ratio, which resulted in more superior performance when compared with all the tested data split was applied in this study (Table 3). The data were split into three (3) sets that is: training (2,300); validation (328); and testing (657), respectively.

Rainfall data were the only input for the model and different input variables of antecedent rainfall were tested in the model. The input variables that gave the optimum model were selected and a total of 100 days of previous rainfall were determined to predict the stream flow at one lead day.

The input data were then pre-processed through normalisation to remove large variations and to enable smooth training of the model. Data normalisation was carried out using the Min–Max and statistical method and the model efficiency was compared using the NSE and RMSE values, as shown in Table 4. The statistical normalisation method was more superior when compared with the Min–Max method (Priddy & Keller 2005). Based on this, the statistical normalisation method was applied to standardise the input and output variables.

To avoid model overfitting, the trial-and-error method (Javan et al. 2015) was applied to determine the optimal number of neurons within the hidden layer. If fewer neurons are used, the network may not be able to capture the very detailed relationship between the indicator and computed output parameters whereas if too many neurons are used, this may result in overtraining of the network (Pramanik et al. 2011; Javan et al. 2015). The model was run with both the training and validation data and their errors monitored during the training stage. The optimal parameters for the ANN model were obtained in the region where validation error was observed to start increasing as the training error reduced. The number of iterations that resulted in the best performance when the model was run with an unseen dataset (testing) was determined as the most optimal.

Furthermore, in this study, a range of neurons (4–30) was tested to determine the suitable number of neurons to use in the model. Results showed that there was no significant change in the accuracy of the model when the number of neurons exceeded 4, which was in agreement with the results of Demirel et al. (2009). Based on this, the ANN model was programmed to use four neurons.

Lastly, the optimal number of epochs (iterations) that adequately generalised the data was determined as 50 (Table 5). The trained ANN was later run for the calibration (2011–2014) and validation (2014–2017) periods which used for the HEC-HMS and MIKE HYDRO models to compare all the models on the same dataset.

Due to the inherent uncertainties associated with ANNs, the interpretability of the model results was investigated using the SHapley additive explanations (SHAP) technique. SHAP originates from ‘game theory’ and constructs an additive interpretation model where all features are regarded as contributors (Wang et al. 2022; Mushtaq et al. 2024). SHAP can quantify the contribution of an input feature to the prediction for an individual sample. The SHAP value obtained for a given prediction describes the contribution to that prediction compared with the average prediction of the given dataset (Molnar 2022). SHAP has been successfully applied to explain the importance of input features to the predictions attained both on the local (individual) and global frame (whole dataset) (Lundberg & Lee 2017). The technique facilitates the correct interpretation of a prediction model's output.

The prediction accuracy of hydrological models must be evaluated in both the calibration and validation phases (Gelete et al. 2023). The use of at least one goodness of fit and one error measure can sufficiently evaluate model performance (Legates & Mccabe 1999). Moriasi et al. (2007) undertook a comprehensive review of hydrological model performance evaluation metrics and recommended the use of NSE, percent bias, and the ratio of the root mean square error (RMSE) to the standard deviation of measured data (RSR). Legates & Mccabe (1999) recommended a combination of relative error that is NSE and the index of agreement and absolute error measures (mean absolute error (MAE) and RMSE) to overcome the weaknesses of correlation-based measures such as the coefficient of determination (R²).

In this study, the performance of the hydrological models was evaluated using NSE (Equation (13)), R² (Equation (14)), and the RMSE measures (Equation (15)) (Seenath et al. 2016; Gelete et al. 2023; Mugume et al. 2024). The NSE, which ranges from minus infinity to 1.0, is a normalised statistic that determines the relative magnitude of the residual variance (‘noise’) compared with the observed data variance (‘information’). NSE indicates how well the plot of observed versus simulated data fits the 1:1 line. Higher values of NSE indicate better agreement, as to the variance in the observed data, subtracted from unity (Nash & Sutcliffe 1970; Legates & Mccabe 1999; Moriasi et al. 2007). NSE values between 0 and 1 are generally acceptable, with 1 as the best value (Gupta & Kling 2011). The NSE helps to capture errors based on the long-term calibration of a model.

The anomalies for rainfall, minimum, and maximum temperature expected in the near-term future (2020–2039) were downloaded for an open-source multi-model ensemble of global climate model results for the case study area that is available on the Climate Change Knowledge Portal (CCKP) (World Bank 2021). The CCKP is an online platform created by the World Bank to provide climate-related information at global and regional scales based on the outputs of the Coupled Model Intercomparison Project Phase 6 (CMIP6). In this study, two future climate change scenarios that are SSP2-4.5 and SSP5-8.5 were chosen and the corresponding anomalies were downloaded for the period 2020–2039 using the period 1995–2014 as the baseline period. The impact of climate change on monthly rainfall, minimum temperature, and maximum temperature was computed for the future 2020–2039 period, consideration of the 10th, 50th, and 90th percentiles (e.g. Patterson et al. 2022). The use of the 10th and 90th percentiles facilitated considering the uncertainty band inherent in future climate change projections. The trained/validated ANN model and the calibrated HEC-HMS models were used for the simulation of stream flow under projected climate change scenarios.

This chapter describes the performance of the individual HEC-HMS, MIKE HYDRO, ANN, and the hybrid HEC-HMS-ANN models during calibration and validation. Furthermore, the ANN model performance during testing and interpretation of ANN model predictions is described. In addition, the results of the climate change impact assessment and the projected stream flows for the River Mayanja catchment are described.

Similar to the HEC-HMS model, the MIKE HYDRO model was calibrated for the period 2011–2014 and validated for the period 2015–2017. The optimised parameters of the MIKE HYDRO model are presented in Supplementary Table S4. The MIKE HYDRO model performed poorly during the calibration period (NSE and R² < 0.5) but produced satisfactory results during the validation period (NSE and R² > 0.5), suggesting that the performance of MIKE HYDRO was less superior when compared with the HEC-HMS model. Furthermore, the MIKE HYDRO model performance in the simulation of low flows was less satisfactory when compared with the corresponding performance obtained using the HEC-HMS model. In addition, the MIKE HYDRO model tended to underestimate the peak flows during some events (refer to Figure 4 and Supplementary Table S5).

The ANN model performed more satisfactorily during the calibration period (NSE and R² > 0.64) and the validation period (NSE and R² > 0.56) when compared with both the HEC-HMS and MIKE HYDRO models (Table 3). However, the ANN model performance, based on the R² coefficient (0.57), was lower than the corresponding value obtained using the MIKE HYDRO model (0.59) during the validation period (refer to Supplementary Figure S2). The study results suggest that the ANN model performed generally well in simulating the general pattern of flow. The model was generally able to simulate the low flows with high levels of accuracy. However, the model did not perform well in simulating peak flows occurring during the simulation period, as the maximum flow is limited to 30 m³/s in the ANN model, compared with the maximum flow of ∼40 m³/s in the observed stream flow data.

The study results suggest that the hybrid HEC-HMS-ANN model performed better than the individual HEC-HMS, MIKE HYDRO, and ANN models during both calibration (NSE and R² > 0.991) and validation (NSE and R² > 0.982) (Table 6). The study results suggest that by combining the strengths of the physically based HEC-HMS model and the ANN models, the resulting performance of the hybrid model is more superior when compared with the individual HEC-HMS and ANN models.

From the results, it is noted that SHAP values for the days when rainfall was received have a positive impact on the output generated while for days where no significant rainfall was received the SHAP values were negative. The results suggest that days that received rainfall led to increased stream flow generation while days that did not receive rainfall led to reduced stream flows. The results further suggest that runoff generated in the River Mayanja catchment system takes approximately 11–19 days to make a significant impact at the point of interest (Kapeeka gauging station).

Furthermore, the results in Figure 6 suggest that although rainfall from the previous 17 and 1 days is relatively the same (41.4 and 40.3 mm, respectively), the impact made on the output from the previous 17 days is significantly greater than that registered by the rainfall received in the previous 1 day (6.07 and 1.71, respectively). In addition, the results of the SHAP analysis also suggest that rainfall from the previous 2–3 months also had a significant influence on the model output (Figures 5 and 6).

Furthermore, the results in Figure 10 suggest that monthly rainfall is expected to increase in January, February, March, August, October, November, and December for both SSP2-4.5 and SSP5-8.5 scenarios. The results also suggest the prediction uncertainty is highest in the dry months of July (−1.6% [−22.4–26.1%]) and December (1.2% [−20.4–72.8%]). For SSP5-8.5, monthly rainfall is anticipated to decrease in May, June, and July with the rest of the months registering increasing rainfall. The results also suggest the prediction uncertainty for the SSP5-8.5 scenario is highest in July (−0.4% [−19.7–31.1%]) and December (0.9% [−21.3–80.0%]). The computed change factors for monthly rainfall, minimum monthly temperature, and maximum monthly temperature are presented in Supplementary Figure S4. The monthly rainfall change factors for the SSP2-4.5 scenario range from a minimum of 0.97 [0.77–1.07] to a maximum of 1.06 [0.96–1.72], while corresponding values for the SSP5-8.5 scenario range from a minimum of 0.95 [0.77–1.05] to a maximum of 1.09 [0.98–1.80]. Furthermore, the study results suggest that the highest climate change factors greater than 1.2 were obtained during the months of July, September, and December for the SSP5-8.5 scenario. On the other hand, the computed change factors for the minimum and maximum monthly temperature were relatively low [0.998–1.002] suggesting that future changes in temperature extremes will be very low.

Overall, a comparison of the projected average monthly rainfall to that of the baseline period shows that the rainfall is projected to increase by 2.1% [−11.4–20.4%] and 3.1% [−14.1–22.9%] for the SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively. These results are relatively consistent with the results obtained by Onyutha et al. (2021) who found that rainfall was projected to increase from January to February and decrease in March to May and June to September and increase in October to December for the SSP2-4.5. A slight decrease in rainfall was observed for the period June to September with an increase in other months for the SSP5-8.5. The projected monthly minimum temperature and maximum temperature slightly increase throughout the year for both scenarios. However, the relative change in minimum and maximum temperature values are low [–0.–5–0.30%] for both SSP2-4.5 and SSP5-8.5 scenarios (Figure 10).

The HEC-HMS model results indicate an increase in stream flows of 18.0% [2.7–41.4%] and 19.3% [1.4–45.2%] considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios. The scaled ANN model results indicate an increase/decrease in stream flows of 15.3% [−17.8–27.2%] and 3.1% [−19.3–30.4%] considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios. On the other hand, the hybrid ANN model results suggest an increase in stream flows of 17.3% [2.2–39.5%] and 18.5% [0.8–42.7%] considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios.

The study results further suggest that both HEC-HMS and the hybrid ANN models led to a slight increase in the low flows (10th percentiles) of up to 2.7 and 1.4% considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively. Furthermore, both models led to significant increases in the peak flows (90th percentiles) of up to 41.4 and 45.2% considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively. The scaled ANN model, unlike the HEC-HMS and hybrid ANN models, resulted in significant decreases in the low flows (10th percentiles) of up to 17.8 and 19.3% considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively.

The physically based HEC-HMS model resulted in satisfactory performance during the calibration and validation periods in contrast to the corresponding results obtained using the conceptual and lumped MIKE HYDRO model. The superior performance of the HEC-HMS model in a tropical region could be attributed to its ability to account for the contribution of the baseflow in the catchment and consideration of canopy processes that influence runoff generation in the catchment (Gumindoga et al. 2017; Sanjay Shekar & Vinay 2021; Tibangayuka et al. 2022). In addition, both HEC-HMS and MIKE HYDRO were able to accurately simulate the low flows during both the calibration and validation periods.

However, both the HEC-HMS and MIKE HYDRO models tended to underestimate the peak flows for some events during the calibration period, which is consistent with the findings of previous studies (Aredo et al. 2021; Gunathilake et al. 2021). In addition, the MIKE HYDRO model also overestimated some peak flows during the validation period. These discrepancies have also been reported in previous studies such as Slieman & Kozlov (2023) and are attributed to the lack of stream flow gauging stations at outlets of catchments, insufficient spatial resolution of existing rainfall, temperature, and soil datasets, relatively low resolution of the utilised digital elevation models, which are vital for estimation of model parameters and limited data on the split between rainfall-runoff and baseflow in gauged rivers (Vilanova et al. 2019).

In future studies, the physically based or conceptual model performance could be enhanced through improved estimation of sensitive model parameters that include percentage imperviousness, storage coefficient, and time of concentration in addition to densification of the meteorological and stream flow gauging stations within catchments to improve the spatial distribution of the observed rainfall, temperature, and stream flow datasets (e.g. Pareta 2023).

In contrast, the study results suggested that the developed ANN model performed slightly better than HEC-HMS and MIKE HYDRO during the calibration and validation periods and was able to sufficiently simulate most of the low flows occurring in the River Mayanja catchment. This was attributed to the presence of a high number of low flows in the training dataset, e.g. Pramanik et al. (2011). However, the ANN model also did not perform satisfactorily well in capturing peak flows for the River Mayanja catchment. This could be attributed to the use of point rainfall that did not effectively represent the spatial rainfall distribution in the catchment. Furthermore, the inadequacy of ANN models in capturing peak flows has been reported in past studies, which attributed the phenomenon to an insufficient number of peak flows in the calibration dataset, leading to the failure of the ANN to establish a strong pattern (Jimeno-Sáez et al. 2018). This, therefore, suggests that the ANN model performance can be significantly improved through the use of longer calibration datasets that contain multiple peaks that are sufficient to establish a strong pattern in the ANN model (Tibangayuka et al. 2022).

Furthermore, the developed hybrid HEC-HMS-ANN model resulted in more superior performance during both calibration and validation periods when compared with the individual HEC-HMS, MIKE HYDRO, and ANN models. In addition, the results of the SHAP model interpretability analysis facilitated an explanation of the significant difference in the resulting ANN and hybrid HEC-HMS-ANN model performance. This difference was attributed to the use of rainfall and stream flow as inputs for the hybrid model, in contrast to the use of a single input (rainfall) for the individual ANN model. In addition, the hybrid model combined the strengths of the physically based HEC-HMS model (detailed mathematical description of physical processes involved in movement and storage of water in a catchment) and the ANN model (ability to accurately simulate complex non-linear processes without the need for detailed knowledge on underlying hydrological processes) and the resulting into more superior performance (e.g. Humphrey et al. 2016).

These results are in agreement with recent studies that suggested that hybrid ANN models are able to exploit the strengths of the individual physically based or conceptual models that utilise mathematical equations to describe the physical processes entailed in the movement and storage of water in catchments and ANN models that have the ability to accurately simulate complex non-linear processes for stream flow prediction without the need for detailed knowledge on underlying hydrological processes (Mount et al. 2016). More so, the performance of the developed hybrid ANN model showed that by improving the model structure to facilitate the use of multiple input datasets, the performance of the ANN models can be significantly improved. The study findings also demonstrate that hybrid ANN models present an opportunity for improved hydrological modelling in data-scarce regions, located in areas with similar climatic zones. This would require prior calibration and validation of hybrid ANN models using available observed rainfall and stream flow data for adjacent gauged catchments located in the same climatic zone as the ungauged catchments being studied.

The study results suggest that using the HEC-HMS model, stream flow is projected to increase by up 18.0% [2.7–41.4%] and 19.3% [1.4–45.2%] by 2039 considering SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively. For the scaled ANN model, the results indicate both increase/decrease stream flow of 15.3% [−17.8–27.2%] and 3.1% [−19.3–30.4%] SSP2-4.5 and SSP5-8.5, respectively, suggesting less satisfactory model performance for future stream flow prediction. The decrease in future stream flow for the scaled ANN model could be attributed to training the ANN using only one model input parameter, which is the projected future rainfall data, as opposed to the HEC-HMS model where future rainfall, temperature, and soil and land use data were utilised as input parameters. The hybrid HEC-HMS-ANN model, on the other hand, addresses this challenge by using input data that consists of both projected future rainfall and the HEC-HMS projected stream flow as inputs for future stream flow simulation.

Furthermore, for the hybrid HEC-HMS-ANN model, the results indicate increases of up to 17.3% [2.2–39.5] and 18.5% [0.8–42.7%] by 2039 considering SSP2-4.5 and SSP5-8.5 future climate change scenarios, respectively. The study results suggest that the developed hybrid ANN model adequately represents the low flows but underpredicts the peak flows. This could be attributed to the training of the ANN model using observed stream flow data with a relatively low number of observed peak flows and lower values of the peak flow magnitudes when compared with the simulated future peak flows.

The results obtained therefore suggest that for the River Mayanja catchment, the developed hybrid ANN model provides highly satisfactory results (model calibration: NSE and R² > 0.99 and validation: NSE and R² > 0.98) and can be used for the simulation of future stream flow in catchments with similar topographic and climatic characteristics. Furthermore, the results agree with similar studies undertaken in the Nile Basin (Gebrechorkos et al. 2023; Tusingwiire et al. 2023; Sempewo et al. 2024).

This study, therefore, suggests that climate change will lead to an increase in available water resources for water supply, irrigation, hydropower production, and other water uses in the catchment. However, the results also confirmed a future increase in the variability of water resources at monthly and seasonal time scales (relatively low increase in low flows of 1.4–2.7% visa vice the significant increase in high flows of 41.4–45.2% for both SSP2-4.5 and SSP5-8.5 future climate change scenarios). These findings therefore point to the need for prioritisation of investments in water storage infrastructure such as dams and reservoirs so as to meet the projected water demands all year round within the case study catchment.

In this study, a hybrid ANN model that combines HEC-HMS and the back propagation multi-layer perceptron FFNN was developed and applied to assess the impact of climate change on future stream flow and water resources availability in a data-scarce River Mayanja catchment in Central Uganda. The performance of the developed hybrid HEC-HMS-ANN model was validated through comparison with individual physically based semi-distributed (HEC-HMS), conceptual and lumped (MIKE HYDRO), and ANN models considering both current and future climate change conditions. Future stream flows were simulated for the near future period using all the models and considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios. Anomalies for future climate change were obtained from the CIMP6 ensemble of global climate models compiled by the World Bank Climate Research Programme and used to project future daily climate conditions.

The study results suggest that the performance of the validated hybrid HEC-HMS-ANN model during calibration and validation (NSE and R² > 0.99) was more superior in predicting stream flows of the River Mayanja catchment when compared with the corresponding performance obtained using individual HEC-HMS (NSE and R² > 0.50), MIKE HYDRO (NSE and R² > 0.42), and ANN models (NSE and R² > 0.56). Using the developed hybrid ANN model, future average daily stream flows are projected to increase by up to 17.3% [2.2–39.5%] and 18.5% [0.8–42.7%] considering the SSP2-4.5 and SSP5-8.5 future climate change scenarios.

In addition, the study has demonstrated that the performance of the hybrid HEC-HMS-ANN model can be improved through the use of multiple and relatively long input datasets so as to establish strong ANN model output patterns that can sufficiently represent both low and peak flows. The study results also suggest that the developed hybrid model combined the strengths of the physically based HEC-HMS model (detailed mathematical description of physical processes involved in movement and storage of water in a catchment) and the ANN model (ability to accurately simulate complex non-linear processes without the need for detailed knowledge on underlying hydrological processes) and the resulting into more superior performance.

The findings of this study demonstrate that hybrid ANN models are suitable for modelling stream flow in catchments with limited observed hydrometeorological datasets. From a modelling perspective, it is also worth noting that MIKE HYDRO is a lumped model with a straightforward structure that is easier to use while HEC-HMS requires a lot more datasets and computations. On the other hand, whereas the developed hybrid HEC-HMS-ANN model is more straightforward, it requires iterative training, testing, and validation. More so, the hybrid ANN model requires both the set-up of the HEC-HMS model and in addition ANN model that uses stream flow output from the HEC-HMS model as one of two inputs. This, therefore, means that ease of model use, modeller experience and set-up should not be used as the main criteria in the selection of a model for a catchment. The selection of a model should also consider other factors such as data availability, length, and spatial distribution of hydrometeorological data. Nonetheless, the calibrated and validated hybrid HEC-HMS-ANN model can be used to more accurately simulate stream flows in adjacent ungauged catchments located in the same climatic zone as the River Mayanja catchment, given access to open-source reanalysis climate datasets (Nakkazi et al. 2022), open-source digital elevation models, soil, and land use and land cover maps.

In addition, this research has demonstrated that ANN models can be developed and applied to support water balance and allocation modelling considering both the current and projected impacts of future climate change on stream flow. The study findings can potentially support the development of water resource modelling guidelines in data-scarce regions that are faced with the challenges of choosing suitable models for different terrains and varying lengths of in situ observed data. Furthermore, this research could inform the identification and prioritisation of potential mitigation and adaptation strategies that are necessary for ensuring water security in view of emerging climate change and urbanisation threats.

However, the performance of the developed HEC-HMS-ANN model was constrained by a limited number of input datasets and an insufficient number of peaks in the calibration dataset. Therefore, future research should focus on enhancing the performance of hybrid models using varying model structures and relatively long calibration and validation datasets that include an adequate number of peaks. Furthermore, future research should investigate the effectiveness of non-linear ensemble models (Gelete et al. 2023) created by training the hybrid ANN using the stream flow from obtained from physically based models in enhancing the performance of hybrid ANN models. Furthermore, future research should focus on the investigation of the effectiveness of hyperparameter tuning methods (Ghimire et al. 2021) for determining the most optimal ANN model parameters during ANN model calibration and validation.

Acknowledgement is given to the Directorate of Water Resources Management (DWRM), Ministry of Water and Environment, Uganda for the provision of the datasets used in the study. The insights of four anonymous reviewers are also gratefully acknowledged.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.