Comparison of the performance of SWAT and hybrid M5P tree models in rainfall–runoff simulation

One of the most crucial hydrological processes, particularly for large-scale operations, is modelling of rainfall and runoff. In addition, nonlinearity and multidimensionality make it very difficult to calculate how rainwater turns into runoff (Ishtiaq et al. 2010). Although there are many different classifications for hydrological models, they have generally been grouped into three categories: empirical or data-driven models, conceptual or grey box models, and physically based or white box models (Willems 2000). Empirical or data-driven models simply link the input conversion functions to the output functions rather than explicitly using rules and processes (Leavesley et al. 2002). The second category comprises conceptual models that are created by understanding the designer of the system model's behaviour rather than on the basis of all physical processes. The third category, theoretical models (physically based models), tries to account for all of the operations in the necessary hydrology system by incorporating physical senses (Moore et al. 1988).

The American Agricultural Research Organization created the hydrological model known as the Soil and Water Assessment Tool (SWAT). The basin-scale framework uses the SWAT model, a conceptual semi-distributed model. This model includes a number of processes such as those related to the weather, hydrology, nutrients, erosion, vegetation, management techniques, and flow direction. As a result, it is widely used everywhere (Gassman et al. 2007). A substantial advancement in the predictors of hydrological events has also been made recently thanks to the development of artificial intelligence techniques like artificial neural networks (ANNs), support vector machine (SVM), and others (Kisi & Cigizoglu 2007; Kisi et al. 2009; Kocabasa et al. 2009; Yang et al. 2009). M5P model tree, a machine learning approach, has gained much popularity in water resources for streamflow prediction in recent years. This is a tree-based model analogous to the linear regression model where parameter spaces are discredited to subspaces for which a local specialized linear regression model is built (Bhattacharya & Solomatine 2005). The approach has wider application in hydrology ranging from stream flow prediction to sediment yield prediction. Shamshirband et al. (2020) used the approach for predicting the hydrological drought index and concluded its superiority over the support vector regression method. The M5P method also performed better in short-time flood forecasting than the ANN method. Similarly, the method has been used to predict the water level of lakes where they edged over random forest, random tree, and k-nearest neighbour methods (Nhu et al. 2020; Ditthakit et al. 2021). M5P has been used both in low-flow forecasting as well as daily flow forecasting with less computation time and reasonable accuracy (Štravs & Brilly 2007; Taghi Sattari et al. 2013).

In river basins all over the world, the SWAT model has been widely used to simulate different types of hydrological processes (Abbaspour et al. 2015; Francesconi et al. 2016; Liu et al. 2016; Malagò et al. 2016; Tuo et al. 2016; Golmohammadi et al. 2017; Duan et al. 2019; Nguyen et al. 2019; Rahman et al. 2020). SWAT is also widely used to evaluate how snow affects the water cycle in mountainous basins (Rostamian et al. 2008; Debele et al. 2010; Troin & Caya 2014; Grusson et al. 2015; Shahid et al. 2021). Many studies have shown that the temperature-index technique, which has been widely utilized to model snow processes in various basins utilizing SWAT (Hock 2003; Walter et al. 2005; Zhang et al. 2008), is astonishingly accurate (Debele et al. 2010; Luo et al. 2013). Although SWAT has demonstrated its ability to simulate hydrological processes, it still requires a variety of geographical data and a thorough description of the numerous physical processes that affect a watershed's hydrological behaviour. ANN models, in contrast, are data driven and do not require spatial information. This is another disadvantage; however, ANN models are useful for assessing and contrasting the modelling of discharge at a single watershed outlet.

Morid et al. (2010) used the ANN and SWAT models simultaneously. They found that ANN outperformed SWAT for basic flow rates in summer, fall, and winter. On the contrary, the SWAT model could perform better modelling in spring when rainfall and sudden peak flow rates were frequent. Bhagwat & Maity (2012) studied the potential to use the least-square SVM to forecast the river flow rate in a catchment basin in India. In Iran, SVM was used to forecast data measurement in the Kashkan catchment basin. The results showed the high accuracy of the model. The artificial neural fuzzy inference system method according to C_means fuzzy clustering. According to frequent applications of the SWAT hydrological model and the time series tool, the main objective of this article is to evaluate the accuracy of SWAT and hybrid M5P tree models in reproducing observed rainfall–runoff patterns and compare the models' performance in predicting runoff in the MH Halli gauging site in the Hemavati River.

In this study, the SWAT model and the M5P model were applied to simulate discharge in the MH Halli station.

SWAT is a semi-distributed hydrologic model that can simulate surface runoff, evapotranspiration, sediment yields, the dissemination of nutrients and pesticides, plant growth, groundwater movement, and estimate reservoir storage over the long term (Grusson et al. 2015). In this study, ArcSWAT 2012 (Arnold et al. 2012) has been used for runoff simulation. After a good model design, the model can effectively mimic vast and complicated watersheds with various management techniques and best management practices. To ensure the reproducibility of research involving the SWAT or similar hydrological models, a ‘proper setup’ encompasses several key steps. It entails comprehensive data collection, including topography, land use, soil properties, and climate data, while ensuring data quality through validation and quality control procedures. It involves characterizing the study area by understanding its physical characteristics, such as size, shape, and topography, mapping the drainage network, analysing land use and land cover, and collecting soil data. A proper parameterization of the hydrological model is essential, involving the configuration of model parameters, calibration, and validation using observed streamflow data. The input data must be meticulously prepared, organized, and formatted for the model, including spatial data input into the SWAT model setup. The researchers should conduct scenario testing and sensitivity analysis to assess various land use or management practices' impact and identify influential model parameters. The model execution and analysis involve running the SWAT model with prepared data, evaluating outputs against observed data, and analysing results. Thus, thorough documentation and reporting of data sources, parameter values, and procedures ensure transparency and facilitate replication by other researchers. This comprehensive approach ensures the rigor and reproducibility of SWAT modelling studies. So it is important that while creating the sub-basins in the SWAT model the study area should thoroughly be investigated, i.e. in a physical sense the distribution of the drainage network and the shape of the basin up to its outlet along with the land use pattern and the soil type.

While generating the sub-basins in the SWAT model, care should be taken that the number of the generated sub-basins neither be very much nor very little because it affects the runoff generation and separation process as well as the simulation of computation time and also creates difficulties while writing the output results. While creating the Hydrologic Response Unit (HRU), it is most important to understand the HRU thresholds and HRU's definition first. HRU is an abbreviation for hydrologic response unit. In hydrology and watershed modelling, an HRU is a fundamental concept used to represent a spatial unit within a watershed. It is a way to partition a watershed into smaller, manageable units based on various landscape characteristics that influence hydrological processes. The HRU concept is essential in models like the SWAT for simulating how water moves through the landscape. Each HRU typically encompasses a specific combination of land use, soil type, slope, and other factors that affect the movement of water, sediment, and nutrients within that unit. HRUs are used to model how rainfall is transformed into runoff, how sediment is eroded and transported, and how nutrients are transported within the watershed. Properly defining HRUs is crucial for accurately representing the complexity of hydrological processes in a watershed. Depending on the modelling needs and data availability, HRUs can be defined in different ways, such as by dominant land use, soil type, slope class, or a combination of these factors. The choice of HRU definition depends on the specific characteristics of the study area and the goals of the modelling exercise.

The SWAT model facilitates the four HRU definitions and two threshold criteria, and in this way as per the thresholds selected, i.e. percentage or area, HRU's definition can be chosen depending on the study area; therefore, a proper investigation of the study area is essential prior to selecting HRU's definition. In the SWAT model, the HRU's definition may be dominant of land use, soils and slopes, dominant of HRUs, target no. of HRU, and multiple HRUs. In this study, we have used multiple HRUs and percentage of thresholds. According to the standards outlined by Her et al. (2015), the values for land use % over sub-basin area, soil class percentage over land use area, and slope class percentage over soil area have been determined. For the SWAT model setup of this study area, we have taken land use and soil data from https://swat.tamu.edu/data/india-dataset/. Since this dataset is easily available and ready to use otherwise, finding out the HSG (Hydrologic Soil Group) is a tedious job which needs an in-depth field investigation of the soil type and multiple infiltration tests for each and every soil type found in the study area. The digital elevation model of 30 m resolution from SRTM has been used for preparing the Shuttle Radar Topography Mission (SRTM) model setup. The Hargreaves method has been used as the potential evapotranspiration (PET) method since this method requires only the temperature as an input for estimating the PET. For reaching channel routing, the Muskingum method has been selected with its default parameter value.

The calibration of model parameters for any hydrological model is an essential part only if the first simulation results are unsatisfactory or expecting more improvements. In this study, we found that the results were satisfactory which are discussed in Section 3. Such type of performance from the model can be obtained only if the model setup has been done in a proper manner as we have explained earlier. Therefore, it was decided that for this setup of the SWAT model and for this study area, no calibration of the parameters is required, which shows that the understanding of the physical meaning of all the input required to the model is necessary while setting up the model.

Quinlan (1992) introduced the M5 tree as a regression decision tree learner (Quinlan 1992). Regression analysis functions are assigned to the terminal nodes of this tree approach, and a multivariate linear regression analysis is fitted to each subspace. The M5 tree scheme, rather than discrete groups, deals with continuous class problems and can handle high-dimensional problems. It shows the piecewise information for each linear model that was used to estimate nonlinear relationships in the dataset.

Daily data on discharge, precipitation, and temperature were first split into two categories: calibration/training and validation/testing. Eight years' worth of data were chosen from the total for calibration, and the remaining 7 years' worth was chosen for testing the constructed models. The statistical parameters for the discharge, rainfall, and temperature datasets' calibration, training, validation, and testing were computed as given in Table 1.

Although the mean and standard deviation for the discharge testing datasets were lower than those for the training, the coefficient of variation (CV) values for the temperature, discharge, and rainfall testing/validation datasets were higher than those for the training (Table 1). In addition, the training dataset has a higher maximum value for the discharge variable. The maximum values in the testing dataset for temperature and rainfall were higher than those in the training dataset.

In fact, the simulation process, which is used to estimate model expectation results, is not possible without model calibration and validation. We have split the available daily time series of the observed flow into two parts, i.e. one for the calibration and the second for a validation process.

By comparing the discharges of the measured flow to the simulated flow in the hydrometric station under consideration, SWAT model validation was carried out over additional periods of the dataset. The validation enabled us to acquire a good model performance for discharges with RMSE and ‘d’ of, respectively, 50.54 and 0.95, in accordance with the performance assessment criteria of the model advised for a monthly time step (Moriasi et al. 2007). The NSE and R² thresholds are 0.74 and 0.91, respectively, and it also assesses the relationship between the two statistical series. The good model calibration and capacity to accurately reflect the flow estimation is also demonstrated by the good agreement between simulations and observations throughout the validation process.

Weka software was used to build the M5P model tree. The user-defined parameter (M) had the best value of 4. As mentioned previously, the training and testing dataset were randomly selected from the 50–50 split. For the sake of simplicity and more precise prediction of the flow, the M5P model itself has been run under two parameter settings named scenario 1 and scenario 2. These scenarios' results were then evaluated using R², RMSE, NSE, and d. The fitting accuracy of the used models for each input composition over the training phase is summarized in Table 2. As given in Table 2, the efficiency fluctuated from one compound to another. The primary reasons for the oscillation are the differences between the effects of each selected input variable on the stream flow prediction. According to Table 2, the best correlation coefficient to estimate discharge in training data was 0.97 for the second scenario.

According to R² values, the Random Forest (RF) model from the second scenario produced the best performance during calibration, followed by the first scenario. Because R² is tuned for differences between the mean and variance of measured and expected quantities, it is vulnerable to outliers and should not be used only for evaluating created models (Legates & McCabe 1999; Kisi & Shiri 2012). As a result, different error measurement indices were used to evaluate the model's performance. Based on RMSE, NSE and d, the M5P (second scenario) was superior to the other types.

In this section, we provide an in-depth discussion of the simulation results obtained from both the SWAT and the M5P models. We aim to elucidate implications of these results and draw meaningful conclusions.

The calibration and validation phases demonstrated a reasonable level of model accuracy, as evidenced by the goodness-of-fit statistics (R², NSE, RMSE, and d). Notably, the model showed its ability to replicate the observed flow observations. The daily hydrographs presented in Figures 4 and 5 further illustrate the model's capability to simulate streamflow. These results indicate that the SWAT model can be applied with acceptable accuracy for discharge assessment in the MH Halli station of the Hemavati River watershed.

Now, we discuss the performance of the M5P model, emphasizing its advantages over the SWAT model. The M5P model, developed using Weka software, exhibited variable efficiency across different input compositions. The best correlation coefficient was achieved in the second scenario of the M5P model as depicted in Table 2, demonstrating the model's sensitivity to input variables. Evaluation metrics (R², RMSE, NSE, and d) revealed the M5P model's superior accuracy during the calibration and validation phases, particularly in the testing stage.

The results clearly indicate that the M5P model outperforms the SWAT model in terms of accuracy, especially in predicting runoff during the testing phase. The evaluation metrics in Table 2 highlight the M5P model's superior performance. This suggests that the M5P model could serve as a promising alternative to the SWAT model for runoff prediction in the MH Halli station.

The superior accuracy of the M5P model during the testing phase underscores its potential as a valuable tool for discharge forecasting in similar watersheds. This study highlights the importance of considering alternative modelling approaches and the need to select the most suitable model based on the specific characteristics of the study area. Finally, this section aims to provide a comprehensive understanding of the simulation results, their significance, and the implications for future research and practical applications. It strengthens the link between the results and the conclusions drawn from this study, ensuring that readers can grasp the key takeaways and their relevance.

The study presented a comparative analysis of the SWAT and the hybrid M5P model for rainfall–runoff simulation in the MH Halli station, Hemavati River watershed, Karnataka, India. While the results and discussion sections have elaborated on the simulation outcomes, let us delve into the rationalization of the conclusions and highlight the advantages of the hybrid M5P model.

Both the SWAT and M5P models demonstrated commendable performance in modelling rainfall and runoff, as evidenced by high correlation coefficients (R²) and NSE values. However, these conclusions are based on the evaluation metrics alone. It is important to clarify that the selection of these models should be context dependent, taking into account the specific research goals and data availability. The assertion that the M5P model may be preferable for assessing the steam flow, particularly in data-scarce regions, needs further clarification. While the M5P model exhibited promising accuracy, the complexity and resource-intensive nature of the model should also be considered in the decision-making process.

The recommendation to use the SWAT model for flood routing and investigations into physical watershed characteristics is valid. However, its suitability is contingent on the availability of comprehensive physical and chemical data for the study area. The suggestion for future research to explore alternative hydrological models such as the MIKE NAM model and the HEC-HMS model is a valuable point. These models may offer further insights into rainfall–runoff processes and enhance water resource management strategies.

The advantages of the hybrid M5P model over the SWAT model, as it is a significant aspect of this study that warrants detailed discussion. The hybrid M5P model's sensitivity to input variables allows for a more in-depth understanding of the factors influencing streamflow prediction. This adaptability is particularly valuable in situations where data availability is limited, as it can leverage available information effectively. The M5P model's superior performance, especially during the testing phase, highlights its potential as a robust tool for discharge forecasting. The model's accuracy, as reflected in metrics like R², RMSE, NSE, and d, positions it as a valuable asset in regions where precise runoff predictions are crucial. The study underscores the importance of considering alternative modelling approaches, and the hybrid M5P model stands out as a viable alternative to the SWAT model in specific scenarios. This flexibility allows researchers and water resource managers to adapt their modelling strategies to suit the unique characteristics of the study area.

In conclusion, this study has highlighted the capabilities and advantages of the hybrid M5P model in the context of rainfall–runoff simulation. While the conclusions are based on rigorous evaluation metrics, it is essential to exercise caution in model selection and to weigh the advantages and complexities associated with each model against the research objectives and data constraints. The hybrid M5P model's adaptability and superior accuracy positions it as a valuable tool in the hydrological modelling setups of hydrologists and water resource managers, particularly in data-scarce or changing climate environments. Future research endeavours should continue to explore and refine hydrological modelling approaches to advance our understanding of runoff processes and improve water resource management strategies.

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

The authors declare there is no conflict.