Projection of monthly surface flows by an optimized SWAT–MLP: a case study

In recent years, population growth and the lack of attention to watershed management plans and the need for food resources have led to watershed residents changing the land use, which could increase the probability of flooding and flood risk. Consequently, one of the most crucial steps for maximizing the use of soil and water reserves is the appropriate handling of basins (Kumari et al. 2020). One of the important factors in water resource management is runoff which is very important in different aspects including flood control and drought. So, runoff forecasting can provide managers and experts with useful information on water resources management to reduce the impact of floods and droughts with proper management (Shirmohammadi et al. 2020). In order to comprehend hydrological activities, what causes them to change and how these patterns of behavior affect water resources, basin models have been created with two main goals in mind. The subsequent goal is to produce hydrological information to create water supplies, and control floods, fluctuations, and runoff projections (Srinivas et al. 2020).

Since it is not possible to measure all the quantities needed to evaluate runoff in watersheds, it is possible to select a model that, while being simple, with the minimum input information can provide an accurate prediction of runoff (Martel et al. 2020). Due to the compatibility that has semi-distributed physical models with the characteristics of the watershed, these models have become more important in recent years. These models can be used to investigate water resource issues such as the environmental impacts, the consequences of global warming on water supplies, and changes in land usage and how to manage watersheds comprehensively (Yuan et al. 2020). Conceptual hydrological models through mathematical formulas are more capable of simulating runoff in the hydrological cycle. One of the continuous and semi-distributed mathematical models is the Soil and Water Assessment Tool (SWAT). For the United States Agricultural Research Service (USARS), Arnold developed an approach that, besides predicting water runoff, also predicts river silt, quality of water, and soil nutrients in agricultural areas (Karki et al. 2020). Evapotranspiration, runoff from surfaces, melting snow, surface infiltration, deep infiltration, groundwater movement, and subsurface flow are the key hydrological procedures that the model analyses (Zeng et al. 2020). According to the literature, the SWAT model has high accuracy in predicting runoff, and most researchers recommend using this model. Newer methods have also been used in recent years, including artificial neural network (ANN) techniques that can simulate various parameters in hydrological research (Gupta et al. 2020).

Runoff simulation has made tremendous strides in recent years, which has caught the interest of several scientists and academics. The ANN method, which is a popular technique among these new techniques, may simulate complicated processes by simulating the human brain (Sameen et al. 2020). In hydrological research, ANNs, which are linear data-driven designs, are frequently utilized. They are also useful instruments for modeling nonlinear structures that may simulate unidentified factors using various constraint kinds, including imperfect and error-prone data. ANNs are employed in the study of hydrology to simulate rainfall, forecast runoff, forecast dam flow, forecast river silt, and more (Chang et al. 2023). In the field of runoff forecasting, various researches have been conducted worldwide. For example, Pradhan et al. (2020) analyzed the effectiveness of the SWAT model and three types of ANN for forecasting flow. According to the findings of the investigation, it was determined that the ANN simulation's amount of coefficient of correlation (R²) and Nash–Sutcliffe Efficiency (NSE) is greater than 0.95. The findings also demonstrated that the ANN model performed better in terms of hydrological indicators while simulating runoff.

Pradhan et al. (2020) evaluated a combination of ANNs with a semi-distributed SWAT hydraulic model, based on hydrological indicators such as annual discharge and baseline flow at different periods. The outcomes displayed that the SWAT technique works enhanced for simulating low flows and the ANN process is more appropriate for simulating high flows.

Kassem et al. (2019) proposed daily runoff prediction in the Khazir watershed using the SWAT model and a combined process by an ANN method. The combined SWAT approach outperforms the standard SWAT framework, according to the findings of statistical indices and significant values.

Kumar et al. (2019) assessed two types of neural networks including the Elman Neural Network (ENN) approach and the ANN method to simulate flow. Based on the findings, it was concluded that the ENN is more effective at forecasting flow than the ANN approach, with maximum proportional error = 0.01, R = 0.93, R² = 0.87, NSE = 0.86, root mean square error (RMSE) = 276.13, and maximum proportional error = 0.86. As a result, they identified the ENN approach as the more efficient framework for flow modeling in the research.

Neto et al. (2019) presented the results of two mathematical models and two computational models for estimating flow in a basin in southern Brazil. The results showed that physical-based models such as SWAT and TOPMODEL perform less well than numerical models such as RT and ANN, but SWAT, TOPMODEL, RT, and ANN models showed satisfactory levels in different management situations.

Koycegiz & Buyukyildiz (2019) investigated the SWAT hydrological method with data-driven models including ANN and Support Vector Machine (SVM) for forecasting runoff. In this study, the result was concluded that data-driven models perform more efficiently in runoff simulation, but they did not show spatially distributed information, whereas the semi-distributed SWAT hydrologic model is capable of doing so.

The ANN-based multi-model ensemble from CMIP6 was used by Ghadimi et al. (2023a) to study the assessment of future rainfall and temperature estimates in Morocco. The research uses ANNs to simulate regional climate and examine the impact of climate change on Morocco. Top models from 15 GCMs are selected, and a multi-model ensemble is built for each climatic parameter. The results show excellent agreement, allowing for future rainfall and temperature estimates under the SSP2-4.5 and SSP5-8.5 scenarios. Temperatures are predicted to rise by up to 5 °C by the end of the century in certain areas. Seasonal variability is discussed, with summer showing similar fluctuations. Precipitation variations are also considered, with Morocco likely experiencing a significant drought by the end of the century.

In the Cape Fear and Pee Dee catchment, Gurley et al. (Gurley et al. 2023) investigated the prediction of future flow and irrigation needs using weather and urban growth. The Coastal Carolinas are under substantial water resource stress due to biological and human demands. The Coastal Carolinas Focus Area Study was started by the U.S. Geological Survey to look at these stresses and how they affect water resources. For the Cape Fear and Pee Dee River Basins, the SWAT model was used to examine future streamflow and irrigation demand under six scenarios. In contrast to developing future scenarios based on forecasts of urban expansion, water demand, and global climate models, historical models were very weakly calibrated. Future studies for large and small regions within the basins are made possible by the calibrated and scenario models, which can simulate flows and water needs in thousands of tiny sub-basins daily.

Mengistu et al. (2023) studied modeling impacts of projected land use and climate changes on the water balance in the Baro basin, Ethiopia. The research examines how the water balance of Ethiopia's Baro basin has been impacted by land development and climate change. Under the CUR and BAU scenarios, the SWAT model predicts a decline in agricultural and forest areas; however, under the RCP4.5 and RCP8.5 scenarios, it predicts a rise in yearly evapotranspiration and a reduction in surface runoff. While the CON scenario would see a 24% fall in yearly SURQ, the BAU scenario would see an increase of 18%. For mitigation and adaptation strategies, it is essential to comprehend these shifts. To increase the resilience of the river basin, the report recommends restoration initiatives and climate-resilient water management techniques.

This study employed a hydrologic simulation using the SWAT framework and a data-driven model including the ANN process for predicting future flow. In this study, a hybrid SWAT model has been proposed and evaluated for performance analysis of the simulations. Also, in the SWAT and ANN process, an optimized algorithm has been proposed in the ANN technique for minimizing the error in the prediction of runoff estimation and to be closer to the observed values. The use of models is appropriate for areas without hydrometric stations and reduces the installation of hydrometric stations in some areas and may save time and cost in some areas, especially areas where hydrometric stations cannot be installed. We have also chosen a different work area, to expand this type of research in different parts of the world.

One of the benefits of the SWAT system's ability for data analysis over yearly, monthly, daily, and hourly timescales (Bo et al. 2022) is that in this analysis it employed monthly interval information to estimate monthly flows. This framework is more effective and user-friendly when run in a shared environment using the ArcGIS software. The ArcGIS 10.2 software and the SWAT 2012 version were used to perform this investigation. Arc SWAT, a graphical interface from SWAT 2012, is a tool that may be added to the Arc Map software.

The scientific name for sunflower is ‘Helianthus annuus’. North America is the primary habitat of this plant.. The leaves and buds of this plant turn toward eastward during the daytime and sunlight, whereas they turn toward westward at sunset. Gomes et al. (2019) provides a novel optimum algorithm that finds an optimal position toward the Sun and is motivated by the unique behavior of the Sun's rays. The term ‘SunFlower Optimization’ (SFO) refers to this. In the suggested technique, pollination of sunflowers occurs at random with a minimal spacing between flower i and flower i + 1. Nevertheless, given that sunflower naturally produces a lot of spores during pollination, so to simplify this algorithm it has been assumed that a spore has been made using the plant spawn. The ‘square inverse square radiation’ is one of the factors to take into account in this method. It reflects the inverse connection between the power of the radiation and the square of the distance so that as the amount of the rays falls, the quantity of the square reduces. The primary purpose of this method is to minimize the distance between the plant and the Sun to absorb more light. Generally, as the plant turns away from the Sun, the amount of radiation it obtains decreases. This method helps the plant to take bigger steps to approach the optimum amount of sunlight (Mengistu et al. 2023).

The population set that the algorithm initiates might be even or randomized. Finding the finest agent of a high value involves evaluating fitness.

It is planned to enable working with numerous suns in a later edition, but SFO restricted it to only one. The result is that, through a random control, every factor (in this case, the sunflower) tilts toward the direction of the sun. In better alignment with the black circle, the circles show the earlier positions of Sun's agents.

Although one of the newest algorithms has a satisfactory solution to optimization problems, it sometimes has problems in local optimization. Recent research has used two methods to solve this problem.

The BP approach is utilized in this study for network learning, as discussed in the previous sections. The slope-decline BP algorithm has several problems as well, one of which is that you can be easily constrained to a small region (Moallem & Razmjooy 2012). These flaws can cause some serious issues with the outcomes of pattern recognition; many solutions have been proposed (Beaumont et al. 2020; Duan et al. 2020; Wengang et al. 2020) Scissors from nearby pens were used in the novel WOA hybrid technique, which was used to reduce the maximum capability rather than slope reduction. Choosing the appropriate fitness performance and selecting the search parameters are the two main goals of employing MSFO in MLP. Thus, MSFO-based MLP can take the following forms:

• (1)

  Calculate the number of initial sunflowers in weight N and evaluate the fitness amount of each MLP/MSFO.

• (2)

  Modify the present efficiency location in accordance with sun and sunflower direction for a fitness score.

• (3)

  Apply additional controllers to the MSFO for each person.

• (4)

  Verify the network has adequate error amount or meets the criterion.

• (5)

  Go to (2) if the criterion situation is not supplied.

• (6)

  If you fit the bill, you must:

• (7)

  End

The SWAT–MLP/MSFO model outperforms the other two recommended models in performance during the calibration period. The results will be determined after analysis. Compared to other models, the statistical results generated from this model show significantly better agreement with the real hydrograph data. The comparison of the hydrographs produced by the three models shows that the SWAT–MLP/MSFO model is more accurate and precise. The statistical indices obtained from the simulations of this model show a significantly better agreement with the hydrograph data, indicating a more accurate picture of the real runoff behavior. On the other hand, the hydrographs produced by SWAT and SWAT–MLP models agree better with the observed hydrograph. The statistical results of these models indicate weaker correlation and more accurate prediction of data patterns. Due to the improved modeling capabilities, the SWAT–MLP/MSFO model performs better than other models in reproducing the observed hydrograph. By combining MLP and MSFO methods, this model provides a more complete and accurate description of more complex hydrological processes. Therefore, the SWAT–MLP/MSFO model provides a more reliable and accurate assessment of runoff behavior during the calibration period and shows a tighter fit with the measured hydrograph. This result emphasizes the potential of the proposed model for reliable hydrological predictions and significantly supports the model's effectiveness.

This chart provides a visual representation of the comparison between the actual data points and the corresponding predictions made by each model. By examining the scatterplot, it is evident that the SWAT–MLP/MSFO model exhibits a significant level of accuracy. The simulated values produced by this model are aligned with the observed data points, resulting in a relatively tight clustering around the 45° line. In contrast, the scatterplots for the other two models, SWAT and SWAT–MLP, show a broader range of points, indicating a lower level of accuracy in their predictions. Deviation from the 45° line indicates a less accurate estimate of the observed data. Findings from correlation coefficients and scatterplot analysis reinforce the superior performance of the SWAT–MLP/MSFO model in predicting runoff results. Its simulation values show a stronger correlation and closer agreement with the observed data, highlighting its accuracy and reliability compared to alternative models.

Table 2 provides information regarding scatter plots and statistical indicators utilized in the calibration process. Each model's observation–simulation equation is included, along with corresponding values for R², RMSE, and NS.

The SWAT model showed a moderate correlation between observed and simulated runoff, with an R² value of 0.73. However, it had a higher degree of prediction inaccuracy and a comparatively elevated RMSE of 2.15. The NS coefficient showed a 0.51 value, suggesting moderate effectiveness in reproducing observed data patterns. The SWAT–MLP model had a higher correlation and a lower RMSE of 1.93, suggesting improved accuracy in replicating observed data patterns. The SWAT–MLP/MSFO model had the most desirable statistical indicators, including an R² value of 0.83, a reduced RMSE of 1.58, and a superior ability to replicate observed data patterns accurately. The findings show that the SWAT–MLP/MSFO model outperforms both the SWAT and SWAT–MLP models in terms of correlation, precision, and effectiveness when simulating runoff behaviors during the calibration phase.

Also, the increased efficiency of the models is shown through a comprehensive analysis of key numerical indicators, as presented in Table 3. Table 3 briefly summarizes the results of various statistical indicators and provides valuable insights into the performance of each model.

By closely examining the results, it is evident that the SWAT–MLP/MSFO model in the validation step shows significant simulation capabilities compared to the alternative models. The statistical indicators shown in Table 3 clearly confirm this claim. In particular, the R² value of 0.77 shows a strong correlation between predicted and observed runoff data, indicating the model's ability to capture the underlying patterns and dynamics accurately. The RMSE value of 2.21 shows a reasonable level of accuracy achieved by the SWAT–MLP/MSFO model and establishes its reliability in runoff forecasting. Furthermore, the NSE value of 0.61 indicates the satisfactory performance of the model, indicating its ability to replicate the observed data with reasonable fidelity. Finally, the residual error (RE) value of −0.1 shows the minimum bias in the SWAT–MLP/MSFO model predictions, which indicates a balanced representation of the runoff phenomenon.

The effectiveness of the SWAT framework and its two variants, SWAT–MLP and SWAT–MLP/MSFO, in estimating monthly runoff was assessed in this study. The selection of the model with the greatest forecast flow was the aim of this study. So, in this study, a multiple-layer per neural network model was utilized in addition to a watershed model like SWAT. In order to improve the quality and accuracy of the runoff simulation findings, the study also applied a novel optimized approach called the MSFO. Statistics metrics such as RMSE, NSE, and coefficient of correlation (R²) were utilized to assess how well each model performed during flow modeling. The SWAT–MLP/MSFO model has the best values for each of these indices, according to the results of these measurements. The simulation and observation findings revealed that this model better reflects the linearity. The outcomes demonstrated that the hydrological model works better when coupled with an ANN model. Additionally, it produces more accurate and realistic results when used with a customized algorithm that has been tailored for the hydrological model.

Data cannot be made publicly available; readers should contact the corresponding author for details.

The authors declare there is no conflict.