Comparison of the Effectiveness of Artificial Neural Networks and Elastic Net Regression in Surface Runoff Modeling

Comparison of the Effectiveness of Artificial Neural Networks and Elastic Net Regression in Surface Runoff Modeling | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Comparison of the Effectiveness of Artificial Neural Networks and Elastic Net Regression in Surface Runoff Modeling Rafał Buczyński This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-4441223/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract This study examines the comparative performance of Artificial Neural Networks and Elastic Net Regression in predicting surface runoff in urban stormwater catchments. Utilizing the Storm Water Management Model, a dataset of over 100,000 samples was prepared, incorporating diverse catchment parameters such as impervious surface percentage, overland flow path width, slope, Manning’s coefficients, and depression storage depths. Both models were developed and tuned to enhance runoff prediction accuracy. An assessment was carried out to gauge the predictive accuracy, computational efficiency, and ability to withstand data noise of the models. The Artificial Neural Networks demonstrated significant advantages in handling complex, non-linear relationships inherent in hydrological data, resulting in higher predictive accuracy and stability. Elastic Net Regression, while useful, exhibited limitations, particularly in lower runoff scenarios due to its regularization constraints. The outcomes highlight the relative advantages and drawbacks of each modeling technique, offering crucial perspectives for enhancing water resource management in urban settings. Runoff Subcatchments SWMM Regression ANN ElasticNet Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction Hydrology is the scientific study of water within the Earth's system, which includes its distribution, movement, and quality. The discipline of surface hydrology involves the description of processes that dictate the distribution of rainfall, the penetration of water into the ground, and the routing of surplus precipitation across land planes leading to channels, eventually reaching the mouth of a watershed (Johnson, Julien, Molnar, Watson, 2000 ). Phenomena such as surface runoff play a crucial role in managing water resources and planning to mitigate the impact of extreme events, such as floods or droughts. Accurately modeling and predicting surface runoff is essential for effectively planning urban infrastructure, engineering activities, and managing risks associated with extreme hydrological events. Models of surface runoff and risk assessments related to this process heavily rely on surface runoff field observations (Dehotin et al., 2015 ). One of the major hydrological issues is runoff simulation uncertainty caused by frozen soil moisture parameterization (Pitman et al., 1999 ). The hydrogeological characteristics of a catchment landscape influence its hydrological response. The analysis of these features yields a fundamental comprehension of catchment hydrology highlighting its primary constituents - surface runoff and infiltration (Beighley, Dunne, Melack, 2005 ). Surface runoff has a significant impact on surface water quality due to the transport of pollutants. Therefore, it is crucial to accurately forecast this phenomenon from an environmental standpoint. Assessment of the effects of land cover change on hydrology is often hindered by insufficient field measurements that characterize runoff generation processes (Molina et al., 2007 ). The Storm Water Management Model (SWMM) program is widely used to manage rainwater in urban areas. It offers simulation capabilities for hydrological, hydraulic, and pollutant transport processes. However, its complexity and computational demands have led experts to search for alternative approaches to model this phenomenon. Artificial intelligence techniques are one way to make runoff predictions for vast areas. In hydrology and environmental studies, models use four primary artificial intelligence methods. These comprise classifiers and machine learning techniques like artificial neural networks, decision trees, and support vector machines. Additionally, there are approaches based on fuzzy logic, which employ fuzzy sets, evolutionary algorithms utilizing evolutionary computing, and models that use wavelet transforms for non-stationarity analysis of data (Yaseen, El-shafie, Jaafar, Afan, Sayl, 2015 ). Over the past few years, there has been an increasing interest in utilizing artificial neural networks (ANN) for hydraulic modeling. ANNs possess the capability to estimate nonlinear relationships and adapt to changing circumstances, making them highly compatible for analyzing and predicting phenomena based on various factors, frequently with nonlinear interrelations. In hydrology, ANNs have the potential to enhance forecast accuracy and reduce computation time as compared to traditional modeling approaches. ANNs are utilized for predicting water flow, estimating soil moisture, and forecasting precipitation. The structure of an ANN model differs based on the particular application. Essentially, it is composed of interlinked layers of synthetic neurons, which are trained using input and output data (Zhang, Patuwo, Hu, 1998 ). Artificial neural networks were developed based on the biological neural networks in the human brain, therefore representing a mathematical abstraction of models of human cognition or neuroscience (Kubat, 1999 ). ANNs comprise nodes, cells or neurons that process information and transmit signals to one another through weighted connections. The node transforms the input data via a nonlinear activation function to generate an output signal (Govindaraju, 2000 ). It is crucial to explain technical term abbreviations when they are first introduced. Muftah, Rowan, and Butler ( 2022 ) found that the application of ANN algorithms in the classification and segmentation of aerial photos enables the prediction of surface runoff values from building roofs with over 90% accuracy, a valuable tool in urban areas. Additionally, this approach provides information on the volumetric intensity of rainfall, which can aid in urban infrastructure planning. Artificial neural networks are utilized to forecast complex phenomena that are challenging to describe with computational systems, improving data clarity and enabling easy combination of machine learning models. ANNs are increasingly being applied in hydraulics to create expert systems for predicting the impact of surface runoff on infrastructure. ElasticNet regression is gaining recognition as an analytical technique for modeling complex data sets in various fields, including hydrology. By combining the advantages of ridge and lasso regression, ElasticNet effectively solves problems of multicollinearity and over-fitting, which are crucial in hydrological data analysis (Zou, Hastie, 2005). The Elastic Net regression's capability to simultaneously select variables and regularize proves to be highly beneficial in hydrological modeling, which encompasses various factors that impact surface runoff dynamics (Worland, Farmer, Kiang, 2018). Its application in forecasting river runoff rates displays superior results compared to classical linear regression models, underscoring its potential in hydrological forecasting (Sayari, Meymand, Aldallal, Zounemat-Kermani, 2022). Ahmed et al. (2019) confirmed the usefulness of ElasticNet in environmental sciences by modeling different water quality parameters, underscoring its role in environmental monitoring. The mathematical underpinnings of ElasticNet regression, grounded in regularization and optimization theory, furnish a robust framework for addressing the difficulties involved in multidimensional data spaces (Hastie, Tibshirani, Wainwright, 2015). ElasticNet plays a vital role in machine learning, specifically in the domain of feature selection and dimensionality reduction, as emphasized by James, Witten, Hastie, Tibshirani (2013). The adaptability of ElasticNet proves advantageous in dealing with complex variable interactions, specifically those related to land use and changing climatic conditions impacting surface runoff. Its efficacy in processing intricate data sets positions it as a crucial tool for hydrological analysis, surpassing the limitations present in traditional models (Abed, Imteaz, Ahmed, Huang, 2021). Additionally, incorporating ElasticNet into hydrological modeling aligns with current computing trends. Its compatibility with large datasets and ability to identify significant predictors satisfy the demands of current data-intensive research. This is particularly noteworthy in the age of big data, where the amount and complexity of data continually expand (Jordan, Mitchell, 2015). This paper presents the results of an analysis of the relationships between individual catchment parameters modeled using the Storm Water Management Model program and their effects on surface runoff from stormwater catchments. The article provides insight into the relationship between selected catchment parameters and surface runoff dynamics. A study comparing the effectiveness of ElasticNet regression and artificial neural networks in modeling and predicting surface runoff is presented. The primary objective of the paper is to determine which of these regression methods provides greater accuracy, stability, and computational efficiency in the analysis of hydrologic data. It is assumed that the analysis of hydrological data is possible using machine learning methods such as ElasticNet regression and artificial neural networks. The use of these techniques is expected to be a good complement to classical numerical methods in hydrology, helping to improve the accuracy and efficiency of surface runoff forecasting. 2. Theoretical background 2.1. Storm Water Management Model In hydrology, a drainage basin is a land unit with a defined area. Its beginning point is determined by the lowest receiver, and its end is determined by the watershed, which separates surface runoff. The catchment's shape is a physiographic parameter that influences the surge's nature, the culmination's size, and the wave's length. Catchment geometry is typically used more frequently in studies, as it is easier to determine. The Storm Water Management Model is an accurate and suitable hydrological-hydraulic water quality simulation model (Shinma, Reis, 2011 ). The SWMM program uses a non-linear reservoir model to determine the flow of rainwater runoff that flows into the network node from the catchment area (Rossman, 2010 ). The definitive outflow rate is therefore determined by formula (1). $$Q=W \frac{{\left(h-{h}_{p}\right)}^{5/3}}{{n}_{p}} {i}_{p}^{1/2}$$ 1 Where Q is the authoritative runoff flow rate (m3/s), W is the hydraulic width of the catchment area (m), h is the precipitation height (m), hp is the surface retention height (m), n_p is the surrogate coefficient of roughness of the catchment area (s/m1/3), and ip is the average slope of the catchment area (-). SWMM has an extensive interface on catchment areas. Based on Rossman ( 2010 ), Table 1 was compiled showing the most important parameters. Table 1 Basic catchment parameters in the Storm Water Management Model program. Feature name Feature description Area Actual catchment area. Width Characteristic overland flow path width for surface runoff Slope Average percentage slope of the catchment area PercImperv Percentage of land area (not including any LID) that is impervious. N-Imperv Manning's n for overland flow over the impervious portion of the subcatchment. N-Perv Manning's n for overland flow over the impervious portion of the subcatchment. Dstore-Imperv Depth of depression storage on the impervious portion of the subcatchment (millimeters). Dstore-Perv Depth of depression storage on the pervious portion of the subcatchment (millimeters). PctZero Percentage of impervious area without depression storage. Infiltration Data Infiltration model „Modified Green-Ampt”. 2.2. Artificial neural networks Artificial neural networks are a type of computational models inspired by the structure and functioning of biological neural networks found in the brains of living organisms. They are adaptive learning systems capable of processing input data, analyzing signals and generating output information (Herberg, 2023 ). ANNs are particularly useful for complex and fuzzy relationships between input and output data, making them an attractive tool for prediction and classification problems (Seyedashraf, Bottacin-Busolin, Harou, 2021 ). The basic element of an ANN is an artificial neuron, whose task is to simulate the functions of its biological counterpart. In regression models, a neuron consists of multiple inputs, a summation function, an activation function and one output. The inputs are weighted according to weights, which are modified during the learning process. The summation function calculates the weighted sum of the input signals, and the activation function introduces nonlinearity by converting the weighted sum to the output of the neuron (Herberg, 2023 ). The architecture of a neural network usually consists of layers with a minimum of one neuron. There are three main types of layers: input layer, hidden layers and output layer. The input layer receives signals, hidden layers process them, and the output layer generates the model's response. The number of hidden layers and the number of neurons in each layer affect the network's ability to model complex relationships (Kim, Keum, Han, 2019 ). Network learning involves updating the weights of neurons to minimize the error between predicted and actual values. The most popular learning algorithm in ANNs is the back-propagation algorithm, which modifies the weights in the network in an iterative manner, starting from the output layer and then propagating the error to the hidden layers (Mendrofa, Hertono, Handari, 2023 ). Considering a simple neuron with activation function f, weights W, thresholds b and loss function L, the propagation can be described by formulas 2 and 3. ΔW = -η ∂L/∂W (2) Δb = -η ∂L/∂b (3) Where η is the learning rate. The gradients ∂L/∂W and ∂L/∂b can be calculated using the chain rule (4). ∂L/∂W = ∂L/∂a * ∂a/∂W ∂L/∂b = ∂L/∂a * ∂a/∂b (4) Where "a" is the value of the neuron's activation before applying the activation function, and ∂L/∂a is the gradient of the loss function relative to the neuron's activation. Their values are calculated recursively as from the output layer to the input layer, making it possible to efficiently calculate gradients for the entire network. Then, the weights (5) and thresholds (6) are updated based on the calculated gradients, and the process is repeated for multiple epochs or learning iterations. Repeating the process of optimizing the weights and thresholds of the neural network, minimizing the loss function leads to finding the optimal model for the problem under consideration. W = W + ΔW (5) b = b + Δb (6) 2.3. ElasticNet The ElasticNet regression model is a regression analysis technique that combines features of Lasso regression and Ridge regression to achieve flexibility and efficiency in modeling complex relationships. This model is particularly useful in situations where the data are colinear or have a large number of predictors relative to the number of observations. Formally, the optimization problem for ElasticNet is defined by Eq. 7 : $${min}_{{\beta }_{0}\beta }\left\{\frac{1}{2n} \sum _{i=1}^{n}{\left({y}_{i}-{\beta }_{0}-{x}_{i}^{T}\beta \right)}^{2}+\lambda \left(\left(1-\alpha \right)\left|\right|\beta {\left|\right|}_{2}^{2}+\alpha \left|\right|\beta {\left|\right|}_{1}\right)\right\}$$ 7 Where \({y}_{i}\) is the value of the dependent variable, \({x}_{i}\) is the vector of independent variables for the i-th observation, \({\beta }_{0}\) i β are the estimated parameters of the model. The parameter λ is used to control the strength of regularization, while α allows balancing between the regularization elements L1 and L2. A key element in the context of this model is its ability to deal effectively with colinearity and high dimensionality in the data. With the combination of L1 and L2 norms, the model is able to perform variable selection as in Lasso regression and stabilize parameter estimation as in Ridge regression. Algorithms such as the coordination gradient method are often used to solve this optimization problem. It is worth noting that although the model is linear in its predictors, its ability to effectively model complex relationships in the data, resulting from the regularization used, makes it useful in a variety of scientific and engineering applications. 3. Materials and methods 3.1 Dataset The dataset was created through simulations in SWMM 5.2.2 following Table 2 . The simulations were conducted on an urban catchment of 5 hectares, featuring an existing rainfall collector. The model rainfall, totaling 100 mm, lasted for 12 hours. Calculations and input file loading, as well as report analysis, were executed with the PySWMM 1.2.0 package. Table 2 Ranges of simulated data Subcatchment Feature Values Width [m] [1, 250 ,500, 750, 1000] Slope [%] [1, 10, 20, 40, 60, 80, 100] PercImperv [%] [1, 10, 20, 40, 60, 80, 100] N-Imperv, N-Perv [-] [0.015, 0.24, 0.4, 0.8] D-Imperv, D-Perv [m] [0.0013, 0.0025, 0.0051, 0.0076] PctZero [%] [1, 10, 20, 40, 60, 80, 100] The study utilized 103,073 samples to analyze fundamental catchment parameters, including the percentage of impervious surface (PercImperv), width of overland flow path (Width), slope of land (PercSlope), Manning's coefficients for impervious (N-Imperv) and permeable (N-Perv) surfaces, depression storage depth in the impervious sub-catchment (D-Imperv) and permeable (D-Perv), and catchment runoff (Runoff). For descriptive statistics, please refer to Table 3 . Table 3 Descriptive statistics of the dataset. PercImperv Width PercSlope N-Imperv N-Perv D-Imperv D-Perv PctZero Runoff count 103073 103073 103073 103073 103073 103073 103073 103073 103073 mean 42.90 481.56 42.81 0.40 0.40 0.18 0.18 49.98 3.67 std 34.64 359.30 34.74 0.32 0.32 0.10 0.10 35.07 1.51 min 1 1 1 0.01 0.015 0.05 0.05 1 0.03 25% 10 250 10 0.015 0.015 0.05 0.05 25 3.71 50% 40 500 40 0.4 0.4 0.2 0.2 50 4.4 75% 80 750 80 0.8 0.8 0.3 0.3 75 4.56 max 100 1000 100 0.8 1 0.3 0.3 100 4.85 3.2 Analysis of catchment area features Understanding the connections between catchment parameters and surface runoff is a crucial aspect of hydrological studies for urban infrastructure planning, water engineering, and managing the risk of extreme hydrological events. To clarify these relationships, a correlation analysis was conducted using data obtained from the SWMM program with simulations performed utilizing the pyswmm 1.2.0 and swmmio 0.6.0 packages. Our analysis identified a significant positive correlation between the surface runoff from storm catchments and the "Width," "Slope," and "PercImperv" parameters. This was evidenced by Spearman correlation coefficients of 1.0 (P-value: 0.0), indicating a deterministic linear relationship (Fig. 4–6). Technical term abbreviations have been explained upon first usage. In contrast, the parameters "N-Imperv," "N-Perv," "D-Imperv," and "D-Perv" displayed a complete negative correlation with surface runoff, as shown by Spearman correlation coefficients of -1.0 (P-value: 0.0). This indicates that as these parameters increase, runoff decreases systematically (Fig. 7–11). These strong correlations emphasize the substantial effect of impermeable surfaces on runoff, with a nearly perfect correlation coefficient (Spearman Correlation: 0.99, P-value: 0.0) for the "PercImperv" parameter specifically. This metric represents the percentage of the catchment area that is impervious and directly contributes to the volume of runoff generated during rainfall events. The negative correlations of "N-Imperv," "N-Perv," "D-Imperv," and "D-Perv" indicate their role in mitigating runoff. These strong correlations demonstrate the importance of accurately parameterizing catchments in hydrological modeling and highlight the sensitivity of runoff to these catchment characteristics. Incorporating a comprehensive set of factors that influence surface runoff, including terrain, soil type, land cover, meteorological conditions, and human activities can significantly enhance the accuracy of modeling and predicting hydrological phenomena. Therefore, it is essential to include as many relevant influencing factors as possible in hydrological studies to guarantee the robustness and reliability of predictive models. 3.3 Structure of the Neural Network Model The neural network architecture utilized in this study is designed to predict surface runoff based on catchment attributes. The architecture is composed of the following layers: Normalization Layer: The initial layer is a preprocessing normalization layer. This layer scales and centers the features based on the computed mean and standard deviation from the training data. It has 17 non-trainable parameters, reflecting the statistical parameters used for normalization. Input Layer: The first dense layer acts as the input layer with 8 neurons. This is equal to the number of features in the dataset, ensuring each feature is adequately represented. It uses a Rectified Linear Unit (ReLU) activation function. Hidden Layers: Two hidden layers follow the input layer, each containing 8 neurons. These layers also use the ReLU activation function, which helps the model learn non-linear relationships in the data. Output Layer: The final layer is a dense layer with a single neuron, which outputs the predicted value for surface runoff. This layer also utilizes the ReLU activation function to ensure non-negative output values. The model is compiled using the Adam optimizer and employs a mean squared error loss function for backpropagation. The model's architecture totals 242 parameters, of which 225 are trainable. Early stopping and batch size of 32 are implemented to optimize the training process. 3.4 Structure of the ElasticNet Regression Model The ElasticNet regression model is utilized in this study to predict surface runoff based on various catchment characteristics. The model integrates several fundamental elements and is implemented using Python's scikit-learn library. Preprocessing: Standardization of the predictor variables is performed using the StandardScaler class, which normalizes the feature set to a mean of zero and a standard deviation of one. This ensures homogeneity in the predictor space and improves the model's convergence speed. Hyperparameters: An alpha parameter set to 0.01 and an l1_ratio of 0.2 are used. The former controls the amount of regularization, while the latter balances the L1 and L2 penalties, providing a compromise between ridge and lasso regression techniques. Data partitioning: An 80 − 20 data partitioning scheme is employed, allowing rigorous model evaluation on out-of-sample data. Optimization Algorithm: By default, the Coordinate Descent Optimization algorithm is used to minimize the objective function. Predictive Variables: The model incorporates eight predictor variables representing various watershed attributes, demonstrating its applicability in capturing the multifaceted nature of hydrologic systems. Outcome Variable: The model is trained to predict a single outcome, surface runoff. 4. Results The aim of this research is to assess the usefulness of ElasticNet regression models and artificial neural networks in hydrological catchment data analysis. The dataset utilized in this study comprises 103,073 samples generated by simulations in SWMM 5.2.2, as outlined in Table 2 . The simulations were carried out in an urban catchment spanning 5 hectares, which has a pre-existing rainfall collector. The total model rainfall was 100 mm over a period of 12 hours. The data set was randomly partitioned into training and testing sets at an 80:20 ratio. The PySWMM 1.2.0 package was utilized to perform calculations, load input files, and analyze the reports. The target variable for prediction is 'Runoff.' The TensorFlow and Keras libraries were utilized to develop the ANN model, while the SciKit-Learn library was employed to prepare the ElasticNet model. The Elastic Net model's hyperparameters were optimized using the Grid Search technique. This model assesses a predetermined set of parameter values αi and l1_ratio via 5-fold cross-validation to gauge the efficacy of each pairing. For the ANN model, a manual optimization of the architectural design was executed. 4.1. Performance metrics Both models underwent evaluation using a set of performance measures, which included mean squared error (MSE), R2 score, Index of Agreement (d), Scatter Index (SI), and Root Mean Square Error (RMSE). Additionally, inference time was utilized as a performance indicator. Table 4 presents a summary of the metrics for both models, providing a thorough overview of their forecasting precision and computational efficiency. Table 4 Summary of performance metrics Model name MSE R2 Score Index of Agreement (d) Scatter Index (SI) RMSE Inference Time ElasticNet 1.035 0.550 0.837 0.277 1.017 0.004 ANN 0.010 0.996 0.999 0.030 0.109 1.396 4.2. Model evaluation The Fig. 12 illustrates the accuracy of the ANN and ElasticNet models in predicting outflow. The points on the graph represent the actual versus predicted values, and the regression line indicates the ideal model fit. The ANN model displays impressive predictive accuracy, with a dense concentration of points near the regression line, supported by an MSE of 0.010 and an R2 Score of 0.996. Moreover, the accuracy of the model is reinforced by its near-perfect Index of Agreement (0.999), low Scatter Index (0.030), and minimal RMSE (0.109). ElasticNet model showcases more scatter in the points, especially at lower outflow values, indicating a less precise fit to the dataset. This is supported by its higher MSE of 1.035, lower R2 Score of 0.550, and larger RMSE of 1.017. Statistical analysis of the error distribution for the ANN and ElasticNet models was performed (Fig. 13 ). Parameters such as the mean, median and standard deviation of the error were calculated. For the ANN model, the mean error was − 0.001 m³/s, with a standard deviation of 0.115 m³/s, 90% of the errors were within a narrow range of -0.203 to 0.201 m³/s, indicating the high precision of the model. For the ElasticNet model, the average error was higher at -0.014 m³/s, with a standard deviation of 0.600 m³/s. 90% of the errors oscillated in a much wider range of -1.041 to 1.013 m³/s. These statistics confirm that the ANN model shows higher precision and is more stable in predicting runoff compared to the ElasticNet model, which is particularly noticeable in the context of a smaller spread of errors around zero. 4.3. Comparative analysis of prediction error When analyzing prediction errors, the ANN model surpasses the ElasticNet model, especially regarding error distribution and precision. The ANN model maintains a narrow error range and greater stability in predicting runoff, which is highlighted by the reduced spread of errors around zero and superior performance across all assessed metrics. To further understand the performance differences between the ANN and ElasticNet models, a detailed error analysis was conducted. A histogram of error differences (Fig. 14 , left) reveals a mean error difference of 0.850 m³/s and a standard deviation of 0.564 m³/s. The dot plot (Fig. 14 , right) shows 15% of cases exceeding the error difference threshold set at the 85th percentile (1.528 m³/s). These observations indicate where the ANN model achieved higher precision and stability compared to the ElasticNet model. Conclusion This study compared ElasticNet regression and Artificial Neural Networks to predict surface runoff. The main objective was to determine which method produces the most precise, stable, and computationally efficient forecasts for hydrological data. The SSN model, constructed with normalizing, hidden, and output layers architecture, displayed a notably superior fit to the data based on the MSE and R2 score values (0.010 and 0.996, respectively). Despite the ElasticNet model's flexibility and ability to handle colinearity, it produced significantly lower performance indicators (MSE = 1.035, R2 Score = 0.550). On the other hand, the SSN model had a high precision rate with 90% of the errors being within a narrow range. However, for the ElasticNet model, the error range was much wider, which limits its practical application. Notably, the performance of ElasticNet was undermined particularly at lower runoff values due to its regularization effect resulting in underfitting. This underfitting stems from the regularization process that may oversimplify the model by reducing the coefficients of less crucial predictors, thus failing to account for the intricate relationship between catchment features and runoff. Additionally, as small flow scenarios involve non-linear dynamics, including the interplay between soil moisture and infiltration rates, ElasticNet regression's linear nature is inadequate to handle such complexities. In contrast, ANNs possess non-linear processing capabilities that make them better equipped for these situations. Therefore, the study findings recommend utilizing ANNs to predict surface runoff. Artificial neural networks exhibit superior ability in detecting and interpreting the intricate interconnections and nonlinear associations among catchment parameters. This grants them efficacy in fulfilling current analytic necessities and positions them as a valuable tool for forthcoming research pursuits and pragmatic applications in the realm of water resource management. Due to the increasing complexity of urban hydrology, the incorporation of artificial neural networks into operational systems has become a promising advancement for predicting and managing surface runoff. This approach provides enhanced precision and adaptability. Declarations Competing Interests The authors have no relevant financial or non-financial interests to disclose. Funding The authors declare that no funds, grants, or other support were received during the preparation of this manuscript. Author Contribution R.B. Conceptualization, methods, software, simulation, validation, writing Data Availability The data and code have been uploaded to a public github repository - https://github.com/BuczynskiRafal/SurfaceRunoff-Modeling-ANN-ElasticNet-Comparison References Johnson, B. E., Julien, P. Y., Molnar, D. K., & Watson, C. C. (2000). THE TWO-DIMENSIONAL UPLAND EROSION MODEL CASC2D‐SED 1. JAWRA Journal of the American Water Resources Association , 36 (1), 31–42. Molina, A., Govers, G., Vanacker, V., Poesen, J., Zeelmaekers, E., & Cisneros, F. (2007). Runoff generation in a degraded Andean ecosystem: Interaction of vegetation cover and land use. Catena , 71 (2), 357–370. Dehotin, J., Breil, P., Braud, I., de Lavenne, A., Lagouy, M., & Sarrazin, B. (2015). Detecting surface runoff location in a small catchment using distributed and simple observation method. Journal of Hydrology , 525 , 113–129. Pitman, A. J., Slater, A. G., Desborough, C. E., & Zhao, M. (1999). Uncertainty in the simulation of runoff due to the parameterization of frozen soil moisture using the Global Soil Wetness Project methodology. Journal of Geophysical Research: Atmospheres , 104 (D14), 16879–16888. Beighley, R. E., Dunne, T., & Melack, J. M. (2005). Understanding and modeling basin hydrology: interpreting the hydrogeological signature. Hydrological Processes: An International Journal , 19 (7), 1333–1353. Yaseen, Z. M., El-shafie, A., Jaafar, O., Afan, H. A., & Sayl, K. N. (2015). Artificial intelligence based models for stream-flow forecasting: 2000–2015. Journal of Hydrology , 530 , 829–844. 10.1016/j.jhydrol.2015.10.038 . Zhang, G., Patuwo, B. E., & Hu, M. Y. (1998). Forecasting with artificial neural networks:: The state of the art. International journal of forecasting , 14 (1), 35–62. Kubat, M. (1999). Neural networks: A comprehensive foundation by Simon Haykin, Macmillan, 1994, ISBN 0-02-352781-7. The Knowledge Engineering Review, 13(4), 409–412. 10.1017/S0269888998214044 . Govindaraju, R. S. (2000). Artificial neural networks in hydrology. II: Hydrologic applications. Journal of Hydrologic Engineering , 5 (2), 124–137. 10.1061/ (ASCE)1084-0699(2000)5:2(124). Muftah, H., Rowan, T. S. L., & Butler, A. P. (2022). Towards open-source LOD2 modelling using convolutional neural networks. Modeling Earth Systems and Environment , 8 (2), 1693–1709. 10.1007/s40808-021-01159-8 . Shinma, T. A., & Reis, L. F. R. (2011). Multiobjective automatic calibration of the storm water management model (SWMM) using non-dominated sorting genetic algorithm II (NSGA-II). In World Environmental and Water Resources Congress 2011: Bearing Knowledge for Sustainability (pp. 598–607). Rossman, L. A. (2010). Storm water management model user's manual, version 5.0 (p. 276). National Risk Management Research Laboratory, Office of Research and Development, US Environmental Protection Agency. Herberg, E. (2023). Neural Network Architectures. arXiv preprint arXiv:2304.05133. Seyedashraf, O., Bottacin-Busolin, A., & Harou, J. J. (2021). A Disaggregation‐Emulation Approach for Optimization of Large Urban Drainage Systems. Water Resources Research , 57(8), e2020WR029098. Kim, H. I., Keum, H. J., & Han, K. Y. (2019). Real-time urban inundation prediction combining hydraulic and probabilistic methods. Water , 11 (2), 293. Mendrofa, G. A., Hertono, G. F., & Handari, B. D. (2023). Ensemble Learning Model on Artificial Neural Network-Backpropagation (ANN-BP) Architecture for Coal Pillar Stability Classification. arXiv preprint arXiv:2303.16524. Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-4441223","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":307571761,"identity":"2ad69ecd-be86-4621-a14f-19f2f0b01d3f","order_by":0,"name":"Rafał Buczyński","email":"data:image/png;base64,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","orcid":"","institution":"Bialystok University of Technology","correspondingAuthor":true,"prefix":"","firstName":"Rafał","middleName":"","lastName":"Buczyński","suffix":""}],"badges":[],"createdAt":"2024-05-18 13:33:38","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-4441223/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-4441223/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":58053652,"identity":"6a775fe8-7c2c-4f95-ab3a-f851491cc192","added_by":"auto","created_at":"2024-06-10 13:34:34","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":27070,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 4 Dependence of runoff on subcatchment width.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/181e447697ad90a90b46c91a.png"},{"id":58053655,"identity":"99de3375-0c36-4831-a5e1-5a1c0e5d87d0","added_by":"auto","created_at":"2024-06-10 13:34:35","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":30525,"visible":true,"origin":"","legend":"\u003cp\u003eFig.5 Dependence of runoff on subcatchment imprevious.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/ea6df938f7eed6e0bb900315.png"},{"id":58054124,"identity":"ba56237d-8a3e-4730-bc7b-76d403ea0788","added_by":"auto","created_at":"2024-06-10 13:42:34","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":28153,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 6 Dependence of runoff on subcatchment slope.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/6459e54359be6f61a84e368b.png"},{"id":58054533,"identity":"aabc3d7e-e7a5-43ae-9188-fe2ab021f819","added_by":"auto","created_at":"2024-06-10 13:50:34","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":30950,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 7 Dependence of runoff on subcatchment N-Imperv.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/44d9369d5311fe7089e38609.png"},{"id":58053647,"identity":"ea58b3d2-e42a-46d2-9c45-7085c1810629","added_by":"auto","created_at":"2024-06-10 13:34:34","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":29930,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 8 Dependence of runoff on subcatchment N-Perv.\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/2fbd878a0018a0ca1eae9901.png"},{"id":58053645,"identity":"82dc6e78-8bbd-4c38-a761-5627d8e0eded","added_by":"auto","created_at":"2024-06-10 13:34:34","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":31462,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 9 Dependence of runoff on subcatchment D-Imperv.\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/3bde9293ccc4d36f5eec06c1.png"},{"id":58054128,"identity":"0e5485e5-af7c-4166-a67a-c9da248c7d0f","added_by":"auto","created_at":"2024-06-10 13:42:34","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":33346,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 10 Dependence of runoff on subcatchment D-Perv.\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/dbf7a3e8cde52b0a9cffc38f.png"},{"id":58053649,"identity":"f7a37e9b-83c1-4b67-b114-41e33fc29cc1","added_by":"auto","created_at":"2024-06-10 13:34:34","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":28244,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 11 Dependence of runoff on subcatchment PctZero.\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/4cae0cc623d2589c7758d65d.png"},{"id":58054126,"identity":"ad7465c2-3043-427a-9158-137a2f6048cf","added_by":"auto","created_at":"2024-06-10 13:42:34","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":132345,"visible":true,"origin":"","legend":"\u003cp\u003eFig. 12. Comparison of flow forecasting accuracy by ANN and ElasticNet models with test data. In each graph, points represent actual data versus predicted values. The regression line represents a perfect fit. The ANN model achieves high prediction accuracy MSE =0.996, R2=0.996. The ElasticNet model has significant prediction error especially at low flows MSE =1.035, R2=0.550.\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/88c61c9038b7f740312937af.png"},{"id":58054534,"identity":"6d4cd2a3-ab00-454e-afd2-961efb26020a","added_by":"auto","created_at":"2024-06-10 13:50:34","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":47581,"visible":true,"origin":"","legend":"\u003cp\u003eFigure 13: Statistical analysis of the error distribution for the ANN and ElasticNet models. For the ANN model, the mean error is -0.001 m³/s with a standard deviation of 0.115 m³/s. The median error is -0.002 m³/s, and 90% of the errors are between -0.203 and 0.201 m³/s. For the ElasticNet model, the median error is -0.014 m³/s with a standard deviation of 0.600 m³/s. The median error for this model is -0.016 m³/s, and the 90% error oscillates between -1.041 and 1.013 m³/s.\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/f5c8f66f3cb6a4a09eb588e0.png"},{"id":58053654,"identity":"07aad487-df23-465b-878b-3bae35affd19","added_by":"auto","created_at":"2024-06-10 13:34:35","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":185313,"visible":true,"origin":"","legend":"\u003cp\u003eFig 14. Analysis of error differences between ANN and ElasticNet models. The first graph shows a histogram of error differences, expressed in units of [m³/s]. The red line indicates the threshold set at the 85th percentile, which is 1.528 m³/s. The second graph illustrates the distribution of error differences for individual samples. The average error difference is 0.850 m³/s, with a standard deviation of 0.564 m³/s. About 15% of the cases exceed the error difference threshold, indicating significant differences in model performance.\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/0e43c3bd7721acb472cdbb2f.png"},{"id":59753325,"identity":"793a876e-f300-4be9-a956-2cd6ce7f39ed","added_by":"auto","created_at":"2024-07-06 00:16:33","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1035203,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-4441223/v1/22acc4d8-fa05-45f8-8f5b-bd711f8f078e.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"\u003cp\u003eComparison of the Effectiveness of Artificial Neural Networks and Elastic Net Regression in Surface Runoff Modeling\u003c/p\u003e","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eHydrology is the scientific study of water within the Earth's system, which includes its distribution, movement, and quality. The discipline of surface hydrology involves the description of processes that dictate the distribution of rainfall, the penetration of water into the ground, and the routing of surplus precipitation across land planes leading to channels, eventually reaching the mouth of a watershed (Johnson, Julien, Molnar, Watson, \u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). Phenomena such as surface runoff play a crucial role in managing water resources and planning to mitigate the impact of extreme events, such as floods or droughts. Accurately modeling and predicting surface runoff is essential for effectively planning urban infrastructure, engineering activities, and managing risks associated with extreme hydrological events.\u003c/p\u003e \u003cp\u003eModels of surface runoff and risk assessments related to this process heavily rely on surface runoff field observations (Dehotin et al., \u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e2015\u003c/span\u003e). One of the major hydrological issues is runoff simulation uncertainty caused by frozen soil moisture parameterization (Pitman et al., \u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). The hydrogeological characteristics of a catchment landscape influence its hydrological response. The analysis of these features yields a fundamental comprehension of catchment hydrology highlighting its primary constituents - surface runoff and infiltration (Beighley, Dunne, Melack, \u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e2005\u003c/span\u003e). Surface runoff has a significant impact on surface water quality due to the transport of pollutants. Therefore, it is crucial to accurately forecast this phenomenon from an environmental standpoint. Assessment of the effects of land cover change on hydrology is often hindered by insufficient field measurements that characterize runoff generation processes (Molina et al., \u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2007\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe Storm Water Management Model (SWMM) program is widely used to manage rainwater in urban areas. It offers simulation capabilities for hydrological, hydraulic, and pollutant transport processes. However, its complexity and computational demands have led experts to search for alternative approaches to model this phenomenon. Artificial intelligence techniques are one way to make runoff predictions for vast areas. In hydrology and environmental studies, models use four primary artificial intelligence methods. These comprise classifiers and machine learning techniques like artificial neural networks, decision trees, and support vector machines. Additionally, there are approaches based on fuzzy logic, which employ fuzzy sets, evolutionary algorithms utilizing evolutionary computing, and models that use wavelet transforms for non-stationarity analysis of data (Yaseen, El-shafie, Jaafar, Afan, Sayl, \u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e2015\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eOver the past few years, there has been an increasing interest in utilizing artificial neural networks (ANN) for hydraulic modeling. ANNs possess the capability to estimate nonlinear relationships and adapt to changing circumstances, making them highly compatible for analyzing and predicting phenomena based on various factors, frequently with nonlinear interrelations. In hydrology, ANNs have the potential to enhance forecast accuracy and reduce computation time as compared to traditional modeling approaches. ANNs are utilized for predicting water flow, estimating soil moisture, and forecasting precipitation. The structure of an ANN model differs based on the particular application. Essentially, it is composed of interlinked layers of synthetic neurons, which are trained using input and output data (Zhang, Patuwo, Hu, \u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e1998\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eArtificial neural networks were developed based on the biological neural networks in the human brain, therefore representing a mathematical abstraction of models of human cognition or neuroscience (Kubat, \u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e1999\u003c/span\u003e). ANNs comprise nodes, cells or neurons that process information and transmit signals to one another through weighted connections. The node transforms the input data via a nonlinear activation function to generate an output signal (Govindaraju, \u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e2000\u003c/span\u003e). It is crucial to explain technical term abbreviations when they are first introduced. Muftah, Rowan, and Butler (\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e2022\u003c/span\u003e) found that the application of ANN algorithms in the classification and segmentation of aerial photos enables the prediction of surface runoff values from building roofs with over 90% accuracy, a valuable tool in urban areas. Additionally, this approach provides information on the volumetric intensity of rainfall, which can aid in urban infrastructure planning. Artificial neural networks are utilized to forecast complex phenomena that are challenging to describe with computational systems, improving data clarity and enabling easy combination of machine learning models. ANNs are increasingly being applied in hydraulics to create expert systems for predicting the impact of surface runoff on infrastructure.\u003c/p\u003e \u003cp\u003eElasticNet regression is gaining recognition as an analytical technique for modeling complex data sets in various fields, including hydrology. By combining the advantages of ridge and lasso regression, ElasticNet effectively solves problems of multicollinearity and over-fitting, which are crucial in hydrological data analysis (Zou, Hastie, 2005). The Elastic Net regression's capability to simultaneously select variables and regularize proves to be highly beneficial in hydrological modeling, which encompasses various factors that impact surface runoff dynamics (Worland, Farmer, Kiang, 2018). Its application in forecasting river runoff rates displays superior results compared to classical linear regression models, underscoring its potential in hydrological forecasting (Sayari, Meymand, Aldallal, Zounemat-Kermani, 2022). Ahmed et al. (2019) confirmed the usefulness of ElasticNet in environmental sciences by modeling different water quality parameters, underscoring its role in environmental monitoring.\u003c/p\u003e \u003cp\u003eThe mathematical underpinnings of ElasticNet regression, grounded in regularization and optimization theory, furnish a robust framework for addressing the difficulties involved in multidimensional data spaces (Hastie, Tibshirani, Wainwright, 2015). ElasticNet plays a vital role in machine learning, specifically in the domain of feature selection and dimensionality reduction, as emphasized by James, Witten, Hastie, Tibshirani (2013). The adaptability of ElasticNet proves advantageous in dealing with complex variable interactions, specifically those related to land use and changing climatic conditions impacting surface runoff. Its efficacy in processing intricate data sets positions it as a crucial tool for hydrological analysis, surpassing the limitations present in traditional models (Abed, Imteaz, Ahmed, Huang, 2021). Additionally, incorporating ElasticNet into hydrological modeling aligns with current computing trends. Its compatibility with large datasets and ability to identify significant predictors satisfy the demands of current data-intensive research. This is particularly noteworthy in the age of big data, where the amount and complexity of data continually expand (Jordan, Mitchell, 2015).\u003c/p\u003e \u003cp\u003eThis paper presents the results of an analysis of the relationships between individual catchment parameters modeled using the Storm Water Management Model program and their effects on surface runoff from stormwater catchments. The article provides insight into the relationship between selected catchment parameters and surface runoff dynamics. A study comparing the effectiveness of ElasticNet regression and artificial neural networks in modeling and predicting surface runoff is presented. The primary objective of the paper is to determine which of these regression methods provides greater accuracy, stability, and computational efficiency in the analysis of hydrologic data. It is assumed that the analysis of hydrological data is possible using machine learning methods such as ElasticNet regression and artificial neural networks. The use of these techniques is expected to be a good complement to classical numerical methods in hydrology, helping to improve the accuracy and efficiency of surface runoff forecasting.\u003c/p\u003e"},{"header":"2. Theoretical background","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1. Storm Water Management Model\u003c/h2\u003e \u003cp\u003eIn hydrology, a drainage basin is a land unit with a defined area. Its beginning point is determined by the lowest receiver, and its end is determined by the watershed, which separates surface runoff. The catchment's shape is a physiographic parameter that influences the surge's nature, the culmination's size, and the wave's length. Catchment geometry is typically used more frequently in studies, as it is easier to determine. The Storm Water Management Model is an accurate and suitable hydrological-hydraulic water quality simulation model (Shinma, Reis, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e2011\u003c/span\u003e). The SWMM program uses a non-linear reservoir model to determine the flow of rainwater runoff that flows into the network node from the catchment area (Rossman, \u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e). The definitive outflow rate is therefore determined by formula (1).\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$Q=W \\frac{{\\left(h-{h}_{p}\\right)}^{5/3}}{{n}_{p}} {i}_{p}^{1/2}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere Q is the authoritative runoff flow rate (m3/s), W is the hydraulic width of the catchment area (m), h is the precipitation height (m), hp is the surface retention height (m), n_p is the surrogate coefficient of roughness of the catchment area (s/m1/3), and ip is the average slope of the catchment area (-).\u003c/p\u003e \u003cp\u003eSWMM has an extensive interface on catchment areas. Based on Rossman (\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e2010\u003c/span\u003e), Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e was compiled showing the most important parameters.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBasic catchment parameters in the Storm Water Management Model program.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eFeature name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFeature description\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eArea\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eActual catchment area.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCharacteristic overland flow path width for surface runoff\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlope\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eAverage percentage slope of the catchment area\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePercImperv\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePercentage of land area (not including any LID) that is impervious.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN-Imperv\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eManning's n for overland flow over the impervious portion of the subcatchment.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN-Perv\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eManning's n for overland flow over the impervious portion of the subcatchment.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDstore-Imperv\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDepth of depression storage on the impervious portion of the subcatchment (millimeters).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDstore-Perv\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDepth of depression storage on the pervious portion of the subcatchment (millimeters).\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePctZero\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePercentage of impervious area without depression storage.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eInfiltration Data\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eInfiltration model \u0026bdquo;Modified Green-Ampt\u0026rdquo;.\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Artificial neural networks\u003c/h2\u003e \u003cp\u003eArtificial neural networks are a type of computational models inspired by the structure and functioning of biological neural networks found in the brains of living organisms. They are adaptive learning systems capable of processing input data, analyzing signals and generating output information (Herberg, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). ANNs are particularly useful for complex and fuzzy relationships between input and output data, making them an attractive tool for prediction and classification problems (Seyedashraf, Bottacin-Busolin, Harou, \u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e2021\u003c/span\u003e). The basic element of an ANN is an artificial neuron, whose task is to simulate the functions of its biological counterpart. In regression models, a neuron consists of multiple inputs, a summation function, an activation function and one output. The inputs are weighted according to weights, which are modified during the learning process. The summation function calculates the weighted sum of the input signals, and the activation function introduces nonlinearity by converting the weighted sum to the output of the neuron (Herberg, \u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e2023\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eThe architecture of a neural network usually consists of layers with a minimum of one neuron. There are three main types of layers: input layer, hidden layers and output layer. The input layer receives signals, hidden layers process them, and the output layer generates the model's response. The number of hidden layers and the number of neurons in each layer affect the network's ability to model complex relationships (Kim, Keum, Han, \u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e2019\u003c/span\u003e). Network learning involves updating the weights of neurons to minimize the error between predicted and actual values. The most popular learning algorithm in ANNs is the back-propagation algorithm, which modifies the weights in the network in an iterative manner, starting from the output layer and then propagating the error to the hidden layers (Mendrofa, Hertono, Handari, \u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e2023\u003c/span\u003e). Considering a simple neuron with activation function f, weights W, thresholds b and loss function L, the propagation can be described by formulas 2 and 3.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Taba\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΔW = -η \u0026part;L/\u0026part;W\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(2)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eΔb = -η \u0026part;L/\u0026part;b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(3)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere η is the learning rate. The gradients \u0026part;L/\u0026part;W and \u0026part;L/\u0026part;b can be calculated using the chain rule (4).\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabb\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026part;L/\u0026part;W = \u0026part;L/\u0026part;a * \u0026part;a/\u0026part;W\u003c/p\u003e \u003cp\u003e\u0026part;L/\u0026part;b = \u0026part;L/\u0026part;a * \u0026part;a/\u0026part;b\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(4)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eWhere \"a\" is the value of the neuron's activation before applying the activation function, and \u0026part;L/\u0026part;a is the gradient of the loss function relative to the neuron's activation. Their values are calculated recursively as from the output layer to the input layer, making it possible to efficiently calculate gradients for the entire network. Then, the weights (5) and thresholds (6) are updated based on the calculated gradients, and the process is repeated for multiple epochs or learning iterations. Repeating the process of optimizing the weights and thresholds of the neural network, minimizing the loss function leads to finding the optimal model for the problem under consideration.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"No\" id=\"Tabc\" border=\"1\"\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eW\u0026thinsp;=\u0026thinsp;W\u0026thinsp;+\u0026thinsp;ΔW\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(5)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eb\u0026thinsp;=\u0026thinsp;b\u0026thinsp;+\u0026thinsp;Δb\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e(6)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e2.3. ElasticNet\u003c/h2\u003e \u003cp\u003eThe ElasticNet regression model is a regression analysis technique that combines features of Lasso regression and Ridge regression to achieve flexibility and efficiency in modeling complex relationships. This model is particularly useful in situations where the data are colinear or have a large number of predictors relative to the number of observations. Formally, the optimization problem for ElasticNet is defined by Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e7\u003c/span\u003e:\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${min}_{{\\beta }_{0}\\beta }\\left\\{\\frac{1}{2n} \\sum _{i=1}^{n}{\\left({y}_{i}-{\\beta }_{0}-{x}_{i}^{T}\\beta \\right)}^{2}+\\lambda \\left(\\left(1-\\alpha \\right)\\left|\\right|\\beta {\\left|\\right|}_{2}^{2}+\\alpha \\left|\\right|\\beta {\\left|\\right|}_{1}\\right)\\right\\}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e7\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({y}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the value of the dependent variable, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({x}_{i}\\)\u003c/span\u003e\u003c/span\u003e is the vector of independent variables for the i-th observation, \u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\beta }_{0}\\)\u003c/span\u003e\u003c/span\u003e i β are the estimated parameters of the model. The parameter λ is used to control the strength of regularization, while α allows balancing between the regularization elements L1 and L2.\u003c/p\u003e \u003cp\u003eA key element in the context of this model is its ability to deal effectively with colinearity and high dimensionality in the data. With the combination of L1 and L2 norms, the model is able to perform variable selection as in Lasso regression and stabilize parameter estimation as in Ridge regression. Algorithms such as the coordination gradient method are often used to solve this optimization problem. It is worth noting that although the model is linear in its predictors, its ability to effectively model complex relationships in the data, resulting from the regularization used, makes it useful in a variety of scientific and engineering applications.\u003c/p\u003e \u003c/div\u003e"},{"header":"3. Materials and methods","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Dataset\u003c/h2\u003e \u003cp\u003eThe dataset was created through simulations in SWMM 5.2.2 following Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The simulations were conducted on an urban catchment of 5 hectares, featuring an existing rainfall collector. The model rainfall, totaling 100 mm, lasted for 12 hours. Calculations and input file loading, as well as report analysis, were executed with the PySWMM 1.2.0 package.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eRanges of simulated data\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"2\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSubcatchment Feature\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eValues\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eWidth [m]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[1, 250 ,500, 750, 1000]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSlope [%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[1, 10, 20, 40, 60, 80, 100]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePercImperv [%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[1, 10, 20, 40, 60, 80, 100]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN-Imperv, N-Perv [-]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[0.015, 0.24, 0.4, 0.8]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eD-Imperv, D-Perv [m]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[0.0013, 0.0025, 0.0051, 0.0076]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePctZero [%]\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e[1, 10, 20, 40, 60, 80, 100]\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe study utilized 103,073 samples to analyze fundamental catchment parameters, including the percentage of impervious surface (PercImperv), width of overland flow path (Width), slope of land (PercSlope), Manning's coefficients for impervious (N-Imperv) and permeable (N-Perv) surfaces, depression storage depth in the impervious sub-catchment (D-Imperv) and permeable (D-Perv), and catchment runoff (Runoff). For descriptive statistics, please refer to Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eDescriptive statistics of the dataset.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"10\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c10\" colnum=\"10\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003ePercImperv\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWidth\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePercSlope\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eN-Imperv\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eN-Perv\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eD-Imperv\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eD-Perv\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003ePctZero\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c10\"\u003e \u003cp\u003eRunoff\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ecount\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e103073\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emean\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e42.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e481.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e42.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e49.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e3.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003estd\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e34.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e359.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e34.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.32\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e35.07\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e1.51\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emin\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e25%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e250\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.015\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e25\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e3.71\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e50%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e40\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.4\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e75%\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e750\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e75\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.56\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003emax\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1000\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e100\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c10\"\u003e \u003cp\u003e4.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Analysis of catchment area features\u003c/h2\u003e \u003cp\u003eUnderstanding the connections between catchment parameters and surface runoff is a crucial aspect of hydrological studies for urban infrastructure planning, water engineering, and managing the risk of extreme hydrological events. To clarify these relationships, a correlation analysis was conducted using data obtained from the SWMM program with simulations performed utilizing the pyswmm 1.2.0 and swmmio 0.6.0 packages. Our analysis identified a significant positive correlation between the surface runoff from storm catchments and the \"Width,\" \"Slope,\" and \"PercImperv\" parameters. This was evidenced by Spearman correlation coefficients of 1.0 (P-value: 0.0), indicating a deterministic linear relationship (Fig.\u0026nbsp;4\u0026ndash;6). Technical term abbreviations have been explained upon first usage. In contrast, the parameters \"N-Imperv,\" \"N-Perv,\" \"D-Imperv,\" and \"D-Perv\" displayed a complete negative correlation with surface runoff, as shown by Spearman correlation coefficients of -1.0 (P-value: 0.0). This indicates that as these parameters increase, runoff decreases systematically (Fig.\u0026nbsp;7\u0026ndash;11).\u003c/p\u003e \u003cp\u003eThese strong correlations emphasize the substantial effect of impermeable surfaces on runoff, with a nearly perfect correlation coefficient (Spearman Correlation: 0.99, P-value: 0.0) for the \"PercImperv\" parameter specifically. This metric represents the percentage of the catchment area that is impervious and directly contributes to the volume of runoff generated during rainfall events. The negative correlations of \"N-Imperv,\" \"N-Perv,\" \"D-Imperv,\" and \"D-Perv\" indicate their role in mitigating runoff. These strong correlations demonstrate the importance of accurately parameterizing catchments in hydrological modeling and highlight the sensitivity of runoff to these catchment characteristics.\u003c/p\u003e \u003cp\u003eIncorporating a comprehensive set of factors that influence surface runoff, including terrain, soil type, land cover, meteorological conditions, and human activities can significantly enhance the accuracy of modeling and predicting hydrological phenomena. Therefore, it is essential to include as many relevant influencing factors as possible in hydrological studies to guarantee the robustness and reliability of predictive models.\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Structure of the Neural Network Model\u003c/h2\u003e \u003cp\u003eThe neural network architecture utilized in this study is designed to predict surface runoff based on catchment attributes. The architecture is composed of the following layers:\u003c/p\u003e \u003cp\u003eNormalization Layer: The initial layer is a preprocessing normalization layer. This layer scales and centers the features based on the computed mean and standard deviation from the training data. It has 17 non-trainable parameters, reflecting the statistical parameters used for normalization.\u003c/p\u003e \u003cp\u003eInput Layer: The first dense layer acts as the input layer with 8 neurons. This is equal to the number of features in the dataset, ensuring each feature is adequately represented. It uses a Rectified Linear Unit (ReLU) activation function.\u003c/p\u003e \u003cp\u003eHidden Layers: Two hidden layers follow the input layer, each containing 8 neurons. These layers also use the ReLU activation function, which helps the model learn non-linear relationships in the data.\u003c/p\u003e \u003cp\u003eOutput Layer: The final layer is a dense layer with a single neuron, which outputs the predicted value for surface runoff. This layer also utilizes the ReLU activation function to ensure non-negative output values.\u003c/p\u003e \u003cp\u003eThe model is compiled using the Adam optimizer and employs a mean squared error loss function for backpropagation. The model's architecture totals 242 parameters, of which 225 are trainable. Early stopping and batch size of 32 are implemented to optimize the training process.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Structure of the ElasticNet Regression Model\u003c/h2\u003e \u003cp\u003eThe ElasticNet regression model is utilized in this study to predict surface runoff based on various catchment characteristics. The model integrates several fundamental elements and is implemented using Python's scikit-learn library.\u003c/p\u003e \u003cp\u003ePreprocessing: Standardization of the predictor variables is performed using the StandardScaler class, which normalizes the feature set to a mean of zero and a standard deviation of one. This ensures homogeneity in the predictor space and improves the model's convergence speed.\u003c/p\u003e \u003cp\u003eHyperparameters: An alpha parameter set to 0.01 and an l1_ratio of 0.2 are used. The former controls the amount of regularization, while the latter balances the L1 and L2 penalties, providing a compromise between ridge and lasso regression techniques.\u003c/p\u003e \u003cp\u003eData partitioning: An 80\u0026thinsp;\u0026minus;\u0026thinsp;20 data partitioning scheme is employed, allowing rigorous model evaluation on out-of-sample data.\u003c/p\u003e \u003cp\u003eOptimization Algorithm: By default, the Coordinate Descent Optimization algorithm is used to minimize the objective function.\u003c/p\u003e \u003cp\u003ePredictive Variables: The model incorporates eight predictor variables representing various watershed attributes, demonstrating its applicability in capturing the multifaceted nature of hydrologic systems.\u003c/p\u003e \u003cp\u003eOutcome Variable: The model is trained to predict a single outcome, surface runoff.\u003c/p\u003e \u003c/div\u003e"},{"header":"4. Results","content":"\u003cp\u003eThe aim of this research is to assess the usefulness of ElasticNet regression models and artificial neural networks in hydrological catchment data analysis. The dataset utilized in this study comprises 103,073 samples generated by simulations in SWMM 5.2.2, as outlined in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The simulations were carried out in an urban catchment spanning 5 hectares, which has a pre-existing rainfall collector. The total model rainfall was 100 mm over a period of 12 hours. The data set was randomly partitioned into training and testing sets at an 80:20 ratio. The PySWMM 1.2.0 package was utilized to perform calculations, load input files, and analyze the reports. The target variable for prediction is 'Runoff.' The TensorFlow and Keras libraries were utilized to develop the ANN model, while the SciKit-Learn library was employed to prepare the ElasticNet model. The Elastic Net model's hyperparameters were optimized using the Grid Search technique. This model assesses a predetermined set of parameter values αi and l1_ratio via 5-fold cross-validation to gauge the efficacy of each pairing. For the ANN model, a manual optimization of the architectural design was executed.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e4.1. Performance metrics\u003c/h2\u003e \u003cp\u003eBoth models underwent evaluation using a set of performance measures, which included mean squared error (MSE), R2 score, Index of Agreement (d), Scatter Index (SI), and Root Mean Square Error (RMSE). Additionally, inference time was utilized as a performance indicator. Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e presents a summary of the metrics for both models, providing a thorough overview of their forecasting precision and computational efficiency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSummary of performance metrics\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"7\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eModel name\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eR2 Score\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eIndex of Agreement (d)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eScatter Index (SI)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eRMSE\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eInference Time\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElasticNet\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e1.035\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.550\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.837\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.277\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.017\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.004\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eANN\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.996\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.999\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.030\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.109\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e1.396\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e4.2. Model evaluation\u003c/h2\u003e \u003cp\u003eThe Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e12\u003c/span\u003e illustrates the accuracy of the ANN and ElasticNet models in predicting outflow. The points on the graph represent the actual versus predicted values, and the regression line indicates the ideal model fit. The ANN model displays impressive predictive accuracy, with a dense concentration of points near the regression line, supported by an MSE of 0.010 and an R2 Score of 0.996. Moreover, the accuracy of the model is reinforced by its near-perfect Index of Agreement (0.999), low Scatter Index (0.030), and minimal RMSE (0.109). ElasticNet model showcases more scatter in the points, especially at lower outflow values, indicating a less precise fit to the dataset. This is supported by its higher MSE of 1.035, lower R2 Score of 0.550, and larger RMSE of 1.017.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eStatistical analysis of the error distribution for the ANN and ElasticNet models was performed (Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e13\u003c/span\u003e). Parameters such as the mean, median and standard deviation of the error were calculated. For the ANN model, the mean error was \u0026minus;\u0026thinsp;0.001 m\u0026sup3;/s, with a standard deviation of 0.115 m\u0026sup3;/s, 90% of the errors were within a narrow range of -0.203 to 0.201 m\u0026sup3;/s, indicating the high precision of the model. For the ElasticNet model, the average error was higher at -0.014 m\u0026sup3;/s, with a standard deviation of 0.600 m\u0026sup3;/s. 90% of the errors oscillated in a much wider range of -1.041 to 1.013 m\u0026sup3;/s. These statistics confirm that the ANN model shows higher precision and is more stable in predicting runoff compared to the ElasticNet model, which is particularly noticeable in the context of a smaller spread of errors around zero.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec14\" class=\"Section2\"\u003e \u003ch2\u003e4.3. Comparative analysis of prediction error\u003c/h2\u003e \u003cp\u003eWhen analyzing prediction errors, the ANN model surpasses the ElasticNet model, especially regarding error distribution and precision. The ANN model maintains a narrow error range and greater stability in predicting runoff, which is highlighted by the reduced spread of errors around zero and superior performance across all assessed metrics.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eTo further understand the performance differences between the ANN and ElasticNet models, a detailed error analysis was conducted. A histogram of error differences (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e14\u003c/span\u003e, left) reveals a mean error difference of 0.850 m\u0026sup3;/s and a standard deviation of 0.564 m\u0026sup3;/s. The dot plot (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e14\u003c/span\u003e, right) shows 15% of cases exceeding the error difference threshold set at the 85th percentile (1.528 m\u0026sup3;/s). These observations indicate where the ANN model achieved higher precision and stability compared to the ElasticNet model.\u003c/p\u003e "},{"header":"Conclusion","content":" \u003c/p\u003e \u003cp\u003eThis study compared ElasticNet regression and Artificial Neural Networks to predict surface runoff. The main objective was to determine which method produces the most precise, stable, and computationally efficient forecasts for hydrological data. The SSN model, constructed with normalizing, hidden, and output layers architecture, displayed a notably superior fit to the data based on the MSE and R2 score values (0.010 and 0.996, respectively). Despite the ElasticNet model's flexibility and ability to handle colinearity, it produced significantly lower performance indicators (MSE\u0026thinsp;=\u0026thinsp;1.035, R2 Score\u0026thinsp;=\u0026thinsp;0.550). On the other hand, the SSN model had a high precision rate with 90% of the errors being within a narrow range. However, for the ElasticNet model, the error range was much wider, which limits its practical application. Notably, the performance of ElasticNet was undermined particularly at lower runoff values due to its regularization effect resulting in underfitting. This underfitting stems from the regularization process that may oversimplify the model by reducing the coefficients of less crucial predictors, thus failing to account for the intricate relationship between catchment features and runoff. Additionally, as small flow scenarios involve non-linear dynamics, including the interplay between soil moisture and infiltration rates, ElasticNet regression's linear nature is inadequate to handle such complexities. In contrast, ANNs possess non-linear processing capabilities that make them better equipped for these situations. Therefore, the study findings recommend utilizing ANNs to predict surface runoff. Artificial neural networks exhibit superior ability in detecting and interpreting the intricate interconnections and nonlinear associations among catchment parameters. This grants them efficacy in fulfilling current analytic necessities and positions them as a valuable tool for forthcoming research pursuits and pragmatic applications in the realm of water resource management. Due to the increasing complexity of urban hydrology, the incorporation of artificial neural networks into operational systems has become a promising advancement for predicting and managing surface runoff. This approach provides enhanced precision and adaptability.\u003c/p\u003e \u003c/div\u003e"},{"header":"Declarations","content":"\u003cp\u003e \u003ch2\u003eCompeting Interests\u003c/h2\u003e \u003cp\u003eThe authors have no relevant financial or non-financial interests to disclose.\u003c/p\u003e \u003c/p\u003e\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThe authors declare that no funds, grants, or other support were received during the preparation of this manuscript.\u003c/p\u003e\u003ch2\u003eAuthor Contribution\u003c/h2\u003e\u003cp\u003eR.B. Conceptualization, methods, software, simulation, validation, writing\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e\u003cp\u003eThe data and code have been uploaded to a public github repository - https://github.com/BuczynskiRafal/SurfaceRunoff-Modeling-ANN-ElasticNet-Comparison\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJohnson, B. E., Julien, P. Y., Molnar, D. K., \u0026amp; Watson, C. C. (2000). THE TWO-DIMENSIONAL UPLAND EROSION MODEL CASC2D‐SED 1. \u003cem\u003eJAWRA Journal of the American Water Resources Association\u003c/em\u003e, \u003cem\u003e36\u003c/em\u003e(1), 31\u0026ndash;42.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMolina, A., Govers, G., Vanacker, V., Poesen, J., Zeelmaekers, E., \u0026amp; Cisneros, F. (2007). Runoff generation in a degraded Andean ecosystem: Interaction of vegetation cover and land use. \u003cem\u003eCatena\u003c/em\u003e, \u003cem\u003e71\u003c/em\u003e(2), 357\u0026ndash;370.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eDehotin, J., Breil, P., Braud, I., de Lavenne, A., Lagouy, M., \u0026amp; Sarrazin, B. (2015). Detecting surface runoff location in a small catchment using distributed and simple observation method. \u003cem\u003eJournal of Hydrology\u003c/em\u003e, \u003cem\u003e525\u003c/em\u003e, 113\u0026ndash;129.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003ePitman, A. J., Slater, A. G., Desborough, C. E., \u0026amp; Zhao, M. (1999). Uncertainty in the simulation of runoff due to the parameterization of frozen soil moisture using the Global Soil Wetness Project methodology. \u003cem\u003eJournal of Geophysical Research: Atmospheres\u003c/em\u003e, \u003cem\u003e104\u003c/em\u003e(D14), 16879\u0026ndash;16888.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eBeighley, R. E., Dunne, T., \u0026amp; Melack, J. M. (2005). Understanding and modeling basin hydrology: interpreting the hydrogeological signature. \u003cem\u003eHydrological Processes: An International Journal\u003c/em\u003e, \u003cem\u003e19\u003c/em\u003e(7), 1333\u0026ndash;1353.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYaseen, Z. M., El-shafie, A., Jaafar, O., Afan, H. A., \u0026amp; Sayl, K. N. (2015). Artificial intelligence based models for stream-flow forecasting: 2000\u0026ndash;2015. \u003cem\u003eJournal of Hydrology\u003c/em\u003e, \u003cem\u003e530\u003c/em\u003e, 829\u0026ndash;844. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1016/j.jhydrol.2015.10.038\u003c/span\u003e\u003cspan address=\"10.1016/j.jhydrol.2015.10.038\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhang, G., Patuwo, B. E., \u0026amp; Hu, M. Y. (1998). Forecasting with artificial neural networks:: The state of the art. \u003cem\u003eInternational journal of forecasting\u003c/em\u003e, \u003cem\u003e14\u003c/em\u003e(1), 35\u0026ndash;62.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKubat, M. (1999). Neural networks: A comprehensive foundation by Simon Haykin, Macmillan, 1994, ISBN 0-02-352781-7. The Knowledge Engineering Review, 13(4), 409\u0026ndash;412. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1017/S0269888998214044\u003c/span\u003e\u003cspan address=\"10.1017/S0269888998214044\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGovindaraju, R. S. (2000). Artificial neural networks in hydrology. II: Hydrologic applications. \u003cem\u003eJournal of Hydrologic Engineering\u003c/em\u003e, \u003cem\u003e5\u003c/em\u003e(2), 124\u0026ndash;137. \u003cdiv class=\"ExternalRefDOI\"\u003e10.1061/\u003c/div\u003e(ASCE)1084-0699(2000)5:2(124).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMuftah, H., Rowan, T. S. L., \u0026amp; Butler, A. P. (2022). Towards open-source LOD2 modelling using convolutional neural networks. \u003cem\u003eModeling Earth Systems and Environment\u003c/em\u003e, \u003cem\u003e8\u003c/em\u003e(2), 1693\u0026ndash;1709. \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.1007/s40808-021-01159-8\u003c/span\u003e\u003cspan address=\"10.1007/s40808-021-01159-8\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eShinma, T. A., \u0026amp; Reis, L. F. R. (2011). Multiobjective automatic calibration of the storm water management model (SWMM) using non-dominated sorting genetic algorithm II (NSGA-II). In World Environmental and Water Resources Congress 2011: Bearing Knowledge for Sustainability (pp. 598\u0026ndash;607).\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eRossman, L. A. (2010). \u003cem\u003eStorm water management model user's manual, version 5.0\u003c/em\u003e (p. 276). National Risk Management Research Laboratory, Office of Research and Development, US Environmental Protection Agency.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eHerberg, E. (2023). Neural Network Architectures. arXiv preprint arXiv:2304.05133.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eSeyedashraf, O., Bottacin-Busolin, A., \u0026amp; Harou, J. J. (2021). A Disaggregation‐Emulation Approach for Optimization of Large Urban Drainage Systems. \u003cem\u003eWater Resources Research\u003c/em\u003e, 57(8), e2020WR029098.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eKim, H. I., Keum, H. J., \u0026amp; Han, K. Y. (2019). Real-time urban inundation prediction combining hydraulic and probabilistic methods. \u003cem\u003eWater\u003c/em\u003e, \u003cem\u003e11\u003c/em\u003e(2), 293.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eMendrofa, G. A., Hertono, G. F., \u0026amp; Handari, B. D. (2023). Ensemble Learning Model on Artificial Neural Network-Backpropagation (ANN-BP) Architecture for Coal Pillar Stability Classification. arXiv preprint arXiv:2303.16524.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Runoff, Subcatchments, SWMM, Regression, ANN, ElasticNet","lastPublishedDoi":"10.21203/rs.3.rs-4441223/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-4441223/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThis study examines the comparative performance of Artificial Neural Networks and Elastic Net Regression in predicting surface runoff in urban stormwater catchments. Utilizing the Storm Water Management Model, a dataset of over 100,000 samples was prepared, incorporating diverse catchment parameters such as impervious surface percentage, overland flow path width, slope, Manning\u0026rsquo;s coefficients, and depression storage depths. Both models were developed and tuned to enhance runoff prediction accuracy. An assessment was carried out to gauge the predictive accuracy, computational efficiency, and ability to withstand data noise of the models. The Artificial Neural Networks demonstrated significant advantages in handling complex, non-linear relationships inherent in hydrological data, resulting in higher predictive accuracy and stability. Elastic Net Regression, while useful, exhibited limitations, particularly in lower runoff scenarios due to its regularization constraints. The outcomes highlight the relative advantages and drawbacks of each modeling technique, offering crucial perspectives for enhancing water resource management in urban settings.\u003c/p\u003e","manuscriptTitle":"Comparison of the Effectiveness of Artificial Neural Networks and Elastic Net Regression in Surface Runoff Modeling","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-06-10 13:34:30","doi":"10.21203/rs.3.rs-4441223/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"568df8cf-f444-4098-af1e-428e6ef912d5","owner":[],"postedDate":"June 10th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2024-07-11T10:55:22+00:00","versionOfRecord":[],"versionCreatedAt":"2024-06-10 13:34:30","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-4441223","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-4441223","identity":"rs-4441223","version":["v1"]},"buildId":"qtupq5eGEP_6zYnWcrvyt","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}