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Measurement inaccuracies and the absence of precise parameters value in conceptual and analytical models pose challenges in simulating the rainfall–runoff modeling (RRM). Accurate prediction of water resources, especially in water scarcity conditions, plays a distinctive and pivotal role in decision-making within water resource management. The significance of machine learning models (MLMs) has become pronounced in addressing these issues. In this context, the forthcoming research endeavors to model the RRM utilizing four MLMs: Support Vector Machine, Gene Expression Programming (GEP), Multilayer Perceptron, and Multivariate Adaptive Regression Splines (MARS). The simulation was conducted within the Malwathu Oya watershed, employing a dataset comprising 4,765 daily observations spanning from July 18, 2005, to September 30, 2018, gathered from rainfall stations, and Kappachichiya hydrometric station. Of all input combinations, the model incorporating the input parameters Qt−1, Qt−2, and R̄t was identified as the optimal configuration among the considered alternatives. The models' performance was assessed through root mean square error (RMSE), mean average error (MAE), coefficient of determination (R2), and developed discrepancy ratio (DDR). The GEP model emerged as the superior choice, with corresponding index values (RMSE, MAE, R2, DDRmax) of (43.028, 9.991, 0.909, 0.736) during the training process and (40.561, 10.565, 0.832, 1.038) during the testing process. HIGHLIGHTS ML models for forecasting streamflow in the Malwathu Oya River basin were evaluated.; Rainfall for several stations was used in model development.; The GEP model showcased the best predictability of streamflow.; Research findings help the proposed Malwathu Oya development scheme.;

Streamflow, a pivotal variable in water resources management, holds profound significance in shaping the decision-making processes of hydrologic projects. This paper tries to delve into the exploration of the stage-discharge relationship using three machine learning methods (MLMs) namely multi-layer neural networks (MLNN), radial basis neural networks (RBNN), and neuro-fuzzy systems (ANFIS) to predict and simulate mean daily stage-discharge data derived from two monitoring stations, Bulakbasi and Karaozü, Kizilirmak River, Turkey. Root mean square error (RMSE), Mean absolute percentage error (MAPE), coefficient of determination (R2), and the Developed Discrepancy Ratio (DDR) metrics were utilized to MLMs' performance assessment. The performance evaluation indices (RMSE, MAEP, R2, DDR) for the preeminent MLNN model applied to Bulakhbashi and Karasu stations were determined as (0.29, 1.57, 0.9998, 17.62) and (1.71, 6.56, 0.9980, 6.65), respectively. The MLNN model contributed to a notable enhancement in the RMSE performance index for the aforementioned stations, exhibiting improvements of 87% and 56%, respectively. These results affirm the MLNN's proficiency in accurately capturing the stage-discharge at both monitoring stations.

The intricate calculation of bed sediment load (BSL), which is influenced by hydraulic, hydrological, and sedimentary factors, is vital for informed decision-making in water resource management. Machine learning models, which are gaining popularity due to their accessibility and ability to reveal complex relationships, play a significant role in tackling these challenges. The efficacy of gene expression programming (GEP) models, support vector machines (SVMs), multi-layer perceptron (MLP), and multivariate adaptive regression splines (MARS) has been assessed through measured data of number 540 obtained from six rivers, namely Oak Creek, Nahal Yatir, Sagehen Creek, Elbow River, Jacoby River, and Goodwin Creek from 1954 to 1992. The assessment of model performance has been conducted utilizing root mean square error (RMSE), R2, Nash–Sutcliffe coefficient (NSE), and developed discrepancy ratio (DDR) as indices. Following data normalization within the range of 0–1, the data models underwent training and testing processes with a partition ratio of 80% for training and 20% for testing. Four dimensionless parameters, denoted as Fr = U/√gy, U/U*, Se, and ω = τU/γs√gyDs3, were employed as inputs in the models. The outcomes indicate that they exhibit superior performance compared to other methods, as evidenced by the following metrics in predicting BSL during the test stage: RMSE = 1.4088, NSE = 0.73054, R2 = 0.8729, and maximum QDDR(max) = 1.9564. HIGHLIGHTS The present work proposes BSL prediction using field data from six rivers.; Four machine learning models including SVM, GEP, MLP and MARS are employed to forecast BSL.; A variety of inputs is implemented for each MLMs to find optimum output.; Statistical indices are used to opt for superior MLMs for BSL prediction.;

Abstract The study focuses on the critical concern of designing secure and resilient bridge piers, especially regarding scour phenomena. Traditional equations for estimating scour depth are limited, often leading to inaccuracies. To address these shortcomings, modern data-driven models (DDMs) have emerged. This research conducts a comprehensive comparison involving DDMs, including support vector machine (SVM), gene expression programming (GEP), multilayer perceptron (MLP), gradient boosting trees (GBT) and multivariate adaptive regression spline (MARS) models, against two regression equations for predicting scour depth around cylindrical bridge piers. Evaluation employs statistical indices, such as root-mean-square error (RMSE), coefficient of determination (R 2), mean average error (MAE) and normalized discrepancy ratio (S (DDRmax)), to assess their predictive performance. A total of 455 datasets from previous research papers are employed for assessment. Dimensionless parameters Froude number $$\left( {Fr = \frac{U}{{\sqrt {gy} }}} \right)$$ F r = U gy , Pier Froude number $$Fr_{P} = \frac{U}{{\sqrt {g^{\prime } D} }}$$ F r P = U g ′ D , and the ratio of scour depth to pier diameter $$(\frac{\text{y}}{{\text{D}}})$$ ( y D ) are carefully selected as influential model inputs through dimensional analysis and the gamma test. The results highlight the superior performance of the SVM model. In the training phase, it exhibits an RMSE of 0.1009, MAE of 0.0726, R2 of 0.9401, and SDDR of 2.9237. During testing, the SVM model shows an RMSE of 0.023, MAE of 0.017, R2 of 0.984, and SDDR of 5.301. Additionally, it has an average error of − 0.065 and a total error of − 20.642 in the training set and an average error of − 0.005 and a total error of − 0.707 in the testing set. Conversely, the M5 model exhibits the lowest accuracy. The statistical metrics unequivocally establish the SVM model as significantly outperforming the experimental models, placing it in a higher echelon of predictive accuracy.

Flip-bucket spillways are utilized in hydraulic engineering to diminish the kinetic energy of flowing water by redirecting the flow jet into the air. In the downstream stailing basin with low tail-water, sediment particles movement results in scour hole formation, posing a threat to spillway stability. The accurate prediction of scour hole depth is a crucial area of the present research work. This study endeavors to employ four data-driven models (DDMs), namely Support Vector Machine (SVM), Gene Expression Programming (GEP), Multilayer Perceptron (MLP), and Multivariate Adaptive Regression Splines (MARS), in combination with five selected empirical equations. The objective is to accurately predict scour depth utilizing field-collected data from site number 84. Relative scour depth, dsH1, was simulated based on the readily extracted parameter i.e. Froude number, Fr=qgH13. The evaluation of model performance was conducted using fundamental metrics, including root mean square error (RMSE), coefficient of determination (R2), mean average error (MAE), and the maximum value of the developed discrepancy ratio (DDRmax). Among the DDMs, the MARS model demonstrated superior performance in both the training and testing phases. In the training phase, it yielded metrics (RMSE = 0.08665, MAE = 0.05714, R2 = 0.99169, DDRmax = 4.519), and in the testing phase, it produced metrics (RMSE = 0.0252, MAE = 0.0170, R2 = 0.09933, DDRmax = 9.144). This exceptional performance of the MARS model surpassed the initially selected (Wu, 1973) [1] experimental model, which exhibited metrics (RMSE = 0.39667, MAE = 0.17463, R2 = 0.96172, DDR = 1.428). The evaluation indices conclusively establish the MARS method's absolute superiority over the experimental approach proposed by Wu (1973) [1].

Contamination and seawater intrusion are esteemed as chief issues of coastal aquifers resulting from unscientific utilization, non-standard monitoring network and improper management. In the present study, an optimum monitoring network with appropriate numbers and standard spatial distribution was designed based on a vulnerability map of the Urmia coastal aquifer. A vulnerability map was extracted using a modified GALDIT-iP model and searching optimum network was done based on genetic algorithm (GA). The maximum value of the correlation between electrical conductivity (EC) and vulnerability index, the minimum number of monitoring wells and the highest value of Nash-Sutcliff were utilized for the simultaneous optimization model. The W-weighting coefficient was considered for economical goals and three targets were defined in a general objective function. The results showed that the W-weighting coefficient has a significant effect to determine optimal solution, and the best weighting was opted considering the most optimal response based on the precise of the monitoring network and vulnerability index. An acceptable optimization and validation process was obtained with the predictions of the validation results. For W = 1, the final value of the objective function was obtained 1.791 using 91 wells with a correlation coefficient of 0.935 and Nash-Sutcliff of 0.979, resulting in the appropriate spatial distribution of the wells and reduction of 18 wells from the existing monitoring wells.

As a destructive process, scouring exposes bridge foundations to failure and disastrous consequences. Control structures of various arrangements are capable to change and manage the adverse effects. This paper aims to investigate the effect of submerged vanes of a quasi-triangular arrangement (of heights 0, 4, and 6 cm), eppi, and sills (of height 4.5 and 9 cm) on scour development. All tests were executed in a rectangular slope-less flume covered with sediments of D50=1.8 mm. Temporal and equilibrium scour depth were mapped for Froud numbers: 0.15, 0.2, 0.25, and 0.6. Results clarified the aggregate effect of the eppies on the scour depth due to section contraction. Submerged vanes and sill were set up to deteriorate sediment transport. Although the vane of height 4 cm had the most superior performance, but the sill installation of height 4.5 cm greatly increased vane's effect, so that a remarkable reduction of scour was occurred at the first pier foundation.

As a remarkable parameter, the discharge coefficient (Cd) plays an important role in determining weirs' passing capacity. In this research work, the support vector machine (SVM) and the gene expression programming (GEP) algorithms were assessed to predict Cd of piano key weir (PKW), rectangular labyrinth weir (RLW), and trapezoidal labyrinth weir (TLW) with gathered experimental data set. Using dimensional analysis, various combinations of hydraulic and geometric non-dimensional parameters were extracted to perform simulation. The superior model for the SVM and the GEP predictor for PKW, RLW, and TLW included , and respectively. The results showed that both algorithms are potential in predicting discharge coefficient, but the coefficient of determination (RMSE, R2, Cd(DDR)max) illustrated the superiority of the GEP performance over the SVM. The results of the sensitivity analysis determined the highest effective parameters for PKW, RLW, and TLW in predicting discharge coefficients are , , and Fr respectively. HIGHLIGHTS Three different types of weirs have been studied in this paper.; Two SVM and GEP algorithms have been implemented to predict the discharge coefficient of three weirs.; Eighteen combinations of dimensionless parameters have been tested to achieve optimum prediction of the discharge coefficient.; An equation for a superior model has been extracted to simulate discharge coefficient.;

In this research work, besides analyzing the scour hole at the downstream of the siphon spillway physical model, some equations have been presented to predict scour hole developing. A physical model of siphon spillway along with three flip buckets of angle 30°, 45° and 60° for three types of sedimentary materials of mean size 1.8, 3.5 and 1.4 (mm) were used to study scour hole formation process. Geometric characteristics of the scour hole were collected for four flow discharges of 39.2, 42.12, 42.12, 49.76 (lit/s) and five tail-water depths of 15, 20, 25, 30 and 35 (cm) using a mesh grid size of 10 (cm) ×10 (cm). Three dimensionless parameters were extracted for analyzing experimental results using dimensional analysis. Of all scour hole dimensions, scour depth (ds), scour length (Ls) and distance of downstream hill up to bucket lip (L6) were adjusted for numerical modeling. Results showed that increasing flow rate causes growth and developing of scour hole geometric properties simultaneously. Increasing the particle size showed an inverse relationship with three dimensions of the scour hole. Also, the reduction of the bucket's angle led to a reduction in ds, Ls and L6. The maximum correlation coefficient obtained between ds, Ls and L6 with particle size, flip bucket angle and discharge/tailwater, respectively. Finally, predictors were presented to describe above-mentioned dimensions of scour hole dimensions.

In this paper, two groups of datasets including Froehlich (1988) and USGS were implemented to simulate scour depth for bridge piers of three shapes (circular, sharp-nose and rectangular) using support vector machine (SVM) algorithm. The results of the SVM were compared with gene expression programming (GEP) and the non-linear regression model. Independent parameters extracted using dimensional analysis were Froud number (Fr), the ratio of pier length to pier width (L/b), the ratio of sediment particle diameters (d50/d84), the ratio of sediment mean size to pier width (d50/b) and attack angle of water flow (α). Different combinations of independent variables were used to achieve optimum performance of the simulator. The results showed that among three simulators, the SVM algorithm had the best performance to predict local scour depth. The sensitivity analysis revealed that among independent parameters, the descending order of effectivity was Fr, sediment size, L/b, and α.