Hydrological droughts are characterized based on their duration, severity, and magnitude. Among the most critical factors, precipitation, evapotranspiration, and runoff are essential in modeling the droughts. In this study, three indices of drought, i.e., Standardized Precipitation Index (SPI), Standardized Streamflow Index (SSI), and Standardized Precipitation Evapotranspiration Index (SPEI), are modeled using Support Vector Regression (SVR), Gene Expression Programming (GEP), and M5 model trees (MT). The results indicate that SPI delivered higher accuracy. Moreover, MT model performed better in predicting SSI by a CC of 0.8195 and a RMSE of 0.8186.

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Owing to the nonlinear and non-stationary nature of the suspended sediment transport in rivers, suspended sediment concentration (SSC) modeling is a challenging task in environmental engineering. Investigation of SSC is of paramount importance in river morphology and hydraulic structures operation. To this end, for SSC modeling, first random forest (RF) and multi-layer perceptron (MLP) standalone models were developed, and then, they were optimized with genetic algorithm (GA) and stochastic gradient descent (SGD) to develop GA-MLP, GA-RF, SGD-MLP, and SGD-RF hybrid models. Variety of input scenarios are implemented for SSC prediction to find the best input combination. The streamflow and SSC data collected from two stations of Minnesota and San Joaquin rivers, respectively, located at South Dakota and California are utilized in the current study. Accuracies of the developed models are examined by means of three performance criteria of correlation coefficient (CC), scattered index (SI), and Willmott's index of agreement (WI). A significant promotion in accuracy of hybrid models has been seen in contrast to their standalone counterparts. As can be deduced from the results, GA-MLP-5 and GA-RF-5 models with CC of 0.950 and 0.944, SI of 0.290 and 0.308, and WI of 0.974 and 0.971, respectively, were found as best models for prediction of SSC at Minnesota river. The developed SGD-MLP-5 and SGD-RF-5 models with CC of 0.900 and 0.901, SI of 0.339 and 0.339, and WI of 0.945 and 0.946, respectively, gave accurate results at San Joaquin river. Through the application of SGD algorithm, the adaptive learning rate, epochs, rho, L1 and L2 were activated and presumed as 0.004, 10, 1, 0.000009 and 0, respectively. The ExpRectifier was considered as san activation operation due to its better efficiency in comparison with its alternatives for predicting SSC in SGD-MLP model. According to the results, the fifth scenario that incorporates SSC t-1 , SSC t-2 , Q t , Q t-1 , and Q t-2 were found superior for SSC modeling in the studied rivers. The recommended hybrid algorithms based on GA and SGD optimization algorithms are proposed as practical tools for solving complex environmental problems.

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