Modeling potential evapotranspiration (ET₀) is an important issue for water resources planning and management projects involving droughts and flood hazards. Evapotranspiration, one of the main components of the hydrological cycle, is highly effective in drought monitoring. This study investigates the efficiency of two machine-learning methods, random vector functional link (RVFL) and relevance vector machine (RVM), improved with new metaheuristic algorithms, quantum-based avian navigation optimizer algorithm (QANA), and artificial hummingbird algorithm (AHA) in modeling ET₀ using limited climatic data, minimum temperature, maximum temperature, and extraterrestrial radiation. The outcomes of the hybrid RVFL-AHA, RVFL-QANA, RVM-AHA, and RVM-QANA models compared with single RVFL and RVM models. Various input combinations and three data split scenarios were employed. The results revealed that the AHA and QANA considerably improved the efficiency of RVFL and RVM methods in modeling ET₀. Considering the periodicity component and extraterrestrial radiation as inputs improved the prediction accuracy of the applied methods.

The prediction of wave parameters has a great significance in the coastal and offshore engineering. For this purpose, several models and approaches have been proposed to predict wave parameters, such as empirical, soft computing, and numerical based approaches. Recently, soft computing techniques such as recurrent neural networks (RNN) have been used to develop sea wave prediction models. In this study, the RNN for wave prediction based on the data gathered and the measurement of the sea waves in the Caspian Sea, in the north of Iran is used for this study. The efficiency of RNNs for 3, 6, and 12 hourly and diurnal wave prediction using correlation coefficients is calculated to be 0.96, 0.90, 0.87, and 0.73, respectively. This indicates that wave prediction by using RNNs yields better results than the previous neural network approaches.

The prediction of ocean waves is a highly challenging task in coastal and water engineering in general due to their very high randomness. In the present case study, an analysis of wind, sea flow features, and wave height in the southern coasts of the Caspian Sea, especially in the off-coast sea waters of Mazandaran Province in Northern Iran, was performed. Satellite altimetry-based significant wave heights associated with the period of observation in 2016 were validated based on those measured at a buoy station in the same year. The comparative analysis between them showed that satellite-based wave heights are highly correlated to buoy data, as testified by a high coefficient of correlation r (0.87), low Bias (0.063 m), and root-mean-squared error (0.071 m). It was possible to assess that the dominant wave direction in the study area was northwest. Considering the main factors affecting wind-induced waves, the atmospheric framework in the examined sea region with high pressure was identified as the main factor to be taken into account in the formation of waves. The outcomes of the present research provide an interesting methodological tool for obtaining and processing accurate wave height estimations in such an intricate flow playground as the southern coasts of the Caspian Sea.

This study investigates the ability of a new hybrid neuro-fuzzy model by combining the neuro-fuzzy (ANFIS) approach with the marine predators’ algorithm (MPA) in predicting short-term (from 1 h ahead to 1 day ahead) significant wave heights. Data from two stations, Cairns and Palm Beach buoy, were used in assessing the considered methods. The ANFIS-MPA was compared with two other hybrid methods, ANFIS with genetic algorithm (ANFIS-GA) and ANFIS with particle swarm optimization (ANFIS-PSO), in predicting significant wave height for multiple lead times ranging from 1 h to 1 day. The multivariate adaptive regression spline was investigated in deciding the best input for prediction models. The ANFIS-MPA model generally offered better accuracy than the other hybrid models in predicting significant wave height in both stations. It improved the accuracy of ANFIS-PSO and ANFIS-GA by 8.3% and 11.2% in root mean square errors in predicting a 1 h lead time in the test period.