Echo State Network and Sparrow Search: Echo State Network for Modeling the Monthly River Discharge of the Biggest River in Buzău County, Romania

Artificial intelligence (AI) has become an instrument used in all domains with good results. The water resources management field is not an exception. Therefore, in this article, we propose two machine learning (ML) techniques—an echo state network (ESN) and sparrow search algorithm–echo state network (SSA-ESN)—for monthly modeling of the water discharge of one of the biggest rivers in Romania for three periods (S, S1, and S2). In both models, R2 was over 0.989 on the test and training sets and the mean absolute error (MAE) varied between 4.4826 and 7.6038. The performance of the SSA-ESN was similar, but the ESN had the shortest run time. The influence of anomalies on the models’ quality was assessed by running the algorithms on a series without the aberrant values, which were detected by the seasonal hybrid extreme studentized deviate (S-H-ESD) test. The results indicate that removing the anomalies significantly improved both models’ performance, but the run time was increased.