Time series prediction of sound speed profiles in complex shallow water environment

Abstract

Sound speed exhibits significant spatio-temporal variations in shallow waters, particularly in environments with internal solitary waves (ISWs). The temporal prediction of sound speed profiles (SSPs) can be transformed into the prediction of empirical orthogonal function (EOF) coefficients. However, dynamic oceanic phenomena can cause significant variations in the background field and EOFs, leading to representational errors. Studies have shown that the sound speed at the depth corresponding to the extreme point of the first EOF contains the most information, which can effectively reflect the SSP structure. To reduce the impact of the background field and EOF mismatch on SSP prediction accuracy, an indirect approach is proposed. Compared to directly predicting the EOF coefficients using a Long Short-Term Memory (LSTM) network, the indirect approach utilizes historical data to establish the relationship between the depth-fixed sound speed at a specified depth and the EOF coefficients using a back propagation (BP) network. The LSTM then predicts the depth-fixed sound speed for the test set. Finally, the EOF coefficients are obtained from the trained BP network and subsequently used to reconstruct the SSPs. A negative coupling relationship is observed between the first EOF component estimated by the indirect approach and the background field. This relationship causes the mutual cancellation of two error components, ultimately reducing the SSP prediction error. The indirect approach substantially enhances SSP prediction accuracy compared to the direct approach, reducing errors by approximately 0.9 m/s, reaching approximately 0.67 m/s. Moreover, it maintains high prediction accuracy with an error of approximately 0.57 m/s with a representative background field.