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Edited by: Shiqiu Peng, State Key Laboratory of Tropical Oceanography (CAS), China

Reviewed by: Javier Zavala-Garay, Department of Marine and Coastal Sciences, Rutgers, The State University of New Jersey, United States; Chuanyu Liu, Institute of Oceanology (CAS), China

*Correspondence: Guijun Han,

This article was submitted to Ocean Observation, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

At present, many prediction models based on deep learning methods have been widely used in ocean prediction with satisfactory results. However, few deep learning models are used to predict the Kuroshio path south of Japan. In this study, a hybrid deep learning prediction model is constructed based on the long short-term memory (LSTM) neural network, combined with the complex empirical orthogonal function (CEOF) and bivariate empirical mode decomposition (BEMD), called CEOF-BEMD-LSTM. We train the model by using a 50-year (1958-2007) long time series of daily mean positions of the Kuroshio path south of Japan extracted from a regional ocean reanalysis dataset. During the test period of 15 years (2008-2022) by using daily altimetry dataset, our model shows a good performance for the Kuroshio path prediction with the lead time of 120 days, with 0.44° root-mean-square error (RMSE) and 0.75 anomaly correlation coefficient (ACC). This model also has good prediction skill score (SS). Moreover, the CEOF-BEMD-LSTM model successfully hindcasts the formation of the latest Kuroshio large meander since the summer of 2017. Predictions of the Kuroshio path for the coming 120 days (from January1 to April 30, 2023) indicate that the Kuroshio will continue to remain in the state of the large meander. Besides, predictor(s) of the Kuroshio path south of Japan need to be sought and added in future research.

The Kuroshio is the western boundary current of the North Pacific Subtropical Gyre. It originates from the bifurcated North Equatorial Current on the eastern side of the Philippines, flows into the East China Sea

Three typical Kuroshio paths south of Japan: nNLM (red line), oNLM (green line), and tLM (blue line) derived from a regional ocean reanalysis described in section 2.1. Thin black contours are isobaths of 1 000 and 2 000 m.

Numerical prediction plays a dominant role in predicting the variation of the Kuroshio path south of Japan. Several studies used experiments to predict the variability of the Kuroshio path using data assimilation models, and the results showed that the predictive limit for the Kuroshio path south of Japan is about a couple of months (

As one of the most popular and consequential technologies, deep learning methods have been widely used for ocean prediction (

In this study, we present a hybrid deep learning prediction model, combining the complex empirical orthogonal function (CEOF) analysis, bivariate empirical mode decomposition (BEMD) analysis, and LSTM neural network, named CEOF-BEMD-LSTM model, to predict the Kuroshio path south of Japan. The rest of this paper is organized as follows. In section 2, we introduce the data and methods. In section 3, we describe the prediction experiments and results of the Kuroshio path. Summary and discussion are given in section 4.

We use the sea-surface height (SSH) data from an ocean reanalysis dataset, which is produced by a Northwest Pacific regional ocean reanalysis system, called China Ocean ReAnalysis (CORA,

We also use the daily absolute dynamic topography (ADT) data of the Ssalto/Duacs altimeter products from January 2008 to December 2022 from the Copernicus Marine and Environment Monitoring Service (CMEMS) (

In this study, the Kuroshio path south of Japan is defined by the 70-cm SSH isoline and 110-cm ADT isoline, respectively. The discrepancy between the definitions with these two datasets results from different reference mean sea surfaces used (

The empirical orthogonal function (EOF) analysis is widely used in dimensionality reduction and pattern extraction in atmospheric and oceanic sciences (

In this study, the Kuroshio path data can be expressed as matrix

where the dimensions are

The matrix X is first normalized, expressed as X':

where σ is the standard deviation matrix and

In the EOF analysis, the spatial modes (EOFs) and associated temporal coefficients (PCs) are obtained by performing a Jacobi decomposition on the covariance matrix of X'.

In the CEOF analysis, a Hermite matrix (U) is constructed by applying the Hilbert transform to the matrix X'. It can be further expanded as:

where P is composed of the complex EOFs (aka, spatial modes, hereafter CEOFs), while B is composed of the corresponding complex PCs (aka, temporal coefficients, hereafter CPCs). In this study, the temporal coefficients (PCs and CPCs) will be taken as the raw data for the input of the deep learning prediction model. Detailed information about the use of the CEOF analysis in this study is given in sections 3.1 and 3.2.

The empirical mode decomposition (EMD) analysis is an efficient method for data denoising (

After the BEMD analysis, the original signal

In this study, the BEMD analysis is applied to the CPCs. Details about the use of the BEMD analysis in this study are provided in section 3.2.

The LSTM neural network can tackle the long-term dependence of sequence data well, and is regarded as a state-of-the-art method for time series prediction. As a variant of the RNN, it solves the problem of gradient vanishing and gradient explosion that exist in the traditional RNN (

Structure of an LSTM cell.

where _{t}
_{t}
_{t}
_{t}
_{f}
_{i}
_{C}
_{f}
_{i}
_{c}
_{t}
_{t}

In this study, we build a 4-layer deep neural network model to conduct 120-day Kuroshio path prediction experiments based on the LSTM neural network. By trial and error, the size of the time window used to predict the Kuroshio path is set to 30, which means that we use the preceding 30-day Kuroshio path data for prediction. Besides, the adaptive moment estimation (Adam) is taken as the gradient optimization algorithm, which provides an optimized method for solving sparse gradients and noise problems (

To evaluate the performance of the prediction models, we employ root-mean-square error (RMSE), anomaly correlation coefficient (ACC), and prediction skill score (SS) as the evaluation criteria. These calculation formulas are defined as follows:

where ^{th} grid point on the ^{th} day; . ^{th} day, respectively;^{th} grid point; and ACC is the spatial anomaly correlation coefficient of the ^{th} day. ^{th} grid point.

First, we construct the CEOF-LSTM (EOF-LSTM) prediction model, based on the CEOF (EOF) analysis and LSTM neural network only (see

Left panels

In summary, the CEOF analysis is significantly better than the EOF analysis for predicting the Kuroshio path south of Japan. It may be due to these following reasons: The CEOF analysis can resolve propagating wave signals (

To improve the performance of the CEOF-LSTM model, we add the BEMD analysis to the prediction model (

Framework of CEOF-BEMD-LSTM model.

In this section, we compare the predictions of the CEOF-BEMD-LSTM model with those of the CEOF-LSTM model to evaluate the performance of the CEOF-BEMD-LSTM model.

We also calculate the prediction skill score (SS) with each model to further evaluate the predictions. The SS is positive (negative) when the accuracy of the prediction is greater (less) than the accuracy of the climatology (

The latest Kuroshio large meander occurred in August 2017, and is the second Kuroshio large meander in this century. As a unique phenomenon, the Kuroshio large meander has a significant impact on climate change along the southern coast of Japan (

Prediction results of the Kuroshio path with the lead time of 120 days from July 1 (1-day) to October 28 (120-day), 2017

The latest Kuroshio large meander has lasted for five years and remains so. In the final part of this section, we use the CEOF-BEMD-LSTM model to predict the Kuroshio path south of Japan for 120 days from January 1 (1-day) to April 30 (120-day), 2023. The prediction results indicate that the Kuroshio will remain in the state of the large meander (

Prediction results of the Kuroshio path with the lead time of 120 days from January 1 (1-day) to April 30 (120-day), 2023. The solid gray curve represents the truth at lead-time of one day.

In this study, a hybrid deep learning prediction model, called CEOF-BEMD-LSTM model, is developed for predicting the Kuroshio path south of Japan based on the CEOF analysis, BEMD analysis, and LSTM neural network. To evaluate the performance of this model, we use the Kuroshio path data obtained from the CORA reanalysis dataset from 1958 to 2007 (50 years) as a training dataset, and its counterpart from the altimetry data from 2008 to 2022 as a testing dataset, to conduct 120-day Kuroshio path prediction experiments. Prediction results show that the CEOF-BEMD-LSTM model has good performance in the 120-day prediction range evaluated by using two common deterministic skill metrics, the ACC and RMSE. Even when the lead time is 120 days, the RMSE is about 0.44°, which is less than the climatological standard deviation, and the ACC can still reach 0.75, which is greater than 0.6 (a widely used measure for forecast verification;

Comparatively speaking, the prediction range of the traditional numerical prediction is usually 60 days (

Some recent studies showed that the inclusion of appropriate predictors can improve the prediction range of deep learning models (e.g.,

Publicly available datasets were analyzed in this study. This data can be found here:

XW and ZJ constructed the prediction model and conducted the prediction experiments. XW wrote the initial draft and revised the manuscript. GH and WL proposed the main ideas and revised the manuscript. LC and WD provided high-performance data processing and revised the manuscript. All authors contributed to the article and approved the revised version.

This research is sponsored by the National Natural Science Foundation of China (grant 41876014).

The authors thank the following data and tool providers: the National Marine Data and Information Service (

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.