The Rossby Normal Mode as a Physical Linkage in a Machine Learning Forecast Model for the SST and SSH of South China Sea Deep Basin

Machine learning (ML) has been widely applied in Earth sciences, but its black-box nature still remains. Existing techniques for interpretable ML developed by deep learning researchers are not satisfactory in understanding physical problems. In this study, our objective is to establish the physical linkage between features extracted from ML model and results derived from physical equations that describe the problem. This approach aims to provide a more comprehensible way of understanding an ML model. We select a less complex ML forecasting model, consisting of traditional statistical algorithms, which effectively forecast sea surface temperature anomaly (SSTA) and sea level anomaly (SLA) of the South China Sea (SCS) in 30 days ahead. Here, we focus on the SLA prediction and detect the physical mechanism of model capability to predict SCS SLA. Previous study has identified Rossby normal modes as the physical mechanism for long-lived eddies in SCS in previous study. We here demonstrate the relationship between the ML model and Rossby normal modes in SCS in terms of temporal variations and spatial distributions of water mass. The model's skill in predicting Rossby normal modes partially explains its skill in predicting SLA, thereby providing a more transparent and interpretable basis for forecasts in SCS. Machine learning (ML) forecast model has made lots of contributions in the Earth science. However, how it makes decision in each task is poorly understood. Traditional statistical methods are not satisfactory in explaining such models for physical problems. In this study, we aim to interpret the ML model's predictions in a more understandable and transparent manner. With physical equations that describe the problem, we try to understand a less complex ML model which can well forecast surface ocean elements of the South China Sea (SCS). The physical equations describe sea level variation in the SCS. We demonstrate the spatial distribution and temporal variation of Rossby normal modes in the SCS can be found in this ML model with some physical sense, thus providing a clearer understanding of how the ML model operates and arrives at its forecasts. An attempt to explain the Machine learning (ML) model with physicsFeatures in ML model are tested by physical equationsA more transparent and interpretable ML forecast model

Automated summary

This study aims to interpret the predictive ability of machine learning models in Earth sciences and establish a connection between the models and physical mechanisms through physical equations. The research findings show that the ML model's skill in predicting Rossby normal modes partially explains its skill in predicting SLA, providing a clearer understanding of how the model operates and arrives at its forecasts.