Comparison of Dynamic Mode Decomposition and Neural Latent Dynamic Model for Predicting Ocean Stratification in the Bay of Bengal

The world’s oceans are vertically stratified into multiple layers based on density, which is a function of temperature and salinity. Fluid mixing occurs when these layers interact with each other and plays a central role in regulating ocean stratification. This mixing process is highly nonlinear in both space and time and is primarily driven by buoyancy. Exploring its detailed dynamics requires numerical models that simulate the combined effects of ocean surface forcing, wind stress, and turbulent mixing, together with in situ observations such as Conductivity–Temperature–Depth (CTD) profiles, moored instruments, and Argo float measurements. These observations and model outputs generate large, high-dimensional spatio-temporal datasets that are challenging to analyse using traditional approaches alone, motivating the use of data-driven and machine learning methods to efficiently extract dominant patterns and predictive information.

In this work, we explore data-driven reduced-order modelling approaches to analyse and predict ocean stratification in the Bay of Bengal using temperature and salinity fields obtained from the Copernicus Marine Environment Monitoring Service (CMEMS). We employ two methods: (i) Dynamic Mode Decomposition (DMD), which approximates the temporal evolution of the system using a linear operator and extracts physically interpretable spatio-temporal modes, and (ii) Neural Latent Dynamic Model (NLDM) based on an encoder–decoder architecture with nonlinear latent-state evolution. The neural model learns a low-dimensional representation of vertical profiles and propagates them forward in time using nonlinear latent dynamics, enabling a flexible approximation of complex temporal behaviour beyond linear assumptions.

The predictive performance of both approaches is evaluated using daily CMEMS temperature and salinity data for the year 2024, with models trained on 360 days and validated by forecasting the subsequent 6 days. Classical Dynamic Mode Decomposition exhibits forecast root-mean-square errors of approximately 1.01 °C for temperature and 0.31 psu for salinity over the 6-day horizon. In contrast, the neural latent dynamics model achieves substantially lower prediction errors, with corresponding RMSEs of 0.0366 °C and 0.0136 psu. This improvement arises from the ability of the neural latent dynamics framework to represent nonlinear temporal evolution in a reduced latent space, which cannot be captured by the linear evolution assumption inherent in classical DMD.

Keywords : Ocean Stratification, DMD, Ocean Vertical Mixing, Neural Latent Dynamic Model