Onboard forecasting is challenging but essential for unmanned autonomous ocean platforms. Due to the numerous operational constraints of these platforms, efficient adaptive Reduced-Order Models (ROMs) are needed. In this work, we employ the incremental Low-Rank Dynamic Mode Decomposition (iLRDMD), which is an adaptive, data-driven, DMD-based ROM that enables efficient forecast compression, transmission, and onboard forecasting. We demonstrate the algorithm on 3D multivariate Hybrid Coordinate Ocean Model (HYCOM) ocean fields in the Middle Atlantic Ridge (MAR) region. We further demonstrate that these iLRDMD ocean forecasts can be used for interdisciplinary applications such as underwater acoustics predictions. Here, acoustics fields computed from the ocean iLRDMD forecasts are compared to those computed from HYCOM fields. We also illustrate the application of a joint ocean-acoustics iLRDMD model for predetermined acoustics configurations. In the MAR region, we find that iLRDMD models are sufficiently accurate and efficient for onboard ocean and acoustic forecasting of temperature, salinity, velocity, and transmission loss fields.

Onboard probabilistic forecasting and data assimilation is challenging for unmanned autonomous platforms. Due to the operational constraints, efficient adaptive reduced order models (ROMs) are needed. To extend the duration for which Dynamic Mode Decomposition (DMD) predictions are accurate, we utilize and augment incremental methods that update the reduced order state but also adapt the DMD. Our adaptive ROM methods are dynamic and stochastic. They update the state, parameters, and basis functions, in response to the changing forecasts, possibly computed in remote centers, and to observations made by the autonomous platforms and by other assets. For the latter, to allow learning even when observations are sparse and multivariate, we employ Bayesian data assimilation. Specifically, we extend the Gaussian Mixture Model – Dynamically Orthogonal (GMM-DO) filter to stochastic DMD forecasts and Bayesian GMM updates of the DMD coefficients, state, and parameters, learning from the limited gappy observation data sets.

We describe and investigate several Dynamic Mode Decomposition (DMD) and reduced order projection methods for regional stochastic ocean predictions. We then showcase some of their results as applied to a 300-member set of ensemble forecasts from the POSYDON-POINT sea experiment in the Middle Atlantic–New York Bight region for the period 23–27 August 2018 as well as to a 42-day data-driven reanalysis from the AWACS–SW06 sea experiment in the Middle Atlantic Bight region for the period 14 August to 24 September 2006. We discuss these results for use by autonomous platforms in uncertain scenarios as well the combination of DMD with ideas from large-ensemble forecasting and Dynamically-Orthogonal (DO) differential equations.