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.