Coupled estimation of internal tides and turbulent motions via statistical modal decomposition

Abstract. We present a data-driven modal-decomposition method that extracts the part of an incoherent internal tidal wave that correlates with the proper orthogonal decomposition (POD) of a turbulent mesoscale flow. This method exploits the a priori knowledge that the incoherent internal tide arises from interactions between an incident wave and the turbulent flow and also exploits the corresponding statistical correlation between the two types of motions. The method is presented and tested in an idealised framework based on the rotating-shallow-water model, where we provide a physical interpretation for the decomposition method based on theoretical considerations. Using idealised simulations with a plane wave propagating through a zonal turbulent jet, we first propose the use of the modal-decomposition method as a data analysis technique to understand how the wave is scattered by the flow. In a second step, we construct an estimation algorithm capable of separating the entangled contributions of the wave and mesoscale motions from a single sea surface height snapshot. This algorithm, which consists of estimating the POD coefficients of the turbulent flow shared by the wave and jet modes, is particularly suitable for configurations where the jet contribution to the sea surface height (SSH) is larger than that of the wave.