A multivariable plane-wave fit technique to extract unidirectional energy fluxes from an internal wave resolving mooring array

Low-mode oceanic internal waves feature complex interference patterns because they propagate in different directions from multiple generation sites.To disentangle their directions, we implement a Multi VARiable Plane (MVARP) wave fit technique, in which a plane wave is simultaneously fit to variables such as perturbation pressure and velocities.MVARP is specifically developed to extract unidirectional low-mode energy fluxes from sparse observations at an Internal Wave Resolving (IWR) array.The IWR array includes a central full-depth mooring measuring velocities, temperature, salinity, and pressure, and a circular array of Current and Pressure-recording Inverted Echo Sounders (CPIESs) measuring bottom velocities and pressure anomalies, and sea surface height inferred from acoustic travel times.We test our MVARP technique on subsampled data from a global Hybrid Coordinate Ocean Model (HYCOM) simulation.We compare the semidiurnal mode-1 unidirectional fluxes from MVARP with these computed with a "state-of-the-art" Directional Fourier Filter (DFF) applied to the gridded HYCOM fields.An optimal IWR array configuration is identified by minimizing residual variance and relative flux vector differences.The MVARP fluxes also agree well with the DFF fluxes, when we move the IWR array stencil over a larger domain.Our MVARP technique has informed the design of an IWR array deployed for 12 months (September 2023-October 2024) off the U.S. West Coast to distinguish far-field from near-field waves and has guided deployments in the equatorial North Pacific (Fall 2024-2025) and the North Pacific south of the Aleutians (July 2025 for 9-12 months).SIGNIFICANCE STATEMENT: Disentangling the directions and energy fluxes of the ocean's internal waves is challenging due to the complexity of the wave field.To address this, we (1) design a mooring array to measure internal waves as a function of depth and horizontal distance, and (2) extend an existing plane wave fitting technique to simultaneously incorporate variables such as velocity and pressure.Using data from a global ocean simulation, we apply this method to extract unidirectional energy fluxes associated with dominant internal waves.The technique also informs the optimal design of the mooring array.We compare the unidirectional fluxes estimated from our method with those obtained using a spectral approach and find strong agreement.