A four-dimensional inversion of the acoustic tomography, satellite altimetry and in situ data using Quasigeostrophic constraints

Abstract

A least square dynamically constrained inversion algorithm (DCIA) is developed for monitoring open ocean eddies in the regions, where open boundaries are the major sources of model forecast uncertainties on time scales larger than one week. We employ a finite-difference quasigeostrophic numerical model to constrain evolution of the ocean state. The inversion algorithm is based upon minimization of a quadratic cost function in the space of initial and boundary conditions for quasigeostrophic equations. The problem is regularized by enforcing smoothness in the fields of vorticity, buoyancy, and vertical velocity. We demonstrate that quasigeostrophic currents in an open ocean 1000 × 1000 km region can be effectively reconstructed using acoustic tomography and satellite altimetry data supported by additional sources of information. Performance of the algorithm is tested in the framework of twin-data experiments and then applied to the real observations. The analyzed observations span over the period of two months and include (i) direct and differential acoustic travel times measured at the array of five acoustic transceivers; (ii) satellite sea surface height measurements; (iii) vertical density profiles, and (iv) current velocities observed by the ship-borne acoustic Doppler current profiler (ADCP). We discuss interpolation properties of the travel time operators, study the impact of various data types on the quality of inversion, and compare performance of the proposed algorithm with the standard least square inversion of the acoustic travel times.