AMODE: An example of tomographic data assimilation
Bruce Cornuelle
Scripps Institution of Oceanography University of California
The Acoustic Mid-Ocean Dynamics Experiment (AMODE) measured time series of both reciprocal acoustic travel times and point temperature measurements from a 700-km diameter array of 6 moorings south of Bermuda during 1991-1992. This covered the 700-km region with about 100 km resolution, re-surveyed several times per day. The increased resolution obtained by modeling the time evolution of the field was adequate to resolve the evolving eddy field. Observations taken over 12 days were combined, using a non-linear quasi-geostrophic ocean model in a 1200 by 1200 km region, to generate improved initializations for predicting the evolving eddy field. Each initialization was performed by calculating the Hessian matrix for the dependence of datum misfit on model initial conditions and inverting the matrix with regularization, taking into account the errors incurred in the linearization of the gradient. This Newton method was iterated to achieve a reduction in the errors due to nonlinearity, and the iteration stopped when errors due to nonlinearity were comparable to the noise in the data.
Predictions of independent data (not used to determine the initialization) test the model dynamics. The rms misfit between data and model forecast was used as the error measure, referenced to a guess of climatological data values, which was defined as zero skill. Initializations derived from 12 days of data forecast the data with skill out to beyond 60 days, in contrast to persistence, which loses all skill after 30 days. The loss of skill can be explored using linearized transition matrices to compute the sensitivity of the forecast field to changes in the initial conditions, just as in the initialization procedure. The loss of predictability is at least partly due to growing unstable modes of the initial eddy field, with the largest 5 modes accounting for almost half the variance after 60 days. [Work supported by ONR.]
