AMODE: An Example of Tomographic Data Assimilation
Bruce D. Cornuelle and Peter F. Worcester (Scripps Institution of Oceanography, UCSD, 9500 Gilman Drive, La Jolla, CA 92093-0230, USA)
email: bcornuelle@ucsd.edu
Brian D. Dushaw, Bruce M. Howe, and Robert C. Spindel (APL, University of Washington, USA)
ABSTRACT
The Acoustic Mid-Ocean Dynamics Experiment (AMODE) measured time series of both reciprocal acoustic travel times and point temperatures 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. 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. The increased resolution obtained by modeling the time evolution of the field was adequate to resolve the evolving eddy field.
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.]
INTRODUCTION
Models provide a simplified dynamical hypothesis for the ocean, suggesting that the ocean evolution can be explained by limited physics and parameters. A correct model is a valuable tool for the interpolation and analysis of data, as well as practical prediction problems, but it is very difficult to obtain adequate data for testing the model, since redundant information must be available to initialize the model and independently check the forecast.
The degree to which the model can be made to fit the observations is ideally a measure of its quality. The final misfit is sensitive to many details, including the resolution of the model and the performance of the fitting algorithm, in addition to the observational error. Perhaps the most interesting source of errors in the fit is incorrect model dynamics. Unfortunately, because of the many sources of error, it is difficult to estimate the errors in then model dynamics given a set of observations. Each source of error must be quantified statistically, and the free parameters in the model must have their uncertainty similarly quantified. A model with many parameters is likely to be able to fit any limited set of observations, regardless of the dynamical validity.
