The uncertainties in the predicted acoustic wavefield associated with the transmission of low- frequency sound from the continental slope, through the shelfbreak front, onto the continental shelf are examined. The locale and sensor geometry being investigated is that of the New England continental shelfbreak with a moored low-frequency sound source on the slope. Our method of investigation employs computational fluid mechanics coupled with computational acoustics. The coupled methodology for uncertainty estimation is that of Error Subspace Statistical Estimation. Specifically, based on observed oceanographic data during the 1996 Shelfbreak Primer Experiment, the Harvard University primitive-equation ocean model is initialized with many realizations of physical fields and then integrated to produce many realizations of a five-day regional forecast of the sound speed field. In doing so, the initial physical realizations are obtained by perturbing the physical initial conditions in statistical accord with a realistic error subspace. The different forecast realizations of the sound speed field are then fed into a Naval Postgraduate School coupled-mode sound propagation model to produce realizations of the predicted acoustic wavefield in a vertical plane across the shelfbreak frontal zone. The combined ocean and acoustic results from this Monte Carlo simulation study provide insights into the relations between the uncertainties in the ocean and acoustic estimates. The modeled uncertainties in the transmission loss estimate and their relations to the error statistics in the ocean estimate are discussed.

The estimation of oceanic environmental and acoustical fields is considered as a single coupled data assimilation problem. The four-dimensional data assimilation methodology employed is Error Subspace Statistical Estimation. Environmental fields and their dominant uncertainties are predicted by an ocean dynamical model and transferred to acoustical fields and uncertainties by an acoustic propagation model. The resulting coupled dominant uncertainties define the error subspace. The available physical and acoustical data are then assimilated into the predicted fields in accord with the error subspace and all data uncertainties. The criterion for data assimilation is presently to correct the predicted fields such that the total error variance in the error subspace is minimized. The approach is exemplified for the New England continental shelfbreak region, using data collected during the 1996 Shelfbreak Primer Experiment. The methodology is discussed, computational issues are outlined and the assimilation of model-simulated acoustical data is carried out. Results are encouraging and provide some insights into the dominant variability and uncertainty properties of acoustical fields.

The efficient interdisciplinary 4D data assimilation with nonlinear models via Error Subspace Statistical Estimation (ESSE) is reviewed and exemplified. ESSE is based on evolving an error subspace, of variable size, that spans and tracks the scales and processes where the dominant errors occur. A specific focus here is the use of ESSE in interdisciplinary smoothing which allows the correction of past estimates based on future data, dynamics and model errors. ESSE is useful for a wide range of purposes which are illustrated by three investigations: (i) smoothing estimation of physical ocean fields in the Eastern Mediterranean, (ii) coupled physical-acoustical data assimilation in the Middle Atlantic Bight shelfbreak, and (iii) coupled physical-biological smoothing and dynamics in Massachusetts Bay.

Data assimilation is a modern methodology of relating natural data and dynamical models. The general dynamics of a model is combined or melded with a set of observations. All dynamical models are to some extent approximate, and all data sets are finite and to some extent limited by error bounds. The purpose of data assimilation is to provide estimates of nature which are better estimates than can be obtained by using only the observational data or the dynamical model. There are a number of specific approaches to data assimilation which are suitable for estimation of the state of nature, including natural parameters, and for evaluation of the dynamical approximations. Progress is accelerating in understanding the dynamics of real ocean biological- physical interactive processes. Although most biophysical processes in the sea await discovery, new techniques and novel interdisciplinary studies are evolving ocean science to a new level of realism. Generally, understanding proceeds from a quantitative description of four-dimensional structures and events, through the identification of specific dynamics, to the formulation of simple generalizations. The emergence of realistic interdisciplinary four-dimensional data assimilative ocean models and systems is contributing significantly and increasingly to this progress.

The effects of a priori parameters on the error subspace estimation and mapping methodology introduced by P. F. J. Lermusiaux et al. is investigated. The approach is three-dimensional, multivariate, and multiscale. The sensitivities of the subspace and a posteriori fields to the size of the subspace, scales considered, and nonlinearities in the dynamical adjustments are studied. Applications focus on the mesoscale to subbasin-scale physics in the northwestern Levantine Sea during 10 February-15 March and 19 March-16 April 1995. Forecasts generated from various analyzed fields are compared to in situ and satellite data. The sensitivities to size show that the truncation to a subspace is efficient. The use of criteria to determine adequate sizes is emphasized and a backof- the-envelope rule is outlined. The sensitivities to scales confirm that, for a given region, smaller scales usually require larger subspaces because of spectral redness. However, synoptic conditions are also shown to strongly influence the ordering of scales. The sensitivities to the dynamical adjustment reveal that nonlinearities can modify the variability decomposition, especially the dominant eigenvectors, and that changes are largest for the features and regions with high shears. Based on the estimated variability variance fields, eigenvalue spectra, multivariate eigenvectors and (cross)-covariance functions, dominant dynamical balances and the spatial distribution of hydrographic and velocity characteristic scales are obtained for primary regional features. In particular, the Ierapetra Eddy is found to be close to gradient-wind balance and coastal-trapped waves are anticipated to occur along the northern escarpment of the basin.