The past two decades have provided an extremely fertile ground for computational ocean acoustics. Thanks to unprecedented developments in the availability of affordable computer power, the field has evolved from being a mere analytical branch of wave propagation physics to being a mature numerical discipline with original contributions of its own. The current computational techniques can be sorted, for the sake of simplicity, into three main branches: propagation models, scattering models, and inversion methods. A brief review of the more numerically mature techniques, namely propagation models and to some extent inversion methods, follows. Pending and upcoming computational challenges are then discussed.

Acoustic propagation numerical models rely on the same underlying multi-dimensional Fourier transform approach to the wave equation. Once the implicit analytical solution to the wave equation is put in integral form, the numerical scheme chosen to perform the integration will determine the type of propagation code: the stationary phase method yields the ray approach, the method of residues yields the normal mode approach, the direct trapezoidal integration rule yields the wavenumber integration approach. The parabolic equation approach stands aside, being based on a factorization of the wave equation differential operator. The reader is referred to [2] for a full discussion. All four classes of codes correspond to specific, partially overlapping regimes determined by parameters such as frequency, range-dependence, elasticity. Provided accurate environmental information is supplied, the appropriate numerical model will predict the acoustic field within a fraction of a decibel. Inversion techniques aim at measuring environmental or source parameters given some acoustic measurements. They can be viewed as a special class of data assimilation algorithms. The first inversion technique, Ocean Acoustic Tomography, is an adaptation of medical and seismic imaging schemes; it relies on a perturbational approach and assumes a good a priori knowledge of the environment [3]. It is the acoustic equivalent of objective analysis techniques used by oceanographers. The other inversion technique, Matched -Field Processing (MFP), leverages the accuracy of modern propagation models by computing a large number of simulated signals assuming different environmental parameters [4]. It then identifies the synthetic signal most closely correlated with the measured one, therefore inferring what the true environment is. MFP has proven to be a very fertile research ground, providing a truly original approach to non-linear inversion problems such as source localization and environmental estimation.

Computational ocean acoustics now stands at a threshold in the history of the discipline. Having to a large extent solved the forward (prediction) problem for a given deterministic environment, it is now severely limited in its ability to accurately represent, store and use complex environmental information for increasingly relevant scenarios such as coastal and basin-scale operations. Further computational bottlenecks include MFP and scattering studies. Environmental uncertainty is dealt with through the use of stochastic formulations, which require significant computational resources. On the other hand, acoustic waves are the only means of remotely sensing the depths of the ocean, and can provide oceanographers and students of the ocean in general with significantly more field data than what is currently available. Much stands to be gained by coupling acoustic and oceanographic models across disciplinary boundaries. The latter will gain access to vast amounts of untapped data and improve current ocean forecasts. The former will gain the much need environmental information necessary to understand and quantify propagation mechanisms and ultimately improve signal processing performance. Some of the computational challenges ocean acoustics will face in order to achieve this multidisciplinary convergence are:

• Acoustic data assimilation. As argued above much stands to be gained by coupling acoustic and oceanographic models. It will enable concurrent progress in both disciplines. A number of issues must be resolved before even tackling the assimilation problem. Data formats and databases must be reconciled, possibly in a distributed manner in order to preserve issues of data ownsership and maintenance. The mutual resolution and sensitivities of acoustic and oceanographic models must be understood. Acoustic models, to take the simplest example, operate on a smaller scale and can be very sensitive to the sub-grid numerical noise of oceanographic model outputs. In order to achieve proper model coupling, the transfer of signal and noise between models and scales must be investigated using an adequate stochastic framework. Once models are coupled, efficient algorithms will be required in order to handle the increased computational complexity as well as the significantly increased amount of data being assimilated.
• Object-oriented computing. All numerical modeling is currently done on a procedural basis, most often in Fortran. This separation of data and processing functions, while very convenient for the direct implementation of relatively simple numerical algorithms, has major and known defaults [1]. An object-oriented methodology must be adopted when combining cross-disciplinary computational modules in order to contain unavoidable bugs and build reliable and maintainable multi-disciplinary computational systems integrating the different physical mechanisms at play, as is the case in ocean data assimilation. The use of object-oriented technique will further benefit the development of hybrid three-dimensional propagation modeling techniques by facilitating the combination of existing separate computation modules such as wavenumber integration and boundary elements. Finally, the use of features such as operator overloading enables the use of a meta-modeling language, whereby the scientist can optimally merge two data sets by simply ``adding'' them and is then free to focus on scientific questions.
• Distributed computing. Given the increasingly multidisciplinary nature of ocean sciences including acoustics, future ocean observing systems will combine a multitude of heterogeneous assets which are distributed in nature. While acoustic data might be acquired on a given node of a generalized observation network, a mobile autonomous underwater vehicle (AUV) might acquire in situ data at a different location, and oceanographic data might be gathered at a third location. AUV navigation as well as real-time data assimilation will entail a large amount of acoustic computations which some nodes, such as the AUV, might not be able to handle. One can then envision a distributed system in which a number of modeling computational tasks are performed on a service basis by the relevant nodes. This approach is also beneficial to MFP, which is an inherently parallel approach. Distributed computing will require some measure of encapsulation readily provided by object-oriented techniques.
• Software metadata. In order to facilitate large scale distributed computing as well as cross-disciplinary interaction among the various ocean sciences, knowledge about existing numerical prediction codes is required. It must list and quantify the actual modeling assets available to the community as well as guide the choice of a potentially inexperienced user. Software metadata would then assist in the localization of all existing modeling assets relevant to a given operational problem, for instance in the course of a real-time environmental assessment exercise. The appropriate model would then be used for the assimilation of data into a complete multi-disciplinary ocean model.

1. Buzzi-Ferraris, G., Scientific C++ -- Building Numerical Libraries the Object-Oriented Way, Addison-Wesley, 1993.
2. Jensen, F. B., Kuperman, W. A., Porter, M. B., and Schmidt, H., Computational Ocean Acoustics, AIP, 1994.
3. Munk, W., Worcester, P., and Wunsch, C., Ocean Acoustic Tomography,Cambridge University Press, 1995.
4. Tolstoy, A., Matched Field Processing for Underwater Acoustics, World Scientific, Singapore, 1993.