RAM to Navy Standard Parabolic Equation: Transition from Research to Fleet Acoustic Model

R.A. Zingarelli and D.B. King
Acoustics Division

Introduction: The Navy Standard Parabolic Equation (NSPE) model is an amalgam of research-oriented underwater acoustic propagation algorithms based on the parabolic equation (PE) approach to solving the forward acoustic wave equation, with various features and input/output routines required for operational use. NSPE originated in the 1980s to fill the need for a standardized low-frequency deep-water acoustic model. In early versions, a split-step Fourier1 solution method (SSF) was combined with an input routine that allowed use of bottom database parameters. Routines that simulate rough wave or ice-covered surfaces, allow directed sound sources, and emulate broadband and beamforming receiver systems were also added.

An assumption inherent in the SSF approach is that there are no vertical discontinuities in the propagation medium. By the 1990s, the emphasis in Naval research had shifted to shallow waters, where interaction with the ocean bottom is more significant and the SSF's water-sediment boundary and single bottom layer approximations are no longer valid. Fortunately, by this time research efforts had produced several other PE models that could numerically handle these discontinuities and provide reliable predictions in shallow water.

The Research Model: One research and development (R&D) model that showed outstanding promise was the Range-dependent Acoustic Model2 (RAM), developed at NRL by Michael Collins. This model is based on a user-selected multiple-term Padé approximation of the PE operator. Because this solution allows range steps much greater than the acoustic wavelength and does not require fine vertical gridding, RAM is a very fast research model.3 Additionally, RAM's grid can be tuned to smoothly trade accuracy and speed as the operational situation requires. Finally, several parallelization methods are applicable, allowing further speed improvements. The odyssey of this model from R&D to operational status represents a first for the Navy because it was done entirely within NRL, with the R&D developer (Collins) playing a key role. The success of this effort establishes a roadmap for future Navy operational models.

Integration and Testing: With RAM's accuracy and speed documented in the peer-reviewed R&D literature, the first step in incorporating it into the operational framework was confirming that the model could work with all necessary features. Some of these required substantial modification; others were simply subroutines that provided specific features.

A major change was in the ocean bottom profile referencing. Originally, bottom layering was indexed relative to the ocean surface within the model; however, Navy databases index relative to the seafloor. Adapting to this convention required shifting the model's internal indexing with bathymetry changes. Collins developed a version of RAM with this capability.

Three items that were easily added were beam sources, seawater volume attenuation, and rough surface losses. Beam sources are accommodated by including them with the original omnidirectional starter in a conditional statement. Volume attenuation was added by including a small complex absorption value in the seawater wavenumber array. Rough surfaces are treated by subroutine calls at each range step that either reduce the field intensity in a surface layer, or directly simulate using conformal mapping.

Another part of incorporating RAM was developing a routine to read from the existing input format, switch on options, and generate an environmental stream for RAM to use. To accomplish this, the entire input is read, then a profile is built at each range where there is a change in the water, bottom, or bathymetry. Figure 11 depicts these additions.

Testing, Optimization, and Formal Acceptance: New capabilities were continuously tested as they were added during development. The completed model was tested using a set of cases designed to cause each routine to be called and verified. Finally the model was tested using 840 environments extracted at random from a shallow-water database to comprehensively simulate real-world use. Once agreement with reference solutions was reached, the grid parameters were repeatedly relaxed and the cases re-run until the model produced acceptable answers in minimum runtime. Testing completed, the model and documentation were submitted to the Oceanographic and Atmospheric Master Library (OAML) secretary for formal review, chiefly to ensure that the added features were correctly implemented. The total process, culminating in NSPE version 5.0, was completed in 18 months.

Fig 11
Acoustic simulation in a simple ocean environment, depicting several of the features required in a Naval operational model: beam source, wind-driven sea surface losses on the first reflection, and loss-vs-angle ocean bottom treatment. Also present but less evident in the simulation are seawater volume attenuation and spherical Earth corrections. Source frequency, angle, and beamwidth are 250 Hz, 5 degrees, and 1.5 degree respectively; water is isovelocity at 1500 m/s and depth is 1000 meters; windspeed is 20 m/s; ocean bottom parameters approximate soft rock.

Continuing Development: Initial comments from the user community were favorable regarding model capabilities, but mixed regarding input/output formats. Complete file compatibility with previous versions had been retained, but at the price of keeping the old punchcard-based input format. In the succeeding version (5.1), we updated the input to a more readable list-based form, and supplied a conversion program for the older format. Runtime is always of concern, and we were able to reduce runtimes by a factor of 5 through several optimizations. Future versions will have further improvements including environmentally sensitive grid tuning and improved indexing techniques. Capabilities in development include improved surface treatments, faster broadband algorithms, and profile range interpolation.

To summarize, NSPE is now a robust and capable model that incorporates one of the fastest and most accurate underwater acoustic models, viz., RAM. In essence, both the ocean acoustics R&D community and the Navy operational community are using the same PE model. The overall NSPE program and file structure have been revamped to modern, maintainable standards. Tools and techniques for upgrading, evaluating, and optimizing newer versions have been developed. Work remains to be done, and the foundation provided by RAM and NSPE 5.1 provide a strong starting point.

Acknowledgments: A special acknowledgment is given to the CNO N096 Standing Acquisition and Coordinating Team (SACT) and the Rapid Transition Process (RTP) program for added support in transitioning the RAM model into NSPE 5.1.

[Sponsored by ONR and SPAWAR]


1 H.K. Brock, "The AESD Parabolic Equation Model," NORDA Technical Note 12, Naval Research Laboratory, Stennis Space Center, MS, January 1978.
2 M.D. Collins, "Generalization of the Split-Step Pade," J. Acoust. Soc. Am. 96, 382-385 (1994).
3 M.D. Collins, R. J. Cederberg, D.B. King, and S.A. Chin-Bing, "Comparison of Algorithms for Solving Parabolic Wave Equations," J. Acoust. Soc. Am. 100, 178-182 (1996)