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Three-dimensional (3D) underwater sound field computations have been used for a few decades to understand sound propagation effects above sloped seabeds and in areas with strong 3D temperature and salinity variations. For an approximate simulation of effects in nature, the necessary 3D sound-speed field can be made from snapshots of temperature and salinity from an operational data-driven regional ocean model. However, these models invariably have resolution constraints and physics approximations that exclude features that can have strong effects on acoustics, example features being strong submesoscale fronts and nonhydrostatic nonlinear internal waves (NNIWs). Here, work to predict NNIW fields to improve 3D acoustic forecasts using an NNIW model nested in a tide-inclusive data-assimilating regional model is reported. The work was initiated under the Integrated Ocean Dynamics and Acoustics project. The project investigated ocean dynamical processes that affect important details of sound-propagation, with a focus on those with strong intermittency (high kurtosis) that are challenging to predict deterministically. Strong internal tides and NNIW are two such phenomena, with the former being precursors to NNIW, often feeding energy to them. Successful aspects of the modeling are reported along with weaknesses and unresolved issues identified in the course of the work.

Duda T.F., W.G. Zhang, K.R. Helfrich, A.E. Newhall, Y.-T. Lin, J.F. Lynch, P.F.J. Lermusiaux, P.J. Haley Jr., J. Wilkin, 2014. *Issues and Progress in the Prediction of Ocean Submesoscale Features and Internal Waves*. OCEANS'14 MTS/IEEE.

Data-constrained dynamical ocean modeling for the purpose of detailed forecasting and prediction continues to evolve and improve in quality. Modeling methods and computational capabilities have each improved. The result is that mesoscale phenomena can be modeled with skill, given sufficient data. However, many submesoscale features are less well modeled and remain largely unpredicted from a deterministic event standpoint, and possibly also from a statistical property standpoint. A multi-institution project is underway with goals of uncovering more of the details of a few submesoscale processes, working toward better predictions of their occurrence and their variability. A further component of our project is application of the new ocean models to ocean acoustic modeling and prediction. This paper focuses on one portion of the ongoing work: Efforts to link nonhydrostatic-physics models of continental-shelf nonlinear internal wave evolution to data-driven regional models. Ocean front-related effects are also touched on.

Regional ocean models have long been integrated with acoustic propagation
and scattering models, including work in the 1990s by Robinson and Lee. However, the
dynamics in these models has been not inclusive enough to represent submesoscale
features that are now known to be very important acoustically. The features include
internal waves, thermohaline intrusions, and details of fronts. In practice, regional models
predict internal tides at many locations, but the nonlinear steepening of these waves and
their conversion to short nonlinear waves is often improperly modeled, because
computationally prohibitive nonhydrostatic pressure is needed. To include the small-scale
internal waves of tidal origin, a nested hybrid model is under development. The approach
is to extract long-wavelength internal tide wave information from tidally forced regional
models, use ray methods or mapping methods to determine internal-tide propagation
patterns, and then solve two-dimensional high-resolution nonhydrostatic wave models to
“fill-in” the internal wave details. The resulting predicted three-dimensional environment
is then input to a fully three-dimensional parabolic equation acoustic code. The output
from the nested ocean model, run in hindcast mode, is to be compared to field data from
the Shallow Water 2006 (SW06) experiment to test and ground truth purposes

Colin, M.E.G.D., T.F. Duda, L.A. te Raa, T. van Zon, P.J. Haley, Jr., P.F.J. Lermusiaux, W.G. Leslie, C. Mirabito, F.P.A. Lam, A.E. Newhall, Y.-T. Lin, J.F. Lynch, 2013. *Time-Evolving Acoustic Propagation Modeling in a Complex Ocean Environment*, Proceedings of OCEANS - Bergen, 2013 MTS/IEEE , vol., no., pp.1,9, 10-14 June 2013, doi: 10.1109/OCEANS-Bergen.2013.6608051.

During naval operations, sonar performance estimates often need to be computed in-situ with limited environmental information. This calls for the use of fast acoustic propagation models. Many naval operations are carried out in challenging and dynamic environments. This makes acoustic propagation and sonar performance behavior particularly complex and variable, and complicates prediction. Using data from a field experiment, we have investigated the accuracy with which acoustic propagation loss (PL) can be predicted, using only limited modeling capabilities. Environmental input parameters came from various sources that may be available in a typical naval operation.

The outer continental shelf shallow-water experimental area featured internal tides, packets of nonlinear internal waves, and a meandering water mass front. For a moored source/receiver pair separated by 19.6 km, the acoustic propagation loss for 800 Hz pulses was computed using the peak amplitude. The variations in sound speed translated into considerable PL variability of order 15 dB. Acoustic loss modeling was carried out using a data-driven regional ocean model as well as measured sound speed profile data for comparison. The acoustic model used a two-dimensional parabolic approximation (vertical and radial outward wavenumbers only). The variance of modeled propagation loss was less than that measured. The effect of the internal tides and sub-tidal features was reasonably well modeled; these made use of measured sound speed data. The effects of nonlinear waves were not well modeled, consistent with their known three-dimensional effects but also with the lack of measurements to initialize and constrain them.

Duda, T.F., Y.-T. Lin, W.G. Zhang, B.D. Cornuelle, P.F.J. Lermusiaux, 2011. *Computational Studies of 3D Ocean sound fields in areas of complex seafloor topography and active ocean dynamics*. Proceedings of the 10th International Conference on Theoretical and Computational Acoustics, NTU, Taiwan, 12pp.

Lermusiaux, P.F.J., J. Xu, C.F. Chen, S. Jan, L.Y. Chiu and Y.-J. Yang, 2010. *Coupled Ocean-Acoustic prediction of transmission loss in a continental shelfbreak region: predictive skill, uncertainty quantification and dynamical sensitivities*. IEEE Transactions, Journal of Oceanic Engineering, 35(4) 895-916. doi:10.1109/JOE.2010.2068611.

In this paper, a method for merging partial overlap- ping time series of ocean profiles into a single time series of profiles using empirical orthogonal function (EOF) decomposition with the objective analysis is presented. The method is used to handle internal waves passing two or more mooring locations from multiple directions, a situation where patterns of variability cannot be accounted for with a simple time lag. Data from one mooring are decomposed into linear combination of EOFs. Objective analysis using data from another mooring and these patterns is then used to build the necessary profile for merging the data, which is a linear combination of the EOFs. This method is applied to temperature data collected at a two vertical moorings in the 2006 New Jersey Shelf Shallow Water Experiment (SW06). Resulting profiles specify conditions for 35 days from sea surface to seafloor at a primary site and allow for reliable acoustic propagation modeling, mode decomposition, and beamforming.

Lam, F.P, P.J. Haley, Jr., J. Janmaat, P.F.J. Lermusiaux, W.G. Leslie, and M.W. Schouten, 2009. *At-sea Real-time Coupled Four-dimensional Oceanographic and Acoustic Forecasts during Battlespace Preparation 2007*. Special issue of the Journal of Marine Systems on "Coastal processes: challenges for monitoring and prediction", Drs. J.W. Book, Prof. M. Orlic and Michel Rixen (Guest Eds.), 78, S306-S320, doi: 10.1016/j.jmarsys.2009.01.029.

Today’s situational awareness requirements in the undersea environment present severe challenges for acoustic communication systems. Acoustic propagation through the ocean environment severely limits the capacity of existing underwater communication systems. Specifically, the presence of internal waves coupled with the ocean sound channel creates a stochastic field that introduces deep fades and significant intersymbol interference (ISI) thereby limiting reliable communication to low data rates. In this paper we present a communication architecture that optimally predistorts the acoustic wave via spatial modulation and detects the acoustic wave with optimal spatial recombination to maximize reliable information throughput. This effectively allows the system to allocate its power to the most efficient propagation modes while mitigating ISI. Channel state information is available to the transmitter through low rate feedback. New results include the asymptotic distribution of singular values for a large number of apertures. Further, we present spatial modulation at the transmitter and spatial recombination at the receiver that asymptotically minimize bit error rate (BER). We show that, in many applications, the number of apertures can be made large enough so that asymptotic results approximate finite results well. Additionally, we show that the interference noise power is reduced proportional to the inverse of the number of receive apertures. Finally, we calculate the asymptotic BER for the sparse aperture acoustic system.

Xu, J., P.F.J. Lermusiaux, P.J. Haley Jr., W.G. Leslie and O.G. Logutov, 2008. *Spatial and Temporal Variations in Acoustic propagation during the PLUSNet-07 Exercise in Dabob Bay. Acoustical Society of America, Proceedings of Meetings on Acoustics (POMA)*. 155th Meeting, Vol. 4. 11pp. doi: 10.1121/1.2988093.

Robinson, A.R. and P.F.J. Lermusiaux, 2004. *Prediction Systems with Data Assimilation for Coupled Ocean Science and Ocean Acoustics*, Proceedings of the Sixth International Conference on Theoretical and Computational Acoustics (A. Tolstoy, et al., editors), World Scientific Publishing, 325-342. Refereed invited Keynote Manuscript.

Lermusiaux, P.F.J., C.-S. Chiu and A.R. Robinson, 2002. *Modeling Uncertainties in the Prediction of the Acoustic Wavefield in a Shelfbreak Environment*. Refereed invited Manuscript, Proceedings of the 5th International conference on theoretical and computational acoustics, May 21-25, 2001. (Eds: E.-C. Shang, Q. Li and T.F. Gao), World Scientific Publishing Co., 191-200.