Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS)

Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part II: Applications

Ali, W.H., and P.F.J. Lermusiaux, 2024. Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part II: Applications. Journal of the Acoustical Society of America 155(1), 656-672. doi:10.1121/10.0024474

The stochastic dynamically orthogonal (DO) narrow-angle parabolic equations (NAPEs) are exemplified and their properties and capabilities are described using three new 2D stochastic range-independent and range-dependent test cases with uncertain sound speed field, bathymetry, and source location. We validate results against ground-truth deterministic analytical solutions and direct Monte Carlo predictions of acoustic pressure and transmission loss fields. We verify the stochastic convergence and computational advantages of the DO-NAPEs and discuss the differences with normal mode approaches. Results show that a single DO-NAPE simulation can accurately predict stochastic range-dependent acoustic fields and their non-Gaussian probability distributions, with computational savings of several orders of magnitude when compared to direct Monte Carlo methods. With their coupling properties and their adaptation in range to the dominant uncertainties, the DO-NAPEs are shown to predict accurate statistics, from mean and variance to multiple modes and full probability distributions, and to provide excellent reconstructed realizations, from amplitudes and phases to other specific properties of complex realization fields.

Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part I: Theory and Schemes

Ali, W.H., and P.F.J. Lermusiaux, 2024. Dynamically Orthogonal Narrow-Angle Parabolic Equations for Stochastic Underwater Sound Propagation. Part I: Theory and Schemes. Journal of the Acoustical Society of America 155(1), 640-655. doi:10.1121/10.0024466

Robust informative acoustic predictions require precise knowledge of ocean physics, bathymetry, seabed, and acoustic parameters. However, in realistic applications, this information is uncertain due to sparse and heterogeneous measurements and complex ocean physics. Efficient techniques are thus needed to quantify these uncertainties and predict the stochastic acoustic wave fields. In this work, we derive and implement new stochastic differential equations that predict the acoustic pressure fields and their probability distributions. We start from the stochastic acoustic parabolic equation (PE) and employ the instantaneously-optimal Dynamically Orthogonal (DO) equations theory. We derive stochastic DO-PEs that dynamically reduce and march the dominant multi-dimensional uncertainties respecting the nonlinear governing equations and non-Gaussian statistics. We develop the dynamical reduced-order DO-PEs theory for the Narrow-Angle PE (NAPE) and implement numerical schemes for discretizing and integrating the stochastic acoustic fields.

A Wide-Area Deep Ocean Floor Mapping System: Design and Sea Tests

Ryu, P., D. Brown, K. Arsenault, B. Cho, A. March, W.H. Ali, A. Charous, and P.F.J. Lermusiaux, 2023. A Wide-Area Deep Ocean Floor Mapping System: Design and Sea Tests. Geomatics 3(1), 290–311. doi:10.3390/geomatics3010016. Special issue "Advances in Ocean Mapping and Nautical Cartography."

Mapping the seafloor in the deep ocean is currently performed using sonar systems on surface vessels (low-resolution maps) or undersea vessels (high-resolution maps). Surface-based mapping can cover a much wider search area and is not burdened by the complex logistics required for deploying undersea vessels. However, practical size constraints for a tow body or hull-mounted sonar array result in limits in beamforming and imaging resolution. For cost-effective high-resolution mapping of the deep ocean floor from the surface, a mobile wide-aperture sparse array with subarrays distributed across multiple autonomous surface vessels (ASVs) has been designed. Such a system could enable a surface-based sensor to cover a wide area while achieving high-resolution bathymetry, with resolution cells on the order of 1 m² at a 6 km depth. For coherent 3D imaging, such a system must dynamically track the precise relative position of each boat’s sonar subarray through ocean-induced motions, estimate water column and bottom reflection properties, and mitigate interference from the array sidelobes. Sea testing of this core sparse acoustic array technology has been conducted, and planning is underway for relative navigation testing with ASVs capable of hosting an acoustic subarray.

Multiscale multiphysics data-informed modeling for three-dimensional ocean acoustic simulation and prediction

Duda, T.F., Y.-T. Lin, A.E. Newhall, K.R. Helfrich, J.F. Lynch, W.G. Zhang, P.F.J. Lermusiaux, and J. Wilkin, 2019. Multiscale Multiphysics Data-Informed Modeling for Three-Dimensional Ocean Acoustic Simulation and Prediction. Journal of the Acoustical Society of America, 146(3), 1996–2015. doi:10.1121/1.5126012

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.

Many Task Computing for Real-Time Uncertainty Prediction and Data Assimilation in the Ocean

Evangelinos, C., P.F.J. Lermusiaux, J. Xu, P.J. Haley, and C.N. Hill, 2011. Many Task Computing for Real-Time Uncertainty Prediction and Data Assimilation in the Ocean. IEEE Transactions on Parallel and Distributed Systems, Special Issue on Many-Task Computing, I. Foster, I. Raicu and Y. Zhao (Guest Eds.), 22, doi: 10.1109/TPDS.2011.64.

Uncertainty prediction for ocean and climate predictions is essential for multiple applications today. Many-Task Computing can play a significant role in making such predictions feasible. In this manuscript, we focus on ocean uncertainty prediction using the Error Subspace Statistical Estimation (ESSE) approach. In ESSE, uncertainties are represented by an error subspace of variable size. To predict these uncertainties, we perturb an initial state based on the initial error subspace and integrate the corresponding ensemble of initial conditions forward in time, including stochastic forcing during each simulation. The dominant error covariance (generated via SVD of the ensemble) is used for data assimilation. The resulting ocean fields are used as inputs for predictions of underwater sound propagation. ESSE is a classic case of Many Task Computing: It uses dynamic heterogeneous workflows and ESSE ensembles are data intensive applications. We first study the execution characteristics of a distributed ESSE workflow on a medium size dedicated cluster, examine in more detail the I/O patterns exhibited and throughputs achieved by its components as well as the overall ensemble performance seen in practice. We then study the performance/usability challenges of employing Amazon EC2 and the Teragrid to augment our ESSE ensembles and provide better solutions faster.

Coupled Ocean-Acoustic prediction of transmission loss in a continental shelfbreak region: predictive skill, uncertainty quantification and dynamical sensitivities

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, we quantify the dynamical causes and uncertainties of striking differences in acoustic transmission data collected on the shelf and shelfbreak in the northeastern Taiwan region within the context of the 2008 Quantifying, Predicting, and Exploiting Uncertainty (QPE 2008) pilot experiment. To do so, we employ our coupled oceanographic (4-D) and acoustic (Nx2-D) modeling systems with ocean data assimilation and a best-fit depth-dependent geoacoustic model. Predictions are compared to the measured acoustic data, showing skill. Using an ensemble approach, we study the sensitivity of our results to uncertainties in several factors, including geoacoustic parameters, bottom layer thickness, bathymetry, and ocean conditions. We find that the lack of signal received on the shelfbreak is due to a 20-dB increase in transmission loss (TL) caused by bottom trapping of sound energy during up-slope transmissions over the complex and deeper bathymetry. Sensitivity studies on sediment properties show larger but isotropic TL variations on the shelf and smaller but more anisotropic TL variations over the shelfbreak. Sediment sound-speed uncertainties affect the shape of the probability density functions of the TLs more than uncertainties in sediment densities and attenuations. Diverse thicknesses of sediments lead to only limited effects on the TL. The small bathymetric data uncertainty is modeled and also leads to small TL variations. We discover that the initial transport conditions in the Taiwan Strait can affect acoustic transmissions downstream more than 100 km away, especially above the shelfbreak. Simulations also reveal internal tides and we quantify their spatial and temporal effects on the ocean and acoustic fields. One type of predicted waves are semidiurnal shelfbreak internal tides propagating up-slope with wavelengths around 40-80 km, horizontal phase speeds of 0.5-1 m/s, and vertical peak-to-peak displacements of isotherms of 20-60 m. These waves lead to variations of broadband TL estimates over 5-6-km range that are more isotropic and on bearing average larger (up to 5-8-dB amplitudes) on the shelf than on the complex shelfbreak where the TL varies rapidly with bearing angles.

Merging Multiple Partial-Depth Data Time Series Using Objective Empirical Orthogonal Function Fitting

Lin, Y.-T., A.E. Newhall, T.F. Duda, P.F. J. Lermusiaux and P.J. Haley, Jr., 2010. Merging Multiple Partial-Depth Data Time Series Using Objective Empirical Orthogonal Function Fitting. IEEE Transactions, Journal of Oceanic Engineering. 35(4) 710-721. doi:10.1109/JOE.2010.2052875.

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.

Automated Sensor Networks to Advance Ocean Science

Schofield, O., S. Glenn, J. Orcutt, M. Arrott, M. Meisinger, A. Gangopadhyay, W. Brown, R. Signell, M. Moline, Y. Chao, S. Chien, D. Thompson, A. Balasuriya, P.F.J. Lermusiaux and M. Oliver, 2010. Automated Sensor Networks to Advance Ocean Science. EOS, Vol. 91, No. 39, 28 September 2010.

Oceanography is evolving from a ship-based expeditionary science to a distributed, observatory- based approach in which scientists continuously interact with instruments in the field. These new capabilities will facilitate the collection of long- term time series while also providing an interactive capability to conduct experiments using data streaming in real time. The U.S. National Science Foundation has funded the Ocean Observatories Initiative (OOI), which over the next 5 years will deploy infrastructure to expand scientists’ ability to remotely study the ocean. The OOI is deploying infrastructure that spans global, regional, and coastal scales. A global component will address planetary- scale problems using a new network of moored buoys linked to shore via satellite telecommunications. A regional cabled observatory will “wire” a single region in the northeastern Pacific Ocean with a high-speed optical and power grid. The coastal component will expand existing coastal observing assets to study the importance of high-frequency forcing on the coastal environment. These components will be linked by a robust cyberinfrastructure (CI) that will integrate marine observatories into a coherent system of systems. This CI infrastructure will also provide a Web- based social network enabled by real- time visualization and access to numerical model information, to provide the foundation for adaptive sampling science. Thus, oceanographers will have access to automated machine-to-machine sensor networks that can be scalable to increase in size and incorporate new technology for decades to come. A case study of this CI in action shows how a community of ocean scientists and engineers located throughout the United States at 12 different institutions used the automated ocean observatory to address daily adaptive science priorities in real time.

At-sea Real-time Coupled Four-dimensional Oceanographic and Acoustic Forecasts during Battlespace Preparation 2007

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.

Systems capable of forecasting ocean properties and acoustic performance in the littoral ocean are becoming a useful capability for scientific and operational exercises. The coupling of a data-assimilative nested ocean modeling system with an acoustic propagation modeling system was carried out at sea for the first time, within the scope of Battlespace Preparation 2007 (BP07) that was part of Marine Rapid Environmental Assessment (MREA07) exercises. The littoral region for our studies was southeast of the island of Elba ( Italy) in the Tyrrhenian basin east of Corsica and Sardinia. During BP07, several vessels collected in situ ocean data, based in part on recommendations from oceanographic forecasts. The data were assimilated into a four- dimensional high-resolution ocean modeling system. Sound-speed forecasts were then used as inputs for bearing- and range-dependent acoustic propagation forecasts. Data analyses are carried out and the set-up of the coupled oceanographic-acoustic system as well as the results of its real-time use are described. A significant finding is that oceanographic variability can considerably influence acoustic propagation properties, including the probability of detection, even in this apparently quiet region around Elba. This strengthens the importance of coupling at-sea acoustic modeling to real-time ocean forecasting. Other findings include the challenges involved in downscaling basin-scale modeling systems to high-resolution littoral models, especially in the Mediterranean Sea. Due to natural changes, global human activities and present model resolutions, the assimilation of synoptic regional ocean data is recommended in the region.

Acoustically Focused Adaptive Sampling and On-board Routing for Marine Rapid Environmental Assessment

Wang, D., P.F.J. Lermusiaux, P.J. Haley, D. Eickstedt, W.G. Leslie and H. Schmidt, 2009. Acoustically Focused Adaptive Sampling and On-board Routing for Marine Rapid Environmental Assessment. Special issue of 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, S393-S407, doi: 10.1016/j.jmarsys.2009.01.037.

Variabilities in the coastal ocean environment span a wide range of spatial and temporal scales. From an acoustic viewpoint, the limited oceanographic measurements and today’s ocean computational capabilities are not always able to provide oceanic-acoustic predictions in high-resolution and with enough accuracy. Adaptive Rapid Environmental Assessment (AREA) is an adaptive sampling concept being developed in connection with the emergence of Autonomous Ocean Sampling Networks and interdisciplinary ensemble predictions and adaptive sampling via Error Subspace Statistical Estimation (ESSE). By adaptively and optimally deploying in situ sampling resources and assimilating these data into coupled nested ocean and acoustic models, AREA can dramatically improve the estimation of ocean fields that matter for acoustic predictions. These concepts are outlined and a methodology is developed and illustrated based on the Focused Acoustic Forecasting-05 (FAF05) exercise in the northern Tyrrhenian sea. The methodology first couples the data-assimilative environmental and acoustic propagation ensemble modeling. An adaptive sampling plan is then predicted, using the uncertainty of the acoustic predictions as input to an optimization scheme which finds the parameter values of autonomous sampling behaviors that optimally reduce this forecast of the acoustic uncertainty. To compute this reduction, the expected statistics of unknown data to be sampled by different candidate sampling behaviors are assimilated. The predicted-optimal parameter values are then fed to the sampling vehicles. A second adaptation of these parameters is ultimately carried out in the water by the sampling vehicles using onboard routing, in response to the real ocean data that they acquire. The autonomy architecture and algorithms used to implement this methodology are also described. Results from a number of real-time AREA simulations using data collected during the Focused Acoustic Forecasting (FAF05) exercise are presented and discussed for the case of a single Autonomous Underwater Vehicle (AUV). For FAF05, the main AREA-ESSE application was the optimal tracking of the ocean thermocline based on ocean-acoustic ensemble prediction, adaptive sampling plans for vertical Yo-Yo behaviors and subsequent onboard Yo-Yo routing.

Path Planning Methods for Adaptive Sampling of Environmental and Acoustical Ocean Fields

Yilmaz, N.K., C. Evangelinos, N.M. Patrikalakis, P.F.J. Lermusiaux, P.J. Haley, W.G. Leslie, A.R. Robinson, D. Wang and H. Schmidt, 2006a. Path Planning Methods for Adaptive Sampling of Environmental and Acoustical Ocean Fields, Oceans 2006, 6pp, Boston, MA, 18-21 Sept. 2006, doi: 10.1109/OCEANS.2006.306841.

Adaptive sampling aims to predict the types and locations of additional observations that are most useful for specific objectives, under the constraints of the available observing network. Path planning refers to the computation of the routes of the assets that are part of the adaptive component of the observing network. In this paper, we present two path planning methods based on Mixed Integer Linear Programming (MILP). The methods are illustrated with some examples based on environmental ocean fields and compared to highlight their strengths and weaknesses. The stronger method is further demonstrated on a number of examples covering multi-vehicle and multi-day path planning, based on simulations for the Monterey Bay region. The framework presented is powerful and flexible enough to accommodate changes in scenarios. To demonstrate this feature, acoustical path planning is also discussed.

Uncertainty Estimation and Prediction for Interdisciplinary Ocean Dynamics

Lermusiaux, P.F.J., 2006. Uncertainty Estimation and Prediction for Interdisciplinary Ocean Dynamics. Refereed manuscript, Special issue on "Uncertainty Quantification". J. Glimm and G. Karniadakis, Eds. Journal of Computational Physics, 217, 176-199. doi: 10.1016/j.jcp.2006.02.010.

Scientific computations for the quantification, estimation and prediction of uncertainties for ocean dynamics are developed and exemplified. Primary characteristics of ocean data, models and uncertainties are reviewed and quantitative data assimilation concepts defined. Challenges involved in realistic data-driven simulations of uncertainties for four-dimensional interdisciplinary ocean processes are emphasized. Equations governing uncertainties in the Bayesian probabilistic sense are summarized. Stochastic forcing formulations are introduced and a new stochastic-deterministic ocean model is presented. The computational methodology and numerical system, Error Subspace Statistical Estimation, that is used for the efficient estimation and prediction of oceanic uncertainties based on these equations is then outlined. Capabilities of the ESSE system are illustrated in three data-assimilative applications: estimation of uncertainties for physical-biogeochemical fields, transfers of ocean physics uncertainties to acoustics, and real-time stochastic ensemble predictions with assimilation of a wide range of data types. Relationships with other modern uncertainty quantification schemes and promising research directions are discussed.