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.

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.

A new generation of efficient parallel, multi-scale, and interdisciplinary ocean models is required for better understanding and accurate predictions. The purpose of this thesis is to quantitatively identify promising numerical methods that are suitable to such predictions. In order to fulfill this purpose, current efforts towards creating new ocean models are reviewed, an understanding of the most promising methods used by other researchers is developed, the most promising existing methods are studied and applied to idealized cases, new methods are incubated and evaluated by solving test problems, and important numerical issues related to efficiency are examined. The results of other research groups towards developing the second generation of ocean models are first reviewed. Next, the Discontinuous Galerkin (DG) method for solving advection-diffusion problems is described, including a discussion on schemes for solving higher order derivatives. The discrete formulation for advection-diffusion problems is detailed and implementation issues are discussed. The Hybrid Discon- tinuous Galerkin (HDG) Finite Element Method (FEM) is identified as a promising new numerical scheme for ocean simulations. For the first time, a DG FEM scheme is used to solve ocean biogeochemical advection-diffusion-reaction equations on a two- dimensional idealized domain, and p-adaptivity across constituents is examined. Each aspect of the numerical solution is examined separately, and p-adaptive strategies are explored. Finally, numerous solver-preconditioner combinations are benchmarked to identify an efficient solution method for inverting matrices, which is necessary for implicit time integration schemes. From our quantitative incubation of numerical schemes, a number of recommendations on the tools necessary to solve dynamical equations for multiscale ocean predictions are provided.

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.

A fundamental requirement in realistic computational geophysical fluid dynamics is the optimal estimation of gridded fields and of spatial-temporal scales directly from the spatially irregular and multivariate data sets that are collected by varied instruments and sampling schemes. In this work, we derive and utilize new schemes for the mapping and dynamical inference of ocean fields in complex multiply-connected domains, study the computational properties of our new mapping schemes, and derive and investigate new schemes for adaptive estimation of spatial and temporal scales.

Objective Analysis (OA) is the statistical estimation of fields using the Bayesian- based Gauss-Markov theorem, i.e. the update step of the Kalman Filter. The existing multi-scale OA approach of the Multidisciplinary Simulation, Estimation and Assimilation System consists of the successive utilization of Kalman update steps, one for each scale and for each correlation across scales. In the present work, the approach is extended to field mapping in complex, multiply-connected, coastal regions and archipelagos. A reasonably accurate correlation function often requires an estimate of the distance between data and model points, without going across complex land- forms. New methods for OA based on estimating the length of optimal shortest sea paths using the Level Set Method (LSM) and Fast Marching Method (FMM) are derived, implemented and utilized in general idealized and realistic ocean cases. Our new methodologies could improve widely-used gridded databases such as the climatological gridded fields of the World Ocean Atlas (WOA) since these oceanic maps were computed without accounting for coastline constraints. A new FMM-based methodology for the estimation of absolute velocity under geostrophic balance in complicated domains is also outlined. Our new schemes are compared with other approaches, including the use of stochastically forced differential equations (SDE). We find that our FMM-based scheme for complex, multiply-connected, coastal regions is more efficient and accurate than the SDE approach. We also show that the field maps obtained using our FMM-based scheme do not require postprocessing (smoothing) of fields. The computational properties of the new mapping schemes are studied in detail. We find that higher-order schemes improve the accuracy of distance estimates. We also show that the covariance matrices we estimate are not necessarily positive definite because the Weiner Khinchin and Bochner relationships for positive definiteness are only valid for convex simply-connected domains. Several approaches to overcome this issue are discussed and qualitatively evaluated. The solutions we propose include introducing a small process noise or reducing the covariance matrix based on the dominant singular value decomposition. We have also developed and utilized novel methodologies for the adaptive estimation of spatial-temporal scales from irregularly spaced ocean data. The three novel methodologies are based on the use of structure functions, short term Fourier transform and second generation wavelets. To our knowledge, this is the first time that adaptive methodologies for the spatial-temporal scale estimation are proposed. The ultimate goal of all these methods would be to create maps of spatial and temporal scales that evolve as new ocean data are fed to the scheme. This would potentially be a significant advance to the ocean community for better understanding and sampling of ocean processes.