In shallow water, a large part of underwater acoustic prediction uncertainties are in- duced by sub-meso-to-small scale oceanographic variabilities. Conventional oceano- graphic measurements for capturing such ocean-acoustic environmental variabilities face the classical conflict between resolution and coverage. The Adaptive Rapid En- vironmental Assessment (AREA) project was proposed to resolve this conflict by optimizing the location of in-situ measurements in an adaptive manner. In this thesis, ideas, concepts and performance limits in AREA are clarified. Both an engineering and a mathematical model for AREA are developed. A modularized AREA simulator was developed and implemented in C++. Philosophies in AREA are discussed. Presumptions about the ocean are made to bridge the gap between the viewpoint in the oceanography community, where the ocean environment is consid- ered to be a deterministic but very complicated system, and that of the underwater acoustic community, where the ocean environment is treated as a random system. At present, how to optimally locate the in-situ measurements made by a single AUV carrying a CTD (conductivity, temperature and depth) sensor is considered in AREA. In this thesis, the AUV path planning is modeled as a Shortest Path problem. However, due to the sound velocity correlation effect, the size of this problem can be very large. A method is developed to simplify the graph for a fast solution. As a significant step, a linear approximation for acoustic Transmission Loss (TL) is investigated numerically and analytically. In addition to following a predetermined path, an AUV can also adaptively gener- ate its path on-board. This adaptive on-board AUV routing problem is modeled using Dynamic Programming (DP) in this thesis. A method based on an optimized prede- termined path is developed to reduce the size of the DP problem and approximately yet efficiently solve it using Pattern Recognition. As a special case, a thermocline- oriented AUV yoyo control and control parameter optimization methods for AREA are also developed. 2 Finally, some AUV control algorithms for capturing fronts are developed. A frame- work for real-time TL forecasts is developed. This is the first time that TL forecasts have been linked with ocean forecasts in real-time. All of the above ideas and methods developed were tested in two experiments, FAF05 in the northern Tyrrhenian Sea in 2005 and MB06 in Monterey Bay, CA in 2006. The latter MB06 sea exercise was a major field experiment sponsored by the Office of Naval Research and the thesis compiles significant findings from this effort.

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 modeling capabilities can’t always provide oceanic-acoustic predictions in sufficient detail and with enough accuracy. Adaptive Rapid Environmental Assessment (AREA) is a new adaptive sampling concept being developed in connection with the emergence of the Autonomous Ocean Sampling Network (AOSN) technology. By adaptively and optimally deploying in-situ measurement resources and assimilating these data in coupled nested ocean and acoustic models, AREA can dramatically improve the ocean estimation that matters for acoustic predictions and so be essential for such predictions. These concepts are outlined and preliminary methods are developed and illustrated based on the Focused Acoustic Forecasting-05 (FAF05) exercise. During FAF05, AREA simulations were run in real-time and engineering tests carried out, within the context of an at-sea experiment with Autonomous Underwater Vehicles (AUV) in the northern Tyrrhenian sea, on the eastern side of the Corsican channel.

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.

THIS REPORT summarizes goals, activities, and recommendations of a workshop on data assimilation held in Williamsburg, Virginia on September 9-11, 2003, and sponsored by the U.S. Office of Naval Research (ONR) and National Science Foundation (NSF). The overall goal of the workshop was to synthesize research directions for ocean data assimilation (DA) and outline efforts required during the next 10 years and beyond to evolve DA into an integral and sustained component of global, regional, and coastal ocean science and observing and prediction systems. The workshop built on the success of recent and existing DA activities such as those sponsored by the National Oceanographic Partnership Program (NOPP) and NSF-Information Technology Research (NSF-ITR). DA is a quantitative approach to optimally combine models and observations. The combination is usually consistent with model and data uncertainties, which need to be represented. Ocean DA can extract maximum knowledge from the sparse and expensive measurements of the highly variable ocean dynamics. The ultimate goal is to better understand and predict these dynamics on multiple spatial and temporal scales, including interactions with other components of the climate system. There are many applications that involve DA or build on its results, including: coastal, regional, seasonal, and inter-annual ocean and climate dynamics; carbon and biogeochemical cycles; ecosystem dynamics; ocean engineering; observing-system design; coastal management; fisheries; pollution control; naval operations; and defense and security. These applications have different requirements that lead to variations in the DA schemes utilized. For literature on DA, we refer to Ghil and Malanotte-Rizzoli (1991), the National Research Council (1991), Bennett (1992), Malanotte- Rizzoli (1996), Wunsch (1996), Robinson et al. (1998), Robinson and Lermusiaux (2002), and Kalnay (2003). We also refer to the U.S. Global Ocean Data Assimilation Experiment (GODAE) workshop on Global Ocean Data Assimilation: Prospects and Strategies (Rienecker et al., 2001); U.S. National Oceanic and Atmospheric Administration-Office of Global Programs (NOAA-OGP) workshop on Coupled Data Assimilation (Rienecker, 2003); and, NOAA-NASA-NSF workshop on Ongoing Analysis of the Climate System (Arkin et al., 2003).

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.