A theoretical synthesis of forward reachability for minimum–time control of anisotropic vehicles operating in strong and dynamic flows is provided. The synthesis relies on the computation of the forward reachable set of states. Using ideas rooted in the theory of non–smooth calculus, we prove that this set is governed by the viscosity solution of an unsteady Hamilton–Jacobi (HJ) equation. We show that the minimum arrival time satisfies a static HJ equation, when a special local controllability condition holds. Results are exemplified by applications to a sailboat moving in a uniform wind–field and autonomous underwater gliders operating in the Sulu Archipelago.

Seaweed biomass presents a substantial opportunity for climate mitigation, yet to realize its potential, farming must be expanded to the expansive open oceans. However, in the open ocean neither anchored farming nor floating farms operating with powerful engines are economically viable. Recent studies have shown that vessels can navigate with low-power engines by going with the flow, utilizing minimal propulsion to strategically leverage beneficial ocean currents. In this work, we focus on low-power autonomous seaweed farms and design controllers that maximize seaweed growth by taking advantage of ocean currents. We first introduce a Dynamic Programming (DP) formulation to solve for the growth-optimal value function when the true currents are known. However, in reality only short-term imperfect forecasts with increasing uncertainty are available. Hence, we present three additional extensions. Firstly, we use frequent replanning to mitigate forecast errors. For that we compute the value function daily as new forecasts arrive, which also provides a feedback policy that is equivalent to replanning on the forecast at every time step. Second, to optimize for long-term growth, we extend the value function beyond the forecast horizon by estimating the expected future growth based on seasonal average currents. Lastly, we introduce a discounted finite-time DP formulation to account for the increasing uncertainty in future ocean current estimates. We empirically evaluate our approach with 30-day simulations of farms in realistic ocean conditions. Our method achieves 95.8% of the best possible growth using only 5-day forecasts. This confirms the feasibility of using low-power propulsion to operate autonomous farms in real-world conditions.

The first steps towards integrating autonomous monitoring, probabilistic forecasting, reachability analysis, and adaptive sampling for the Gulf of Mexico were demonstrated in real-time during the collaborative Mini-Adaptive Sampling Test Run (MASTR) ocean experiment, which took place from February to April 2024. The emphasis of this contribution is on the use of the MIT Multidisciplinary Simulation, Estimation, and Assimilation Systems (MSEAS) including Error Subspace Statistical Estimation (ESSE) large-ensemble forecasting and path planning systems to predict ocean fields and uncertainties, forecast reachable sets and optimal paths for gliders, and guide sampling aircraft and ocean vehicles toward the most informative observations. Deterministic and probabilistic ocean forecasts are exemplified and linked to the variability of the Loop Current (LC) and LC Eddies, demonstrating predictive skill by real-time comparisons to independent data. Risk forecasts in terms of probabilities of currents exceeding 1.5 kt were provided. The most informative sampling patterns for Remote Ocean Current Imaging System (ROCIS) flights were forecast using mutual information between surface currents and density anomaly. Finally, we guided four underwater gliders using probabilistic reachability and path-planning forecasts.

As part of the Mini-Adaptive Sampling Test Run (MASTR) experiment in the Gulf of Mexico (GoM) region from February to April 2024, we demonstrated real-time deterministic and probabilistic reachability analysis and time-optimal path planning to guide a fleet of four ocean gliders. The governing differential equations for reachability analysis and time-optimal path planning were numerically integrated in real-time and forced by currents from our large-ensemble ocean forecasts. We illustrate the real-time deterministic and probabilistic forward reachability analyses, reachability and path planning for glider pickups, time-optimal path planning for gliders in distress, and planning of future glider deployments. Results show that the actual paths of gliders were contained within our reachable set forecasts and in accord with the dynamic reachability fronts. Our time-optimal headings and paths also predicted real glider motions, even for longer-range predictions of weeks to a month duration. Reachability and time-optimal path planning forecasts were successfully employed for glider recovery. They also enabled exploring options for future glider deployments.

General differential equations for multi-objective reachability and optimal planning are used to guide autonomous air and sea drones in hazard-time optimal missions. The vehicles minimize exposure to hazards and travel time, leveraging the dynamic environments with strong flows and steering clear of dynamic hazardous regions. We demonstrate the approach first with an autonomous air drone that crosses the Atlantic Ocean optimizing travel time using trade winds while avoiding hazardous rain storms in the inter-tropical convergence zone. We then consider an air drone that exploits winds and avoids hazardous rains to transport an ocean vehicle to a target destination. The ocean vehicle then completes its own hazard-time optimal mission, leveraging ocean currents and avoiding vessel traffic hazards. In all cases, we predict hazard-time reachable sets, Pareto fronts, and optimal paths. The results highlight the benefits of considering hazards in optimal path planning.

Low-propulsion vessels can take advantage of powerful ocean currents to navigate towards a destination. Recent results demonstrated that vessels can reach their destination with high probability despite forecast errors. However, these results do not consider the critical aspect of safety of such vessels: because their propulsion is much smaller than the magnitude of surrounding currents, they might end up in currents that inevitably push them into unsafe areas such as shallow waters, garbage patches, and shipping lanes. In this work, we first investigate the risk of stranding for passively floating vessels in the Northeast Pacific. We find that at least 5.04% would strand within 90 days. Next, we encode the unsafe sets as hard constraints into Hamilton-Jacobi Multi-Time Reachability to synthesize a feedback policy that is equivalent to re-planning at each time step at low computational cost. While applying this policy guarantees safe operation when the currents are known, in realistic situations only imperfect forecasts are available. Hence, we demonstrate the safety of our approach empirically with large-scale realistic simulations of a vessel navigating in high-risk regions in the Northeast Pacific. We find that applying our policy closed-loop with daily re-planning as new forecasts become available reduces stranding below 1% despite forecast errors often exceeding the maximal propulsion. Our method significantly improves safety over the baselines and still achieves a timely arrival of the vessel at the destination.

The ocean is vast, complex, and increasingly threatened by human activities. There is an urgent need to find complementary ways to gather information and promote the comprehensive understanding and management of the ocean. The global network of subsea cables provides an opportunity to support a holistic ocean observation system. Data gathered from this system can be employed to anticipate and provide warning about hazardous events. Large-scale and widespread ocean monitoring may also enable the oversight and tracing of global phenomena that have local impacts.

The Knowledge and Data from the Deep to Space (K2D) project aims to develop the critical components that will enable the large-scale coupling of autonomous underwater vehicles (AUVs) and subsea cables for global ocean environmental monitoring and multi-hazard warning. Funded by the Fundação para a Ciência e Tecnologia/Massachusetts Institute of Technology Portugal Program and involving teams from Portugal and the United States, the project started in 2021 with a global budget of 1.4 M€ and an estimated duration of three years. Sustained ocean observation systems are scarce, especially those that focus on or near the seafloor. The combination of subsea cables and marine robotics is promising not only because it allows access to remote locations and provides an extensive network (deep sea, open ocean), but also because it combines a large set of capabilities in a highly resource-efficient way, unmatched by any other ocean observation approach. These assets may initiate the first global ocean “nervous system” in the near future.

We obtain, solve, and verify fundamental differential equations for energy-time path planning in dynamic flows. The equations govern the energy-time reachable sets, optimal paths, and optimal controls for autonomous vehicles navigating to any destination in known dynamic environments, minimizing both energy usage and travel time. Based on Hamilton-Jacobi theory for reachability and the level set method, the resulting methodology computes the Pareto optimal solutions to the multi-objective path planning problem, numerically solving the exact equations governing the evolution of reachability fronts and optimal paths in the augmented energy and physical-space domain. Our approach is applicable to path planning in various dynamic flow environments and energy types. We first validate the methodology through a benchmark case of crossing a steady jet for which we compare our results to semi-analytical optimal energy-time solutions. We then consider unsteady flow environments and solve for energy-time optimal missions in a quasi-geostrophic double-gyre flow field. Results show that our theory and schemes can provide all the energy-time optimal solutions and that these solutions can be strongly influenced by unsteady flow conditions.

Long-term and reliable marine ecosystems monitoring is essential to address current environmental issues, including climate change and biodiversity threats. The existing oceans monitoring systems show clear data gaps, particularly when considering characteristics such as depth coverage or measured variables in deep and open seas. Over the last decades, the number of fixed and mobile platforms for in situ ocean data acquisition has increased significantly, covering all oceans’ regions. However, these are largely dependent on satellite communications for data transmission, as well as on research cruises or opportunistic ship surveys, generally presenting a lag between data acquisition and availability. In this context, the creation of a widely distributed network of SMART cables (Science Monitoring And Reliable Telecommunications) – sensors attached to submarine telecommunication cables – appears as a promising solution to fill in the current ocean data gaps and ensure unprecedented oceans health continuous monitoring. The K2D (Knowledge and Data from the Deep to Space) project proposes the development of a persistent oceans monitoring network based on the use of telecommunications cables and Autonomous Underwater Vehicles (AUVs). The approach proposed includes several modules for navigation, communication and energy management, that enable the cost-effective gathering of extensive oceans data. These include physical, chemical, and biological variables, both registered with bottom fixed stations and AUVs operating in the water column. The data that can be gathered have multiple potential applications, including oceans health continuous monitoring and the enhancement of existing ocean models. The latter, in combination with geoinformatics and Artificial Intelligence, can create a continuum from the deep sea to near space, by integrating underwater remote sensing and satellite information to describe Earth systems in a holistic manner.

Techniques for use in connection with determining an optimized route for a vehicle include obtaining a target state, a fixed initial position of the vehicle, and dynamic flow information, and determining an optimized route from the fixed initial position to the target state using the dynamic flow information.

More details can be found here.

For the analysis of dynamical systems, it is fundamental to determine all states that can be reached at any given time. In this work, we obtain and apply new governing equations for reachability analysis over multiple start and terminal times all at once, and for systems operating in time-varying environments with dynamic obstacles and any other relevant dynamic fields. The theory and schemes are developed for both backward and forward reachable tubes with time-varying target and start sets. The resulting value functions elegantly capture not only the reachable tubes but also time-to-reach and time-to-leave maps as well as start time vs. duration plots and other useful secondary quantities for optimal control. We discuss the numerical schemes and computational efficiency. We first verify our results in an environment with a moving target and obstacle where reachability tubes can be analytically computed. We then consider the Dubin’s car problem extended with a moving target and obstacle. Finally, we showcase our multi-time reachability in a non-hydrostatic bottom gravity current system. Results highlight the novel capabilities of exact multi-time reachability in dynamic environments.

In dynamic flow fields such as winds and ocean currents an agent can navigate by going with the flow, only using minimal propulsion to nudge itself into beneficial flows. This navigation paradigm of hitchhiking flows is highly energy-efficient. However, reliable navigation in this setting remains challenging as typically only forecasts are available which differ significantly from the true currents and the forecast error can be larger than can be handled by the actuation of the agent. In this paper, we propose a novel control method for reliable navigation of underactuated agents hitchhiking flows based on imperfect forecasts. In the spirit of Model Predictive Control our method allows for time-optimal replanning at every time step with only one computation per forecast. Using the recent Multi-Time Hamilton-Jacobi Reachability formulation we obtain a value function which is then used for closed-loop control. We evaluate the reliability of our method empirically over a large set of multi-day start-target missions in the ocean currents of the Gulf of Mexico with realistic forecast errors. Our method outperforms the baselines significantly, achieving high reliability, measured as the success rate of navigating from start to target, at low computational cost.

Thanks to the advent of new technologies and higher real-time computational capabilities, the use of unmanned vehicles in the marine domain received a significant burst in the last decade. Ocean and seabed sampling, missions in dangerous areas, and civilians security are just a few of the large number of applications which currently benefit from unmanned vehicles. One of the most actively studied topic is their full autonomy, i.e., the design of marine vehicles capable of pursuing a task while reacting to the changes of the environment without the intervention of humans, not even remote. Environment dynamicity may consist in variations of currents, presence of unknown obstacles, and attacks from adversaries (e.g., pirates). To achieve autonomy in such highly dynamic uncertain conditions, many types of autonomous path planning problems need to be solved. There has thus been a commensurate number of approaches and methods to optimize such path planning. This work focuses on game theoretic ones and provides a wide overview of the current state of the art, along with future directions.

The oceans make this planet habitable and provide a variety of essential ecosystem services ranging from climate regulation through control of greenhouse gases to provisioning about 17% of protein consumed by humans. The oceans are changing as a consequence of human activity but this system is severely under sampled. Traditional methods of studying the oceans, sailing in straight lines, extrapolating a few point measurements have not changed much in 200 years. Despite the tremendous advances in sampling technologies, we often use our autonomous assets the same way. We propose to use the advances in multiplatform, multidisciplinary, and integrated ocean observation, artificial intelligence, marine robotics, new high-resolution coastal ocean data assimilation techniques and computer models to observe and predict the oceans “intelligently”—by deploying self-propelled autonomous sensors and Smallsats guided by data assimilating models to provide observations to reduce model uncertainty in the coastal ocean. This system will be portable and capable of being deployed rapidly in any ocean.

The rising popularity of aquaculture has led to increased research in offshore algae farming. Central to the efficient operation of such farms is the need for (i) accurate models of the dynamic ocean environment including macroalgae ecosystem dynamics and (ii) intelligent path planning algorithms for autonomous vessels that optimally manage and harvest the algae fields. In this work, we address both these challenges. We first integrate our modeling system of the ocean environment with a model for forecasting the growth and decay of algae fields. These fields are then input into our exact optimal path planning, augmented with the optimal harvesting goals and solved using level set methods. The resulting path is a provable time-optimal route for the vehicle to follow under the constraint of having to monitor or harvest a specified amount of the field to collect. To demonstrate the theory, we simulate algal growth in both idealized and realistic data-assimilative dynamic ocean environments and compute the optimal paths for an autonomous collection vehicle. We demonstrate that our theory and schemes can be used to compute the optimal path in a variety of scenarios – harvesting in the case of discrete farms, a large kelp farm field, or large scale dynamic algal bloom fields.

Time-optimal paths are evaluated by VISIR (“discoVerIng Safe and effIcient Routes”), a graph-search ship routing model, with respect to the solution of the fundamental differential equations governing optimal paths in a dynamic wind-wave environment. The evaluation exercise makes use of identical setups: topological constraints, dynamic wave environmental conditions, and vessel-ocean parametrizations, while advection by external currents is not considered. The emphasis is on predicting the time-optimal ship headings and Speeds Through Water constrained by dynamic ocean wave fields. VISIR upgrades regarding angular resolution, time-interpolation, and static navigational safety constraints are introduced. The deviations of the graph-search results relative to the solution of the exact differential equations in both the path duration and length are assessed. They are found to be of the order of the discretization errors, with VISIR’s solution converging to that of the differential equation for sufficient resolution.

Autonomous underwater vehicles (AUVs) operate in the three-dimensional and time-dependent marine environment with strong and dynamic currents. Our goal is to predict the time history of the optimal three-dimensional headings of these vehicles such that they reach the given destination location in the least amount of time, starting from a known initial position. We employ the exact differential equations for time-optimal path planning and develop theory and numerical schemes to accurately predict three-dimensional optimal paths for several classes of marine vehicles, respecting their specific propulsion constraints. We further show that the three-dimensional path planning problem can be reduced to a two-dimensional one if the motion of the vehicle is partially known, e.g. if the vertical component of the motion is forced. This reduces the computational cost. We then apply the developed theory in three-dimensional analytically known flow fields to verify the schemes, benchmark the accuracy, and demonstrate capabilities. Finally, we showcase time-optimal path planning in realistic data-assimilative ocean simulations for the Middle Atlantic Bight region, integrating the primitive-equation of the Multidisciplinary Simulation Estimation and Assimilation System (MSEAS) with the three-dimensional path planning equations for three common marine vehicles, namely propelled AUVs (with unrestricted motion), floats (that only propel vertically), and gliders (that often perform sinusoidal yo-yo motions in vertical planes). These results highlight the effects of dynamic three-dimensional multiscale ocean currents on the optimal paths, including the Gulf Stream, shelfbreak front jet, upper-layer jets, eddies, and wind-driven and tidal currents. They also showcase the need to utilize data-assimilative ocean forecasts for planning efficient autonomous missions, from optimal deployment and pick-up, to monitoring and adaptive data collection.

We combine decision theory with fundamental stochastic time-optimal path planning to develop partial-differential-equations-based schemes for risk-optimal path planning in uncertain, strong and dynamic flows. The path planning proceeds in three steps: (i) predict the probability distribution of environmental flows, (ii) compute the distribution of exact time-optimal paths for the above flow distribution by solving stochastic dynamically orthogonal level set equations, and (iii) compute the risk of being suboptimal given the uncertain time-optimal path predictions and determine the plan that minimizes the risk. We showcase our theory and schemes by planning risk-optimal paths of unmanned and/or autonomous vehicles in illustrative idealized canonical flow scenarios commonly encountered in the coastal oceans and urban environments. The step-by-step procedure for computing the risk-optimal paths is presented and the key properties of the risk-optimal paths are analyzed.

Ocean data assimilation is increasingly recognized as crucial for the accuracy of the real-time ocean prediction systems. Here, the current status of ocean data assimilation in support of the operational demands of analysis and forecasting is reviewed, focusing on the methods currently adopted in operational prediction systems. Significant challenges associated with the most commonly employed approaches are identified and discussed. Overarching issues faced by ocean data assimilation in general are also addressed, and important future directions in response to scientific advances, evolving and forthcoming ocean observing systems and the needs of stakeholders and downstream applications are presented.

Many aspects of geosciences pose novel problems for intelligent systems research. Geoscience data is challenging because it tends to be uncertain, intermittent, sparse, multiresolution, and multiscale. Geosciences processes and objects often have amorphous spatiotemporal boundaries. The lack of ground truth makes model evaluation, testing, and comparison difficult. Overcoming these challenges requires breakthroughs that would significantly transform intelligent systems, while greatly benefitting the geosciences in turn. Although there have been significant and beneficial interactions between the intelligent systems and geosciences communities, the potential for synergistic research in intelligent systems for geosciences is largely untapped. A recently launched Research Coordination Network on Intelligent Systems for Geosciences followed a workshop at the National Science Foundation on this topic. This expanding network builds on the momentum of the NSF EarthCube initiative for geosciences, and is driven by practical problems in Earth, ocean, atmospheric, polar, and geospace sciences. Based on discussions and activities within this network, this article presents a research agenda for intelligent systems inspired by geosciences challenges.

The present paper demonstrates the use of exact equations to predict time-optimal mission plans for a marine vehicle that visits a number of locations in a given dynamic ocean current field. This problem bears close resemblance to that of the classic “traveling salesman”, albeit with the added complexity that the vehicle experiences a dynamic flow field while traversing the paths. The paths, or “legs”, between all goal waypoints are generated by numerically solving the exact time-optimal path planning level-set differential equations. Overall, the planning proceeds in four steps. First, current forecasts for the planning horizon is obtained utilizing our data-driven 4-D primitive equation ocean modeling system (Multidisciplinary Simulation Estimation and Assimilation System; MSEAS), forced by high-resolution tidal and real-time atmopsheric forcing fields. Second, all tour permutations are enumerated and the minimum number of times the time-optimal PDEs are to be solved is established. Third, due to the spatial and temporal dynamics, a varying start time results in different paths and durations for each leg and requires all permutations of travel to be calculated. To do so, the minimum required time-optimal PDEs are solved and the optimal travel time is computed for each leg of all enumerated tours. Finally, the tour permutation for which travel time is minimized is identified and the corresponding time-optimal paths are computed by solving the backtracking equation. Even though the method is very efficient and the optimal path can be computed serially in real-time for common naval operations, for additional computational speed, a high-performance computing cluster was used to solve the level set calculations in parallel. Our equation and software is applied to simulations of realistic naval applications in the complex Philippines Archipelago region. Our method calculates the global optimum and can serve two purposes: (a) it can be used in its present form to plan multiwaypoint missions offline in conjunction with a predictive ocean current modeling system, or (b) it can be used as a litmus test for approximate future solutions to the traveling salesman problem in dynamic flow fields.

Recent advances in probabilistic forecasting of regional ocean dynamics, and stochastic optimal path planning with massive ensembles motivate principled analysis of their large datasets. Specifically, stochastic time-optimal path planning in strong, dynamic and uncertain ocean flows produces a massive dataset of the stochastic distribution of exact timeoptimal trajectories. To synthesize such big data and draw insights, we apply machine learning and data mining algorithms. Particularly, clustering of the time-optimal trajectories is important to describe their PDFs, identify representative paths, and compute and optimize risk of following these paths. In the present paper, we explore the use of hierarchical clustering algorithms along with a dissimilarity matrix computed from the pairwise discrete Frechet distance between all the optimal trajectories. We apply the algorithms to two datasets of massive ensembles of vehicle trajectories in a stochastic flow past a circular island and stochastic wind driven double gyre flow. These paths are computed by solving our dynamically orthogonal level set equations. Hierarchical clustering is applied to the two datasets, and results are qualitatively and quantitatively analyzed.

Accounting for uncertainty in optimal path planning is essential for many applications. We present and apply stochastic level-set partial differential equations that govern the stochastic time-optimal reachability fronts and time-optimal paths for vehicles navigating in uncertain, strong, and dynamic flow fields. To solve these equations efficiently, we obtain and employ their dynamically orthogonal reduced-order projections, maintaining accuracy while achieving several orders of magnitude in computational speed-up when compared to classic Monte Carlo methods. We utilize the new equations to complete stochastic reachability and time-optimal path planning in three test cases: (i) a canonical stochastic steady-front with uncertain flow strength, (ii) a stochastic barotropic quasi-geostrophic double-gyre circulation, and (iii) a stochastic flow past a circular island. For all the three test cases, we analyze the results with a focus on studying the effect of flow uncertainty on the reachability fronts and time-optimal paths, and their probabilistic properties. With the first test case, we demonstrate the approach and verify the accuracy of our solutions by comparing them with the Monte Carlo solutions.With the second, we show that different flow field realizations can result in paths with high spatial dissimilarity but with similar arrival times. With the third, we provide an example where time-optimal path variability can be very high and sensitive to uncertainty in eddy shedding direction downstream of the island. Keywords: Stochastic Path Planning, Level Set Equations, Dynamically Orthogonal, Ocean Modeling, AUV, Uncertainty Quantification

Ocean scientists have dreamed and recently started to realize an ocean observing revolution with autonomous observing platforms and sensors. Critical questions to be answered by such autonomous systems are where, when, and what to sample for optimal information, and how to optimally reach the sampling locations. Definitions, concepts, and progress towards answering these questions using quantitative predictions and fundamental principles are presented. Results in reachability and path planning, adaptive sampling, machine learning, and teaming machines with scientists are overviewed. The integrated use of differential equations and theory from varied disciplines is emphasized. The results provide an inference engine and knowledge base for expert autonomous observing systems. They are showcased using a set of recent at-sea campaigns and realistic simulations. Real-time experiments with identical AUVs in the Buzzards Bay and Vineyard Sound region first show that our predicted time-optimal paths were faster than shortest distance paths. Deterministic and probabilistic reachability and path forecasts issued and validated for gliders and floats in the northern Arabian Sea are then presented. Novel Bayesian adaptive sampling for hypothesis testing and optimal learning are finally shown to forecast the observations most informative to estimate the accuracy of model formulations, the values of ecosystem parameters and dynamic fields, and the presence of Lagrangian Coherent Structures.

The Arabian Sea circulation is forced by strong monsoonal winds and is characterized by vigorous seasonally reversing currents, extreme differences in sea surface salinity, localized substantial upwelling and widespread submesoscale thermohaline structures. Its complicated sea surface temperature patterns are important for the onset and evolution of the Asian Monsoon. Here we describe a program that aims to elucidate the role of upper ocean processes and atmospheric feedbacks in setting the sea surface temperature properties of the region. The wide range of spatial and temporal scales and the difficulty of accessing much of the region with ships due to piracy motivated a novel approach based on state-of-the-art autonomous ocean sensors and platforms. The extensive dataset that is being collected, combined with numerical models and remote sensing data, confirms the role of planetary waves in the reversal of the Somali Current system. These data also document the fast response of the upper equatorial ocean to the monsoon winds through changes in temperature and salinity and the connectivity of the surface currents across the northern Indian Ocean. New observations of thermohaline interleaving structures and mixing in setting the surface temperature properties of the northern Arabian Sea are also discussed.

Where, when, and what to sample, and how to optimally reach the sampling locations, are critical questions to be answered by Autonomous and Lagrangian Platforms and Sensors. For a reproducible scientific sampling approach, answers should be quantitative and provided using fundamental principles. Concepts and recent progress towards this principled approach are first overviewed, focusing on reachability, path planning, and adaptive sampling. Results of a real-time forecasting and planning experiment completed during February-April 2017 for the Northern Arabian Sea Circulation – Autonomous Research program are then presented. The predictive skill, layered fields, and uncertainty estimates obtained using our MIT MSEAS multi-resolution ensemble ocean modeling system are first studied. With such inputs, deterministic and probabilistic three-dimensional reachability forecasts issued daily for gliders and floats are then showcased and validated. Our Bayesian adaptive sampling framework is finally shown to forecast in real-time the observations that are most informative for estimating classic ocean fields but also secondary-variables such as Lagrangian Coherent Structures.

In recent years, the use of autonomous undersea vehicles (AUVs) for highly time-critical at-sea operations involving surface ships has received increased attention, magnifying the importance of optimal interception. Finding the optimal route to a moving target is a challenging procedure. In this work, we describe and apply our exact time-optimal path planning methodology and the corresponding software to such ship interception problems. A series of numerical ship interception experiments is completed in the southern littoral of Massachusetts, namely in Buzzards Bay and Vineyard Sound around the Elizabeth Islands and Martha’s Vineyard. Ocean currents are estimated from a regional ocean modeling system. We show that complex coastal geometry, ship proximity, and tidal current phases all play key roles influencing the time-optimal vehicle behavior. Favorable or adverse currents can shift the optimal route from one island passage to another, and can even cause the AUV to remain nearly stationary until a favorable current develops. We also integrate the Kelvin wedge wake model into our path planning software, and show that considering wake effects significantly complicates the shape of the time-optimal paths, requiring AUVs to execute sequences of abrupt turns and tacking maneuvers, even in highly idealized scenarios. Such behavior is reminiscent of ocean animals swimming in wakes. In all cases, it is shown that our level set partial differential equations successfully guide the time-optimal vehicles through regions with the most favorable currents, avoiding regions with adverse effects, and accounting for the ship wakes when present.

Autonomous underwater vehicles (AUVs) are used to execute an increasingly challenging set of missions in commercial, environmental and defense industries. The resources available to the AUV in service of these missions are typically a limited power supply and onboard sensing of its local environment. Optimal path planning is needed to maximize the chances that these AUVs will successfully complete long endurance missions within their power budget. A time-optimal path planner has been recently developed to minimize AUV mission time required to traverse a dynamic ocean environment at a specified speed through the water. For many missions, time minimization is appropriate because the AUVs operate at a fixed propeller speed. However, the ultimate limiting constraint on AUV operations is often the onboard power supply, rather than mission time. While an empirical or theoretical relationship between mission time and power could be applied to estimate power usage in the path planner, the real power usage and availability on an AUV varies mission-to-mission, as a result of multiple factors, including vehicle buoyancy, battery charge cycle, fin configuration, and water type or quality. In this work, we use data collected from two mid-size AUVs operating in various conditions to learn the mission-to-mission variability in the power budget so that it could be incorporated into the mission planner.

We report the results of sea exercises that demonstrate the real-time capabilities of our fundamental time-optimal path planning theory and software with real ocean vehicles. The exercises were conducted with REMUS 600 Autonomous Underwater Vehicles (AUVs) in the Buzzards Bay and Vineyard Sound Regions on 21 October and 6 December 2016. Two tests were completed: (i) 1-AUV time-optimal tests and (ii) 2-AUV race tests where one AUV followed a time-optimal path and the other a shortest-distance path between the start and finish locations. The time-optimal planning proceeded as follows. We first forecast, in real-time, the physical ocean conditions in the above regions and times utilizing our MSEAS multi-resolution primitive equation ocean modeling system. Next, we planned time-optimal paths for the AUVs using our level-set equations and real-time ocean forecasts, and accounting for operational constraints (e.g. minimum depth). This completed the planning computations performed onboard a research vessel. The forecast optimal paths were then transferred to the AUV operating system and the vehicles were piloted according to the plan. We found that the forecast currents and paths were accurate. In particular, the time-optimal vehicles won the races, even though the local currents and geometric constraints were complex. The details of the results were analyzed off-line after the sea tests.

In this paper, we adopt a reachability-based approach to deal with the pursuit-evasion differential game between two players in the presence of dynamic environmental disturbances (e.g., winds, sea currents). We give conditions for the game to be terminated in terms of reachable set inclusions. Level set equations are defined and solved to generate the reachable sets of the pursuer and the evader. The corresponding time-optimal trajectories and optimal strategies can be retrieved immediately afterwards. We validate our method by applying it to a pursuit-evasion game in a simple flow field, for which an analytical solution is available.We then implement the proposed scheme to a problem with a more realistic flow field.

We integrate data-driven ocean modeling with the stochastic Dynamically Orthogonal (DO) level-set optimization methodology to compute and study energy-optimal paths, speeds, and headings for ocean vehicles in the Middle-Atlantic Bight (MAB) region. We hindcast the energy-optimal paths from among exact time-optimal paths for the period 28 August 2006 to 9 September 2006. To do so, we first obtain a data-assimilative multiscale re-analysis, combining ocean observations with implicit two-way nested multiresolution primitive-equation simulations of the tidal-to-mesoscale dynamics in the region. Second, we solve the reduced-order stochastic DO level-set partial differential equations (PDEs) to compute the joint probability of minimum arrival-time, vehicle-speed time-series, and total energy utilized. Third, for each arrival time, we select the vehiclespeed time-series that minimize the total energy utilization from the marginal probability of vehicle-speed and total energy. The corresponding energy-optimal path and headings are obtained through a particle backtracking equation. Theoretically, the present methodology is PDE-based and provides fundamental energy-optimal predictions without heuristics. Computationally, it is three- to four-orders of magnitude faster than direct Monte Carlo methods. For the missions considered, we analyze the effects of the regional tidal currents, strong wind events, coastal jets, shelfbreak front, and other local circulations on the energy-optimal paths. Results showcase the opportunities for vehicles that intelligently utilize the ocean environment to minimize energy usage, rigorously integrating ocean forecasting with optimal control of autonomous vehicles.

In this paper a reachability-based approach is adopted to deal with the pursuit-evasion dierential game between one evader and multiple pursuers in the presence of dynamic environmental disturbances (e.g., winds, sea currents). Conditions for the game to be terminated are given in terms of reachable set inclusions. Level set equations are defined and solved to generate the forward reachable sets of the pursuers and the evader. The time-optimal trajectories and the corresponding optimal strategies are sub- sequently retrieved from these level sets. The pursuers are divided into active pursuers, guards, and redundant pursuers according to their respec- tive roles in the pursuit-evasion game. The proposed scheme is implemented on problems with both simple and realistic time-dependent flow fields, with and without obstacles.

Regional ocean models are capable of forecasting conditions for usefully long intervals of time (days) provided that initial and ongoing conditions can be measured. In resource-limited circumstances, the placement of sensors in optimal locations is essential. Here, a nonlinear optimization approach to determine optimal adaptive sampling that uses the Genetic Algorithm (GA) method is presented. The method determines sampling strategies that minimize a user-defined physics-based cost function. The method is evaluated using identical twin experiments, comparing hindcasts from an ensemble of simulations that assimilate data selected using the GA adaptive sampling and other methods. For skill metrics, we employ the reduction of the ensemble root-mean-square-error (RMSE) between the “true” data-assimilative ocean simulation and the different ensembles of data-assimilative hindcasts. A 5-glider optimal sampling study is set up for a 400 km x 400 km domain in the Middle Atlantic Bight region, along the New Jersey shelf-break. Results are compared for several ocean and atmospheric forcing conditions.

A stochastic optimization methodology is formulated for computing energy–optimal paths from among time–optimal paths of autonomous vehicles navigating in a dynamic flow field. Based on partial differential equations, the methodology rigorously leverages the level–set equation that governs time–optimal reachability fronts for a given relative vehicle speed function. To set up the energy optimization, the relative vehicle speed is considered to be stochastic and new stochastic Dynamically Orthogonal (DO) level–set equations are derived. Their solution provides the distribution of time–optimal reachability fronts and corresponding distribution of time–optimal paths. An optimization is then performed on the vehicle’s energy–time joint distribution to select the energy–optimal paths for each arrival time, among all stochastic time–optimal paths for that arrival time. Numerical schemes to solve the reduced stochastic DO level–set equations are obtained and accuracy and efficiency considerations are discussed. These reduced equations are first shown to be efficient at solving the governing stochastic level-sets, in part by comparisons with direct Monte Carlo simulations.To validate the methodology and illustrate its overall accuracy, comparisons with `semi–analytical’ energy–optimal path solutions are then completed. In particular, we consider the energy–optimal crossing of a canonical steady front and set up its `semi–analytical’ solution using a dual energy–time nested nonlinear optimization scheme. We then showcase the inner workings and nuances of the energy–optimal path planning, considering different mission scenarios. Finally, we study and discuss results of energy-optimal missions in a strong dynamic double–gyre flow field.

The science of autonomy is the systematic development of fundamental knowledge about autonomous decision making and task completing in the form of testable autonomous methods, models and systems. In ocean applications, it involves varied disciplines that are not often connected. However, marine autonomy applications are rapidly growing, both in numbers and in complexity. This new paradigm in ocean science and operations motivates the need to carry out interdisciplinary research in the science of autonomy. This chapter reviews some recent results and research directions in time-optimal path planning and optimal adaptive sampling. The aim is to set a basis for a large number of vehicles forming heterogeneous and collaborative underwater swarms that are smart, i.e. knowledgeable about the predicted environment and their uncertainties, and about the predicted effects of autonomous sensing on future operations. The methodologies are generic and applicable to any swarm that moves and senses dynamic environmental fields. However, our focus is underwater path planning and adaptive sampling with a range of vehicles such as AUVs, gliders, ships or remote sensing platforms.

We present a novel stochastic optimization method to compute energy-optimal paths, among all time-optimal paths, for vehicles traveling in dynamic unsteady currents. The method defines a stochastic class of instantaneous nominal vehicle speeds and then obtains the energy-optimal paths within the class by minimizing the total time-integrated energy usage while still satisfying the strong-constraint time-optimal level set equation. This resulting stochastic level set equation is solved using a dynamically orthogonal decomposition and the energy-optimal paths are then selected for each arrival time, among all stochastic time-optimal paths. The first application computes energy-optimal paths for crossing a steady front. Results are validated using a semi-analytical solution obtained by solving a dual nonlinear energy-time optimization problem. The second application computes energy-optimal paths for a realistic mission in the Middle Atlantic Bight and New Jersey Shelf/Hudson Canyon region, using dynamic data-driven ocean field estimates.

As the concurrent use of multiple autonomous vehicles in ocean missions grows, systematic control for their coordinated operation is becoming a necessity. Many ocean vehicles, especially those used in longer–range missions, possess limited operating speeds and are thus sensitive to ocean currents. Yet, the effect of currents on their trajectories is ignored by many coordination techniques. To address this issue, we first derive a rigorous level-set methodology for distance–based coordination of vehicles operating in minimum time within strong and dynamic ocean currents. The new methodology integrates ocean modeling, time-optimal level-sets and optimization schemes to predict the ocean currents, the short-term reachability sets, and the optimal headings for the desired coordination. Schemes are developed for dynamic formation control, where multiple vehicles achieve and maintain a given geometric pattern as they carry out their missions. Secondly, we obtain an efficient, non–intrusive technique for level-set-based time–optimal path planning in the presence of moving obstacles. The results are time-optimal path forecasts that rigorously avoid moving obstacles and sustain the desired coordination. They are exemplified and investigated for a variety of simulated ocean flows. A wind–driven double–gyre flow is used to study time-optimal dynamic formation control. Currents exiting an idealized strait or estuary are employed to explore dynamic obstacle avoidance. Finally, results are analyzed for the complex geometry and multi–scale ocean flows of the Philippine Archipelago.

Oceanic fronts, similar to atmospheric fronts, occur at the interface of two fluid (water) masses of varying characteristics. In regions such as these where there are quantifiable physical, chemical, or biological changes in the ocean environment, it is possible—with the proper instrumentation—to track, or map, the front boundary.

In this paper, the front is approximated as an isotherm that is tracked autonomously and adaptively in 2D (horizontal) and 3D space by an autonomous underwater vehicle (AUV) running MOOS-IvP autonomy. The basic, 2D (constant depth) front tracking method developed in this work has three phases: detection, classification, and tracking, and results in the AUV tracing a zigzag path along and across the front. The 3D AUV front tracking method presented here results in a helical motion around a central axis that is aligned along the front in the horizontal plane, tracing a 3D path that resembles a slinky stretched out along the front.

To test and evaluate these front tracking methods (implemented as autonomy behaviors), virtual experiments were conducted with simulated AUVs in a spatiotemporally dynamic MIT MSEAS ocean model environment of the Mid-Atlantic Bight region, where a distinct temperature front is present along the shelfbreak. A number of performance metrics were developed to evaluate the performance of the AUVs running these front tracking behaviors, and the results are presented herein.

This paper presents a novel way to approach the problem of how to adaptively sample the ocean using fleets of underwater gliders. The technique is particularly suited for those situations where the covariance of the field to sample is unknown or unreliable but some information on the variance is known. The proposed algorithm, which is a variant of the well-known fuzzy C-means clustering algorithm, is able to exploit the presence of non-maneuverable assets, such as fixed buoys. We modified the fuzzy C-means optimization problem statement by including additional constraints. Then we provided an algorithmic solution to the new, constrained problem.

The level set methodology for time-optimal path planning is employed to predict collision-free and fastest time trajectories for swarms of underwater vehicles deployed in the Philippine Archipelago region. To simulate the multiscale ocean flows in this complex region, a data-assimilative primitive-equation ocean modeling system is employed with telescoping domains that are interconnected by implicit two-way nesting. These data-driven multiresolution simulations provide a realistic flow environment, including variable large-scale currents, strong jets, eddies, wind-driven currents and tides. The properties and capabilities of the rigorous level set methodology are illustrated and assessed quantitatively for several vehicle types and mission scenarios. Feasibility studies of all-to-all broadcast missions, leading to minimal time transmission between source and receiver locations, are performed using a large number of vehicles. The results with gliders and faster propelled vehicles are compared. Reachability studies, i.e.~determining the boundaries of regions that can be reached by vehicles for exploratory missions, are then exemplified and analyzed. Finally, the methodology is used to determine the optimal strategies for fastest time pick-up of deployed gliders by means of underway surface vessels or stationary platforms. The results highlight the complex effects of multiscale flows on the optimal paths, the need to utilize the ocean environment for more efficient autonomous missions and the benefits of including ocean forecasts in the planning of time-optimal paths.

We develop an accurate partial differential equation based methodology that predicts the time-optimal paths of autonomous vehicles navigating in any continuous, strong and dynamic ocean currents, obviating the need for heuristics. The goal is to predict a sequence of steering directions so that vehicles can best utilize or avoid currents to minimize their travel time. Inspired by the level set method, we derive and demonstrate that a modified level set equation governs the time-optimal path in any continuous flow. We show that our algorithm is computationally efficient and apply it to a number of experiments. First, we validate our approach through a simple benchmark application in a Rankine vortex flow for which an analytical solution is available. Next, we apply our methodology to more complex, simulated flow-fields such as unsteady double-gyre flows driven by wind stress and flows behind a circular island. These examples show that time-optimal paths for multiple vehicles can be planned, even in the presence of complex flows in domains with obstacles. Finally, we present, and support through illustrations, several remarks that describe specific features of our methodology.

We develop and illustrate an efficient but rigorous methodology that predicts the time-optimal paths of ocean vehicles in dynamic continuous flows. The goal is to best utilize or avoid currents, without limitation on these currents nor on the number of vehicles. The methodology employs a new modified level set equation to evolve a wavefront from the starting point of vehicles until they reach their desired goal locations, combining flow advection with nominal vehicle motions. The optimal paths of vehicles are then computed by solving particle tracking equations backwards in time. The computational cost is linear with the number of vehicles and geometric with spatial dimensions. The methodology is applicable to any continuous flows and many vehicles scenarios. Present illustrations consist of the crossing of a canonical uniform jet and its validation with an optimization problem, as well as more complex time varying 2D flow fields, including jets, eddies and forbidden regions.

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.

The Autonomous Ocean Sampling Network Phase Two (AOSN-II) experiment was conducted in and offshore from the Monterey Bay on the central California coast during July 23-September 6, 2003. The objective of the experiment was to learn how to apply new tools, technologies, and analysis techniques to adaptively sample the coastal ocean in a manner demonstrably superior to traditional methodologies, and to use the information gathered to improve predictive skill for quantities of interest to end-users. The scientific goal was to study the upwelling/relaxation cycle near an open coastal bay in an eastern boundary current region, particularly as it developed and spread from a coastal headland. The suite of observational tools used included a low-flying aircraft, a fleet of underwater gliders, including several under adaptive autonomous control, and propeller-driven AUVs in addition to moorings, ships, and other more traditional hardware. The data were delivered in real time and assimilated into the Harvard Ocean Prediction System (HOPS), the Navy Coastal Ocean Model (NCOM), and the Jet Propulsion Laboratory implementation of the Regional Ocean Modeling System (JPL/ROMS).

Two upwelling events and one relaxation event were sampled during the experiment. The upwelling in both cases began when a pool of cold water less than 13^oC appeared near Cape Ano Nuevo and subsequently spread offshore and southward across the bay as the equatorward wind stress continued. The primary difference between the events was that the first event spread offshore and southward, while the second event spread only southward and not offshore. The difference is attributed to the position and strength of meanders and eddies of the California Current System offshore, which blocked or steered the cold upwelled water. The space and time scales of the mesoscale variability were much shorter than have been previously observed in deep-water eddies offshore. Additional process studies are needed to elucidate the dynamics of the flow.

During the August-September 2003 Autonomous Ocean Sampling Network-II experiment, the Harvard Ocean Prediction System (HOPS) and Error Subspace Statistical Estimation (ESSE) system were utilized in real-time to forecast physical fields and uncertainties, assimilate various ocean measurements (CTD, AUVs, gliders and SST data), provide suggestions for adaptive sampling, and guide dynamical investigations. The qualitative evaluations of the forecasts showed that many of the surface ocean features were predicted, but that their detailed positions and shapes were less accurate. The root-mean-square errors of the real-time forecasts showed that the forecasts had skill out to two days. Mean one-day forecast temperature RMS error was 0.26^oC less than persistence RMS error. Mean two-day forecast temperature RMS error was 0.13^oC less than persistence RMS error. Mean one- or two-day salinity RMS error was 0.036 PSU less than persistence RMS error. The real-time skill in the surface was found to be greater than the skill at depth. Pattern correlation coefficient comparisons showed, on average, greater skill than the RMS errors. For simulations lasting 10 or more days, uncertainties in the boundaries could lead to errors in the Monterey Bay region.

Following the real-time experiment, a reanalysis was performed in which improvements were made in the selection of model parameters and in the open-boundary conditions. The result of the reanalysis was improved long-term stability of the simulations and improved quantitative skill, especially the skill in the main thermocline (RMS simulation error 1^oC less than persistence RMS error out to five days). This allowed for an improved description of the ocean features. During the experiment there were two-week to 10-day long upwelling events. Two types of upwelling events were observed: one with plumes extending westward at point Ano Nuevo (AN) and Point Sur (PS); the other with a thinner band of upwelled water parallel to the coast and across Monterey Bay. During strong upwelling events the flows in the upper 10-20 m had scales similar to atmospheric scales. During relaxation, kinetic energy becomes available and leads to the development of mesoscale features. At 100-300 m depths, broad northward flows were observed, sometimes with a coastal branch following topographic features. An anticyclone was often observed in the subsurface fields in the mouth of Monterey Bay.

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.

The goal of adaptive sampling in the ocean is to predict the types and locations of additional ocean measurements that would be most useful to collect. Quantitatively, what is most useful is defined by an objective function and the goal is then to optimize this objective under the constraints of the available observing network. Examples of objectives are better oceanic understanding, to improve forecast quality, or to sample regions of high interest. This work provides a new path-planning scheme for the adaptive sampling problem. We define the path-planning problem in terms of an optimization framework and propose a method based on mixed integer linear programming (MILP). The mathematical goal is to find the vehicle path that maximizes the line integral of the uncertainty of field estimates along this path. Sampling this path can improve the accuracy of the field estimates the most. While achieving this objective, several constraints must be satisfied and are implemented. They relate to vehicle motion, intervehicle coordination, communication, collision avoidance, etc. The MILP formulation is quite powerful to handle different problem constraints and flexible enough to allow easy extensions of the problem. The formulation covers single- and multiple-vehicle cases as well as singleand multiple-day formulations. The need for a multiple-day formulation arises when the ocean sampling mission is optimized for several days ahead. We first introduce the details of the formulation, then elaborate on the objective function and constraints, and finally, present a varied set of examples to illustrate the applicability of the proposed method.

For efficient progress, model properties and measurement needs can adapt to oceanic events and interactions as they occur. The combination of models and data via data assimilation can also be adaptive. These adaptive concepts are discussed and exemplified within the context of comprehensive real-time ocean observing and prediction systems. Novel adaptive modeling approaches based on simplified maximum likelihood principles are developed and applied to physical and physical-biogeochemical dynamics. In the regional examples shown, they allow the joint calibration of parameter values and model structures. Adaptable components of the Error Subspace Statistical Estimation (ESSE) system are reviewed and illustrated. Results indicate that error estimates, ensemble sizes, error subspace ranks, covariance tapering parameters and stochastic error models can be calibrated by such quantitative adaptation. New adaptive sampling approaches and schemes are outlined. Illustrations suggest that these adaptive schemes can be used in real time with the potential for most efficient sampling.

The problem of how to optimally deploy a suite of sensors to estimate the oceanographic environment is addressed. An optimal way to estimate (nowcast) and predict (forecast) the ocean environment is to assimilate measurements from dynamic and uncertain regions into a dynamical ocean model. In order to determine the sensor deployment strategy that optimally samples the regions of uncertainty, a Genetic Algorithm (GA) approach is presented. The scalar cost function is defined as a weighted combination of a sensor suite’s sampling of the ocean variability, ocean dynamics, transmission loss sensitivity, modeled temperature uncertainty (and others). The benefit of the GA approach is that the user can determine “optimal” via a weighting of constituent cost functions, which can include ocean dynamics, acoustics, cost, time, etc. A numerical example with three gliders, two powered AUVs, and three moorings is presented to illustrate the optimization approach in the complex shelfbreak region south of New England.

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.

Oceanographic conditions in the Gulf of Procchio, along the northern Elba coast, are influenced by the circulation in the Corsica channel and the southeastern Ligurian Sea. In order to support ocean prediction by nested models, an initial 4-day CTD survey provided initial ocean conditions. The purposes of the forecasts were threefold: i) in support of AUV exercises; ii) as an experiment in the development of rapid environmental assessment (REA) methodology; and, iii) as a rigorous real time test of a distributed ocean ocean prediction system technology. The Harvard Ocean Prediction System (HOPS) was set up around Elba in a very high resolution domain (225 m horizontally) which was two-way nested in a high resolution domain (675 m) in the channel between Italy and Corsica. The HOPS channel domain was physically interfaced with a one-way nest to the CU-POM model run in a larger Ligurian Sea domain. Eleven nowcasts and 2-3 day forecasts were issued during the period 26 September to 10 October, 2000 for the channel domain and for a Procchio Bay operational sub-domain of the Elba domain.

After initialization with the NRV Alliance, CTD survey data adaptive sampling patterns for nightly excursions of the Alliance were designed on the basis of forecasts to obtain data for assimilation which would most efficiently maintain the structures and variability of the flow in future dynamical forecasts. Images of satellite sea surface temperature were regularly processed and used for track planning and also for model verification. Rapid environmental assessment (REA) techniques were used for data processing and transmission from ship to shore and vice versa for model results. ADCP data validated well the flow in the channel. Additionally and importantly, the direction and strength of the flow in Procchio Bay were correctly forecast by dynamics supported only by external observations. CU-POM model hydrographic and geostrophic flow data was assimilated successfully on boundary strips of the HOPS domain. Flow fields with/without CU-POM nesting were qualitatively similar and a quantitative analysis of differences is under study. A significant result was the demonstration of a powerful and efficient distributed ocean observing and prediction system with in situ data collected in the Ligurian Sea, satellite data collected at SACLANTCEN, forecast modeling at Harvard University and the University of Colorado, and adaptive sampling tracks designed at Harvard. The distributed system functioned smoothly and effectively and coped with the adverse six-hour time difference between Massachusetts and Italy.

We present the high level architecture of a real-time interdisciplinary ocean forecasting system that employs adaptive elements in both modeling and sampling. We also discuss an important issue that arises in creating an integrated, web-accessible framework for such a system out of existing stand-alone components: transparent support for handling legacy binaries. Such binaries, that are most common in scientific applications, expect a standard input stream, maybe some command line options, a set of input files and generate a set of output files as well as standard output and error streams. Legacy applications of this form are encapsulated using XML. We present a method that uses XML documents to describe the parameters for executing a binary.