Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

Stochastic Transport in Upper Ocean Dynamics

This open access proceedings volume brings selected, peer-reviewed contributions presented at the Stochastic Transport in Upper Ocean Dynamics (STUOD) 2021 Workshop, held virtually and in person at the Imperial College London, UK, September 20–23, 2021. The STUOD project is supported by an ERC Synergy Grant, and led by Imperial College London, the National Institute for Research in Computer Science and Automatic Control (INRIA) and the French Research Institute for Exploitation of the Sea (IFREMER). The project aims to deliver new capabilities for assessing variability and uncertainty in upper ocean dynamics. It will provide decision makers a means of quantifying the effects of local patterns of sea level rise, heat uptake, carbon storage and change of oxygen content and pH in the ocean. Its multimodal monitoring will enhance the scientific understanding of marine debris transport, tracking of oil spills and accumulation of plastic in the sea. All topics of these proceedings are essential to the scientific foundations of oceanography which has a vital role in climate science. Studies convened in this volume focus on a range of fundamental areas, including: Observations at a high resolution of upper ocean properties such as temperature, salinity, topography, wind, waves and velocity; Large scale numerical simulations; Data-based stochastic equations for upper ocean dynamics that quantify simulation error; Stochastic data assimilation to reduce uncertainty. These fundamental subjects in modern science and technology are urgently required in order to meet the challenges of climate change faced today by human society. This proceedings volume represents a lasting legacy of crucial scientific expertise to help meet this ongoing challenge, for the benefit of academics and professionals in pure and applied mathematics, computational science, data analysis, data assimilation and oceanography

A complex network theory approach to oceanic and atmospheric transport phenomena

Doctoral thesis 2015. Doctoral Program of Physics (Universitat de les Illes Balears).[EN] The last two decades have seen important advances in the Lagrangian description of transport and mixing in fluid flows driven by concepts from dynamical systems theory, and nowadays several approaches have been developed. Some of such techniques focus on geometric objects - lines, surfaces - separating fluid regions with different properties while others have focussed on computing stretching-like fields in the fluid domain, such as different types of Lyapunov exponents or other Lagrangian descriptors. Finally, there is a line of research focussing on the moving fluid regions themselves, the so-called set-oriented methods. On the other hand many real-world systems can be studied by using the Network paradigm and in the last years Network Theory approaches have been successfully used for geophysical systems in the context of climate networks in which the connections among the different locations represent statistical relationships between climatic time series from these locations, inferred from correlations and other statistical methods. In this thesis we propose a new paradigm linking the network formalism with transport and mixing phenomena in geophysical flows. We analyze directly the network describing the material fluid flow among different locations, which we call flow network. Among other characteristics this network is directed, weighted, spatially embedded and time-dependent. We illustrate the general ideas with an exemplary network derived from a realistic simulation of the surface flow in the Mediterranean sea. We use network-theory tools to analyze them and gain insights into transport processes from a general point of view. We quantitatively relate dispersion and mixing characteristics, classically quantified by Lyapunov exponents, to the degree of the network nodes. A family of network entropies is defined from the network adjacency matrix, and related to the statistics of stretching in the fluid, in particular to the Lyapunov exponent field. We use a network community detection algorithm, Infomap, to partition the network into coherent regions, i.e. areas internally well mixed, but with little fluid interchange between them. We find interesting applications of this approach to marine biology of the Mediterranean Sea. Oceanic dispersal and connectivity have been identified indeed as crucial factors for structuring marine populations and designing Marine Protected Areas (MPAs). Larvae of different pelagic durations and seasons could be modeled as passive tracers advected in a simulated oceanic surface flow from which a flow network is constructed. By ap- plying the Infomap algorithm we extract hydrodynamical provinces from the network that result to be delimited by frontiers which match multi-scale oceanographic features. By examining the repeated occurrence of such boundaries, we identify the spatial scales and geographic structures that would control larval dispersal across the entire seascape. Based on these hydrodynamical units, we study novel connectivity metrics for existing MPAs.We also define node-by-node proxies measuring local larval retention and exchange. From the analysis of such measures we confirm that retention processes are favored along the coastlines while they are weak in the open ocean due to specific oceanographic conditions. Although these proxies were often studied separately in the literature, we demonstrated that they are inter-related under certain conditions and that their integrated analysis leads to a better understanding of metapopulation dynamics, informing both genetic and demographic connectivities. We also consider paths in weighted and directed temporal networks, introducing tools to compute sets of paths of high probability. We quantify the relative importance of the most probable path between two nodes with respect to the whole set of paths, and to a subset of highly probable paths which incorporate most of the connection probability. These concepts are used to provide alternative definitions of betweenness centrality. We apply these tools to the temporal flow network describing surface currents in the Mediterranean sea. Despite the full transport dynamics is described by a very large number of paths we find that, for realistic time scales, only a very small subset of high probability paths (or even a single most probable one) is enough to characterize global connectivity properties of the network. Finally we apply the same analysis to the atmospheric blocking of eastern Europe and western Russia in summer 2010. We compute the most probable paths followed by fluid particles which reveal the Omega-block skeleton of the event. A hierarchy of sets of highly probable paths is introduced to describe transport pathways when the most probable path alone is not representative enough. These sets of paths have the shape of narrow coherent tubes flowing close to the most probable one. Thus, as for the case of Mediterranean Sea, even when the most probable path is not very significant in terms of its probability, it still identifies the geometry of the transport pathwaysI acknowledge also financial support from FEDER and MINECO (Spain) through the ESCOLA (CTM2012- 39025-C02-01) and INTENSE@COSYP (FIS2012-30634) projects, and from European Commission Marie-Curie ITN program (FP7-320 PEOPLE-2011- ITN) through the LINC project (no. 289447).Peer reviewe

Probabilistic regional ocean predictions : stochastic fields and optimal planning

Thesis: Ph. D. in Mechanical Engineering and Computation, Massachusetts Institute of Technology, Department of Mechanical Engineering, 2018.Cataloged from PDF version of thesis. "Submitted to the Department of Mechanical Engineering and Center for Computational Engineering."Includes bibliographical references (pages 253-268).The coastal ocean is a prime example of multiscale nonlinear fluid dynamics. Ocean fields in such regions are complex, with multiple spatial and temporal scales and nonstationary heterogeneous statistics. Due to the limited measurements, there are multiple sources of uncertainties, including the initial conditions, boundary conditions, forcing, parameters, and even the model parameterizations and equations themselves. To reduce uncertainties and allow long-duration measurements, the energy consumption of ocean observing platforms need to be optimized. Predicting the distributions of reachable regions, time-optimal paths, and risk-optimal paths in uncertain, strong and dynamic flows is also essential for their optimal and safe operations. Motivated by the above needs, the objectives of this thesis are to develop and apply the theory, schemes, and computational systems for: (i) Dynamically Orthogonal ocean primitive-equations with a nonlinear free-surface, in order to quantify uncertainties and predict probabilities for four-dimensional (time and 3-d in space) coastal ocean states, respecting their nonlinear governing equations and non-Gaussian statistics; (ii) Stochastic Dynamically Orthogonal level-set optimization to rigorously incorporate realistic ocean flow forecasts and plan energy-optimal paths of autonomous agents in coastal regions; (iii) Probabilistic predictions of reachability, time-optimal paths and risk-optimal paths in uncertain, strong and dynamic flows. For the first objective, we further develop and implement our Dynamically Orthogonal (DO) numerical schemes for idealized and realistic ocean primitive equations with a nonlinear free-surface. The theoretical extensions necessary for the free-surface are completed. DO schemes are researched and DO terms, functions, and operations are implemented, focusing on: state variable choices; DO norms; DO condition for flows with a dynamic free-surface; diagnostic DO equations for pressure, barotropic velocities and density terms; non-polynomial nonlinearities; semi-implicit time-stepping schemes; and re-orthonormalization consistent with leap-frog time marching. We apply the new DO schemes, as well as their theoretical extensions and efficient serial implementation to forecast idealized-to-realistic stochastic coastal ocean dynamics. For the realistic simulations, probabilistic predictions for the Middle Atlantic Bight region, Northwest Atlantic, and northern Indian ocean are showcased. For the second objective, we integrate data-driven ocean modeling with our stochastic DO level-set optimization to compute and study energy-optimal paths, speeds, and headings for ocean vehicles in the Middle Atlantic Bight region. We compute the energy-optimal paths from among exact time-optimal paths. For ocean currents, we utilize a data-assimilative multiscale re-analysis, combining observations with implicit two-way nested multi-resolution primitive-equation simulations of the tidal-to-mesoscale dynamics in the region. 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. For each arrival time, we then select the vehicle-speed 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 be obtained through a particle backtracking equation. 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. For the third objective, we develop and apply stochastic level-set PDEs that govern the stochastic time-optimal reachability fronts and paths for vehicles in uncertain, strong, and dynamic flow fields. To solve these equations efficiently, we again employ their dynamically orthogonal reduced-order projections. We develop the theory and schemes for risk-optimal planning by combining decision theory with our stochastic time-optimal planning equations. The risk-optimal planning proceeds in three steps: (i) obtain predictions of the probability distribution of environmental flows, (ii) obtain predictions of the distribution of exact time-optimal paths for the forecast flow distribution, and (iii) compute and minimize the risk of following these uncertain time-optimal paths. We utilize the new equations to complete stochastic reachability, time-optimal and risk-optimal path planning in varied stochastic quasi-geostrophic flows. The effects of the flow uncertainty on the reachability fronts and time-optimal paths is explained. The risks of following each exact time-optimal path is evaluated and risk-optimal paths are computed for different risk tolerance measures. Key properties of the risk-optimal planning are finally discussed. Theoretically, the present methodologies are PDE-based and compute stochastic ocean fields, and optimal path predictions without heuristics. Computationally, they are several orders of magnitude faster than direct Monte Carlo. Such technologies have several commercial and societal applications. Specifically, the probabilistic ocean predictions can be input to a technical decision aide for a sustainable fisheries co-management program in India, which has the potential to provide environment friendly livelihoods to millions of marginal fishermen. The risk-optimal path planning equations can be employed in real-time for efficient ship routing to reduce greenhouse gas emissions and save operational costs.by Deepak Narayanan Subramani.Ph. D. in Mechanical Engineering and Computatio

Do bacteria thrive when the ocean acidifies? Results from an off-­shore mesocosm study

Marine bacteria are the main consumers of the freshly produced organic matter. In order to meet their carbon demand, bacteria release hydrolytic extracellular enzymes that break down large polymers into small usable subunits. Accordingly, rates of enzymatic hydrolysis have a high potential to affect bacterial organic matter recycling and carbon turnover in the ocean. Many of these enzymatic processes were shown to be pH sensitive in previous studies. Due to the continuous rise in atmospheric CO2 concentration, seawater pH is presently decreasing at a rate unprecedented during the last 300 million years with so-far unknown consequences for microbial physiology, organic matter cycling and marine biogeochemistry. We studied the effects of elevated seawater pCO2 on a natural plankton community during a large-scale mesocosm study in a Norwegian fjord. Nine 25m-long Kiel Off-Shore Mesocosms for Future Ocean Simulations (KOSMOS) were adjusted to different pCO2 levels ranging from ca. 280 to 3000 µatm by stepwise addition of CO2 saturated seawater. After CO2 addition, samples were taken every second day for 34 days. The first phytoplankton bloom developed around day 5. On day 14, inorganic nutrients were added to the enclosed, nutrient-poor waters to stimulate a second phytoplankton bloom, which occurred around day 20. Our results indicate that marine bacteria benefit directly and indirectly from decreasing seawater pH. During both phytoplankton blooms, more transparent exopolymer particles were formed in the high pCO2 mesocosms. The total and cell-specific activities of the protein-degrading enzyme leucine aminopeptidase were elevated under low pH conditions. The combination of enhanced enzymatic hydrolysis of organic matter and increased availability of gel particles as substrate supported higher bacterial abundance in the high pCO2 treatments. We conclude that ocean acidification has the potential to stimulate the bacterial community and facilitate the microbial recycling of freshly produced organic matter, thus strengthening the role of the microbial loop in the surface ocean

Controllability and Stabilization of Kolmogorov Forward Equations for Robotic Swarms

abstract: Numerous works have addressed the control of multi-robot systems for coverage, mapping, navigation, and task allocation problems. In addition to classical microscopic approaches to multi-robot problems, which model the actions and decisions of individual robots, lately, there has been a focus on macroscopic or Eulerian approaches. In these approaches, the population of robots is represented as a continuum that evolves according to a mean-field model, which is directly designed such that the corresponding robot control policies produce target collective behaviours. This dissertation presents a control-theoretic analysis of three types of mean-field models proposed in the literature for modelling and control of large-scale multi-agent systems, including robotic swarms. These mean-field models are Kolmogorov forward equations of stochastic processes, and their analysis is motivated by the fact that as the number of agents tends to infinity, the empirical measure associated with the agents converges to the solution of these models. Hence, the problem of transporting a swarm of agents from one distribution to another can be posed as a control problem for the forward equation of the process that determines the time evolution of the swarm density. First, this thesis considers the case in which the agents' states evolve on a finite state space according to a continuous-time Markov chain (CTMC), and the forward equation is an ordinary differential equation (ODE). Defining the agents' task transition rates as the control parameters, the finite-time controllability, asymptotic controllability, and stabilization of the forward equation are investigated. Second, the controllability and stabilization problem for systems of advection-diffusion-reaction partial differential equations (PDEs) is studied in the case where the control parameters include the agents' velocity as well as transition rates. Third, this thesis considers a controllability and optimal control problem for the forward equation in the more general case where the agent dynamics are given by a nonlinear discrete-time control system. Beyond these theoretical results, this thesis also considers numerical optimal transport for control-affine systems. It is shown that finite-volume approximations of the associated PDEs lead to well-posed transport problems on graphs as long as the control system is controllable everywhere.Dissertation/ThesisDoctoral Dissertation Mechanical Engineering 201

Modelling the ecology, dynamics and assessment of Nephrops norvegicus (Linnaeus 1758) in the waters around Ireland

Nephrops norvegicus is a valuable market species in the North-East Atlantic and it is of economic importance to Ireland. The present study investigated the status of the Aran ground stock, frequently ranked within the top two commercially valuable “fish” landed. Since 2002, under water TV surveys have been developed to provide a fishery independent estimate of burrow abundance in areas that exhibited a steady decrease in Nephrops over two decades contrasting with the increasing landings. In order to identify stock status and provide reliable information to management, we used a number of different approaches in the fields of time series analysis, spatial analysis and fisheries stock assessment. We examined the temporal fluctuations in a 16 year time series of landings in Aran grounds and found fluctuating cycles within an overall decreasing trend. This stock dynamic was also compared with the other main areas of harvest off the coast of Ireland (Smalls ground, Porcupine Bank, and the west Irish Sea) disclosing a regional common trend in the pattern of the stocks for connecting areas. Regional climatic influences (e.g NAO, AO and AMO) have been detected on various time scales ranging from month to years and the time series analysis method appears effective for detecting changes in fishing behaviours. Spatial analysis of the burrow density over the stock area revealed patchy distribution varying in size and intensity over the years with a spatio-temporal trend marked by a depletion of abundance in midfield with noticeable consequences for fishing vessel activity at a regional level. This spatial approach enabled the evaluation of the influence of the mud content of the seabed on the density of burrows and to explore the potential impact of the prevailing current circulation pattern during the planktonic stage of Nephrops on the level of recruitment by using remote sensing data. For an optimal fisheries management strategy, demographic information for the exploited species is necessary and for Nephrops, effective stock assessment is hampered because of the difficulty in age determination. A biomass model with a Schaefer surplus yield component and a data limited CMSY method were chosen to address the lack of age data and to predict biomass and related key fisheries reference points. Both approaches underline the ongoing decline of Nephrops abundance and reveal warning signals of unsustainable fishing exploitation