Papers by Pierre Lermusiaux
Journal Of Geophysical Research: Oceans, Mar 1, 2022
Mediterranean Basin are visible for instance in images of ocean color (Figure ) and sea surface t... more Mediterranean Basin are visible for instance in images of ocean color (Figure ) and sea surface temperature (SST; Figure ). The ocean color imagery presents a large eddy where the larger concentrations of chlorophyll located on its outer part are associated with the WAGF. On the other hand, the SST image shows a penetrating and elongated meander associated with the EAGF that introduces cold water to the interior of the Mediterranean Sea. The scales of interest in this study are 1-100 km in the horizontal, 0-1,000 m in the vertical, and from a day to several weeks in time. While the large spatio-temporal scales are dominated by the effects of Earth's rotation, which constrain the motion to be largely horizontal to satisfy the geostrophic and the thermal wind balance, the ageostrophic motion and vertical velocities become more important at the smallest scales leading to a non-rotational and unbalanced flow. These ocean scales include mesoscale flows (10-100 km, and a few weeks) characterized by a small Rossby number, Ro ≪ 1, and a large Richardson number, Ri = N 2 /U z (where N 2 is the buoyancy frequency and U z is the vertical gradient of the horizontal velocity). At smaller scale, the submesoscale flows (1-10 km, and a few days) occur with 𝐴𝐴 (1) Ro and Ri. These processes are driven by internal instabilities, buoyancy forcing or wind stress at the surface . At the mesoscale, the flow is predominantly two-dimensional as the magnitude of the vertical velocities (W) is several orders of magnitude smaller than the horizontal velocities, 𝐴𝐴 𝐴𝐴≈ (1-10 m/day). Nevertheless, the magnitude of the vertical velocities increases as a smaller spatio-temporal scale is approached. For submesoscale 𝐴𝐴 𝐴𝐴 ≈ (100 m/day) as a result of ageostrophic motions (Mahadevan, 2016). Important efforts have historically been made to measure vertical velocities in the frontal zones of the Alboran Sea . For example, in the Western Alboran Sea, used a quasi-geostrophic omega equation to estimate vertical velocities around 20-30 m/day related to the mesoscale circulation. In the Eastern Alboran Sea, Ruiz et al. ( ) found vertical velocities of 10 m/day associated with a large-scale circulation. The vertical velocities from the quasi-geostrophic omega equation is valid for the mesoscale flow. However, this equation fails to capture 𝐴𝐴 (1) Rossby number dynamics associated with submesoscales. For these small scales better approximations should include the advection of ageostrophic velocities terms . The circulation of the flow at the front is defined primarily by an along-front jet and an across-front ageostrophic secondary circulation (ASC; McWilliams, 2016). The jet separates dense waters with positive relative vertical vorticity (ξ) and light waters with negative ξ; meanwhile, the ASC is characterized by upward velocities in the front's light side and downward velocities in the dense side. The project entitled Coherent Lagrangian Pathways from the Surface Ocean to Interior (CALYPSO, Office of Naval Research initiative (Mahadevan et al., 2021)) addresses the challenges of observing, understanding, and predicting the vertical velocities and three dimensional pathways on subduction processes of the fronts in the Alboran Sea. Within this scope, the focus of this paper is
Journal of the Acoustical Society of America, May 1, 2008
We present the spatial and temporal variability of the acoustic field in Dabob Bay during the PLU... more We present the spatial and temporal variability of the acoustic field in Dabob Bay during the PLUSNet07 Exercise. The study uses a 4-D (3-D in space with 1-D in time) data-assimilative numerical ocean model to provide input to an acoustic propagation model. The ocean physics models (primitive-equations and tidal models) of the Multidisciplinary Simulation, Estimation, and Assimilation System (MSEAS), with CTD data assimilation, provided ocean predictions in the region. The output ocean forecasts had a 300m and 1 to 5m resolution in the horizontal and vertical directions, at 3-hour time intervals within a 15-day period. This environmental data, as the input to acoustic modeling, allowed for the prediction and study of the diurnal and semi-diurnal temporal variations of the acoustic field, as well as the varying spatial structures of the field. Using the CSNAP one-way coupled-normal-mode code, along-and across-sections in the Dabob Bay acoustic field structures at 100, 400, and 900 Hz were forecasted and described twice-daily, for various source depths. Interesting propagation effects, such as acoustic fluctuations with respect to the source depth and frequency as a result of the regional ocean variability, wind forcing, and tidal effects are discussed. The novelty of this work lies in the possibility of accurate acoustic TL prediction in the littoral region by physically coupling the real-time ocean prediction system to real-time acoustic modeling. This work also offers an opportunity to study 4-D acoustic modeling in the future.
To understand the dynamics and health of marine ecosystems such as lagoons and coral reefs as wel... more To understand the dynamics and health of marine ecosystems such as lagoons and coral reefs as well as to understand the impact of human activities on these systems, it is imperative to predict the residence times of water masses and connectivity between ocean domains. In the present work, we consider the pristine lagoons and coral reefs of the Red Sea as an example of such sensitive ecosystems, with a large number of marine species, many of which are unique to the region. To study the residence times and connectivity patterns, we make use of recent advances in dynamic three-dimensional Lagrangian analyses using partial differential equations. Specifically, we extend and apply our novel efficient flow map composition scheme to predict the time needed for any particular water parcel to leave the domain of interest (i.e. a lagoon) as well as the time for any particular water parcel to enter that domain. These spatiotemporal residence time fields along with fourdimensional Lagrangian metrics such as finite time Lyapunov exponent (FTLE) fields provide a quantitative description of the Lagrangian pathways and connectivity patterns of lagoons in the Red Sea.
Global Oceans 2020: Singapore – U.S. Gulf Coast, Oct 5, 2020
We describe and investigate several Dynamic Mode Decomposition (DMD) and reduced order projection... more We describe and investigate several Dynamic Mode Decomposition (DMD) and reduced order projection methods for regional stochastic ocean predictions. We then showcase some of their results as applied to a 300-member set of ensemble forecasts from the POSYDON-POINT sea experiment in the Middle Atlantic-New York Bight region for the period 23-27 August 2018 as well as to a 42-day data-driven reanalysis from the AWACS-SW06 sea experiment in the Middle Atlantic Bight region for the period 14 August to 24 September 2006. We discuss these results for use by autonomous platforms in uncertain scenarios as well the combination of DMD with ideas from large-ensemble forecasting and Dynamically-Orthogonal (DO) differential equations.
To cleanup marine plastics, accurate modeling is needed. We outline and illustrate a new partial-... more To cleanup marine plastics, accurate modeling is needed. We outline and illustrate a new partial-differentialequation methodology for characterizing and modeling plastic transports in time and space (4D), showcasing results for Massachusetts Bay. We couple our primitive equation model for ocean dynamics with our composition based advection for Lagrangian transport. We show that the ocean physics predictions have skill by comparison with synoptic data. We predict the fate of plastics originating from four sources: rivers, beach and nearshore, local Bay, and remote offshore. We analyze the transport patterns and the regions where plastics accumulate, comparing results with and without plastic settling. Simulations agree with existing debris and plastics data. They also show new results: (i) Currents set-up by wind events strongly affect floating plastics. Winds can for example prevent Merrimack outflows reaching the Bay; (ii) There is significant chaotic stirring between nearshore and offshore floating plastics as explained by ridges of Lagrangian Coherent Structures (LCSs); (iii) With 4D plastic motions and settling, plastics from the Merrimack and nearshore regions can settle to the seabed before offshore advection; (iv) Internal waves and tides can bring plastics downward and out of main currents, leading to settling to the deep bottom. (v) Attractive LCSs ridges are frequent in the northern Cape Cod Bay, west of the South Shore, and southern Stellwagen Bank. They lead to plastic accumulation and sinking along thin subduction zones.
Journal Of Geophysical Research: Oceans, Aug 1, 2016
Internal tides in the Middle Atlantic Bight region are found to be noticeably influenced by the p... more Internal tides in the Middle Atlantic Bight region are found to be noticeably influenced by the presence of the shelfbreak front and the Gulf Stream, using a combination of observations, equations, and data-driven model simulations. To identify the dominant interactions of these waves with subtidal flows, vertical-mode momentum and energy partial differential equations are derived for small-amplitude waves in a horizontally and vertically sheared mean flow and in a horizontally and vertically variable density field. First, the energy balances are examined in idealized simulations with mode-1 internal tides propagating across and along the Gulf Stream. Next, the fully nonlinear dynamics of regional tide-mean-flow interactions are simulated with a primitive-equation model, which incorporates realistic summer-mesoscale features and atmospheric forcing. The shelfbreak front, which has horizontally variable stratification, decreases topographic internal-tide generation by about 10% and alters the wavelengths and arrival times of locally generated mode-1 internal tides on the shelf and in the abyss. The (sub)mesoscale variability at the front and on the shelf, as well as the summer stratification itself, also alter internal-tide propagation. The Gulf Stream produces anomalous regions of O(20 mW m 22 ) mode-1 internal-tide energy-flux divergence, which are explained by tide-mean-flow terms in the mode-1 energy balance. Advection explains most tide-mean-flow interaction, suggesting that geometric wave theory explains mode-1 reflection and refraction at the Gulf Stream. Geometric theory predicts that offshore-propagating mode-1 internal tides that strike the Gulf Stream at oblique angles (more than thirty degrees from normal) are reflected back to the coastal ocean, preventing their radiation into the central North Atlantic.
arXiv (Cornell University), Nov 12, 2022
Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to the spa... more Predictive dynamical models for marine ecosystems are used for a variety of needs. Due to the sparse measurements and limited understanding of the myriad of ocean processes, there is however significant uncertainty. There is model uncertainty in the parameter values, functional forms with diverse parameterizations, and level of complexity needed, and thus in the state variable fields. We develop a Bayesian model learning methodology that allows interpolation in the space of candidate dynamical models and discovery of new models from noisy, sparse, and indirect observations, all while estimating state variable fields and parameter values, as well as the joint probability distributions of all learned quantities. We address the challenges of high-dimensional and multidisciplinary dynamics governed by partial differential equations (PDEs) by using state augmentation and the computationally efficient Gaussian Mixture Model -Dynamically Orthogonal filter. Our innovations include stochastic formulation parameters and stochastic complexity parameters to unify candidate models into a single general model as well as stochastic expansion parameters within piecewise function approximations to generate dense candidate model spaces. These innovations allow handling many compatible and embedded candidate models, possibly none of which are accurate, and learning elusive unknown functional forms that augment these models. Our new Bayesian methodology is generalizable and interpretable. It seamlessly and rigorously discriminates among existing models, but also extrapolates out of the space of models to discover new ones. We perform a series of twin experiments based on flows past a ridge coupled with three-to-five component ecosystem models, including flows with chaotic advection. We quantify the learning skill, and evaluate convergence and the sensitivity to hyper-parameters. Our PDE framework successfully discriminates among functional forms and model complexities, and learns in the absence of prior knowledge by searching in dense function spaces. The probabilities of known, uncertain, and unknown model formulations, and of biogeochemical-physical fields and parameters, are updated jointly using Bayes' law. Non-Gaussian statistics, ambiguity, and biases are captured. The parameter values and the model formulations that best explain the noisy, sparse, and indirect data are identified. When observations are sufficiently informative, model complexity and model functions are discovered.
Developing a U.S. Research Agenda to Advance Subseasonal to Seasonal Forecasting
AGU Fall Meeting Abstracts, Dec 17, 2015
Coastal circulation and water transport properties of the Red Sea Project lagoon
Ocean Modelling, 2021
arXiv (Cornell University), Sep 25, 2022
Finite element discretizations of problems in computational physics often rely on adaptive mesh r... more Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies are often heuristic and rely on domain-specific knowledge or trial-and-error. We treat the process of adaptive mesh refinement as a local, sequential decisionmaking problem under incomplete information, formulating AMR as a partially observable Markov decision process. Using a deep reinforcement learning approach, we train policy networks for AMR strategy directly from numerical simulation. The training process does not require an exact solution or a high-fidelity ground truth to the partial differential equation at hand, nor does it require a precomputed training dataset. The local nature of our reinforcement learning formulation allows the policy network to be trained inexpensively on much smaller problems than those on which they are deployed. The methodology is not specific to any particular partial differential equation, problem dimension, or numerical discretization, and can flexibly incorporate diverse problem physics. To that end, we apply the approach to a diverse set of partial differential equations, using a variety of highorder discontinuous Galerkin and hybridizable discontinuous Galerkin finite element discretizations. We show that the resultant deep reinforcement learning policies are competitive with common AMR heuristics, generalize well across problem classes, and strike a favorable balance between accuracy and cost such that they often lead to a higher accuracy per problem degree of freedom.
Toward Dynamic Data-Driven Systems for Rapid Adaptive Interdisciplinary Ocean Forecasting
In this paper, we quantify the dynamical causes and uncertainties of striking differences in acou... more In this paper, we quantify the dynamical causes and uncertainties of striking differences in acoustic transmission data collected on the shelf and shelfbreak in the northeastern Taiwan region within the context of the 2008 Quantifying, Predicting, and Exploiting Uncertainty (QPE 2008) pilot experiment. To do so, we employ our coupled oceanographic (4-D) and acoustic (Nx2-D) modeling systems with ocean data assimilation and a best-fit depth-dependent geoacoustic model. Predictions are compared to the measured acoustic data, showing skill. Using an ensemble approach, we study the sensitivity of our results to uncertainties in several factors, including geoacoustic parameters, bottom layer thickness, bathymetry, and ocean conditions. We find that the lack of signal received on the shelfbreak is due to a 20-dB increase in transmission loss (TL) caused by bottom trapping of sound energy during up-slope transmissions over the complex and deeper bathymetry. Sensitivity studies on sediment properties show larger but isotropic TL variations on the shelf and smaller but more anisotropic TL variations over the shelfbreak. Sediment sound-speed uncertainties affect the shape of the probability density functions of the TLs more than uncertainties in sediment densities and attenuations. Diverse thicknesses of sediments lead to only limited effects on the TL. The small bathymetric data uncertainty is modeled and also leads to small TL variations. We discover that the initial transport conditions in the Taiwan Strait can affect acoustic transmissions downstream more than 100 km away, especially above the shelfbreak. Simulations also reveal internal tides and we quantify their spatial and temporal effects on the ocean and acoustic fields. One type of predicted waves are semidiurnal shelfbreak internal tides propagating up-slope with wavelengths around 40-80 km, horizontal phase speeds of 0.5-1 m/s, and vertical peak-to-peak displacements of isotherms of 20-60 m. These waves lead to variations of broadband TL estimates over 5-6-km range that are more isotropic and on bearing average larger (up to 5-8-dB amplitudes) on the shelf than on the complex shelfbreak where the TL varies rapidly with bearing angles.
Marine Technology Society Journal, May 1, 2021
The oceans make this planet habitable and provide a variety of essential ecosystem services rangi... more 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 integrated ocean dynamics and acoustics project
Journal of the Acoustical Society of America, 2016
The goal of timely and accurate acoustics modeling in the ocean depends on accurate environmental... more The goal of timely and accurate acoustics modeling in the ocean depends on accurate environmental input information. Acoustic propagation modeling has improved to the point of possibly being ahead of ocean dynamical modeling from the standpoint that some significant ocean features having strong acoustic effects are not faithfully reproduced in many models, particularly data-driven ocean models. This in part stems from the fact that ocean models have developed with other goals in mind, but computational limitations also play a role. The Integrated Ocean Dynamics and Acoustics (IODA) MURI project has as its goals improving ocean models, and also making continued improvements to acoustic models, for the purpose of advancing ocean acoustic modeling and prediction capabilities. Two major focuses are improved internal tide forecasting and improved nonlinear internal wave forecasting, which require pushing the state of the art in data-constrained mesoscale feature modeling as well as devel...
High frequency stochastic acoustic wavefront propagation and joint ocean-acoustic inference: The GMM-DO wavefront
Journal of the Acoustical Society of America, Oct 1, 2022
In marine applications, the value of accurate modeling and learning for stochastic acoustic propa... more In marine applications, the value of accurate modeling and learning for stochastic acoustic propagation in uncertain ocean environments cannot be overstated. In this work, we derive stochastic theory and schemes for (i) modeling of high frequency acoustic propagation in uncertain ocean environments and (ii) joint Bayesian assimilation of ocean-acoustic measurements to infer fields, parameters, and uncertain model functions. We first obtain the Dynamically Orthogonal (DO) wavefront equations to solve for the stochastic extension of the Liouville Equation that governs the dynamics of acoustic wavefront in an augmented phase space. These DO wavefront equations provide the prior for the Gaussian Mixture Model—DO (GMM-DO) filter that completes joint physics-acoustics Bayesian inference using sparse observations. Specifically, given a set of receivers, the Eulerian nature of the DO wavefront equations allows for the efficient extraction of arrival time prior probability distributions. The GMM-DO Waverfront filter then combines these joint priors with arrival time measurements using Bayes rule, jointly inferring environmental properties (e.g., unknown source location and/or sound speed field), the acoustic wavefront distribution, and the arrival time distribution itself. We evaluate results using high-frequency applications, illustrating the estimation of mean fields and properties, but also of probability density distributions and model parameterizations.
Twenty-first century outer continental shelf and shelfbreak acoustics research: Methods, tools, and progress
Journal of the Acoustical Society of America, Oct 1, 2022
New findings in outer-shelf and shelfbreak acoustics have been enabled by experimental and comput... more New findings in outer-shelf and shelfbreak acoustics have been enabled by experimental and computational advances over the last 25 years. The details of sound field variability caused by highly dynamic conditions often found in this regime have become measurable through advances in data collection technology. Furthermore, these details can now be computationally modeled more realistically. The coupling of more plentiful data and higher fidelity modeling has uncovered many new behaviors. It has also allowed us to quantify the effects on sound level and phase structure (coherence) of many outer-shelf physical features, as well as the temporal aspects of these variations. Key tools have been vessel dynamic positioning, underwater position finding, small mobile platforms, high-capacity multichannel receive arrays, data-assimilating regional ocean dynamical models, nonlinear wave modeling, and three-dimensional acoustic propagation modeling. Examples from the published work of the authors, and the work of others, of how these advances have fostered new knowledge of specific processes will be presented, as well as present-day challenges inspired by recent findings.
Incremental Low-Rank Dynamic Mode Decomposition Model for Efficient Forecast Dissemination and Onboard Forecasting
OCEANS 2022, Hampton Roads, Oct 17, 2022
High-Performance Visualization for Ocean Modeling
OCEANS 2022, Hampton Roads, Oct 17, 2022
Stochastic sound propagation using dynamically orthogonal parabolic equations
Journal of the Acoustical Society of America, Oct 1, 2021
Accurate modeling of underwater acoustic propagation is challenging due to the complex ocean phys... more Accurate modeling of underwater acoustic propagation is challenging due to the complex ocean physics and acoustic dynamics and the need for resolving the wavelength of the propagating acoustic wave over large distances. These challenges are further amplified by the incomplete knowledge of the ocean environment and the acoustic parameters. These complexities thus lead to many sources of uncertainties in the governing models. In this work, we use our stochastic Dynamically Orthogonal (DO) framework to represent these uncertainties probabilistically in the acoustic Parabolic Equation (PE). These equations optimally represent the dominant uncertainties in the sound speed, density, bathymetry, and acoustic pressure fields. Starting from the governing PE, we derive range-evolution DO differential equations for the mean field, stochastic modes, and coefficients, hence preserving the nonlinearities and capturing the non-Gaussian statistics. The DO equations are implemented for the narrow-angle PE and higher-order Padé wide-angle PEs and are applied in range-dependent canonical test cases and realistic ocean environments with uncertain source location, source frequency, sound speed, and/or bathymetry fields. We highlight the computational advantages of our framework by comparing it to Monte Carlo predictions and show convergence of the probability density functions as the number of samples and/or modes is increased.
Uploads
Papers by Pierre Lermusiaux