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In this work, we study a three-wave kinetic equation with resonance broadening arising from the theory of stratified ocean flows. Unlike Gamba-Smith-Tran(On the wave turbulence theory for stratified flows in the ocean, Math. Models Methods Appl. Sci. 30 (2020), no.1, 105--137), we employ a different formulation of the resonance broadening, which makes the present model more suitable for ocean applications. We establish the global existence and uniqueness of strong solutions to the new resonance broadening kinetic equation.
In this paper, we detail the high-performance implementation of our spaceborne radar simulator for satellite oceanography. Our software simulates the sea surface and the signal to imitate, as far as possible, the measurement process, starting from its lowest level mechanisms. In this perspective, raw data are computed as the sum of many illuminated scatterers, whose time-evolving properties are related to the surface roughness, topography, and kinematics. To achieve efficient performance, we intensively use GPU computing. Moreover, we propose a fast simulation mode based on the assumption that the instantaneous Doppler spectrum within a range gate varies on a timescale significantly larger than the PRI. The sea surface can then be updated at a frequency much smaller than the PRF, drastically reducing the computational cost. When the surface is updated, Doppler spectra are computed for all range gates. Signals segments are then obtained through 1D inverse Fourier transforms and pondered to ensure a smooth time evolution between surface updates. We validate this fast simulation mode with a radar altimeter simulation case of the Sentinel-3 SRAL instrument, showing that simulated raw d
Machine learning (ML) refers to computer algorithms that predict a meaningful output or categorize complex systems based on a large amount of data. ML is applied in various areas including natural science, engineering, space exploration, and even gaming development. This review focuses on the use of machine learning in the field of chemical and biological oceanography. In the prediction of global fixed nitrogen levels, partial carbon dioxide pressure, and other chemical properties, the application of ML is a promising tool. Machine learning is also utilized in the field of biological oceanography to detect planktonic forms from various images (i.e., microscopy, FlowCAM, and video recorders), spectrometers, and other signal processing techniques. Moreover, ML successfully classified the mammals using their acoustics, detecting endangered mammalian and fish species in a specific environment. Most importantly, using environmental data, the ML proved to be an effective method for predicting hypoxic conditions and harmful algal bloom events, an essential measurement in terms of environmental monitoring. Furthermore, machine learning was used to construct a number of databases for variou
An algorithm for determining stationary periods for time series of random sea waves is proposed in this work. This is a problem in which changes between stationary sea states are usually slow and segmentation procedures based on change-point detection frequently give poor results. The method is based on a new procedure for time series clustering, built on the use of the total variation distance between normalized spectra as a measure of dissimilarity. The oscillatory behavior of the series is thus considered the central characteristic for classification purposes. The proposed algorithm is compared to several other methods which are also based on features extracted from the original series and the results show that its performance is comparable to the best methods available and in some tests it performs better. This clustering method may be of independent interest.
We review the study of rogue waves and related instabilities in optical and oceanic environments, with particular focus on recent experimental developments. In optics, we emphasize results arising from the use of real-time measurement techniques, whilst in oceanography we consider insights obtained from analysis of real-world ocean wave data and controlled experiments in wave tanks. Although significant progress in understanding rogue waves has been made based on an analogy between wave dynamics in optics and hydrodynamics, these comparisons have predominantly focused on one-dimensional nonlinear propagation scenarios. As a result, there remains significant debate about the dominant physical mechanisms driving the generation of ocean rogue waves in the complex environment of the open sea. Here, we review state-of-the-art of rogue wave studies in optics and hydrodynamics, aiming to clearly identify similarities and differences between the results obtained in the two fields. In hydrodynamics, we take care to review results that support both nonlinear and linear interpretations of ocean rogue wave formation, and in optics, we also summarise results from an emerging area of research ap
Small satellites and autonomous vehicles have greatly evolved in the last few decades. Hundreds of small satellites have been launched with increasing functionalities, in the last few years. Likewise, numerous autonomous vehicles have been built, with decreasing costs and form-factor payloads. Here we focus on combining these two multifaceted assets in an incremental way, with an ultimate goal of alleviating the logistical expenses in remote oceanographic operations. The first goal is to create a highly reliable and constantly available communication link for a network of autonomous vehicles, taking advantage of the small satellite lower cost, with respect to conventional spacecraft, and its higher flexibility. We have developed a test platform as a proving ground for this network, by integrating a satellite software defined radio on an unmanned air vehicle, creating a system of systems, and several tests have been run successfully, over land. As soon as the satellite is fully operational, we will start to move towards a cooperative network of autonomous vehicles and small satellites, with application in maritime operations, both \textit{in-situ} and remote sensing.
Observations of quasi-periodic oscillations (QPOs) in the luminosity from many accreting neutron stars (NS) have led us to investigate a source of periodicity prevalent in other stars: non-radial oscillations. After summarizing the structure of the atmosphere and ocean of an accreting NS, we discuss the various low l g-modes with frequencies in the 1-100 Hz range. Successful identification of a non-radial mode with an observed frequency would yield new information about the thermal and compositional makeup of the NS, as well as its radius. We close by discussing how rapid rotation changes the g-mode frequencies.
To build insight into the atmosphere and ocean, it is useful to apply qualitative reasoning to predict the geophysical fluid dynamicss of worlds radically different from our own such as exoplanets, earth in Nuclear Winter, other solar system worlds, and far future terrestial climates. Here, we look at atmospheric and oceanic dynamics on a flat earth, that is a disc-shaped planet rather like Sir Terry Pratchet's fantasy Discworld. Altough this has the disadvantage that this geometry is a completely imaginary, there is a rich larray of videos by flat earth proponents whose errors illuminate how concepts can be misconceived and misapplied by amateurs and freshman science studients. As such, this case is very useful to geophysics instructors. We show that weather and ocean flows on a flat, nonrotating earth and a rotating spherical planet are wildly different. These differences are a crushing debunk of the flat earh heresy, if one were needed. The "high contrast" of these very different atmospheres and oceans is valuable in instilling the open-mindedness that is essential in understanding excoplanets and Nuclear Winter and Post-Climate-Apocalypse earth.
We consider the assimilation of Lagrangian data into a primitive equations circulation model of the ocean at basin scale. The Lagrangian data are positions of floats drifting at fixed depth. We aim at reconstructing the four-dimensional space-time circulation of the ocean. This problem is solved using the four-dimensional variational technique and the adjoint method. In this problem the control vector is chosen as being the initial state of the dynamical system. The observed variables, namely the positions of the floats, are expressed as a function of the control vector via a nonlinear observation operator. This method has been implemented and has the ability to reconstruct the main patterns of the oceanic circulation. Moreover it is very robust with respect to increase of time-sampling period of observations. We have run many twin experiments in order to analyze the sensitivity of our method to the number of floats, the time-sampling period and the vertical drift level. We compare also the performances of the Lagrangian method to that of the classical Eulerian one. Finally we study the impact of errors on observations.
Echo-sounder data registered by buoys attached to drifting FADs provide a very valuable source of information on populations of tuna and their behaviour. This value increases whenthese data are supplemented with oceanographic data coming from CMEMS. We use these sources to develop Tuna-AI, a Machine Learning model aimed at predicting tuna biomass under a given buoy, which uses a 3-day window of echo-sounder data to capture the daily spatio-temporal patterns characteristic of tuna schools. As the supervised signal for training, we employ more than 5000 set events with their corresponding tuna catch reported by the AGAC tuna purse seine fleet.
A defining feature of the present-day global overturning circulation (GOC) is the absence of deep water formation in the Pacific, in contrast to the Atlantic. This asymmetry, associated with higher surface salinities in the North Atlantic, is reflected in the Atlantic Meridional Overturning Circulation (AMOC) and the lack of a Pacific overturning (PMOC). A commonly cited explanation is the asymmetry in surface freshwater fluxes, with the Pacific receiving more freshwater per unit area than the Atlantic. Here, we develop a two-basin conceptual ocean model, consisting of a wide and a narrow basin. The model admits three states: sinking confined to the narrow basin, sinking confined to the wide basin, and sinking in both basins. We analyze the (co-)existence of these states as a function of freshwater asymmetry and hydrological cycle strength, defined as the longitudinally symmetric freshwater flux. For a weak hydrological cycle, representative of warm Pliocene-like climate conditions, sinking occurs in both basins, with symmetry breaking only when one basin is sufficiently more evaporative. For intermediate conditions, representative of the present-day climate, the basin with slightl
Rogue waves are extreme ocean events characterized by the sudden formation of anomalously large crests, and remain an important subject of investigation in oceanography and mathematics. A central problem is to quantify the probability of their formation under random Gaussian sea initial data. In this work, we rigorously characterize the tail-probability for the formation of rogue waves of the pure gravity water wave equations in deep water, the most accurate quasilinear PDE modeling waves in open ocean. This large deviation result rigorously proves various conjectures from the oceanography literature in the weakly nonlinear regime. Moreover, the result holds up to the optimal timescales allowed by deterministic well-posedness theory. The proof shows that rogue waves most likely arise through "dispersive focusing", where phase quasi-synchronization produces constructive amplification of the water crest. The main difficulty in justifying this mechanism is propagating statistical information over such long timescales, which we overcome by combining normal forms and probabilistic methods. Unlike prior work, this novel approach does not require approximate solutions to be Gaussian. Our
Bathymetry reconstruction is an important problem in various fields, including oceanography and environmental monitoring. This paper presents a Bayesian inference approach to reconstructing bathymetries from point measurements of the water height. We test the method for parameterized and discretized bathymetries with synthetic data to evaluate its performance and limitations. Our results indicate that the Bayesian framework provides a robust approach to bathymetry reconstruction. Finally, we use the framework to reconstruct a real-world bathymetry in a wave flume from experimental measurements and compare its performance to an adjoint optimization method. The Bayesian approach improves the normalized root mean squared error (NRMSE) of the reconstruction and provides better qualitative features, while also quantifying uncertainty.
Melting is omnipresent in nature and technology, with applications ranging from metallurgy, biology, food science, and latent thermal energy storage to oceanography, geophysics, and climate science, and occurring on all scales from sub-millimeter to global scales. The key objective is to understand the rate at which an object melts as a function of its size and of the ambient conditions. To achieve this it is important to be able to extrapolate from small scale experiments and observations to large or even global scales. This is done by scaling laws. However, these are only meaningful if there is no transition from one scaling relation to another one. Here we show, however, that for both fixed and freely-advected melting objects immersed in a turbulent flow a melting transition does exist, namely from slow melting at the small scales to fast melting at the large scales. We do so by controlled melting experiments and corresponding direct numerical simulations, covering four orders of magnitude in scale. The transition corresponds to the transition from a laminar-type boundary layer around the melting object to a turbulent-type boundary layer, i.e., from so-called classical turbulenc
This paper explores the versatility and depth of Bayesian modeling by presenting a comprehensive range of applications and methods, combining Markov chain Monte Carlo (MCMC) techniques and variational approximations. Covering topics such as hierarchical modeling, spatial modeling, higher-order Markov chains, and Bayesian nonparametrics, the study emphasizes practical implementations across diverse fields, including oceanography, climatology, epidemiology, astronomy, and financial analysis. The aim is to bridge theoretical underpinnings with real-world applications, illustrating the formulation of Bayesian models, elicitation of priors, computational strategies, and posterior and predictive analyses. By leveraging different computational methods, this paper provides insights into model fitting, goodness-of-fit evaluation, and predictive accuracy, addressing computational efficiency and methodological challenges across various datasets and domains.
Data assimilation is widely used in many disciplines such as meteorology, oceanography, and robotics to estimate the state of a dynamical system from noisy observations. In this work, we propose a lightweight and general method to perform data assimilation using diffusion models pre-trained for emulating dynamical systems. Our method builds on particle filters, a class of data assimilation algorithms, and does not require any further training. As a guiding example throughout this work, we illustrate our methodology on GenCast, a diffusion-based model that generates global ensemble weather forecasts.
Despite decades of ship-based observations at the Bermuda Atlantic Timeseries Study (BATS) site, ambiguities linger in our understanding of the region's annual carbon cycle. Difficulties reconciling geochemical estimates of annual net community production (ANCP) with direct measurements of nutrient delivery and carbon exports (EP) have implied either an insufficient understanding of these processes, and/or that they are playing out on shorter time and spatial scales than resolved by monthly sampling. We address the latter concern using autonomous underwater gliders equipped with biogeochemical sensors to quantify ANCP from mass balances of oxygen (O2) and nitrate (NO3) over a full annual cycle. The timing, amplitude and distribution of O2 production, consumption, and NO3 fluxes reaffirm ideas about strong seasonality in physical forcing and trophic structure creating a dual system: i.e. production fueled by NO3 supplied to the photic zone from deeper layers in the first half of the year, versus being recycled within the upper ocean during the second half. The evidence also supports recently proposed hypotheses regarding the production and recycling of carbon with non-Redfield chara
The shoaling of high-amplitude Internal Solitary Waves (ISWs) of depression in the South China Sea (SCS) is examined through large-scale parallel turbulence-resolving high-accuracy/resolution simulations. A select, near-isobath-normal, bathymetric transect of the gentle SCS continental slope is employed together with stratification and current profiles obtained by in-situ measurements. Three simulations of separate ISWs with initial deep-water amplitudes in the range [136m, 150m] leverage a novel wave-tracking capability for a propagation distance of 80km and accurately reproduce key features of in-situ-observed phenomena with significantly higher spatiotemporal resolution. The interplay between convective and shear instability and the associated turbulence formation and evolution, as a function of deep-water ISW amplitude are further studied in-part revealing processes previously not observed in the field. Across all three waves, the convective instability develops in a similar fashion. Heavier water entrained from the wave rear plunges into its interior, giving rise to transient, yet distinct, subsurface vortical structures. Ultimately, a gravity current is triggered which horizo
Underwater gliders have been widely used in oceanography for a range of applications. However, unpredictable events like shark strikes or remora attachments can lead to abnormal glider behavior or even loss of the instrument. This paper employs an anomaly detection algorithm to assess operational conditions of underwater gliders in the real-world ocean environment. Prompt alerts are provided to glider pilots upon detecting any anomaly, so that they can take control of the glider to prevent further harm. The detection algorithm is applied to multiple datasets collected in real glider deployments led by the University of Georgia's Skidaway Institute of Oceanography (SkIO) and the University of South Florida (USF). In order to demonstrate the algorithm generality, the experimental evaluation is applied to four glider deployment datasets, each highlighting various anomalies happening in different scenes. Specifically, we utilize high resolution datasets only available post-recovery to perform detailed analysis of the anomaly and compare it with pilot logs. Additionally, we simulate the online detection based on the real-time subsets of data transmitted from the glider at the surfacing
We study the Stokes-transport system in a two-dimensional channel with horizontally moving boundaries, which serves as a reduced model for oceanography and sedimentation. The density is transported by the velocity field, satisfying the momentum balance between viscosity, pressure, and gravity effects, described by the Stokes equation at any given time. Due to the presence of moving boundaries, stratified densities with the Couette flow constitute one class of steady states. In this paper, we investigate the asymptotic stability of these steady states. We prove that if the stratified density is close to a constant density and the perturbation belongs to the Gevrey-3 class with compact support away from the boundary, then the velocity will converge to the Couette flow as time approaches infinity. More precisely, we prove that the horizontal perturbed velocity decays as $\frac{1}{\langle t\rangle^3}$ and the vertical perturbed velocity decays as $\frac{1}{\langle t\rangle^4}$.