Real Ocean Research Articles

Semantic Segmentation of Mesoscale Eddies in the Arabian Sea: A Deep Learning Approach

Detecting mesoscale ocean eddies provides a better understanding of the oceanic processes that govern the transport of salt, heat, and carbon. Established eddy detection techniques rely on physical or geometric criteria, and they notoriously fail to predict eddies that are neither circular nor elliptical in shape. Recently, deep learning techniques have been applied for semantic segmentation of mesoscale eddies, relying on the outputs of traditional eddy detection algorithms to supervise the training of the neural network. However, this approach limits the network’s predictions because the available annotations are either circular or elliptical. Moreover, current approaches depend on the sea-surface height, temperature, or currents as inputs to the network, and these data may not provide all the information necessary to accurately segment eddies. In the present work, we have trained a neural network for the semantic segmentation of eddies using human-based—and expert-validated—annotations of eddies in the Arabian Sea. Training with human-annotated datasets enables the network predictions to include more complex geometries, which occur commonly in the real ocean. We then examine the impact of different combinations of input surface variables on the segmentation performance of the network. The results indicate that providing additional surface variables as inputs to the network improves the accuracy of the predictions by approximately 5%. We have further fine-tuned another pre-trained neural network to segment eddies and achieved a reduced overall training time and higher accuracy compared to the results from a network trained from scratch.

An unsteady RANS simulation of the performance of an oscillating hydrofoil at a high Reynolds number

The oscillating hydrofoil has been widely used in ocean engineering applications such as ships, underwater vehicles and ocean energy devices. However, Reynolds number of existing research are lower than real ocean applications.This study reports our recent numerical effort in studying a sinusoidally oscillating hydrofoil under unsteady conditions by solving the Reynolds-averaged Navier–Stokes equations. By using experimental test data, the numerical method is well validated. Three wake patterns are identified to fundamentally affect the propulsive performance of the oscillating hydrofoil. Only the wake in the reverse von Kármán vortex street pattern is found to generate thrust for purely oscillating motion. The leading-edge vortex is demonstrated todirectly influence the pressure distribution over the foil’s surface but not the thrust.Furthermore, impact of 3D effect on vortex shedding on the hydrodynamic performance of the hydrofoil is presented. This study is expected to provide guidance on both academics and industries in relevant fields.

Application to the World Ocean of the Theory of Transformation of a Mesoscale Vortex into a Submesoscale Vortex Thread When the Vortex Elongates by an Inhomogeneous Barotropic Flow

This paper is a continuation of the authors’ research [5]. We apply some aspects of the theory about strong horizontal stretching of large-scale mesoscale eddies in the World ocean based on ‘the ellipsoidal eddies’ theory to the ocean conditions. Two areas are considered, characterized by increased eddy manifestation. They are the Lofoten Basin in the Norwegian Sea and the Agulhas Current area. We also discuss the condition of the Atlantic Ocean and the World Ocean. The main purpose of this paper is to check the feasibility of the physical conditions for unbounded eddy elongation in the real ocean and estimate the fraction of mesoscale ocean eddies that are elongating into filaments and redistributing energy from the mesoscale to the submesoscale. We estimate the share of eddies in the World Ocean that are strongly elongated. We propose the maps of the geographical location of unlimited eddy elongation zones and give the interpretation of the obtained results. We also describe the effect of a decrease in the vortices’ self-energy due to the tensile action of the background flow. We suppose that it is a possible mechanism for energy transfer from the vortex to the flow and a manifestation of the negative viscosity effect.

A new hypothesis on the intrusion of the Loop Current

The unsteady and inviscid shallow water equations of motion and continuity for a northward moving Loop Current (LC) on the f-plane were integrated to derive an equation for the rate of LC area increase. The dA/dt, where A is the LC surface area, is a function of kinetic energy change across the LC and absolute vorticity. This equation agrees with previous results and is proposed as a new hyphothesis to explain the LC intrusion: a reduction in kinetic energy from west to east across the LC causes mass to be stored inside the Gulf of Mexico (GOM) because the outflow is smaller than the inflow and is manifested as a positive dA/dt indicating a growing and intruding LC into the GOM. The necessary kinetic energy reduction for driving the LC intrusion is caused by relative vorticity and dissipative energy mechanisms. Observations from the intruding LC showed a horizontal reduction of kinetic energy as suggested herein. We discussed that relative vorticity, dissipative forces, and baroclinic and baratropic instabilities induce a kinetic energy reduction across the LC causing an intrusion. Because of the possibility of several kinetic and potential energy-changing mechanisms acting jointly, finding a single mechanism or “trigger” to explain the LC intrusion seems difficult. Additionally, it seems that the relative vorticity values within the LC act to keep dA/dt close to its steady state value. The proposed hypothesis sheds light on the correlation between the LC intrusion and relative vorticity found by Candela et al. (2002). This hypothesis is diagnostic in the sense that it suggests a mechanism or mechanisms that induce a kinetic energy reduction across the LC and the intrusion. Numerical models are ideally suited to evaluate such mechanism(s), to verify the hypothesis, and help design field experiments to test it in the real ocean.

Atmospheric correction algorithm based on the interpolation of ultraviolet and shortwave infrared bands.

Traditional atmospheric correction algorithms of ocean color remote sensing are mostly based on the extrapolation of aerosol scattering radiance from a reference band (near infrared, shortwave infrared, or ultraviolet bands), which inevitably leads to the problem of extrapolation error amplification with the increase of extrapolation spectral distance. In this study, we propose a practical interpolation-based algorithm (named the UV-SWIR-AC algorithm) using three reference bands (one ultraviolet and two shortwave infrared bands) for turbid waters. According to 6SV radiative transfer simulations with 15 customized aerosol types, we establish a fitting function framework for the aerosol scattering radiance in the wavelength range of 322-1643 nm. We apply the UV-SWIR-AC algorithm to the real satellite ocean color data observed by the Second-Generation Global Imager aboard the Global Change Observation Mission-Climate (SGLI/GCOM-C) and compare the retrieved remote sensing reflectance with the in-situ data from the observation platform of Hangzhou Bay in the East China Sea and typical bays. The results show that the UV-SWIR-AC algorithm can achieve a better performance than the traditional, extrapolation-based algorithm in turbid waters. Moreover, in the typical regional analysis, this new algorithm also demonstrates a high applicability. The UV-SWIR-AC algorithm should be helpful to improve the atmospheric correction accuracy for next-generation ocean color missions (e.g., NASA's Plankton, Aerosol, Cloud, ocean Ecosystem (PACE) mission and China's Haiyang-1E/F (HY-1E/F) mission) with wider spectral ranges from the ultraviolet to shortwave infrared wavelengths.

Interactions Between Internal Tidal Bores and Submesoscale Currents on the Continental Shelf

AbstractA realistic simulation of Central California reveals interactions between shoaling internal tidal bores and submesoscale currents on the inner‐shelf (approximately 30–60 m depth). These interactions comprise collisions between internal tidal upwelling, “forward” bores (FBs) with submesoscale currents (SMCs) in the form of surface layer density fronts or filaments with downwelling secondary circulation. Along‐shore oriented FBs collide with both cross‐shore (perpendicular interaction) or along‐shore (parallel interaction) oriented SMCs. In perpendicular interaction, FBs colliding into cross‐shore oriented SMCs refract around the offshore tip of the downwelling front or filament. SMCs generally survive perpendicular interaction, despite partial disruption of downwelling secondary circulation by FBs. An example of parallel interaction demonstrates regional wind regulating the competition between FBs and SMCs to set cross‐shore stratification structure. This example comprises (a) blocking of FB propagation by elevated mixing (strong wind) and dense filament formation on the inner‐shelf and (b) the subsequent destruction of the dense filament that is initiated by a decrease in vertical mixing (weakening wind) and completed by renewed FB propagation underneath it. For both perpendicular and parallel interaction, FB propagation is modulated by a varying medium introduced by SMC density and current structure. The computational evidence of these interactions corroborates recent observations of interactions between small‐scale, nearshore currents in the real ocean. This study motivates further exploration of interactions between fronts, filaments, internal tidal bores, and vortices in the nearshore.

A guided-liquid-based hybrid triboelectric nanogenerator for omnidirectional and high-performance ocean wave energy harvesting

Ocean wave energy is a promising clean and renewable energy source to mitigate the global energy crisis and environmental issues. Here, a guided-liquid-based isotropic triboelectric–electromagnetic-hybrid nanogenerator (iTEHG) is developed for efficient and sustainable harvesting of omnidirectional ocean wave energy. The fully-enclosed iTEHG is based on a triboelectric nanogenerator (TENG) and electromagnetic generator (EMG), with the structure design of a unique concentric circular electrode pair built on a tilted satellite-dish-inspired plate for gravity-guided motion of the liquid. The newly-designed ocean wave harvester solves the wear and insufficient contact problems of mainstream solid–solid-interfaced TENGs, prolonging the device lifetime, and improves controllability of liquid compared with other solid–liquid-interfaced TENGs. This produces immediate power and current densities of 7.25 µW·cm–3 and 4.85 µA·cm–3 with undifferentiated 360° coverage. The iTEHG can charge a 0.1 F supercapacitor to 3.1 V and continuously drive a wireless thermometer for over 26 min. It exhibits superior performance for practical applications in real ocean environments, proven by continuously driving 320 high luminosity LEDs in Sanya Bay, China, even during quiet periods of ocean activity. The proposed design is expected to have a broad prospect for future blue energy harvesting and inspire development of self-sufficient ocean sensors.

Inversion models of internal solitary wave propagation speed in ocean based on least squares method and support vector machine

The propagation speed is one of the important parameters of the internal solitary wave (ISW). How to obtain the ISW speed through optical remote sensing images accurately and quickly is an important problem to be solved. In this paper, we simulate ISW optical remote sensing imaging, obtain an experimental database, and build the ISW speed inversion model based on a single-scene optical remote sensing image by using the least squares method and the support vector machine. The accuracy of the ISW speed inversion model is tested by using MODIS Image and GF-4 image data of the South China Sea. The study results are shown below. The least squares ISW speed inversion model can give the regression equation, which is more intuitive and has less accuracy in the water depth ranging from 300 m to 399 m, while the support vector machine ISW speed inversion model has high accuracy in the water depth ranging from 400 m to 1200 m and from 83 m to 299 m. Therefore, the two kinds of ISW speed inversion models have different advantages, and can be applied to the inversion of the ISW speed in the real ocean.

A novel filtering method for geodetically determined ocean surface currents using deep learning

Abstract Determining an accurate picture of ocean currents is an important societal challenge for oceanographers, aiding our understanding of the vital role currents play in regulating Earth’s climate, and in the dispersal of marine species and pollutants, including microplastics. The geodetic approach, which combines satellite observations of sea level and Earth’s gravity, offers the only means to estimate the dominant geostrophic component of these currents globally. Unfortunately, however, geodetically-determined geostrophic currents suffer from high levels of contamination in the form of geodetic noise. Conventional approaches use isotropic spatial filters to improve the signal-to-noise ratio, though this results in high levels of attenuation. Hence, the use of deep learning to improve the geodetic determination of the ocean currents is investigated. Supervised machine learning typically requires clean targets from which to learn. However, such targets do not exist in this case. Therefore, a training dataset is generated by substituting clean targets with naturally smooth climate model data and generative machine learning networks are employed to replicate geodetic noise, providing noisy input and clean target pairs. Prior knowledge of the geodetic noise is exploited to develop a more realistic training dataset. A convolutional denoising autoencoder (CDAE) is then trained on these pairs. The trained CDAE model is then applied to unseen real geodetic ocean currents. It is demonstrated that our method outperforms conventional isotropic filtering in a case study of four key regions: the Gulf Stream, the Kuroshio Current, the Agulhas Current, and the Brazil-Malvinas Confluence Zone.

A new combined ZK-mZK dynamic model for Rossby solitary wave

In this article, using multi-scale and perturbation methods, a partial differential model of Rossby solitary waves with complete Coriolis force effect is obtained, which is called the combined ZK-mZK equation. This equation can reflect the prop?agation characteristics of Rossby waves in space, and is more suitable for real oceans and atmosphere than the (1+1)-dimensional model. According to the pa?rameter composition of the new model, it can be seen that the effect of the complete Coriolis force affects not only the longitudinal structure of the model, but also the amplitude structure of the non-linear long wave.

Realistic ocean initial condition for stimulating the successful prediction of extreme cold events in the 2020/2021 winter

In the first half of winter 2020/2021, several unprecedented cold events occurred in most parts of China and caused record-breaking low temperatures in many cities. However, seasonal predictions related to the onset and evolution of extreme cold events are still challenging. In this study, we first evaluated the short-term climate prediction skills in winter of the CAS-ESM-c global coupled model and revealed the key dynamic processes of the onset and development of 2020/2021 extreme cold events based on the ensemble forecasts starting on October 1st, 2020. Under the background provided by the synergistic effect of the warm Arctic and the cold tropical Pacific (La Niña), the model captured the abnormal meridional atmospheric pattern well, including the intensification of the Ural Blocking High and the negative phase of the Arctic Oscillation, forecasted the negative geopotential height anomalies over the Eastern Asian region, and finally, successfully predicted the outbreak of cold waves in December 2020 two months in advance. Moreover, the dominant differences in the initial ocean fields between the best and the worst forecast members were further compared to isolate the triggering factor for predicting cold events by CAS-ESM-c. The initial warm sea surface temperature over the Barents Sea can gradually form a meridional pattern between the warm Arctic and the cold Asian continent, which could lead to a reduction in the large-scale meridional temperature gradient at mid-high latitudes and weaken the atmospheric baroclinicity with more conducive to the southward outbreak of cold waves, highlighting that realistic Arctic ocean conditions in autumn can be reasonably assimilated into coupled models to stimulate the successful prediction of extreme cold events in the 2020/2021 winter.

Subglacial hydrology modulates basal sliding response of the Antarctic ice sheet to climate forcing

Abstract. Major uncertainties in the response of ice sheets to environmental forcing are due to subglacial processes. These processes pertain to the type of sliding or friction law as well as the spatial and temporal evolution of the effective pressure at the base of ice sheets. We evaluate the classic Weertman–Budd sliding law for different power exponents (viscous to near plastic) and for different representations of effective pressure at the base of the ice sheet, commonly used for hard and soft beds. The sensitivity of the above slip laws is evaluated for the Antarctic ice sheet in two types of experiments: (i) the ABUMIP experiments in which ice shelves are instantaneously removed, leading to rapid grounding-line retreat and ice sheet collapse, and (ii) the ISMIP6 experiments with realistic ocean and atmosphere forcings for different Representative Concentration Pathway (RCP) scenarios. Results confirm earlier work that the power in the sliding law is the most determining factor in the sensitivity of the ice sheet to climatic forcing, where a higher power in the sliding law leads to increased mass loss for a given forcing. Here we show that spatial and temporal changes in water pressure or water flux at the base modulate basal sliding for a given power, especially for high-end scenarios, such as ABUMIP. In particular, subglacial models depending on subglacial water pressure decrease effective pressure significantly near the grounding line, leading to an increased sensitivity to climatic forcing for a given power in the sliding law. This dependency is, however, less clear under realistic forcing scenarios (ISMIP6).

Interaction of Rossby waves with the Gulf Stream and Kuroshio using altimetry in a framework of a vortex layer model

In this paper, we show the potential of satellite altimetry to study the interaction of Rossby waves with the shear flow. The Miles-Ribner approach, which was developed in gas dynamics in the 1960 s, is used to describe Rossby waves interacting with the Gulf Stream and Kuroshio areas. The region of interaction is approximated by a nonzonal vortex layer. We apply the main formulations of the problem of a nonzonal vortex layer on the β-plane in the formulation of Miles-Ribner to observations in the real ocean. Earlier, we showed that the interaction of waves with a nonzonal flow gives rise to a new class of solutions, which is absent in the case of a zonal flow. This new class of solutions can be interpreted as the pure emission of Rossby waves by the nonzonal flow. We apply this theoretical approach to the areas of the Gulf Stream and Kuroshio as well. We use for analysis altimetry data available at Copernicus Marine Environment Monitoring Service. The analysis of Hovmöller diagrams in the areas under consideration confirms the previously obtained theoretical conclusions of the problem of the interaction of planetary waves with a nonzonal flow on the β-plane in the formulation of Miles-Ribner. The incident waves, as well as refracted and reflected waves are distinguished. The speed of refracted and reflected waves exceeds the speed of incident waves, which confirms the conclusions about the existence of mechanisms for the amplification of planetary waves when they interact with a nonzonal flow.

Applying dynamical systems techniques to real ocean drifters

Abstract. This paper presents the first comprehensive comparison of several different dynamical-systems-based measures of stirring and Lagrangian coherence, computed from real ocean drifters. Seven commonly used methods (finite-time Lyapunov exponent (FTLE), trajectory path length, trajectory correlation dimension, trajectory encounter volume, Lagrangian-averaged vorticity deviation, dilation, and spectral clustering) were applied to 144 surface drifters in the Gulf of Mexico in order to map out the dominant Lagrangian coherent structures. Among the detected structures were regions of hyperbolic nature resembling stable manifolds from classical examples, divergent and convergent zones, and groups of drifters that moved more coherently and stayed closer together than the rest of the drifters. Many methods highlighted the same structures, but there were differences too. Overall, five out of seven methods provided useful information about the geometry of transport within the domain spanned by the drifters, whereas the path length and correlation dimension methods were less useful than others.

Dynamic mode decomposition for underwater acoustics on autonomous platforms

A sufficiently accurate representation of the ocean physics is needed for reliable underwater acoustics forecasting. Ocean physics are often simulated by high-dimensional data-assimilative numerical ocean simulations. Due to operational constraints such as computing, memory, communication-bandwidth, etc., it is infeasible to run these numerical simulations onboard the platforms. In this work, we employ the onboard data-assimilative incremental, Low-Rank Dynamic Mode Decomposition (iLRDMD) for forecast transmission, onboard computation, and data assimilation. The iLRDMD is an adaptive reduced-order model (ROM) that uses proper orthogonal decomposition (POD) and DMD for compression and transmission of high-fidelity ocean forecast to communication-disadvantaged platforms. It provides reduced-order onboard forecasting and also enables efficient updates of the DMD model itself from inputs from remote centers. Finally, when sparse observations are made by the platform, the iLRDM uses Bayesian data assimilation to correct both the forecasts and the DMD model. We demonstrate the use of deterministic and data-assimilative iLRDMD forecasted ocean fields for underwater acoustics computations in real ocean examples. We further explore the use of our adaptive ROM for joint reduction of the ocean physics and acoustics fields.

Adaptive variational Hamiltonian Monte Carlo sampling with application to ocean acoustics

The Hamiltonian Monte Carlo (HMC) algorithm is a variant Markov Chain Monte Carlo (MCMC) excelling at sampling high dimensional target distributions. The HMC explores a distribution as a particle trajectory in a Hamiltonian system by augmenting distribution parameters with auxiliary momentum variables. A particle trajectory is numerically integrated from initial point to some distant low-correlation point. Projecting back to parameter space yields a proposal point with high acceptance probability leading to faster exploration of the target distribution. The Leap-frog integrator is commonly used for its volume preservation (symplecticity) and reversibility traits that maintain the detailed balance condition of MCMC. Although effective, Leap-frog has sensitivity to choice of integration step-size and number of integration steps. Poor choices cause slow exploration or bias when regions of the distribution are not explored. Adaptive step methods could remove step size issues and explore regions of a distribution where Leap-frog fails. Existing adaptive methods self-adjust step-size while maintaining symplecticity and reversibility. In this work, we apply adaptive step methods to simulated target distributions and real world ocean acoustic data and compare performance. [Work supported by Office of Naval Research.]

Learning coordinate systems for fast and accurate acoustic modeling

Many popular numerical methods, such as finite difference and spectral methods, rely on simple domain geometry and environmental smoothness. Unfortunately, these features are rarely found in real-world simulations. We propose learning coordinate transformations with deep neural networks to facilitate acoustic modeling in complex media. Using automatic differentiation, we obtain new coordinate systems by solving various optimization problems that map the computational domain to a rectangular grid. Different choices of the objective function are utilized to attain different goals, including (i) mapping complicated boundaries such as the seafloor to straight lines and (ii) reducing the rank of two-dimensional slices of the refractive index. The first choice allows for domain decomposition to accurately model sharp discontinuities in density and sound speed. The second drastically accelerates a non-intrusive reduced-order modeling technique referred to as the dynamical low-rank approximation. Using realistic ocean test cases, we compare the performance of our learned coordinate systems with domain decomposition to the classic approach of smoothing sharp discontinuities, and we compare full-rank, low-rank, and coordinate-system-accelerated low-rank solutions of the three-dimensional parabolic wave equation.

A new method to estimate the speed of internal solitary waves based on a single optical remote sensing image

ABSTRACT It is imperative to estimate the energy of internal solitary waves (ISWs) in the real ocean. The energy of ISW is related to speed and amplitude. It is a problem to obtain the propagation speed of ISW from a single optical remote sensing image. Generally, the nonlinear phase speed (NPS) of ISW can be regarded as the propagation speed of ISW. This paper proposes a new inversion approach for NPS of ISW based on an optical remote sensing image. The simulation platform of optical remote sensing was used to conduct the ISW experiment in the laboratory, and the data were obtained by a series of experiments. Three NPS inversion models of ISW are investigated by support vector regression (SVR), Random forest (RF) and Deep neural network (DNN) based on a single optical remote sensing image. The accuracy of the inversion models was verified by the in-situ data of GF-1 satellite images, GF-4 satellite images and Moderate-resolution Imaging Spectroradiometer (MODIS) images. In the verification results, the SVR inversion model has high accuracy in different sea areas and water depths. The RF and DNN inversion models both have high inversion accuracy in the water depth range of 93–299 m in the South China Sea. Compared with the other two traditional methods for calculating ISW NPS, the SVR inversion model still has the highest accuracy. The results showed that the NPS models of ISW are suitable and effective.

Vertical Structure of Barotropic‐to‐Baroclinic Tidal Energy Conversion on a Continental Slope

AbstractHorizontal distribution of the vertically integrated barotropic‐to‐baroclinic energy conversion has been widely studied to examine the generation of internal tides at steep topography. The vertical structure of the energy conversion that provides insights into the associated dynamics, however, is masked by the often used depth‐integrated approach. Here, we reveal the vertical profile of barotropic‐to‐baroclinic energy conversion by employing an idealized ocean model in a slope‐shelf context forced by M2 barotropic tidal flow. The model shows two vertically separated hotspots of energy conversion, one near the sloping bottom and the other at the thermocline, resulting from the stronger vertical velocity and enhancement of the density perturbation, respectively. Isolation of the hotspots demonstrates that baroclinic energy generated in the bottom layer radiates toward onshore and offshore primarily in the form of internal wave beams, whereas that generated at the thermocline propagates away in the form of internal wave modes. Although energy converted at the thermocline contributes to only a small portion of the total energy conversion, it plays an important role in onshore baroclinic energy radiation and can be significantly affected by the internal wave activity at the bottom layer. With a fixed bottom topography, the percentage of baroclinic energy generated at the thermocline is linearly related to a body force exerted by the barotropic tidal flow over topography that can be estimated analytically. This provides a convenient way to estimate the overall barotropic‐to‐baroclinic energy conversion over a continental slope in the real ocean by measuring the energy conversion in the thermocline only.

On Characterizing Ocean Kinematics from Surface Drifters

Abstract Horizontal kinematic properties, such as vorticity, divergence, and lateral strain rate, are estimated from drifter clusters using three approaches. At submesoscale horizontal length scales , kinematic properties become as large as planetary vorticity f, but challenging to observe because they evolve on short time scales . By simulating surface drifters in a model flow field, we quantify the sources of uncertainty in the kinematic property calculations due to the deformation of cluster shape. Uncertainties arise primarily due to (i) violation of the linear estimation methods and (ii) aliasing of unresolved scales. Systematic uncertainties (iii) due to GPS errors, are secondary but can become as large as (i) and (ii) when aspect ratios are small. Ideal cluster parameters (number of drifters, length scale, and aspect ratio) are determined and error functions estimated empirically and theoretically. The most robust method—a two-dimensional, linear least squares fit—is applied to the first few days of a drifter dataset from the Bay of Bengal. Application of the length scale and aspect-ratio criteria minimizes errors (i) and (ii), and reduces the total number of clusters and so computational cost. The drifter-estimated kinematic properties map out a cyclonic mesoscale eddy with a surface, submesoscale fronts at its perimeter. Our analyses suggest methodological guidance for computing the two-dimensional kinematic properties in submesoscale flows, given the recently increasing quantity and quality of drifter observations, while also highlighting challenges and limitations. Significance Statement The purpose of this study is to provide insights and guidance for computing horizontal velocity gradients from clusters (i.e., three or more) of Lagrangian surface ocean drifters. The uncertainty in velocity gradient estimates depends strongly on the shape deformation of drifter clusters by the ocean currents. We propose criteria for drifter cluster length scales and aspect ratios to reduce uncertainties and develop ways of estimating the magnitude of the resulting errors. The findings are applied to a real ocean dataset from the Bay of Bengal.