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Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry
Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e, depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder and the bathymetry inversion problem is derived on the low-dimensional latent space in a Hierarchical Bayesian setting. Further, the reformulation allows variational inference with a small number (e.g., $\mathscr{O}$ (100) of ROM runs and efficient uncertainty quantification. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.
A Numerical Study of Hypoxia in Chesapeake Bay Using an Unstructured Grid Model: Validation and Sensitivity to Bathymetry Representation
A three-dimensional unstructured-grid hydrodynamic and water quality model (Semi-implicit Cross-scale Hydroscience Intergrated System Model-Integrated Compartment Model) is applied successfully for Chesapeake Bay. The model is validated with observations of salinity, chlorophyll-a, dissolved oxygen, nutrients, and phytoplankton productions from the year 1991 to 1995 for the mainstem and some major tributaries, based on multiple model skill scores. Model experiments are conducted to test the importance of having (1) an accurate representation of bathymetry to correctly predict hypoxia and other processes and (2) a high-resolution model grid for tributaries to correctly simulate water quality variables. Further, comparison with the model experiment results with bathymetry smoothing indicates that bathymetry smoothing, as commonly used for many systems, changes the stratification and lateral circulation pattern, resulting in more salt intrusion into shallow water regions, and an increase in the freshwater age. Consequently, a model with bathymetry smoothing can lead to an unrealistic prediction of the distribution of hypoxia and phytoplankton production. Local grid refinement shows significant improvement of model simulations on local stratification and water quality variables. Overall, the use of high-resolution unstructured grid model leads to a faithful representation of the complex geometry, and thus a seamless cross-scale capability for simulating water quality processes in the Bay including tributaries and tidal creeks.
Automated Model for Improved Mapping of Country-Scale High-Resolution Coastal Bathymetry
Accurate and up-to-date maps of coastal bathymetry are critical for a variety of sectors from vessel navigation to port construction and are increasingly vital to inform coastal infrastructure management amid accelerating sea-level rise and more frequent and severe storm-surge events. The primary challenges to accurate and efficient bathymetric mapping from optical remote sensing are: accurately modeling light attenuation in both the atmosphere and water column; and inefficient data processing pipelines for highresolution satellite imagery. To address the effects of light attenuation within the water-column we have developed a novel physics-based bathymetry model that accounts for variations in water-column inherent optical properties on a pixel-by-pixel basis in optically-shallow aquatic environments, which represents a major advancement. For applications to satellite imagery, we have developed a software package that automatically applies the robust 6S atmospheric correction algorithm, estimates the bottom depth from the physics-based bathymetry model, which corrects for attenuation by suspended particulate matter and colored dissolved organic matter in the water column on a pixel-by-pixel basis, and leverages highperformance computing for rapid application to region-scale (e.g., CONUS) 2-meter resolution imagery datasets. Our approach is tailored to sensors that collect data at two-meter resolution with high return times for frequent updates. We mapped 591 WorldView satellite images for Florida, North Carolina, and Alaska and validated the maps against LiDAR-derived bathymetry data. Results show median RMSE of 1.75, 1.59, and 2.67 meters, respectively. By combining the strengths of Oak Ridge National Laboratory in high-performance computing and remote-sensing science with the water-column modeling expertise of Scripps Institution of Oceanography we advance the state of bathymetric mapping capability.
High Spatial Melt Rate Variability Near the Totten Glacier Grounding Zone Explained by New Bathymetry Inversion
Totten Glacier is a fast-moving East Antarctic outlet with the potential for significant future sea-level contributions. We deployed four autonomous phase-sensitive radars on its ice shelf to monitor ice-ocean interactions near its grounding zone and made active source seismic observations to constrain gravity-derived bathymetry models. We observe an asymmetry in basal melting with mean melt rates along the grounding zone differing by up to 20 m/a. Our new bathymetry model reveals that this melt rate asymmetry coincides with an asymmetry in water column thickness and that the low-melting ice-shelf portion is shielded from the main cavity circulation. A 2-year record yields year-to-year melt rate variability of 7–9 m/a with no seasonal cycle. Our results highlight the key role of bathymetry near grounding lines for accurate modeling of ice-shelf melt, and the importance of sustained multi-year monitoring, especially at ice-shelf cavities where the dominant melt rate drivers vary primarily inter-annually.
Seabed bathymetry and friction modeling in MoorDyn
This paper presents the implementation and verification of a seabed bathymetry feature and seabed friction feature to the open-source, lumped-mass mooring system dynamics modeler, MoorDyn, which is part of the National Renewable Energy Laboratory’s aero-hydro-servo-elastic simulation tool, OpenFAST. Variations in seabed slope, as well as the frictional effects of mooring lines moving along the seabed, will affect the mooring line tensions of a floating platform and the consequent platform response. These new features are especially relevant for modeling mooring systems in deep-water coastal areas where seabed depth can change significantly over an entire mooring footprint. The bathymetry feature models the seabed as a rectangular grid of variable water depths in place of the existing, uniform water depth in MoorDyn. The friction force is primarily represented as a Coulombic friction force, or the product of a kinetic friction coefficient and the seabed contact normal force, with the ability to differentiate between transverse and axial motion of a line node on the seabed in any bathymetry grid. These capabilities were tested by running MoorDyn and OpenFAST simulations over a variety of seabed and environmental conditions; the resulting fairlead tensions, node tensions, and mooring line kinematics were verified against equivalent OrcaFlex simulations. The results match closely, meaning the features are verified, which will increase the overall fidelity of OpenFAST and FAST.Farm simulations.
Millinocket Stream, Maine Velocity and Bathymetry Measurements 2021
ORPC staff collected site characterization data on Millinocket Stream, downstream of the hydropower station at the former Great Northern Paper Mill site in Millinocket, Maine. Bathymetry was collected with a SonTek M9 using HydroSurveyor software package and velocity was collected using the SonTek M9 RiverSurveyor software package. Bathymetry only was collected on 9/30/21. Bathymetry and velocity were collected on 10/21/21.
An entropy stable nodal discontinuous Galerkin method for the two dimensional shallow water equations on unstructured curvilinear meshes with discontinuous bathymetry
We design an arbitrary high-order accurate nodal discontinuous Galerkin spectral element approximation for the non-linear two dimensional shallow water equations with non-constant, possibly discontinuous, bathymetry on unstructured, possibly curved, quadrilateral meshes. The scheme is derived from an equivalent flux differencing formulation of the split form of the equations. We prove that this discretization exactly preserves the local mass and momentum. Furthermore, combined with a special numerical interface flux function, the method exactly preserves the mathematical entropy, which is the total energy for the shallow water equations. By adding a specific form of interface dissipation to the baseline entropy conserving scheme we create a provably entropy stable scheme. That is, the numerical scheme discretely satisfies the second law of thermodynamics. Finally, with a particular discretization of the bathymetry source term we prove that the numerical approximation is well-balanced. We provide numerical examples that verify the theoretical findings and furthermore provide an application of the scheme for a partial break of a curved dam test problem.
Wave–current interaction in the presence of a three-dimensional bathymetry: Deep water wave focusing in opposing current conditions
Large scale experiments were carried out in the Ocean Engineering Basin FIRST, France. A tri-dimensional bathymetry consisting of two symmetrical submerged mounds was displayed on the flat bed on both sides of the basin. Regular waves of frequency corresponding to deep water conditions above the bathymetry were generated in opposing current conditions. A strong tri-dimensional behaviour is observed for the wave amplitude, leading to a strong focusing (up to twice the incident amplitude) of the wave energy towards the central deeper zone. This amplification cannot be ascribed to the increase of the current intensity in the main wave direction, nor to a current gradient normally to the wave direction. A wave phase gradient, normal to its main direction, is observed up-wave (or downstream) the mounds. This phase lag depends on the wave amplitude, it is the higher for the moderate amplitude case. The experimental data are compared with calculations of a refraction-diffraction model assuming a depth-averaged current. If the model qualitatively predicts the wave amplification in the centerline of the basin, discrepancies are observed in the vicinity of the depth changes. The observed mean current vertical profile shape is then supposed to play a significant role in the wave focusing, especially near the steep slopes down-stream the mounds. In addition, the waves are found to modify substantially both horizontal and vertical current fields.
Efficient Modeling of Floating Wind Arrays Including Current Loads and Seabed Bathymetry
Capabilities for modeling the effects of seabed bathymetry and current drag loads on a floating wind farm are now available in an open-source model for quasi-static analysis. In this model, mooring lines and dynamic cables are represented by a quasi-static solver that can quickly represent complex mooring/cabling arrangements and arrays of floating bodies. To account for seabed bathymetry, we expand the model to include a surface mesh that captures changes in water depth over a rectangular grid. We formulate modifications to the catenary equations that capture a mooring line's profile and tensions when contacting a slope seabed. To account for current drag loads on mooring lines and dynamic cables, we formulate a novel technique that rotates the reference frame so that the vector sum of the the weight and the current force are used in the catenary equations, while accounting for the seabed orientation. To complete the system, current drag loads on floating substructures are handled by inclusion of strip-theory drag calculations. These new capabilities are verified by comparing with results from the established offshore dynamics models MoorDyn and OrcaFlex in equivalent steady-state scenarios. The results show very good agreement for both sloped seabeds and current loads. With computation times of the quasi-static model typically under one second, the model additions are a useful capability toward rapidly evaluating a floating wind array's response to environmental loads under realistic site conditions.
Efficient Modeling of Floating Wind Arrays Including Current Loads and Seabed Bathymetry: Preprint
Capabilities for modeling the effects of seabed bathymetry and current drag loads on a floating wind farm are now available in an open-source model for quasi-static analysis. In this model, mooring lines and dynamic cables are represented by a quasistatic solver that can quickly represent complex mooring/cabling arrangements and arrays of floating bodies. To account for seabed bathymetry, we expand the model to include a surface mesh that captures changes in water depth over a rectangular grid. We formulate modifications to the catenary equations that capture a mooring line's profile and tensions when contacting a slope seabed. To account for current drag loads on mooring lines and dynamic cables, we formulate a novel technique that rotates the reference frame so that the vector sum of the the weight and the current force are used in the catenary equations, while accounting for the seabed orientation. To complete the system, current drag loads on floating substructures are handled by inclusion of strip-theory drag calculations. These new capabilities are verified by comparing with results from the established offshore dynamics models MoorDyn and OrcaFlex in equivalent steady-state scenarios. The results show very good agreement for both sloped seabeds and current loads. With computation times of the quasi-static model typically under one second, the model additions are a useful capability toward rapidly evaluating a floating wind array's response to environmental loads under realistic site conditions.
Radar imaging of shallow water bathymetry: A case study in the Yangtze Estuary
This study focuses on 2-dimensional (2-D) radar imaging of bathymetric features in the shallow water of the Yangtze Estuary using synthetic aperture radar (SAR) observations and model simulations. A validated 2-D shallow water numerical model simulates the barotropic current velocity, and the simulated current fields together with the relevant parameters of radar observations are then invoked in the radar imaging model as the input. The results show that variations in the simulated image intensity are mainly dominated by distinct radar backscatter anomalies caused by wave-current interactions in the vicinity of rapidly changing underwater topographies. The comparison between the simulated and observed SAR images shows a reasonable agreement, demonstrating that our approach may be implemented to monitor changes in the shallow water bathymetry of the Yangtze Estuary in the future.
A high accuracy/resolution spectral element/Fourier–Galerkin method for the simulation of shoaling non-linear internal waves and turbulence in long domains with variable bathymetry
A high-order hybrid continuous-Galerkin numerical method, designed for the simulation of non-linear, non -hydrostatic internal waves and turbulence in long computational domains with complex bathymetry, is presented. The spatial discretization in the non-periodic wave-propagating directions, utilizes the nodal spectral element method. Such a high-order element-based discretization allows the highly accurate representation of complex domain geometry along with the flexibility of concentrating resolution in areas of interest. Under the assumption of the normal-to-isobath propagation of non-linear internal waves, a third periodic direction is incorporated via a Fourier-Galerkin discretization. The distinct non-hydrostatic nature of non-linear internal waves and, any instabilities and turbulence therein, necessitates the numerically challenging solution of the pressure Poisson problem. A defining feature of this work is the application of a domain decomposition approach, combined with block-Jacobi/deflation-based preconditioning to the pressure Poisson problem. Such a combined approach is particularly suitable for the long high aspect-ratio complex domains of interest and enables the efficient high-accuracy reproduction of the non-hydrostatic dynamics of non-linear internal waves. Implementation details are also described in the context of the stability of the solver and its parallelization strategy. A series of benchmarks of increasing complexity demonstrate the robustness of the flow solver. The benchmarks culminate with the three-dimensional simulation of a convectively breaking mode-one non-linear internal wave over a realistic South-China-Sea bathymetric transect and background current/stratification profiles.
Numerical Mixing Suppresses Submesoscale Baroclinic Instabilities Over Sloping Bathymetry
Abstract The impacts of spurious numerical salinity mixing on the larger‐scale flow and tracer fields are characterized using idealized simulations. The idealized model is motivated by realistic simulations of the Texas‐Louisiana shelf and features oscillatory near‐inertial wind forcing. can exceed the physical mixing from the turbulence closure in frontal zones and within the mixed layer. This suggests that simulated mixing processes in frontal zones are driven largely by . Near‐inertial alongshore wind stress amplitude is varied to identify a base case that maximizes the ratio of to in simulations with no prescribed horizontal mixing. We then test the sensitivity of the base case with three tracer advection schemes (MPDATA, U3HC4, and HSIMT) and conduct ensemble runs with perturbed bathymetry. Instability growth is evaluated using the volume‐integrated eddy kinetic energy and available potential energy . While all schemes have similar total mixing, the HSIMT simulations have over double the volume‐integrated and 20% less relative to other schemes, which suppresses the release of and reduces the by roughly 25%. This results in reduced isohaline variability and steeper isopycnals, evidence that enhanced suppresses instability growth. Differences in and between the MPDATA and U3HC4 simulations are marginal. However, the U3HC4 simulations have 25% more . Experiments with variable horizontal viscosity and diffusivity coefficients show that small amounts of prescribed horizontal mixing improve the representation of the ocean state for all advection schemes by reducing the and increasing the .
Automated remote sensing tools to counter illicit maritime activity: vessel detection, bathymetry and topography from WorldView imagery
Illicit maritime activity, such as piracy and smuggling, is a global issue that often occurs in areas where interdiction authorities are sparse, ground-based monitoring technologies like radar lack range and coverage, and dark vessels abound. Our objective was to assess vessel congregation patterns, identify likely beaching areas based on terrain maps, and use them to narrow the search for potential smuggling transfer and overland routes in a specific region along the Puntland coast of Somalia. To accomplish this goal, we developed automated protocols applied to WorldView satellite imagery for (1) vessel detection and size classification, (2) shallow-water bathymetric characterization, and (3) coastal topography mapping. Utilizing a single sensor for vessel detection and topographic and bathymetric extraction at high spatial resolution and at a high re-visit rate provides a simplification to near-shore characterization for monitoring purposes. The extracted topography and bathymetry are then presented as a single, comprehensive perspective of a coastal region. The vessel-detection algorithm identified all vessels larger than approximately 15 metres in length (35 of 35), but misidentified six artefacts (i.e. false positives), resulting in an overall accuracy of 85%. The combined vessel and terrain maps facilitated the identification of a potential beaching and overland transportation route location.
The measurement of depth of water in oceans, seas, or lakes - GEBCO bathymetry gridded data for North Sea / Baltic Sea - Derived Data
This dataset contains global bathymetry, or water depth, measurements from the General Bathymetric Chart of the Oceans (GEBCO), converted into the format needed for WRF's Pre-processing System (WPS). The data are read in for the use of a depth-dependent water surface roughness scheme.
Block Island Bathymetry Data
This dataset contains bathymetric data for the Block Island region used in acoustic propagation modeling, including water depth measurements, coastline boundaries, and processed bathymetry datasets from multiple sources and resolutions.
Changes to Subaqueous Delta Bathymetry Following a High River Flow Event, Wax Lake Delta, USA
Not provided.