Surface Elevation Measurements Research Articles

A comparative study of mass balance in the Lambert Glacier and Amery Ice Shelf along the Chinese inland traverse during 2019–2023 using altimetry, gravity, and in-situ observations

Abstract. The new photon-counting laser altimetry satellite ICESat-2 was successfully launched on September 15, 2018 with an unprecedented ice surface elevation measurement accuracy of 2–4 cm. It is meaningful for accurately estimating volumetric changes in the Antarctic Ice Sheet. Cross-validation of different types of data, especially comparison with in-situ data, is important for the ice sheet mass balance results of a new satellite. This paper proposes an elevation-difference method of grid elevation change rate model, based on ICESat-2 ATL11 elevation time series data, to distinguish the linear change trend of ice sheet surface elevation from the elevation change resulting from periodic precipitation. In order to compare the estimated elevation-change rate with the flux computed from in-situ snow stake velocity measurements and GRACE-FO gravity survey data, we made corrections for firn air content, elastic, and glacier isostatic adjustment. Based on the ATL11 data from 2019 to 2023, our results show that the ice sheet change in Basin 11 along the CHINARE traverse is from ~0.019 m yr−1 to ~0.121 m yr−1, and the mass balance in the upstream of the traverse in Basin 11 is ~1.9±0.2 Gt yr−1. It is comparable to ~2.4±1.2 Gt yr−1 from GRACE-FO during the same time period. Furthermore, the flux across traverse-11.9±1.1 Gt yr−1 is comparable to that of ~-9.7±0.9 Gt yr−1 across the same flux gate during 1997–2009 which is calculated based on GNSS-derived ice velocity observations, considering the time period difference and uncertainties.

Generation of High‐Resolution Water Surface Slopes From Multi‐Mission Satellite Altimetry

AbstractFor nearly three decades, satellite radar altimetry has provided measurements of the water surface elevation (WSE) of rivers. These observations can be used to calculate the water surface slope (WSS), which is an essential parameter for estimating flow velocity and river discharge. In this study, we calculate a non time‐varying high‐resolution WSS of 11 Polish rivers based on multi‐mission altimetry observations from 11 satellites in the period from 1994 to 2023. The proposed approach is based on a weighted least squares adjustment with an additional Laplace condition and an a priori gradient condition. The processing is divided into river sections not interrupted by dams and reservoirs. After proper determination of the WSE for each river kilometer (bin), the WSS between adjacent bins is calculated. To assess the accuracy of the estimated WSS, it is compared with slopes between gauge stations, which are referenced to a common vertical datum. Such gauge stations are available for 8 studied rivers. The root mean squared error (RMSE) ranges from 4 mm/km to 77 mm/km, with an average of 27 mm/km. However, the mean RMSE decreases to 11 mm/km when the 2 mountain rivers are excluded. The WSS accuracies are also compared with slope data sets based on digital elevation models, ICESat‐2 altimetry, and lidar. For 6 rivers the estimated WSS shows the highest accuracy. The improvement was particularly significant for mountain rivers. The proposed approach allows an accurate, non time‐varying high‐resolution WSS even for small and medium‐sized rivers and can be applied to almost any river worldwide.

Current-distorted wave diffraction patterns in the near-field of a monopile in coastal seas

The simultaneous impact of a wave field in the diffraction regime and a perpendicular intersecting current on a cylinder reflects a common application case for wave-current-structure interaction with offshore wind turbines in the German North Sea. Although existing literature has thoroughly investigated structural impacts from both waves and currents individually, the complex interplay between both forcings in the near-field of an offshore monopile has not been explored as thoroughly in the past. Only little is understood concerning the resulting nonlinear 3D interaction. This laboratory study evaluates the physical insights of a broad range of wavelength-dependent pile diameters, i.e., 0.14<diameterD/wavelengthL<0.25. The study focuses on surface elevation characteristics, documented either qualitatively using video recordings or quantitatively by surface elevation measurements in close vicinity of the pile. Within the experimental boundaries of this initial study, a current-induced, D/L-dependent asymmetry in crest amplitudes is documented. These distorted diffraction patterns are explained to originate from non-linear wave–current–structure interactions, which are not represented by existing design approaches. The findings further suggest that in this context, secondary load cycle dynamics are of practical relevance to the design and operation of offshore structures.

Remotely sensed land‐cover change and floodplain disturbance following upstream‐migrating river avulsions in tropical rainforests

AbstractThe displacement of a river to a new position within its adjacent floodplain is called avulsion, and here we examine how a newly recognized style, called retrogradational avulsion, affects the surrounding floodplain in tropical rainforests using remote sensing. Retrogradational avulsions begin with a channel blockage that causes self‐propagating upstream dechannelization and flooding. While this flooding results in vegetation die‐off and floodplain sedimentation, few quantitative measurements of disturbance by retrogradational avulsions exist. Here, we first focus on land‐cover change following a single retrogradational avulsion in Papua New Guinea from 2012 to 2021. During the avulsion, the river dechannelized 892 m upstream, and the parent channel width doubled. Using maximum likelihood image classification, we observed healthy vegetation fluctuated around 4.3 km2, vegetation regrowth peaked in 2017 at 3.2 km2, dead vegetation peaked in 2013 at 2.1 km2, and visible extent of deposited sediment was greatest in 2015 at 0.44 km2. We also examined 19 other retrogradational avulsions in Papua New Guinea and South America using NDVI. The area of floodplain disturbance (i.e., vegetation die‐off and possible sedimentation) for each avulsion ranged from &lt;1 to &gt;13 km2 and scaled with the dechannelization area. Comparing our plan‐view disturbance results with FABDEM digital‐elevation data and ICESat‐2 surface elevation measurements, we hypothesize floodplain disturbance extent is a function of topographic relief. Our results also suggest that retrogradational avulsions, on average, perturb larger areas of forest compared to blowdowns, suggesting this might be an important disturbance regime that influences gap‐filling regeneration in tropical rainforests.

Propagating speedups during quiescence escalate to the 2020–2021 surge of Sít’ Kusá, southeast Alaska

Abstract We use satellite image processing techniques to measure surface elevation and velocity changes on a temperate surging glacier, Sít’ Kusá, throughout its entire 2013–2021 surge cycle. We present detailed records of its dynamic changes during quiescence (2013–2019) and its surge progression (2020–2021). Throughout quiescence, we observe order-of-magnitude speedups that propagate down-glacier seasonally from the glacier's upper northern tributary, above a steep icefall, into the reservoir zone for the surging portion of the glacier. The speedups initiate in fall and gradually accelerate through winter until they peak in late spring, ~1 − 2 months after the onset of melt. Propagation distance of the speedups controls the distribution of mass accumulation in the reservoir zone prior to the surge. Furthermore, the intensity and propagation distance of each year's speedup is correlated with the positive degree day sum from the preceding melt season, suggesting that winter melt storage drives the seasonal speedups. We demonstrate that the speedups are kinematically similar to the 2020–2021 surge, differing mainly in that the surge propagates past the dynamic balance line at the lower limit of the reservoir zone, likely triggered by the exceedance of a tipping point in mass accumulation and basal enthalpy in the reservoir zone.

Measurements and Modeling of Pore‐Pressure Gradients in the Swash Zone Under Large‐Scale Laboratory Bichromatic Waves

AbstractThe present work presents physical laboratory measurements of surface elevation and pore water pressures in a fine sand bed under bichromatic waves in a large‐scale laboratory experiment. This was done at three cross‐shore locations in the swash zone, with pressures being measured at different depths in the bed. The measurements show that the pore pressure signal decays and shifts with increased depth. These measurements are used to validate a practical model, based on the theory of Yamamoto et al. (1978, https://doi.org/10.1017/S0022112078003006) and Guest and Hay (2017, https://doi.org/10.1002/2016JC012257). The model corresponds well with the measurements (nRMSE &lt; 0.2 and R2 &gt; 0.95 for most probes) and shows that a frequency‐based model can reproduce the pressures in the bed, despite the bed being exposed during dry periods. Furthermore, the model provides the opportunity to calculate pressure gradients, both throughout the bed and at the bed surface. These modeled pressure gradients at the bed surface show that the vertical pressure gradient can have an important impact on the Shields parameter, thereby influencing sediment transport.

Experimental and numerical investigation on hydrodynamic performance of a 3D land-fixed OWC wave energy converter

The hydrodynamic performance of a land-fixed oscillating water column (OWC) wave energy device was thoroughly investigated under various wave conditions and geometric parameters through both experimental and numerical studies in a three-dimensional (3D) wave tank. The study involved the measurement and comparison of water surface elevation, air pressure in the OWC chamber, and hydrodynamic efficiency with the results obtained from the 3D Higher-Order Boundary Element Method (HOBEM). The influences of 3D effects, incident wave amplitude, front wall draught, and incident wave angle on the hydrodynamic performance of the OWC device were analyzed. The results demonstrate that, under actual sea conditions, the 3D effects significantly affect the hydrodynamic efficiency of the OWC, making it exceed unity near the resonance frequency. On the other hand, the incident wave angle was found to have minimal effect on the resonant frequency and varied trend of efficiency. However, the hydrodynamic efficiency decreases with increasing incident wave angle. These results highlight the importance of the consideration of the 3D effects and incident wave angles in optimizing the design and performance of fixed OWC wave energy devices.

Predicting the occurrence of rogue waves in short-crested mixed seas

ABSTRACT In this paper we have for the first time proposed a novel transformed Gaussian process method for the estimation of rogue wave occurrence in a short crested mixed sea. The saddle point approximation of a specific joint density is utilised to further improve the computational efficiency of the proposed method. The proposed method has been applied to forecast the rogue wave occurrence in four short-crested mixed sea states, two with directional wave spectra based on measured surface elevation data at the coast of Yura, and another two with typical directional bimodal wave spectra. It is shown in these four cases that the proposed method can offer more accurate forecasting results than those obtained from the linear simulation method, from the transformation based on Hermite polynomials and from using the Rayleigh distribution model. It is also demonstrated that the proposed method is more efficient than the nonlinear simulation method.

Evaluation of snow depth retrievals from ICESat-2 using airborne laser-scanning data

Abstract. The unprecedented precision of satellite laser altimetry data from the NASA ICESat-2 mission and the increasing availability of high-resolution elevation datasets open new opportunities to measure snow depth in mountains, a critical variable for ecosystem and water resource monitoring. We retrieved snow depth over the upper Tuolumne basin (California, USA) for 3 years by differencing ICESat-2 ATL06 snow-on elevations and various snow-off digital elevation models. Snow depth derived from ATL06 data only (snow-on and snow-off) offers a poor temporal and spatial coverage, limiting its potential utility. However, using a digital terrain model from airborne lidar surveys as the snow-off elevation source yielded a snow depth accuracy of ∼ 0.2 m (bias) and precision of ∼ 1 m (random error) across the basin, with an improved precision of 0.5 m for low slopes (&lt; 10∘), compared to eight reference airborne lidar snow depth maps. Snow depths derived from ICESat-2 ATL06 and a satellite photogrammetry digital elevation model have a larger bias and reduced precision, partly induced by increased errors in forested areas. These various combinations of repeated ICESat-2 snow surface elevation measurements with satellite or airborne products will enable tailored approaches to map snow depth and estimate water resource availability in mountainous areas with limited snow depth observations.

Energy Transfer and Reverse Flow Characteristics in the Interaction Process between Non-Breaking Solitary Wave and a Steep Seawall: A Case Study

This study utilized a two-dimensional numerical viscous wave tank to simulate the run-up and run-down processes of non-breaking solitary waves on a steep seawall. The research aimed to investigate the transformation between wave potential energy and kinetic energy, the evolution mechanisms of the wave and flow fields, and the correlation between the dynamic pressure gradient and the reverse flow near the sloping bed. The numerical model results were consistent with laboratory measurements of free surface elevations and flow velocity profiles, demonstrating the accuracy of the numerical model. This study focused on a solitary wave with a wave-height-to-water-depth ratio of 0.15, propagating on a representative seawall with a steep slope of 1:3 along the western coast of Taiwan. The simulation results indicate that the maximum run-up height occurs when the potential energy is at its highest. Undertow is caused by the adverse pressure gradient within the flow field, and the dynamic pressure on the sloping bed is directly proportional to the free surface elevation. Therefore, by observing the spatial changes in the free surface elevation, we can indirectly determine the occurrence time of undertow.

Continuum and discrete element modelling for describing coupled hydro-mechanical effects of earthworm burrow coatings on soil shrinkage

Structured soils with earthworm burrows are locally heterogeneous due to coatings along these biopore walls that are superimposed on the inter- and intra-aggregate pore network of the soil matrix. The partially compacted finer-textured and organic matter-rich coatings can limit the flow exchange between the macropores and the soil matrix during preferential flow. Still unknown are dynamic hydro-mechanical interrelations in coating and matrix domains that affect stress–strain behaviour at the macroscopic scale. Such hydro-mechanic interactions may be described with the discrete element method (DEM) coupled with a two-phase pore finite volume (2PFV) approach if relevant pore structures are represented in the model. The objective was to develop a coupled DEM-2PFV model together with a parameterization procedure. Major task was to create a parameterization procedure to calibrate micro parameters of the model by macro properties quantified from drainage experiments of soil samples with earthworm burrow wall coatings.The solid phase was modelled by particle aggregation creating inter and intra-aggregate pore network for the soil matrix in a cube of about 5 cm edge length and one side with the coating structure. This DEM model was coupled with a 2PFV model to simulate hydro-mechanic effects during drainage. Sand box drainage experiments were carried out on soil matrix and biopore samples with laser surface elevation measurements to obtain the mechanical stress–strain macro parameters necessary for model calibration. The poly-dispersed DEM-2PFV model was able to describe effects of two-phase air–water flow on stress–strain macro parameters. The micro parameters (i.e., particle stiffness and bond strength) of the pore scale model were obtained from macro parameters of the primary and secondary stress–strain stages by training a random forest meta-estimator. The model was able to reproduce the pore network of coating material and the inter- and intra-aggregate pore network of the matrix that are dynamically changing with the effective stress. The machine learning model revealed that the bond strength among particles within aggregates governed the shrinkage of soil matrix, while the particle stiffness of the coating material reduced the susceptibility of aggregate breakage producing a more stable inter-aggregated pore network during the drainage process. This study confirmed that coating material present in biopore surface increases the horizontal soil hydro structural stability. The microscale hydro-mechanic modelling can be useful for finding flow exchange parameters inputs for upscaled models and correlating pore-scale parameters to experimentally determined stress–strain macro parameters.

A Framework for Estimating Global River Discharge From the Surface Water and Ocean Topography Satellite Mission

AbstractThe Surface Water and Ocean Topography (SWOT) mission will vastly expand measurements of global rivers, providing critical new data sets for both gaged and ungaged basins. SWOT discharge products (available approximately 1 year after launch) will provide discharge for all river that reaches wider than 100 m. In this paper, we describe how SWOT discharge produced and archived by the US and French space agencies will be computed from measurements of river water surface elevation, width, and slope and ancillary data, along with expected discharge accuracy. We present for the first time a complete estimate of the SWOT discharge uncertainty budget, with separate terms for random (standard error) and systematic (bias) uncertainty components in river discharge time series. We expect that discharge uncertainty will be less than 30% for two‐thirds of global reaches and will be dominated by bias. Separate river discharge estimates will combine both SWOT and in situ data; these “gage‐constrained” discharge estimates can be expected to have lower systematic uncertainty. Temporal variations in river discharge time series will be dominated by random error and are expected to be estimated within 15% for nearly all reaches, allowing accurate inference of event flow dynamics globally, including in ungaged basins. We believe this level of accuracy lays the groundwork for SWOT to enable breakthroughs in global hydrologic science.

River hydraulic modeling with ICESat-2 land and water surface elevation

Abstract. Advances in geodetic altimetry instruments are providing more accurate measurements, thus enabling satellite missions to produce useful data for narrow rivers and streams. Altimetry missions produce spatially dense land and water surface elevation (WSE) measurements in remote areas where in situ data are scarce that can be combined with hydraulic and/or hydrodynamic models to simulate WSE and estimate discharge. In this study, we combine ICESat-2 (Ice, Cloud and land Elevation Satellite) land and water surface elevation measurements with a low-parameterized hydraulic calibration to simulate WSE and discharge without the need for surveyed cross-sectional geometry and a rainfall–runoff model. ICESat-2 provides an opportunity to map river cross-sectional geometry very accurately, with an along-track resolution of 0.7 m, using the ATL03 product. These measurements are combined with the inland water product ATL13 to calibrate a steady-state hydraulic model to retrieve unobserved hydraulic parameters such as river depth or the roughness coefficient. The low-parameterized model, together with the assumption of steady-state hydraulics, enables the application of a global search algorithm for a spatially uniform parameter calibration at a manageable computational cost. The model performance is similar to that reported for highly parameterized models, with a root mean square error (RMSE) of around 0.41 m. With the calibrated model, we can calculate the WSE time series at any chainage point at any time for an available satellite pass within the river reach and estimate discharge from WSE. The discharge estimates are validated with in situ measurements at two available gauging stations. In addition, we use the calibrated parameters in a full hydrodynamic model simulation, resulting in a RMSE of 0.59 m for the entire observation period.

Statistical and Dynamical Characteristics of Extreme Wave Crests Assessed with Field Measurements from the North Sea

Abstract Wave crests of unexpected height and steepness pose a danger to activities at sea, and long-term field measurements provide important clues for understanding the environmental conditions that are conducive to their generation and behavior. We present a novel dataset of high-frequency laser altimeter measurements of the sea surface elevation gathered over a period of 18 years from 2003 to 2020 on an offshore platform in the central North Sea. Our analysis of crest height distributions in the dataset shows that mature, high sea states with high spectral steepness and narrow directional spreading exhibit crest height statistics that significantly deviate from standard second-order models. Conversely, crest heights in developing sea states with similarly high steepness but wide directional spread correspond well to second-order theory adjusted for broad frequency bandwidth. The long-term point time series measurements are complemented with space–time stereo video observations from the same location, collected during five separate storm events during the 2019/20 winter season. An examination of the crest dynamics of the space–time extreme wave crests in the stereo video dataset reveals that the crest speeds exhibit a slowdown localized around the moment of maximum crest elevation, in line with prevailing theory on nonlinear wave group dynamics. Extending on previously published observations focused on breaking crests, our results are consistent for both breaking and nonbreaking extreme crests. We show that wave crest steepness estimated from time series using the linear dispersion relation may overestimate the geometrically measured crest steepness by up to 25% if the crest speed slowdown is not taken into account. Significance Statement Better understanding of the statistics and dynamical behavior of extreme ocean surface wave crests is crucial for improving the safety of various operations at sea. Our study provides new, long-term field evidence of the combined effects of wave field steepness and directionality on the statistical distributions of crest heights in storm conditions. Moreover, we show that the dynamical characteristics of extreme wave crests are well described by recently identified nonlinear wave group dynamics. This finding has implications, for example, for wave force calculations and the treatment of wave breaking in numerical wave models.

Ship waves in rivers: Environmental criteria and analysis methods for measurements

AbstractA literature review shows that the most important physical quantities determining environmental impact of ship waves in a waterway are the fluid velocities, maximum and minimum water levels, and size of drawdown events. Fluid velocity can vary strongly in the vertical so that the usual measurements at a single point are not enough unless made near where the effects are most important, often the bed. Customary use of wave height as a measure of impact has been misleading, because the all‐important fluid velocity is of a scale given by wave height divided by wave period. A good and simple estimate of the surface velocity as a disturbance scale is shown to be given by the time derivative of the free surface height. The most important role of linear wave theory is to explain and understand the physics and measurement procedures, such as done here in several places. Its use for obtaining numerical results is criticised. Instead, three integral measures of impact are proposed, all of which use surface elevation measurements and which require no essential mathematical approximations or wave‐by‐wave analysis. The methods are applied to a study of ship waves on the Danube River. A number of results are presented, including examination of the effects of measurement frequency. After a ship passage, due to repeated shoreline reflections of the wake waves, the river is brought into a long‐lasting state of short‐crested disturbances, with finite fluid velocities. The environmental consequences of this might be important. After the primary and secondary ship waves it could be called the tertiary wave system.

A Modified Frequency Distribution Function of Wave-Breaking-Induced Energy Dissipation.

A nonlinear frequency-domain model and a probabilistic wave breaking model have been employed together to simulate the propagation of nearshore wave breaking and to provide estimates of related statistical quantities such as skewness and asymmetry. This combination of models requires a pre-specification of the frequency dependence of dissipation. Prior work has suggested that a frequency-squared weighting for the dissipation term is most appropriate via physical arguments. However, the original frequency distribution function significantly underpredicts the higher-order moments, particularly the accuracy of asymmetry predictions is in need of further improvement. An intensity of frequency dependence for the breaking-induced damping coefficient is introduced here to further adjust the dissipation function in order to increase the accuracy of asymmetry predictions. By correcting the frequency dependence function with a new form of frequency dependence in the breaking coefficient, the model results are in better agreement with the measurements of the spectrum and higher-order statistics, as well as with the free surface elevation measurements. It is also seen from testing the model with three different cases that the more evident the influence of the breaking mechanism is on the wave transformation process, the more pronounced the contribution of this modification is.

The Impact of Systematic Attitude Error on the Measurement of Interferometric Radar Altimeter

Altimetric error has always been the significant performance parameter of the interferometric radar altimeter (IRA), particularly in the observation of sub-mesoscale ocean dynamic processes in which a higher accuracy of sea surface elevation (SSE) measurement is needed. The systematic attitude error of IRA associated with platform altitude, roll, pitch, and yaw errors is a remarkable source of altimetric error. However, the coupling attitude altimetric error is still less discussed up to now. In this paper, we focus on the study of the coupling attitude altimetric error and its related position-shifting, which are all induced by the attitude errors. The theoretical formulas of the coupling attitude altimetric error were derived, and the theoretical analysis demonstrates that the coupling attitude altimetric error is no longer along the range direction of the IRA image rigorously due to the change of the radar beam pointing. Based on theoretical formulas proposed by this study, the coupling attitude altimetric error and its related position-shifting are simulated and verified by using attitude data recorded by an airborne position and orientation system (POS) of three airborne experiments. The experimental results illustrate that the simulated coupling attitude altimetric errors are consistent with the measurements of the airborne experiments.

Quantifying Lidar Elevation Accuracy: Parameterization and Wavelength Selection for Optimal Ground Classifications Based on Time since Fire/Disturbance

Pre- and post-fire airborne lidar data provide an opportunity to determine peat combustion/loss across broad spatial extents. However, lidar measurements of ground surface elevation are prone to uncertainties. Errors may be introduced in several ways, particularly associated with the timing of data collection and the classification of ground points. Ground elevation data must be accurate and precise when estimating relatively small elevation changes due to combustion and subsequent carbon losses. This study identifies the impact of post-fire vegetation regeneration on ground classification parameterizations for optimal accuracy using TerraScan and LAStools with airborne lidar data collected in three wavelengths: 532 nm, 1064 nm, and 1550 nm in low relief boreal peatland environments. While the focus of the study is on elevation accuracy and losses from fire, the research is also highly pertinent to hydrological modelling, forestry, geomorphological change, etc. The study area includes burned and unburned boreal peatlands south of Fort McMurray, Alberta. Lidar and field validation data were collected in July 2018, following the 2016 Horse River Wildfire. An iterative ground classification analysis was conducted whereby validation points were compared with lidar ground-classified data in five environments: road, unburned, burned with shorter vegetative regeneration (SR), burned with taller vegetative regeneration (TR), and cumulative burned (both SR and TR areas) in each of the three laser emission wavelengths individually, as well as combinations of 1550 nm and 1064 nm and 1550 nm, 1064 nm, and 532 nm. We find an optimal average elevational offset of ~0.00 m in SR areas with a range (RMSE) of ~0.09 m using 532 nm data. Average accuracy remains the same in cumulative burned and TR areas, but RMSE increased to ~0.13 m and ~0.16 m, respectively, using 1550 nm and 1064 nm combined data. Finally, data averages ~0.01 m above the field-measured ground surface in unburned boreal peatland and transition areas (RMSE of ~0.19 m) using all wavelengths combined. We conclude that the ‘best’ offset for depth of burn within boreal peatlands is expected to be ~0.01 m, with single point measurement uncertainties upwards of ~0.25 m (RMSE) in areas of tall, dense vegetation regeneration. The importance of classification parameterization identified in this study also highlights the need for more intelligent adaptative classification routines, which can be used in other environments.

Three-dimensional coupling between Boussinesq (FEM) and Navier–Stokes (particle based) models for wave structure interaction

The paper presents coupling between a mesh-based finite-element model for Boussinesq equations (FEBOUSS Agarwal et al., 2022) with a meshless local Petrov–Galerkin model for the Navier–Stokes equations (MLPG_R Agarwal et al., 2021) in 3D. Boussinesq equation models are widely used for simulating wave-propagation over large domains with uneven topography using a 2D surface mesh. Mesh-less models inherently capture large free-surface deformations and have shown promise in simulating wave-structure interaction, run-up and breaking phenomenon. The hybrid approach in this paper assumes a 3D MLPG_R sub-domain surrounded by the 2D mesh of FEBOUSS. The coupling interface in MLPG_R consists of relaxation zones that can be placed along multiple boundaries of the sub-domain for exchanging particle velocity from FEBOUSS. This hybrid model is therefore capable of simulating directional waves, that has not been reported previously.The paper first presents the procedure for calculating the depth-resolved velocities in 3D from the Boussinesq model. The resultant velocities are compared against theory, experiments and other models. The following sections present the coupling algorithm along a single and multiple coupling interfaces in MLPG_R. Validation results for this hybrid model are provided using surface elevation and velocity measurements for regular waves, including directional cases. In general, the results from the hybrid model are reported to have marginal over-prediction of peaks compared to purely MLPG_R simulation. Finally, the interaction of a vertical cylinder with direction regular wave is simulated using the 3D hybrid model.

A new Contour-Based combined matching algorithm for underwater Terrain-Aided strapdown inertial navigation system

Terrain-aided strapdown inertial navigation system is a geophysical field positioning technique for long-endurance underwater vehicles, whose key technology is the matching algorithm. Aiming at transcending the limitations of current batch matching algorithms in accuracy due to local convergence and neglect of the SINS continuous trajectory information, we propose a two-stage combined matching algorithm. First, a coarse matching position is obtained based on the terrain mean factor search and the maximum likelihood estimation utilizing the multi-beam measured surface elevations. Then we implement the contour-based fine matching by introducing inertial constraint and proportionality factor, and propose a new numerical solution for the trajectory transformation matrix, where the proportionality factor and transformation matrix are both solvable independently. Finally, the simulations and field test results on real grid maps with 10 m resolution show that the proposed algorithm is superior to the previous algorithms and its feasibility in practical applications, and the matching accuracy reaches 1–2 grids.