Elevation Time Series Research Articles

Numerical method for the characterization of sea states using realistic irregular waves on computational fluid dynamics simulations for application on wave energy converters

Energy demand grows along with technological advances, industrial expansion, and global urbanization. To supply this demand sustainably, there are several attempts to harness energy from renewable sources, among them, wave energy. The study of wave energy availability in energy conversion devices primarily focuses on two major areas: analysis of the fluid-dynamic behavior of the devices and the simulation of sea states to estimate theoretical energy potential. Despite advancements in both fields, there is a lack of methodologies that effectively integrate realistic irregular wave simulations and fluid-dynamic analysis of energy conversion devices. This research aims to integrate these areas by employing the WaveMIMO methodology, in which a sea state spectrum is converted into a statistically equivalent time series of water free surface elevation, then applied as an estimation of the velocity field in the water column to generate irregular waves. This study focuses on the development of a methodology to characterize the wave climate in the city of Rio Grande, in southern Brazil, for the year 2014, using a histogram to classify sea states according to their significant wave height and mean wave period, thus producing a bivariate histogram of wave conditions. A sea state spectrum was obtained for each pair of wave height and period and simulated using the computational fluid dynamics software Fluent to reproduce the realistic irregular waves of this sea state. The results indicated that the methodology for categorizing the sea state based on a histogram proved to be a computationally efficient alternative for the numerical simulation of wave climates in a given location for a long period of time, reducing the simulation time needed to approximately 0.5% of the total amount. In addition, an application of this methodology to investigate the wave energy conversion employing an oscillating water column device is presented as supplementary material.

Faster than real-time, phase-resolving, data-driven model of wave propagation and wave–structure interaction

A machine learning time-series prediction approach is proposed for wave propagation and wave load prediction. Under unidirectional wave conditions and variable bathymetry, given a wave gauge upstream, a model is shown to reproduce wave elevation or wave forces downstream under irregular steep and either non-breaking or breaking conditions. Attempts to perform the opposite calculation, predicting upstream conditions from downstream measurements, results in higher error, likely due to information loss under breaking conditions. For choice of machine learning approach, comparisons show that the Time-series Dense Encoder (TiDE) approach results in a good balance between model complexity, stability, computational time, and error. Over a flat bottom, time-series of wave elevation can be predicted up to 10 wavelengths away, though with a degraded accuracy compared to shorter distances. Similar results are shown for time-series of forces on a vertical cylinder, showing better results than a simple Morison approach, as used in engineering tools such as OpenFAST, but with a similarly fast computational time. Generalizations show that training on irregular wave data permit extrapolations to periodic wave cases. Finally, the same method also is also demonstrated at field-scale, comparing results between two offshore buoys.

Validation and Analysis of the ICESat-2 ATL11 Product: A Case Study of Lake Vostok

Elevation changes are crucial input data for mass balance assessment based on satellite altimetry. However, due to the accuracy limitations of altimetry data and mass conversion models, a significant uncertainty remains in estimating the mass balance of the Antarctic ice sheet, especially in East Antarctica. The ICESat-2 photon altimetry satellite enhances the precision of ice sheet surface elevation measurements to an accuracy of 2–4 cm. This improvement is particularly beneficial for detecting subtle elevation changes in East Antarctica. The ATL11 product from ICESat-2 offers a time series of ice surface elevations across Antarctica, enabling direct calculation of elevation change rates. To evaluate the capability of the ATL11 product in accurately depicting detailed elevation changes within the local terrain, we selected the Vostok Subglacial Lake as the validation region. Our research involves comparing fitted surface elevation change rates with in-situ data, while also considering surface mass balance, wind, and surface elevation to analyze the factors contributing to small differences in elevation changes within the local lake area. This analysis aims to identify the factors contributing to the minor variations in elevation changes within the local lake area. According to our analysis, the Vostok Lake surface elevation change rate is 2.00 ± 0.77 cm yr−1 from April 2019 to June 2023, with an average period of 356 ± 81 days. The results demonstrate that the ATL11 elevation product sequence has the potential to accurately characterize subtle elevation changes and seasonal variations in the Antarctic ice sheet.

Data Assimilation and Parameter Identification for Water Waves Using the Nonlinear Schrödinger Equation and Physics-Informed Neural Networks

The measurement of deep water gravity wave elevations using in situ devices, such as wave gauges, typically yields spatially sparse data due to the deployment of a limited number of costly devices. This sparsity complicates the reconstruction of the spatio-temporal extent of surface elevation and presents an ill-posed data assimilation problem, which is challenging to solve with conventional numerical techniques. To address this issue, we propose the application of a physics-informed neural network (PINN) to reconstruct physically consistent wave fields between two elevation time series measured at distinct locations within a numerical wave tank. Our method ensures this physical consistency by integrating residuals of the hydrodynamic nonlinear Schrödinger equation (NLSE) into the PINN’s loss function. We first showcase a data assimilation task by employing constant NLSE coefficients predetermined from spectral wave properties. However, due to the relatively short duration of these measurements and their possible deviation from the narrow-band assumptions inherent in the NLSE, using constant coefficients occasionally leads to poor reconstructions. To enhance this reconstruction quality, we introduce the base variables of frequency and wavenumber, from which the NLSE coefficients are determined, as additional neural network parameters that are fine tuned during PINN training. Overall, the results demonstrate the potential for real-world applications of the PINN method and represent a step toward improving the initialization of deterministic wave prediction methods.

GNSS elevation time series prediction model based on multiple gate recurrence unit and temporal convolutional networks parallel

GNSS elevation time series prediction model based on multiple gate recurrence unit and temporal convolutional networks parallel

Spatiotemporal variability in surface velocity of large tributary-bearing glaciers of the Indian Himalayas inferred from SAR polarimetry

ABSTRACT Glacier pattern changes directly indicate variability in local climatic circumstances. The present study dealt with the proposition and estimation of spatiotemporal glacier movement using a synthetic aperture radar-derived polarimetric tracking method which revealed improved estimates over four selected large tributary-bearing glaciers (Siachen, Bara Shigri, Gangotri, and Zemu) in the Indian Himalayas. The average estimated velocities in 2021–2022 for the four glaciers were 0.13, 0.06, 0.08 and 0.09 m/day. The thick debris cover hindered the movement temporally in the middle and lower reaches of the glaciers. The effect of meltwater influx along the tributary confluence zone was also witnessed over the glaciers. Comparison and validation with the US National Aeronautics and Space Administration (NASA) Inter-mission Time Series of Land Ice Velocity and Elevation (ITS_LIVE) products has shown the utility of the proposed method in studying the contributions of active feeding tributaries of the glaciers in the ablation zone.

Elevation Changes of A’nyemaqen Snow Mountain Revealed with Satellite Remote Sensing

A’nyemaqen Snow Mountain (ASM) is the largest glacier area in the Yellow River source area and has been experiencing significant ablation in recent years. To investigate spatial–temporal elevation changes in ASM, a 21–year Digital Elevation Model (DEM) time series was obtained using the MicMac ASTER (MMASTER) algorithm and ASTER L1A V003 data. It covers the period from January 2002 to January 2023. The mean elevation of ASM decreased by −7.88 ± 3.37 m during this period, with highly spatial variation. The elevation decrease occurred mainly in the lower elevations and opposite in the higher elevations. The corresponding elevation decrease was −12.99 ± 11.29 and −4.45 ± 11.36 m at the southern Yehelong Glacier and the northern Weigeledangxiong Glacier, respectively. Moreover, there exists a temporal variation in ASM. The maximum elevation was observed in February for both ASM and the southern Yehelong Glacier but March for Weigeledangxiong Glacier, with about 1 month lagged. With the elevation time series and climate data from ERA5 datasets, we applied the random forest technique and found that the temperature is the main factor to elevation change in ASM. Furthermore, the response of elevation changes to temperature appeared with a lag and varied with the location. Based on the elevation time series, the ARIMA model was further used to forecast the elevation changes in the next 5 years. All regions will experience the elevation decrease, with a mean decline −1.74 ± 0.39 m and a corresponding rate −0.35 ± 0.08 m/a in ASM. This is similar to that of −0.38 ± 0.16 m/a between 2002 and 2003, showing its stability in the near future.

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.

Statistically assessing vertical change on a sandy beach from permanent laser scanning time series

In the view of climate change, understanding and managing effects on coastal areas and adjacent cities is essential. Permanent Laser Scanning (PLS) is a successful technique to not only observe notably sandy coasts incidentally or once every year, but (nearly) continuously over extended periods of time. The collected point cloud observations form a 4D point cloud data set representing the evolution of the coast provide the opportunity to assess change processes at high level of detail. For an exemplary location in Noordwijk, The Netherlands, three years of hourly point clouds were acquired on a 1 km long section of a typical Dutch urban sandy beach. Often, the so-called level of detection is used to assess point cloud differences from two epochs. To explicitly incorporate the temporal dimension of the height estimates from the point cloud data set, we revisit statistical testing theory. We apply multiple hypothesis testing on elevation time series in order to identify different coastal processes, like aeolian sand transport or bulldozer works. We then estimate the minimal detectable bias for different alternative hypotheses, to quantify the minimal elevation change that can be estimated from the PLS observations over a certain period of time. Additionally, we analyse potential error sources and influences on the elevation estimations and provide orders of magnitudes and possible ways to deal with them. Finally we conclude that elevation time series from a long term PLS data set are a suitable input to identify aeolian sand transport with the help of multiple hypothesis testing. In our example case, slopes of 0.032 m/day and sudden changes of 0.031 m can be identified with statistical power of 80% and with 95% significance in 24-h time series on the upper beach. In the intertidal area the presented method allows to classify daily elevation time series over one month according to the dominating model (sudden change or linear trend) in either eroding or accreting behaviour.

Wave measurements using open source ship mounted ultrasonic altimeter and motion correction system during the one ocean circumnavigation

This study reviews the design and signal processing of ship borne ultrasonic altimeter wave measurements. The system combines a downward facing ultrasonic altimeter to capture the sea surface elevation as a time series, and an inertial measurement unit to compensate for the ship’s motion. The methodology is cost-effective, open source, and adaptable to various ships and platforms. The system was installed on the barque Statsraad Lehmkuhl and recorded data continuously during the 20-month One Ocean Expedition. Results from 1-month crossing of the Tropical Atlantic are presented here. The one-dimensional wave spectrum and associated wave parameters are obtained from the sea surface elevation time series. The observed significant wave height agrees well with satellite altimetry and a spectral wave model. The agreement between observations and the spectral wave model is better for the mean wave period than the peak period. We perform Doppler shift corrections to improve wave period estimates by accounting for the speed of the ship relative to the waves. This correction enhances the accuracy of the mean period, but not the peak period. We suggest that the Doppler correction could be improved by complementing the data sources with directional wave measurements from a marine X-band radar.

Measurements of nearshore ocean-surface kinematics through coherent arrays of free-drifting buoys

Abstract. Surface gravity wave breaking occurs along coastlines in complex spatial and temporal patterns that significantly impact erosion, scalar transport, and flooding. Numerical models are used to predict wave breaking and associated processes but many lack sufficient evaluation with observations. To fill the need for more nearshore wave measurements, we deployed coherent arrays of small-scale, free-drifting buoys named microSWIFTs. The microSWIFT is a small buoy equipped with a GPS module to measure the buoy's position, horizontal velocities, and an inertial measurement unit (IMU) to directly measure the buoy's rotation rates, accelerations, and heading. Measurements were collected over a 27 d field experiment in October 2021 at the US Army Corps of Engineers Field Research Facility in Duck, NC. The microSWIFTs were deployed as a series of coherent arrays, meaning they all sampled simultaneously with a common time reference, leading to a rich spatial and temporal dataset during each deployment. Measurements spanned offshore significant wave heights ranging from 0.5 to 3 m and peak wave periods ranging from 5 to 15 s over the entire experiment. The completed dataset consists of 67 deployment files that contain 971 drift tracks that contain all associated data. We use an attitude and heading reference system (AHRS) 9-degrees-of-freedom Kalman filter to rotate the measured accelerations from the reference frame of the buoy to the Earth reference frame. We then use the corrected accelerations to compute the vertical velocity and sea-surface elevation. We give example evaluations of wave spectral energy density estimates from individual microSWIFTs compared with a nearby acoustic wave and current (AWAC) sensor. A zero-crossing algorithm is applied to each buoy time series of sea-surface elevation to extract realizations of measured surface gravity waves, yielding 116 307 wave realizations throughout the experiment. We also compute significant wave height estimates from the aggregate wave realizations and compare these estimates with the nearby AWAC estimates. An example of spatial variability in cross-shore velocity and vertical acceleration is explored. Wave-breaking events, detected by high-intensity vertical acceleration peaks, are explored, and the cross-shore distribution of all breaking events detected in the experiment is shown. A total of 3419 wave-breaking events were detected across the entire experiment. These data are available at https://doi.org/10.5061/dryad.hx3ffbgk0 (Rainville et al., 2023) and will be used to investigate nearshore wave kinematics, transport of buoyant particles, and wave-breaking processes.

Constructal Design Applied to an Oscillating Water Column Wave Energy Converter Device under Realistic Sea State Conditions

In this work, we conducted a numerical analysis of an oscillating water column (OWC) wave energy converter (WEC) device. The main objective of this research was to conduct a geometric evaluation of the device by defining an optimal configuration that maximized its available hydrodynamic power while employing realistic sea data. To achieve this objective, the WaveMIMO methodology was used. This is characterized by the conversion of realistic sea data into time series of the free surface elevation. These time series were processed and transformed into water velocity components, enabling transient velocity data to be used as boundary conditions for the generation of numerical irregular waves in the Fluent 2019 R2 software. Regular waves representative of the sea data were also generated in order to evaluate the hydrodynamic performance of the device in comparison to the realistic irregular waves. For the geometric analysis, the constructal design method was utilized. The hydropneumatic chamber volume and the total volume of the device were adopted as geometric constraints and remained constant. Three degrees of freedom (DOF) were used for this study: H1/L is the ratio between the height and length of the hydropneumatic chamber, whose values were varied, and H2/l (ratio between height and length of the turbine duct) and H3 (submergence depth of hydropneumatic chamber) were kept constant. The best performance was observed for the device geometry with H1/L= 0.1985, which presented an available hydropneumatic power Phyd of 29.63 W. This value was 4.34 times higher than the power generated by the worst geometry performance, which was 6.83 W, obtained with an H1/L value of 2.2789, and 2.49 times higher than the power obtained by the device with the same dimensions as those from the one on Pico island, which was 11.89 W. When the optimal geometry was subjected to regular waves, a Phyd of 30.50 W was encountered.

Phase-resolved wave prediction with linear wave theory and physics-informed neural networks

Deterministic wave elevation prediction is crucial for improving the power generation efficiency of offshore energy structures (OESs). Although phase-resolved wave models may predict deterministic wave information, a comprehensive understanding of wave theory and mathematics is necessary to guarantee their accuracy. Inspired by the capability of physics-informed neural networks (PINNs) in solving physical equations, we propose an irregular long-crested wave prediction model named LWT-PINN that combines the linear wave theory (LWT) with PINNs. To the best of our knowledge, this is the first time that PINNs are used to predict waves. Five sets of wave elevation time series with steepness ranging from 0.0174 to 0.0349 are generated in a wave basin to optimize and evaluate the LWT-PINN. The computing time for LWT-PINN is 0.13 s, close to real-time. When predicting downstream wave elevation, the LWT-PINN significantly outperforms the linear wave prediction (LWP) model in terms of accuracy and prediction length. Specifically, the LWT-PINN achieves satisfactory accuracy with only 100 s upstream wave elevation, whereas the LWP requires 175 s; LWT-PINN’s high-precision prediction duration is 13.7 s, which is 2.5 times longer than that of LWP (5.5 s). Moreover, LWT-PINN can provide wave autoregressive predictions of around 5 s without the aid of statistical methods, which offers a new direction for developing wave autoregressive prediction methods. The excellent performance of the proposed model can substantially assist the stable operation of OESs.

Computing River Discharge Using Water Surface Elevation Based on Deep Learning Networks

Accurately computing river discharge is crucial, but traditional computing methods are complex and need the assistance of many other hydraulic parameters. Therefore, it is of practical value to develop a convenient and effective auto-computation technique for river discharge. Water surface elevation is relatively easy to obtain and there is a strong relationship between river discharge and water surface elevation, which can be used to compute river discharge. Unlike previous usage of deep learning to predict short-term river discharge that need multiple parameters besides water level, this paper proved that deep learning has the potential to accurately compute long-term river discharge purely based on water level. It showed that the majority of relative errors on the test dataset were within ±5%, particularly it could operate continuously for almost one year with high precision without retraining. Then, we used BiGRU to compute river flow with different hyperparameters, and its best RMSE, NSE, MAE, and MAPE values were 256 m3/s, 0.9973, 207 m3/s, and 0.0336, respectively. With this data-driven based technology, it will be more convenient to obtain river discharge time series directly from local water surface elevation time series accurately in natural rivers, which is of practical value to water resources management and flood protection.

A study of the potential effects of deepening the Corpus Christi Ship Channel on hurricane storm surge

We present a case study of the potential impact on hurricane storm surge due to deepening the Corpus Christi Ship Channel through Aransas Pass in the region of Corpus Christi and Port Aransas, Texas. Our investigation is based on numerical mathematical models of the circulation of coastal water due to Hurricane Harvey and a synthetic hurricane derived from Harvey. The circulation models are based on the numerical solution of the shallow water equations using finite element and finite difference techniques. The shallow water equations are solved within the framework of the widely used ADvanced CIRCulation (ADCIRC) numerical model. From the models, we ascertain maximum storm surge as well as elevation time series at critical locations in the study region. To assess the effects of a deeper channel, we compare the model outputs for current and proposed future channels. The model results indicate that the changes to maximum storm surge magnitude are small and in large portions of the study area the models indicate a reduction in surge magnitude. However, there are some local areas where the models results show an increase of up to 30 centimeters in a synthetic extreme storm scenario.

Scattering of Long Waves by Freely Oscillating Submerged Plates

Abstract We consider a horizontal, submerged plate in shallow water that is allowed to oscillate in the vertical direction due to the wave loads. The plate is attached to a linear spring and damper to control the oscillations. The focus of the study is on the transformation of the wave field by the submerged oscillating plate. To estimate energy scattering, wave reflection and transmission coefficients are determined from four wave gauges: two placed upwave and two placed downwave of the oscillating plate. The flow is governed by the nonlinear level I Green–Naghdi (GN) equations, coupled with the equations of the vertical oscillations of the plate. Time series of water surface elevation recorded at gauges upwave and downwave of the plate obtained by the GN model are compared with the available laboratory experiments and other data, and very good agreement is observed. Wave reflection and transmission coefficients are then determined for a range of involved parameters, including wave conditions (wavelength and wave height), initial submergence depth of the plate, plate length, and the spring-damper system attached to the plate. It is found that a submerged oscillating plate can have a remarkable effect on the wave field and that nonlinearity plays an important role in this wave–structure interaction problem. Discussion is provided on how the wave reflection and transmission coefficients vary with the wave conditions, plate characteristics, initial submergence depth, and spring-damper system properties.

Stereo Reconstruction Method for 3D Surface Wave Fields around a Floating Body Using a Marker Net in a Wave Tank

Spatial wave fields around floating bodies are important for the understanding of hydrodynamics, and particularly the wave drift forces, of floating bodies in waves; however, experimental measurement of these fields is challenging. This paper presents a stereo reconstruction method for three-dimensional (3D) surface wave fields around floating bodies in a wave tank. Styrofoam markers were attached to a flexible net in a regular grid, called a marker net, and were placed on the water surface to be used as targets for stereo cameras (SCs). A thin plate spline was applied to the markers detected by the SCs to reconstruct the 3D surface wave profile around a floating body model. The proposed method was validated by measuring the wave field around a cylindrical floating body with a footing at its bottom. These experiments were conducted under regular wave incidence conditions. A wave elevation time series measured using a servo-controlled wave gauge was used as the benchmark data. The 3D surface wave field reconstruction method was applied under three different conditions: without the model, with a fixed model, and with a freely oscillating model. The results showed reliable reconstructions of the scattering and radiation waves. The marker net’s effects on the floating body’s motion and the surrounding wave fields were shown to be negligible by comparing the results acquired with and without the marker net.

Determining Undersampled Coastal Tidal Harmonics Using Regularized Least Squares

AbstractSatellite altimetry, which measures water level with global coverage and high resolution, provides an unprecedented opportunity for a wide and refined understanding of the changing tides in the coastal area. But its sampling frequency is too low to satisfy the Nyquist frequency requirement and too few data points per year are available to recognize a sufficient number of tidal constituents to capture the trend of tidal changes on a yearly basis. To address these issues, a novel regularized least‐square approach is developed to relax the sampling interval limit to the range of 9–11 days, reaching the revisit time of the existing satellites. In this method, the prior information of the regional tidal amplitudes is used to support a least square analysis to obtain the amplitudes of the tidal constituents for water elevation time series of different lengths and time intervals. Synthetic data experiments performed in Delaware Bay and Galveston Bay showed that the proposed method can determine the tidal amplitudes with high accuracy and the sampling interval can be extended to the application level of major altimetry satellites. The proposed algorithm was further validated using the data of the altimetry mission, Jason‐3, to show its applicability to irregular and noisy data. The new method could help identify the changing tides with sea‐level rise and anthropogenic activities in coastal areas, informing coastal flooding risk assessment and ecosystem health analysis.

The Effect of Gravel and Sand Mining on Groundwater and Surface Water Regimes—A Case Study of the Velika Morava River, Serbia

This paper describes how uncontrolled and illegal mining of sand and gravel can affect surface water and groundwater regimes in places where there is a hydraulic connection between them, based on a case study of the Velika Morava River in Serbia. Also, a change in cross-profile geometry, as a result of anthropogenic and natural factors, hinders the preparation of this river for inclusion among Serbia’s waterways. The Velika Morava River’s navigability would enable the development of waterborne transportation for both merchant ships and vessels of the Serbian Armed Forces River Flotilla. Correlations between water levels at gauging stations, as well as correlations between groundwater levels and river water levels at gauging stations, are used to show the dependence of these parameters on the change in the river bed profile after sand and gravel mining at the locations near gauging stations. In addition, the homogeneity of time-series of average annual elevations and the variance of the water levels of the Velika Morava River, measured in gauging stations during different periods, are statistically analyzed. The deepening of the Velika Morava riverbed where it was indiscriminately excavated in the 1980s led to the disruption of the groundwater regime and the hydraulic connection with the river, which lowered the water table of the aquifer used for the public water supply, as well as causing a number of other negative consequences.

Investigation of Numerical Irregular Wave Generation Using Transient Discrete Data as Boundary Conditions of Prescribed Velocity

This work presents a two-dimensional numerical analysis of a wave channel. The goal is to investigate a methodology that uses transient velocity data as means to impose velocity boundary condition for generating numerical waves. To do so, a numerical wave channel was simulated using irregular waves. These waves were obtained using the WaveMIMO methodology, which converts sea data from a spectral model into time series of free surface elevation, and then converts this elevation into transient discrete wave velocity data. For the numerical analysis, computational fluid dynamics ANSYS Fluent software was employed, which is based on the finite volume method. The computational domain and mesh were generated using GMSH software, and the nonlinear multiphase model volume of fluid (VOF) was applied to tackle water-air interaction. In general, the results obtained through the use of discrete data as velocity boundary condition presented a good agreement with free surface elevation converted from the spectral model, and the tests performed provided further insight into the parameters which affect this methodology. Since many studies use regular waves, the proposed investigation stands out for its capacity to improve the use of realistic sea state data in numerical simulations of wave energy converters.