Wave Height Measurements Research Articles

Waveform of the Reflected Impulse at the Oblique Sounding of the Sea Surface

The height of sea waves is one of the most important characteristics describing the wave climate of the ocean. At the present, the main radar for remote measurement of wave heights is an altimeter. Measurements are performed at the vertical sounding (incidence angle equal to zero). The Brown model was developed to describe the waveform of the reflected impulse at the vertical sounding. There is no theoretical model for the case of oblique sounding. In the Kirchhoff approximation, the theoretical task about waveform of the reflected impulse at oblique sounding was considered. In the result of the investigation, the analytical formula for the waveform of the reflected impulse for oblique sounding at the small incidence angles (< 12◦) for a microwave radar with a narrow antenna beam was obtained. The waveform of the reflected impulse depends on the width of antenna beam, incidence angle, impulse duration, significant wave height (SWH), altitude of the radar, mean square slopes of large-scale, in comparison with radar wavelength, sea waves. It is shown that possibility exist to retrieve SWH using waveform the reflected impulse at the oblique sounding.

Wave height distribution for plunging breakers induced by air bubbles

This study highlights the wave height distributions based on plunging breaking waves and air bubble effects in the surf zone. Wave height distributions predicted previously by different models have been reformulated in terms of air bubble effects. Some of the most commonly applied wave height distributions are judged using laboratory observations in a custom-built wave flume. Results have revealed a notable deviation from the Rayleigh distribution, with the proposed model demonstrating a closer match to experimental data, particularly for larger wave heights. Probability densities of larger wave heights are reduced significantly by entrained air bubbles, leading to measured wave heights below Rayleigh distribution predictions. In addition, the different wave height parameters derived from the proposed model exhibited good agreement with laboratory data compared to the Rayleigh distribution. Furthermore, theoretical analysis shows the scale parameter's dependence on the decay coefficient, aligning well with measurements and simplifying the proposed distribution to a one-parameter model. Again, based on the error analysis, the proposed model's results show good performance compared to others.

Waveform of the Reflected Impulse at the Oblique Sounding of the Sea Surface

The height of sea waves is one of the most important characteristics describing the wave climate of the ocean. At the present, the main radar for remote measurement of wave heights is an altimeter. Measurements are performed at the vertical sounding (incidence angle equal to zero). The Brown model was developed to describe the waveform of the reflected impulse at the vertical sounding. There is no theoretical model for the case of oblique sounding. In the Kirchhoff approximation, the theoretical task about waveform of the reflected impulse at oblique sounding was considered. In the result of the investigation, the analytical formula for the waveform of the reflected impulse for oblique sounding at the small incidence angles (< 12◦) for a microwave radar with a narrow antenna beam was obtained. The waveform of the reflected impulse depends on the width of antenna beam, incidence angle, impulse duration, significant wave height (SWH), altitude of the radar, mean square slopes of large-scale, in comparison with radar wavelength, sea waves. It is shown that possibility exist to retrieve SWH using waveform the reflected impulse at the oblique sounding.

“Assessing the wave power density in the Atlantic French façade from high-resolution CryoSat-2 SAR altimetry data”

The wave energy resource potential and trends are assessed in coastal areas of the Atlantic French Façade. High-resolution satellite altimetry sea state estimates (significant wave height and backscatter coefficient) are used, taking advantage of the time and spatial coverage of ESA's CryoSat-2 mission data processed with the coastal zone SAMOSA + waveform retracker algorithm. Due to this novel retracker specifically designed for challenging regions like the coastal zone, the successful measurements of the significant wave height in the coastal zone allows us to solve previously difficult coastal issues such as land and calm water interference in the altimetry footprint. The study comprises 12 years, from January 2011 to December 2022, and applies a relatively simple empirical model to estimate the wave power density. Results are analyzed by season, showing the time of the year and location where the resource is abundant and identifying potential reserves of wave power. The highest value of the mean wave power density (27.1 kW/m) over the 12 years is found in the western sector and to the south of Belle-Île-en-mer, whereas the autumn, in which sea state conditions are less harsh for the extraction activity, appears as the most favorable season for extracting the wave resource. In conclusion, according to the estimated positive trend of wave power density, the wave resource is abundant in nearshore regions of the Atlantic French Façade and promising in view of its future exploitation. The study highlights the importance of an innovative methodology and the role of satellite data in enhancing the accuracy of wave energy assessments.

Adaptation Of Different Scales In The Same 3D Physical Model To Assess The Different Armour Sizes

While assessing the breakwater stability through a 3D physical model, the normal practice is to modify the structure element if the breakwater is unstable. However, casting a larger number of different sizes of concrete armour is time-consuming and costly. Therefore, the present study assessed the utilisation of the constructed model with 6.5T(1:41.37) to represent the 10.0T(1:47.82) and 12.5T(1:51.51) tetrapod (TTP) armours by using 88g TTP units in the model. Only the stability of the main armour at the roundhead was considered with new scales. Further, the same structure freeboard in the prototype was considered for new scales. Since the measured wave heights at the breakwater including the wave reflection from the structure, wave condition at the paddles were considered while selecting the input signals for the new scales during the trial runs. The selected inputs for the trail runs were verified with the post-calibration done for a 1:51.51 scale. Originally proposed 6.5T units were replaced by the hydraulically stable 12.5T units at the roundhead based on the model results done with different scales.

Development and Validation of an Instrument for Wave Height Measurement with Encoder Sensors and Accelerometer

Ocean waves play a significant role in coastal dynamics and the management of coastal development activities. However, there are limited instruments to measure the wave height, particularly in developing countries. This study introduces a novel instrument design for simple and cost-effective wave height measurement. The proposed instrument combines a Hall-effect sensor and an accelerometer to capture the rise and fall of a buoy in response to wave movements. The Hall-effect sensor as a rotary encoder detects the rotation of the buoy while the accelerometer measures the tilt of the instrument caused by ocean waves. The instrument is constructed using PVC pipes and incorporates long-range (LoRa) communication technology for real-time monitoring. Experimental tests were conducted at a study site in Banyuwangi Regency, Indonesia, where the performance of the instrument was compared with an ultrasonic sensor-based instrument. The results validate the effectiveness of the proposed instrument design for wave height measurement. The collected data were transmitted via the LoRa communication system, enabling convenient monitoring and analysis of sea-level changes. The valuable contribution of the instrument to the field stems from its precision in measuring the wave height, adaptability to diverse conditions, and potential applicability in shallow waters.

MEMS Differential Pressure Sensor with Dynamic Pressure Canceler for Precision Altitude Estimation.

Atmospheric pressure measurements based on microelectromechanical systems (MEMSs) can extend accessibility to altitude information. A differential pressure sensor using a thin cantilever and an air chamber is a promising sensing element for sub-centimeter resolution. However, its vulnerability to wind and the lack of height estimation algorithms for real-time operation are issues that remain to be solved. We propose a sensor "cap" that cancels the wind effect and noise by utilizing the airflow around a sphere. A set of holes on the spherical cap transmits only the atmospheric pressure to the sensor. In addition, we have developed a height estimation method based on a discrete transfer function model. As a result, both dynamic pressure and noise are suppressed, and height is estimated under a 5 m/s wind, reconstructing the trajectory with an estimation error of 2.8 cm. The developed sensing system enhances height information in outdoor applications such as unmanned aerial vehicles and wave height measurements.

Acoustical effects of extreme weather events

The transfer of water from evaporating regions to precipitating regions drives the global water cycle, and understanding its dynamics is essential in determining how weather patterns will respond to changes in global climate. An intensification of the global water cycle has been reported using 50-year sea surface salinity data (Durack and Wijffels, 2010, J. Climate) with the consequence of more frequent extreme weather events. However, data under extreme weather conditions over the ocean are rare and a lot of physics remains to be investigated. As part of the Ocean Climate Stations that NOAA is maintaining, the 1-year data presented here are from Ocean Station Papa (50°N, 145°W), including measurements of wind speed, rain rate, currents, wave height and direction, bubble plume spatial structure and dynamics, and ambient noise for wind speeds up to 25 m/s. This full suite of data enables the study of the statistical properties of bubble plumes, their relation to meteorological parameters, and how to take them into account in ambient noise prediction, especially under severe weather conditions. Knowledge gained through this unique dataset can be critical for understanding air–sea interaction, validating satellite rain products, and predicting the ambient noise field under extreme weather conditions.

PHYSICS-INFORMED DEEP LEARNING OF NEARSHORE WAVE PROCESSES

The paper introduces the NWnets, a physics-informed deep learning model for reconstructing nearshore wave fields and mapping bathymetry. The physics encoded into the deep neural networks are the wave energy balance equation and dispersion relation. Insights into the model capability are gained through application of the NWnets to a laboratory experiment of wave transformation over a circular shoal. If the bathymetry and discrete measurements of wave height are available, the NWnets model is capable of simulating nearshore wave transformation. Moreover, the extended NWnets can be used for depth inversion if the bathymetry is unknown. Two methods for simultaneously estimating water depths and surface waves are presented. If surface wave number and limited wave height measurements are available from remote sensing platforms, the first method employs wave numbers and scarce measurements of wave height as training data. The second method utilizes scarce wave height and limited water depth measurements as training points to reconstruct bathymetry and wave fields. The results show that both methods are capable of simultaneously mapping the bathymetry and waves when the locations of training points are appropriately distributed.

Evaluation of Spectral Wave Models Physics as Applied to a 100‐Year Southern Hemisphere Extra‐Tropical Cyclone Sea State

AbstractExtreme significant wave height estimates, and their probability of exceedance, are fundamental offshore and coastal engineering design parameters. These estimates are characterized by uncertainty due to an incomplete understanding of the atmosphere‐ocean energy and momentum exchanges during intense storms. This particularly affects extreme wave statistics of ocean regions exposed to large and frequent synoptic disturbances such as Extra‐Tropical Cyclones (ETCs). In this work, we assessed the performance of global phase‐averaged spectral wave models in representing the 1 in 100‐year sea state generated by a Southern Ocean ETC in April 2021. We collected in situ and remote sensing observations, from the storm generation region to its decaying phase and the impact on South‐East Australian coastlines. We compared the observations with a suite of reanalysis and hindcast global wave model data sets. While comparing well for wind speed up to 20 m/s, the models presented differences in solving the air‐sea momentum exchange between the atmosphere and the ocean for wind speed velocities between 20 and 35 m/s, which are a distinctive characteristic of ETCs. Despite marked differences in the storm generation region, the models converged to a similar representation of the swell systems impacting the South‐East Australian coastlines, as demonstrated by a comparison with deep‐water buoy observations close to the coastlines. Furthermore, we found that the energy of the ERA5 reanalysis, which assimilates satellite wave height measurements is quickly dispersed and, as such, of little advantage in representing the 9.9 m significant wave heights that impacted the South‐East Australian coastlines on 10 April 2021.

The Study of the Bistatic Cross-Correlation Function of Two Signals Separated in Frequency Reflected by the Water Surface

The purpose of this study is to analyze the applicability conditions for the significant wave height (SWH) measurement approach based on measuring the cross-correlation function of two signals with similar frequencies reflected by the sea surface in the bistatic problem statement (the transmitting antenna and the receiving antenna are separated in space). When implementing this approach, the modulus of the normalized cross-correlation function for several pairs of signals with different frequency bases will be measured in the experiment. The advantage of this approach over the traditional method for radar altimetry, based on the analysis of the shape of the reflected pulse, is the high accuracy in measuring the SWH for weak waves. In the bistatic formulation of the problem, an important advantage of the approach under study is the possibility of obtaining analytical formulas for solving the direct problem. This paper presents the derivation of a formula for the modulus of the normalized cross-correlation function of reflected signals, which expresses an explicit relationship with the parameters of sea waves and the measurement geometry in the bistatic formulation of the problem. This paper considers the influence on the modulus of the normalized cross-correlation function of the antenna patterns of the transmitting and receiving antennas, the distances to the sea surface, the wave slope variances, the SWH and the frequency base of the transmitted signals. The optimal variants of the measurement scheme are discussed. The results and conclusions obtained can be easily expanded to underwater acoustic sounding.

How useful are mispointing phase SARAL/AltiKa geophysical products for ocean applications?

SARAL/AltiKa, the first microwave altimeter operating at Ka-band frequency, recently completed nine years of operations in orbit. During these years, it has catered to many applications related to operational oceanography, climate sciences, hydrology and cryosphere. More specifically, in oceanography, SARAL has contributed immensely to operational wave and circulation modelling, eddy detection/tracking, ocean current generation and many more. However, since Feb 2019, SARAL has moved from the drifting phase (DP) to the mispointing phase (MP) due to the malfunctioning of the star sensor of the spacecraft. In this study, we analyse the instrument’s performance and its waveforms during its ongoing MP. We find out that during the MP, significant wave height (SWH) measurements are anomalously high between 18 and 24 m, and wind speed measurements are between 16 and 19 m/s. In sea surface height anomaly (SSHA), there is a steady rise in negative values during the MP. In the return waveform, ∼15% degradation in Brown-type waveforms in the open ocean region is noticed. These changes significantly impact the SARAL applications. Two important applications of wave forecast and eddy detection are discussed here as examples. Following this, we also recommend using provided quality flags so that the data can be further explored for various ocean applications.

A comparison of an operational wave–ice model product and drifting wave buoy observation in the central Arctic Ocean: investigating the effect of sea-ice forcing in thin ice cover

A prototype OpenMetBuoy (OMB) was deployed alongside a commercial buoy in the central Arctic Ocean, north of the Laptev Sea, where there are historically no wave observations available. The inter-buoy comparison showed that the OMB measured wave heights and periods accurately, so the buoy data were used to study the predictability of a wave–ice model. The first event we studied was when both buoys observed a sudden decrease in significant wave heights Hm0, which was caused by the change of wind directions from along the ice edge to off-ice wind. The Arctic Ocean Wave Analysis and Forecast wave–ice model product (ARC MFC) underestimated the Hm0 on the account of the fetch being constrained by the inaccurate model representation of an ice tongue. The second case was an on-ice wave event as new ice formed. In this instance, the ARC MFC wave–ice model product largely underestimated the downwind buoy Hm0. Model sea-ice conditions were examined by comparing the ARC MFC sea-ice forcing with the neXtSIM sea-ice model product, and our analysis revealed the ARC MFC did not resolve thin ice thickness distribution for ice types like young and grey ice, typically less than 30 cm. The ARC MFC model’s wave dissipation rate has a sea-ice thickness dependence and overestimated wave dissipation in thin ice cover; sea-ice forcing that can resolve the thin thickness distribution is needed to improve the predictability. This study provides an observational insight into better predictions of waves in marginal ice zones when new ice forms.

Simultaneous mapping of nearshore bathymetry and waves based on physics-informed deep learning

This paper uses physics-informed neural networks (PINNs) to simultaneously determine nearshore water depths and wave height fields based on remote sensing of the ocean surface with limited or sparse measurements. Two methods that integrate the knowledge of water wave mechanics and fully connected neural networks are introduced. The first method utilizes observed wave celerity fields and scarce measurements of wave height as training data. The model performance was examined with linear waves over an alongshore varying barred beach and nonlinear waves over an alongshore uniform barred beach. The second method uses scarce wave height and water depth measurements as training points, and the model performance was investigated with water waves over a circular shoal and the alongshore varying barred beach. One advantage of applying PINNs to solve bathymetry inversion problems is that wave height and bathymetry can be simultaneously estimated by PINN models. Thus, the impact of wave amplitude dispersion on depth inversion in nonlinear wave systems can be considered without measuring the entire wave height field. Overall, this study demonstrates the potential of the inverse PINN model as a promising tool for estimating nearshore bathymetry and reconstructing wave fields using observations from different remote sensing platforms.

An experimental study on capacitive and ultrasonic measurement principles and uncertainty assessment in laboratory wave measurements

Many studies in ocean engineering and related fields need physical wave modelling in controlled environments. Monitoring the free surface elevation over time is essential to forming accurate waves. Various wave height measurement instruments can be used to determine the free surface elevation. However, measurements based on only one principle might lead to uncertain results. This study aims to compare measurements taken with capacitance-type and ultrasonic-type wave height gauges for the same wave models and analyze uncertainty in wave modelling. Nine different wave cases were tested using three-wave heights and three-wave frequencies. In a two-dimensional wave flume, the amplitude and frequency of the waves were controlled with a mechanical wave generator. The Guide on the Expression of Uncertainty in Measurement (GUM) presented by the Joint Committee for Guides in Metrology (JCGM) was used following ITTC procedures and guidelines. The processes for acquiring data, selecting data intervals, estimating amplitude and frequency, and analyzing uncertainty are presented and discussed. The measurements by the ultrasonic-type wave height gauge required a different input stroke for the wave generator and had more uncertainties associated with the amplitude of the measured waves. The findings highlight that identifying differences in measurement principles is significant for wave modelling.

An intermediate water gravity wavelength and wave height measurement inside a large wave flume tank

This paper discusses an intermediate water gravity wavelength and wave height measurement method. Three methods were used to obtain wave height, wavelength, and period. Firstly, conventional methods used two Honeywell pressure sensors mounted at the bottom of the wave tank at two different locations. Secondly, using the transfer function of the flap wavemaker (the relationship between wave height and the wave paddle stroke). Thirdly, the Laser Sheet technique (PIV image processing technique). The significant wave height and period from pressure reading sensors of regular gravity waves were obtained from the Raleigh distribution and Zero up crossing technique. Wavelength was obtained indirectly by using a dispersion relationship that was solved by using the Newton Raphson numerical method from both the pressure sensors and the transfer function of the flap wavemaker. This experiment was focused on getting the direct value of wave measurements by developing an image processing technique in a clear large wave flume tank to replace the conventional methods and eliminate the error that may produce by using the numerical methods. The PIV setup with the CCD camera was used to capture wave images. The image processing technique based on Canny edge detection with constant threshold value was used to detect the edge of the waves. The experimental result showed a good agreement between the results obtained from these three methods, with the percent of error up to 8.683%.

Understanding ecosystem services for climate change resilience in coastal environments: a case study of low-canopy sub-tidal seagrass beds in Fiji

The Pacific Island Countries (PICs) are exposed to extreme wave conditions which are projected to be exacerbated by rising sea levels due to climate change, prompting the need for strategic planning of coastal communities and assets. Nature-based protection has been proposed as a sustainable solution to promote the resilience of coastal areas from physical impacts such as wave-induced erosion. In this study, we investigate the potential coastal protection service of shallow sub-tidal low-canopy seagrass beds, dominated by Halodule uninervis, on the rate of wave height and wave energy reduction on a barrier and fringing reefs. The data was collected using bottom-mounted pressure sensors to measure wave height and energy reduction as waves moved toward the shoreline across the seagrass beds. The results show that on average, the seagrass beds were able to reduce wave height by 30% and energy by 47% in both reef environments. These reduction rates are strongly influenced by water depth, seagrass characteristics and local reef conditions. Based on these results, seagrasses can strengthen the resilience of coastal shorelines to wave erosion, thus conserving healthy low-canopy seagrass habitats has measurable benefits for shoreline protection in Fiji and other PICs.

Analysis of extreme wind wave based on weibull and fisher tippett I (gumbel) distribution

Extreme waves are an important factor in coastal structures both offshore structures and onshore structure design. However, due to the difficulty of measuring ocean waves, many areas still do not have measured wave height data. Data processing is required to transform the measured wind data into wind-wave value in order to solve this issue. This study aims to analyze extreme waves based on wind data from BMKG Panjang and BMKG Radin Inten II stations. For analysis of determination of extreme waves can be done by using Fisher Tippet Type I (Gumbel) and Weibull methods. The result show that Weibull method gives the higher value than Gumbel method, with the maximum percentage of 43.04% at the 2-year return period.

A Multidecadal Assessment of Mean and Extreme Wave Climate Observed at Buoys off the U.S. East, Gulf, and West Coasts

The current understanding of wind-generated wave climate from buoy-based measurements is mainly focused on a limited number of locations and has not been updated to include measurements in the past decade. This study quantifies wave climate variability and change during the historical period of 1980–2020 through a comprehensive analysis of wave height measurements at 43 buoys off the U.S. Pacific, Atlantic, and Gulf of Mexico Coasts. Variabilities and trends in the annual and monthly mean and 95th percentile significant wave heights (SWH) and the number of extreme wave events are quantified for the cold and warm seasons. We calculate the SWH long-term and decadal trends, and temporal variabilities using the ordinary least squares regression and coefficient of variation, respectively. Independent extreme wave events are identified using a method based on the peaks-over-threshold and the autocorrelation function, which accounts for the geographical variation in the timespan between independent extreme events. Results show that the warm season’s interannual variabilities in monthly and annual SWH are smaller in the Pacific while larger in the Atlantic and Gulf, with the largest variabilities observed at buoys in the Gulf and lower latitudes of the Atlantic. Strong significant alternating decadal trends in SWH are found in the Pacific and Atlantic regions. Buoys in the Atlantic and Gulf regions have experienced higher numbers of extreme wave events (anomalies) compared to the Pacific region. In general, the long-term trend in the number of extreme events during the cold season is positive at buoys located at higher latitudes but negative at lower latitudes.

Characterization and classification of wave storm events and wave climate on the Sea of Marmara

This study aims to conduct a wave climate study and provide a detailed analysis of wave storm events on the Sea of Marmara based on a 40-year (1979–2018) hindcast dataset. The accuracy of the used dataset was initially investigated in terms of both climatic and storm conditions using five-year (2013–2017) measurements of significant wave height (Hm0) at the Silivri buoy station. For the wave climate, the measurements’ 5-year mean and maximum Hm0 values were compared with SWAN hindcasts. To detect wave storm events from a time series, a critical value was determined by using the mean and standard deviation of the measurements. After that, the corresponding hindcasted storms with the measurements were detected. This analysis showed that the hindcasts are compatible with the measurements not only for climatic conditions but also for storm conditions. Monthly and annual variations of mean and maximum Hm0 were examined based on a 40-year long-term wave dataset and different return period Hm0 values based on annual maximums were determined at various locations. Wave storm events in the long-term analysis have been characterized and classified based on the storm energy density (Es) in five storm categories according to their energy. Temporal analysis of wave storm events shows that there has been an increase in the number and severity of storm events in recent years. The middle regions of the sea and the northeastern coasts of Marmara Island and Kapıdağ Peninsula are the most affected regions by extreme sea conditions.