Buoy Motion Research Articles

Wave Heights during Hurricane Katrina: An Evaluation of PPP and PPK Measurements of the Vertical Displacement of the GPS Antenna

Abstract In August 2005 the eye of Hurricane Katrina passed 49 n mi to the west of a 3-m discus buoy operated by the Central Gulf of Mexico Ocean Observing System (CenGOOS). Buoy motions were measured with a strapped-down 6 degrees of freedom accelerometer, a three-axis magnetometer, and a survey-grade GPS receiver. The significant wave heights were computed from the buoy’s accelerometer record and from the dual-frequency GPS measurements that were processed in two different ways. The first method was postprocessed kinematic (PPK) GPS, which requires another GPS receiver at a fixed known location, and the other was precise point positioning (PPP) GPS, which is another postprocessed positioning technique that yields absolute rather than differential positions. Unlike inertial measurement units, either GPS technique can be used to obtain both waves and water levels. The purpose of this note is to demonstrate the excellent reliability and accuracy of both methods for determining wave heights and periods from a GPS record. When the motion of the GPS antenna is properly understood as the motion of the buoy deck and not the true vertical motion of the sea surface, the GPS wave heights are as reliable as a strapped-down 1D accelerometer.

A Comparison of Methods for Determining Significant Wave Heights—Applied to a 3-m Discus Buoy during Hurricane Katrina

Abstract In August 2005, the eye of Hurricane Katrina passed 90 km to the west of a 3-m discus buoy deployed in the Mississippi Sound and operated by the Central Gulf of Mexico Ocean Observing System (CenGOOS). The buoy motions were measured with a strapped-down, 6 degrees of freedom accelerometer, a three-axis magnetometer, and from the displacement of a GPS antenna measured by postprocessed-kinematic GPS. Recognizing that an accelerometer experiences a large offset due to gravity, the authors investigated four different means of computing wave heights. In the most widely used method for a buoy with a strapped-down, 1D accelerometer, wave heights are overestimated by 26% on average and up to 56% during the peak of the hurricane. In the second method, the component of gravity is removed from the deck relative z-axis accelerations, requiring pitch and roll information. This is most similar to the motion of the GPS antenna and reduces the overestimation to only 5% on average. In the third method, the orientation data are used to obtain a very accurate estimate of the vertical acceleration, reducing the overestimation of wave heights to 1%. The fourth method computes an estimate of the true earth-referenced vertical accelerations using the accelerations from all three axes but not the pitch and roll information. It underestimates the wave heights by 2.5%. The fifth method uses the acceleration from all three axes and the pitch and roll information to obtain the earth-referenced vertical acceleration of the buoy, the most accurate measure of the true wave vertical acceleration. The primary conclusion of this work is that the measured deck relative accelerations from a strapped-down, 1D accelerometer must be tilt corrected in environments of high wave heights.

Identification of breaking events from the responses of a data buoy

Conventional data buoys record wave spectral parameters such as the significant height, peak period, and mean direction. Information about the existence of wave groups and breaking waves is also important for the design of ocean structures. To derive such information from data buoy measurements, understanding of the motion characteristics of data buoys under a variety of wave conditions is essential. In the present study, the motion characteristics of a scale-modelled discus data buoy were tested under the action of deep-water breaking waves of different intensities, covering spilling to steep plunging types. The laboratory generation of breaking waves was based on the constructive wave—wave interaction method. The buoy heave and pitch motions were measured using potentiometers and non-contact motion-capturing cameras. The measured time series of the breaking-wave surface elevation and the resulting buoy motions were analysed by continuous wavelet transformation and phase—time methods. A closer insight into the wavelet phases reveals that the breaking events leave a constant phase variation over a wider range of higher frequencies. Through appropriate filtering of the localized frequencies, the phase—time method could also be adopted to detect breaking events in the time histories of the measured wave elevation and motion response. The details of the model, instrumentation, testing conditions, and analysis are presented and discussed in this paper.

Bragg scattering and wave-power extraction by an array of small buoys

Future designs of systems for power extraction from ocean waves will likely involve a periodic array of absorbing units. We report an asymptotic theory of scattering and radiation by a linear array of heaving buoys in a channel and attached to power-takeoff devices. The spacing between buoys is assumed to be comparable to the incident wavelength and sea depth but much greater than the buoy size. The effects of extraction rate on the buoy motion, transmission and reflection coefficients for a range of frequencies in and outside the band gap are studied. It is found that strong reflection for frequencies inside the band gap of Bragg resonance reduces the extraction efficiency significantly. For comparison an alternate theory for the efficiency away from the band gap is derived using Froude–Krylov approximation. The predictions confirms and complements the asymptotic theory.

漂流ブイの上下揺れに及ぼす粘性流体力の影響

In recent years, a system to measure sea conditions in real time for carrying in a buoy is developed. In this system, wave conditions, those are wave height, period and direction, are obtained from calculating the buoy's motion equation with its accurate response operator functions using measured buoy's motion. Therefore, it is necessary to take the functions in design stage, in order to design for an optimum form of buoy for installed sea area. First, the accuracy of an existing motion calculation program based on potential theory is checked. It is found that the calculation overestimates the harmonic heaving amplitude for some buoy.Then, in order to understand the reasons, the characteristics of the hydrodynamic forces acting on buoy are investigated with a forced heaving motion test. From the flow observation around a buoy using visualization technique, large vortexes shedding under the body in the moment when buoy has maximum upward velocity are observed, and it is confirmed that viscous drag acts on buoy. Using a vertical cylinder model, the viscous drag coefficient acting on aft-body in the moment when the model has maximum upward velocity is measured by the forced heaving motion test for several KC numbers and 2D CFD calculation based on CIP method is also carried out, and the characteristics of the viscous drag are investigated and an empirical estimation formula is presented. Finally, a motion calculation including the viscous drag is carried out and the results are compared with measured results. It is confirmed that the calculated results are improved and shows good agreement with measured results.

Experimental results of rectification and filtration from an offshore wave energy system

The present paper presents results from a wave energy conversion that is based on a direct drive linear generator. The linear generator is placed on the seabed and connected to a buoy via a rope. Thereby, the natural wave motion is transferred to the translator by the buoy motion. When using direct drive generators, voltage and current output will have varying frequency and varying amplitude and the power must be converted before a grid connection. The electrical system is therefore an important part to study in the complete conversion system from wave energy to grid connected power. This paper will bring up the first steps in the conversion: rectification and filtration of the power. Both simulation studies and offshore experiments have been made. The results indicate that this kind of system works in a satisfactory way and a smooth DC power can be achieved with one linear generator.

Nearshore Wave Measurement Using Single-Video Images of Buoy Motions

This paper presents a wave measurement technique based on single-video monitoring of moored buoys. A simple photogrammetry is proposed, with a constraint that the distance from video camera to buoy should be predetermined. The distance is approximated to a constant under the condition that it is much greater than the range of the buoy motion. Image coordinates of a buoy are mapped onto a spherical surface without significant errors in vertical ground coordinates. Wave characteristics are comparable to those from a bottom pressure gauge, indicating that the video technique has the potential to remotely measure waves in coastal environments. We anticipate our finding to be a starting point for an economic instrument of wave measurement through development of an automated image processing technique.

Terminal control in sea observation systems with mobile platforms for data collection

The expediency of application of terminal control in sea observation systems is shown on the example of a system of profile measurements of the ocean environment constructed on the basis of controlled diving buoys, sea probes. The model of motion of a diving buoy with controlled buoyancy is given. The control law is synthesized according to basic ideas [1], as applied to the digital controller. A method of choosing the controller parameters is proposed, and an algorithm for program implementation of the synthesized control law is developed. It is shown that the constructed iterative algorithm of calculation of the control signal possesses the adaptability property. The results of simulation of control processes under the action of perturbations on the system and variation of the plant parameters are presented.

Application of fluid–structure interaction simulation of an ocean wave energy extraction device

A numerical technique that employs a computational fluid dynamics (CFD) code is used to perform coupled fluid–structure interaction simulation of a wave energy device in order to assess power output in a 3D numerical wave flume. The current method determines the motion of the buoy from the dynamic solution of the fluid flow problem and the dynamic buoy motion problem rather than prescribing the motion of the buoy. The power output of the device is calculated for different wave conditions. The technique was expanded for an array of two buoys to determine the interference between them.

ブイの動揺を考慮したＧＰＳ波浪計による洋上風観測

Newly developed GPS buoy system, applying the RTK-GPS techniques to measure the exact movement of the offshore floating buoy, is supposed to be the future principal offshore wave and tsunami observation equipment for Japanese NOWPHAS (Nationwide Ocean Wave information network for Ports and HArbourS). By installing a wind gauge at the top of the buoy, offshore wind information is also applicable, which is important for various offshore economical activities such as fishery, clean energy development etc., with proper correction of the observed data with consideration of the buoy motion effects. This paper introduces results of study on buoy motion correcting methods by using proto-type data obtained off-Muroto-Misaki.

Tsunami Wave Interaction with Data Buoys

To plan for proper mitigation measures, one should have an advanced knowledge of the phenomenon of tsunami propagation from the deep ocean to coastal waters. There are a few methods to predict tsunamis in the ocean waters; one method is the effective use of data buoy measurements. Although data buoys have been used along the Indian waters there has been a tremendous growth in the number of buoy deployment recently. Under the National Data Buoy Programme (NDBP) of India, the 2.2 m diameter discus data buoys were deployed along the east and west coasts of India for measuring meteorological and ocean parameters. It would be advantageous if these buoys could be efficiently used to measure rare events such as tsunamis. Understanding the dynamic behavior of the buoy is of prime importance if a tsunami warning system is to be successful. This may be accomplished through experimental or numerical studies. A comprehensive experimental study has been conducted to understand the dynamic behavior of a wave rider buoy exposed to a variety of waves. It is common that tsunami waves are represented in terms of shallow water waves, namely solitary and cnoidal waves. Hence, in the present study, the discus type data buoy is scale modeled and tested under the action of solitary and cnoidal waves in the laboratory. The time histories of wave elevations, as well as heave and pitch motions of the buoy model, were analyzed through a spectral approach as well as through wavelet transformations. The wavelet approach gives more detailed insight into the spectral characteristics of the buoy motion in the time scale. The harmonic analyses were performed for the cnoidal wave elevations and subsequent motion characteristics that give an insight into the energy variations. The details of the model, instrumentation, testing conditions and the results are presented in this paper.

Image processing for video images of buoy motion

In this paper, image processing technique that reduces video images of buoy motion to yield time series of image coordinates of buoy objects will be investigated. The buoy motion images are noisy due to time-varying brightness as well as non-uniform background illumination. The occurrence of boats, wakes, and wind-induced white caps interferes significantly in recognition of buoy objects. Thus, semiautomated procedures consisting of object recognition and image measurement aspects will be conducted. These offer more satisfactory results than a manual process. Spectral analysis shows that the image coordinates of buoy objects represent wave motion well, indicating its usefulness in the analysis of wave characteristics.

부설 수심의 변화에 따른 파랑 중 원통형 부체의 운동 및 계류삭 장력 해석

침하식 가두리 시설의 안정성 평가를 위한 기초 단계로서 일방향 규칙파 중 2점 계류된 원통형 부체를 대상으로 부설 수심의 변화에 따른 부체의 동적 거동 및 계류삭에 작용하는 장력 산정에 관한 수치 계산을 수행하였다. 수치 계산 결과, 수면 상에 설치된 부체를 수면 아래의 약 1/2되는 수층까지 침하 시킨 경우 그것은 동적 거동과 파력은 초기 상태에 비해 각각 최대 50%와 77%까지 감소되어 시설물을 수중으로 침하 시키면 그것의 안정성 유지에 매우 효과적임을 확인할 수 있었다. 또한 부체의 전 후단 변위 및 계류삭에 작용하는 장력의 최대치는 부체의 고유 주기의 영향으로 인해 그것은 길이 d 에 대한 파장 <TEX>${\lambda}$</TEX>의 비 즉, d/<TEX>${\lambda}$</TEX>가 약 0.66에서 나타났으며, 이와 같은 현상은 기존 수리 모형실험 결과와 비교적 잘 일치하였다. 그러나 본 수치 계산의 신뢰성 확인을 위해서는 수리 모형실험을 통해 부체의 고유 주기와 작용 파고에 대한 전 후단 변위 등에 대한 충분한 검토가 요구된다. This paper presents a method analyzing the motion of cylindrical buoy moored at 2 points and tensions action on each mooring line under the action of periodic waves. It was found that submersible buoy was more effective than floating one in the severe conditions considering its dynamic motions, wave forces, and mooring line tensions. The wave induced its dynamic responses and mooring line tensions peak when the ratio d/<TEX>${\lambda}$</TEX> of the buoy length d to the waves length <TEX>${\lambda}$</TEX> was 0.66 due to its natural frequency. The results of this study were in agreement with the existing measurement ones, however, further verifications are needed considering resonance of cylindrical buoy and its displacements to wave height by a series of model tests.

Modelling of hydraulic performance and wave energy extraction by a point absorber in heave

The feasibility of energy extraction from sea waves has been investigated, with special attention to potential applications in the Belgian coastal area of the North Sea. The performance of heaving point absorbers in wave conditions that are representative for the considered area is calculated by means of a linear theory. The geometry of the heaving buoy, the external damping and a supplementary inertia are considered as variable parameters to optimise the absorption system. Further, the numerical results are validated by means of physical model testing. The resulting power absorption performance appears to be wave height dependent. For regular waves of relatively small amplitude the absorption length significantly exceeds the absorber diameter and diminishes with larger wave heights. In irregular waves, the absorption length is estimated to reach 60% of the buoy diameter. The comparison between experimental and numerical data shows discrepancies that are primarily related to two issues that inversely affect the absorber effectiveness. Firstly, significant vortex shedding and viscous losses occurring with significant buoy motion reduce the power extraction. Secondly, the actual decrease in absorbed power due to the mistuning effect in irregular waves is smaller as revealed from computational prediction. Regarding the significant motion, restrictions must be included in order to avoid slamming of the buoy. This may be achieved by increasing the external damping compared to the theoretical optimal values or, alternatively, by increasing the draft of the buoy. The adaptation of the draft is also shown as a measure to increase the overall absorber efficiency in natural seaways. In the end, considering the frequency of occurrence of the wave spectra, optimal characteristics for the point absorber are determined. An optimal absorber is evaluated as rated to a 100 kW, with an annual average power capture of about 30 kW or 263 MWh per year per point absorber unit.

A New Lagrangian Model of Arctic Sea Ice

A new Lagrangian sea ice model for the Arctic Ocean has been developed to accommodate the assimilation of integral measures of ice displacement over periods of days or weeks. The model is a two-layer (thick ice and open water) dynamic model with 600‐700 cells spaced at roughly 100 km. The force balance equation is solved for each cell with standard wind and water stress terms, a Coriolis term, and an internal ice stress term. The internal stress is found using a viscous‐plastic rheology and an elliptical yield curve. The strain rate is determined by the ‘‘Smoothed Particle Hydrodynamics’’ formalism, which determines the spatial derivatives of the velocity by a weighted summation of the velocities of adjacent cells. A length scale of 150 km is used. The model is driven with observed geostrophic winds and climatological-mean ocean currents. Ice growth and melt are found from a seasonal- and thickness-based lookup table because the current focus is on the model dynamics. The model ice velocity simulations are compared to observed buoy motion. Over the 5-yr period 1993‐97 the correlation of the daily averaged model velocity with buoy velocities is R 5 0.76 (N 5 42 553, rms difference 5 0.072 m s21, speed bias 51 0.009 m s21, angle bias 5 8.08). This compares favorably with the correlation of a state-of-the-art Eulerian coupled ice‐ocean model, where R 5 0.74 in the summer and 0.66 in the winter over the same 5-yr period.

Assimilation of ice motion observations and comparisons with submarine ice thickness data

Aided by submarine observations of ice thickness for model evaluation, we investigate the effects of assimilating buoy motion data and satellite SSM/I (85 Ghz) ice motion data on simulation of Arctic sea ice. The sea‐ice model is a thickness and enthalpy distribution model and is coupled to an ocean model. Ice motion data are assimilated by means of optimal interpolation. Assimilating motion data, particularly from drifting buoys, significantly improves the modeled ice motion, reducing the error to 0.04 m s−1 from 0.07 m s−1 and increasing the correlation with observations to 0.90 from 0.66. Without data assimilation, the modeled ice moves too slowly with excessive stoppage. Assimilation leads to more robust ice motion with substantially reduced stoppage, which in turn leads to strengthened ice outflow at Fram Strait and enhanced ice deformation everywhere. Enhanced deformation doubles the production of ridged ice to an Arctic Ocean average of 0.77 m yr−1, and raises the amount of ridged ice to half the total ice volume per unit area of 2.58 m. Assimilation also significantly alters the spatial distribution of ice mass and brings the modeled ice thickness into better agreement with the thickness observed in four recent submarine cruises, reducing the error to 0.66 m from 0.76 m, and increasing the correlation with observations to 0.65 from 0.45. Buoy data are most effective in reducing model errors because of their small measurement error. SSM/I data, because of their more complete spatial coverage, are helpful in regions with few buoys, particularly in coastal areas. Assimilating both SSM/I and buoy data combines their individual advantages and brings about the best overall model performance in simulating both ice motion and ice thickness.

Sea‐ice deformation rates from satellite measurements and in a model

The deformation of sea ice is an important element of the Arctic climate system because of its influence on the ice‐thickness distribution and on the rates of ice production and melt. New data obtained from the Radarsat Geophysical Processor System (RGPS) using satellite synthetic aperture radar images of the ice offers an opportunity to compare observations of the ice deformation to estimates obtained from models. The RGPS tracks tens of thousands of points, spaced roughly at 10‐km intervals, for an entire season in a Lagrangian fashion. The deformation is computed from cells formed by the tracked points, typically at 3‐day intervals. We used a coupled ice/ocean model with ice‐thickness and enthalpy distributions that covers the entire Arctic Ocean with a 40‐km grid. Model‐only and model‐with‐data‐assimilation runs were analysed. The data assimilation runs were analysed in order to determine the validity of the comparison techniques and to find the comparisons under the best of circumstances, when many buoy measurements are available for assimilation. This step is necessary because the RGPS and model data differ in spatial and temporal sampling characteristics. The assimilated data included buoy motion and Special Sensor Microwave/Imager (SSM/I)‐derived ice motion. The Pacific half of the Arctic Basin was analysed for a 10‐month period in 1997 and 1998. Comparisons of ice velocity observations to the modelled velocities showed excellent agreement from the model‐with‐data‐assimilation run but poorer agreement for the model‐only run. At a scale of 320 km, the deformation from the data assimilation run was in modest agreement with the observations but where many buoys were available for assimilation the agreement was quite good. Both model runs showed poor agreement during summer. Comparisons of the deformation distribution functions suggest why the agreements were poor even though the velocity agreements were good. Decreasing the ice strength parameter in the model improved the deformation comparisons for the model‐only runs.

LINEAR VIBRATION CHARACTERISTICS OF CABLE–BUOY SYSTEMS

A theoretical model for the linear vibration of a cable tensioned by a subsurface buoy is developed. The equilibrium of the cable–buoy system subject to drag is evaluated using an approximate closed-form solution whose range of validity is confirmed through comparison with numerical solutions. The three-dimensional equations of cable–buoy motion are linearized about this equilibrium and then used to assess vibration characteristics. The characteristic equations for the natural frequencies of both in-plane and out-of-plane vibration modes are derived. The in-plane natural frequency spectrum exhibits the curve veering phenomena due to asymmetry of the associated mode shapes. Parameter studies reveal the dependencies of the in-plane and out-of-plane vibration modes on the cable tension, the buoy mass, and the current velocity.

A Study for Development of a Wave Observation Platform

A wave observation buoy has been developed, which uses a system where incident wave height in the ocean can be obtained from the heave motion of the buoy measured using a gyro system and the heave response function determined through theoretical calculations and model experiments.The accuracy of the theoretical calculation of the response function of the buoy motion was first confirmed by model experiments in a wave tank. Next, the validity of the method was verified by comparing the time series of irregular wave profiles measured with a wave height meter fixed in the wave tank and a reproduced series using the heave motion of the buoy model measured with a motion sensor and the response function.A real buoy was designed and constructed based on these studies and has been moored in the sea near Ishigaki Island since March of 2001.Finally, the wave data obtained using the above method were compared with those directly obtained from motions measured with a gyro and the relative wave height measured with a wave sensor fixed to the buoy, and the results were discussed.

The quality of sea ice velocity estimates

Several aspects of observed and estimated velocities for Arctic sea ice are explored. The long‐term mean ice motion field and associated variance are derived using 15 years (over 85,000 observations) of daily buoy motions. The mean field is separated into the part due to long‐term currents and internal ice stress and the part due to mean winds. The velocity variance is partitioned into “linear” and “nonlinear” parts. The linear response has no trend over the 15 years examined. For a 5‐year subset of the buoy data, an ice‐ocean model with constant air‐drag parameters is used to estimate daily ice velocities at the buoy locations, and then the linear relationship between the modeled velocities and the geostrophic winds is examined. Compared with buoy velocities, the modeled velocities have a larger variance and larger linear response to the winds. In a parameter study, the effects of seasonally varying air‐drag coefficients, increased ice strength, and different ocean currents are examined. Seasonally varying air drag, with smaller average magnitude than the standard value, significantly improves the match of total, linear, and nonlinear variances between observed and modeled velocities. The model simulations with varying air drag also have a smaller root‐mean‐square daily velocity error. Comparison of daily large‐scale deformations shows that the day‐to‐day deformations are not modeled well but generally have means and standard deviations within ±50% of the observed values. No one version of the model is consistently better than the others at matching the means and standard deviations of the observed daily divergence, vorticity, and shear. Ice thickness is sensitive to the model parameters varied, with 5‐year average thicknesses ranging from 2.2 to 3.4 m for the various simulations.