Average Wave Period Research Articles

Artificial neural network to translate offshore satellite wave data to coastal locations

Owing to the spatial averaging involved in satellite sensing, use of observations so collected is often restricted to offshore regions. This paper discusses a technique to obtain significant wave heights at a specified coastal site from their values gathered by a satellite at deeper offshore locations. The technique is based on the approach of Artificial Neural Network (ANN) of Radial Basis Function (RBF) and Feed-forward Back-propagation (FFBP) type. The satellite-sensed data of significant wave height; average wave period and the wind speed were given as input to the network in order to obtain significant wave heights at a coastal site situated along the west coast of India. Qualitative as well as quantitative comparison of the network output with target observations showed usefulness of the selected networks in such an application vis-à-vis simpler techniques like statistical regression. The basic FFBP network predicted the higher waves more correctly although such a network was less attractive from the point of overall accuracy. Unlike satellite observations collection of buoy data is costly and hence, it is generally resorted to fewer locations and for a smaller period of time. As shown in this study the network can be trained with samples of buoy data and can be further used for routine wave forecasting at coastal locations based on more permanent flow of satellite observations.

RELATING DEEP WATER WAVES WITH COASTAL WAVES USING ANN

ABSTRACT This paper presents a technique to obtain significant wave heights at coastal locations from their values sensed at deeper locations with the help of a satellite. It is based on the approach of neural networks. A Satisfactory mapping between deep- water-buoy measurements and corresponding shallow-water-buoy observations first ensured applicability of the method. Thereafter, the satellite data of significant wave height; average wave period and wind speed were given as input in order to obtain significant wave heights at a coastal location along the west coast of India. This effort initially involved use of a common feed forward network trained using variants of back-propagation algorithms (FFBP) and later that of the radial basis function (RBF) and adaptive neuro-fuzzy inference system (ANFIS). Qualitative as well as quantitative comparison of the network output with target observations showed usefulness of neural networks in such an application. Great variations in the result accuracy were not noticed when newer architectures of RBF and ANFIS were adopted in place of the basic FFBP. Unlike satellite observations collection of buoy data is costly and hence it is generally resorted to fewer locations and for a smaller period of time. As shown in this study the network can be trained with samples of buoy data and can be further used for routine wave forecasting at coastal locations based on more permanent flow of satellite observations. The wave rider buoy can be discarded or redeployed elsewhere.

Wave parameter estimation using neural networks

At different stages of wave analysis and wave-based structural design it becomes necessary to know interrelationships among certain characteristic wave parameters. This knowledge is currently obtained by using empirical spectral or statistical regression schemes, which may suffer from uncertainties and approximations. This paper presents an alternative to them, which is based on the neural network approach. Networks were developed in order to estimate values of average zero-cross wave period, peak-spectral period, maximum spectral energy density and maximum wave height from the given value of significant wave height and also to evaluate spectral width parameter from the spectral narrowness parameter. They were trained with respect to observed data at an offshore site along the east coast of India. The trained network when tested revealed that it formed a useful tool in exploring the interdependency in between the parameters. When the underlying relation structure was hazier and uncertain the neural networks were more accurate than the statistical non-linear regression methods in estimating one parameter from the specified value of the other.

On the distributions of wave periods, wavelengths, and amplitudes in a random wave field

On the basis of a narrow‐band Gaussian process, two theoretical probability density functions (PDFs) are derived by applying an approximate Hilbert transform to the process represented by a general form. The first PDF is for the joint distribution of the wave period τ and amplitude ρ of sea waves. It has the same merits as the PDF previously derived by Longuet‐Higgins [1983], in being asymmetric in τ and depending only on the spectral width parameter ν, but gains an advantage that it predicts an exactly Rayleigh distribution of ρ and so facilitates its handling in theory and application in practice. In virtue of the advantage, a relatively simple conditional PDF of τ assuming ρ is derived, which may be used to predict an arbitrarily defined characteristic conditional wave period assuming the wave height from the average wave period. The second PDF is for the joint distribution of wavelengths and amplitudes in a unidirectional Gaussian wave field with narrow spectrum. It has the same form as the first PDF but depends only on the parameter μ defined by μ2 = m0m4/m22 − 1, where mn is the nth moment of spectrum. From this joint PDF, a PDF for the distribution of wavelengths of sea waves is also derived. Numerical simulation and laboratory experiments of wind waves and their results are reported. It is shown that the PDFs derived in this paper give fairly good fits to the simulated data and suitably filtered laboratory data.

Stokes Correction for Nonlinearity of Wave Crests in Heavy Seas

The application of Stokes fifth-order wave theory to random deep-water waves is considered in connection with nonlinearity in crest amplitudes. The theory is shown to apply, on average, to crest amplitudes and wave heights, although differences exist for individual waves as a result of variation in wave frequency. Corrections to the Rayleigh law and associated predictions of fractions of waves exceeding crest threshold levels are shown to be in close agreement with measurements for heavy seas when the significant wave height and average wave period are specified accurately.

Large Wave Tank Dispersant Effectiveness Testing in Cold Water

ABSTRACT Research experiments were completed to determine the viability of using chemical dispersants on two crude oils in very cold water conditions. Tests were completed at Ohmsett (the National Oil Spill Response Test Facility in Leonardo, New Jersey) in late February and early March of 2002. Ohmsett is a large outdoor, above-ground concrete tank (203 m long by 20 m wide by 3.4 m deep) filled with 9.84 million gallons of salt water. The tank has a wave-generating paddle, a wave-dissipating beach, and mobile bridges that transport equipment over its surface. A refrigeration unit was installed to ensure that the water was kept at near freezing temperatures during the entire test program. A total of twelve large-scale tests were completed. Corexit 9500 and Corexit 9527 were applied to fresh and weathered Hibernia and Alaska North Slope crude oils, on cold water (-0.5 to 2.4 °C), at dispersant-to-oil ratios (DORs) ranging from 1:14 to 1:81. The average wave amplitude for the tests ranged between 16.5 and 22.5 cm and the average wave period was between 1.7 and 1.9 seconds. The effectiveness of the dispersant in each test was documented through extensive video records and by measurement of the residual oil remaining within the containment boom at the end of each test. The results clearly show that both dispersants were effective in dispersing the two crude oils tested in cold-water conditions.

Noise-driven wave transitions on a vertically falling film

We decipher the rich and complex two-dimensional wave transition and evolution dynamics on a falling film both theoretically and numerically. Small-amplitude white noise at the inlet is filtered by the classical linear instability into a narrow Gaussian band of primary frequency harmonics centred about ωm. Weakly nonlinear zero-mode excitation and a secondary modulation instability then introduce a distinct characteristic modulation frequency Δ [Lt ] ωm. The primary wave field evolves into trains of solitary pulses with an average wave period of 2π/ωm. Abnormally large ‘excited’ pulses appear within this train at a relative frequency of Δ/ωm due to the modulation. The excited pulses travel faster than the equilibrium ones and eliminate them via coalescence to coarsen the pulse field downstream. The linear coarsening of wave period downstream is a universal (0.015/〈u〉) s cm−1 and the final wave frequency is the modulation frequency Δ for 0.1 < δ < 0.4 where 〈u〉 is the flat-film average Nusselt velocity, δ = (3R2/W)1/3/15 is a normalized Reynolds number, R is the flat-film Reynolds number and W the Weber number.

Analysis of Wave Directional Spreading Using Neural Networks

The short-term directional spreading of wave energy at a given location is popularly modeled with the help of the Cosine Power model. This model is oriented mainly around value of the spreading parameter involved in its expression. This paper describes how a representative spreading parameter could be arrived at from easily available wave parameters such as significant wave height and average zero-cross wave period, using the technique of neural networks. It is shown that training of the network with the help of observed directional wave (e.g., heave-pith-roll buoy) data could be used to establish dependency of the spreading parameter on more commonly available unidirectional wave parameters derived from, for example, pressure gauge data. It is found that such a procedure involving neural networks is much more accurate and reliable than the conventional approach based on statistical linear regression.

Observations of the quasi-2-day wave in the mesosphere and lower thermosphere over Yamagawa and Wakkanai

[1] Mesospheric/lower thermospheric (MLT) winds observed at Yamagawa (31.2°N, 130.6°E) and Wakkanai (45.4°N, 141.7°E), using the spaced-antenna technique, have been analyzed to study features of the quasi-2-day oscillations. We have used 4–5 years (1996–2000) of near-continuous data for the analysis. Our results are consistent with the reports at other midlatitude sites. The analysis reveals that the wave features observed at these two stations are similar. The occurrence of the wave event (probably the same) is seen at both stations during the same days. The wave is found every year with the maximum amplitude in the summer months. The meridional component has larger amplitudes than the zonal component. Comparing the amplitudes at the two stations, we find that the values observed at Yamagawa are larger than those at Wakkanai. The amplitude appears to attain its maximum value at around 90 km at both stations. Substantial year-to-year variations are observed in the 2-day wave amplitude. The average wave period observed at Yamagawa and Wakkanai is approximately 48 hours. The study also explores the dependence of the 2-day wave on the background atmospheric circulation. However, further analysis on wave events is needed to obtain a better understanding of this aspect. The results of the present study are also compared with the earlier meteor radar observations in Kyoto, Japan, and some other midlatitude observations. Further coordinated studies are suggested to investigate horizontal structure and generating mechanism of the 2-day wave.

Neural networks for wave forecasting

The physical process of generation of waves by wind is extremely complex, uncertain and not yet fully understood. Despite a variety of deterministic models presented to predict the heights and periods of waves from the characteristics of the generating wind, a large scope still exists to improve on the existing models or to provide alternatives to them. This paper explores the possibility of employing the relatively recent technique of neural networks for this purpose. A simple 3-layered feed forward type of network is developed to obtain the output of significant wave heights and average wave periods from the input of generating wind speeds. The network is trained with different algorithms and using three sets of data. The results show that an appropriately trained network could provide satisfactory results in open wider areas, in deep water and also when the sampling and prediction interval is large, such as a week. A proper choice of training patterns is found to be crucial in achieving adequate training.

An Estimation of Ocean Wave Characteristics Based on Measured Ship Motions (4th Report)

It is well known that a ship can be regarded as a type of wave recorder and, under the assumption of linear superposition, wave spectra can thus be estimated from measured ship motions. Based on this idea, the evaluation of directional wave spectra has been extensively carried out in recent years. However, when a ship is traveling with an advance speed in following seas, there is a range of the encounter frequency of the ship, which cannot be related to the wave frequency by a single-value transformation. In the previous paper, we proposed a method to overcome this difficulty, and evaluated one-dimensional wave spectrum by using nonlinear programming.In this paper, we extend the method used for the estimation of one-dimensional wave spectrum to evaluate the directional wave spectrum. The capability of this approach has been discussed by comparing the estimated average wave periods and significant wave heights with those evaluated from the so-called SMB Method and the observation data written in logbook.

Coherent structures, self-similarity, and universal roll wave coarsening dynamics

Beyond their inception region from wide-banded inlet noise, roll waves on an inclined plane increase their amplitude and separation downstream in a scale-invariant linear manner by as much as one order of magnitude. Analysis of a set of dissipative hydraulic equations shows that this self-similar coarsening dynamics is driven by irreversible coalescence events between localized roll waves. By exploiting the localized structure of the roll waves and certain symmetries of the hydraulic equations to simple affine coordinate stretching by the substrate thickness, the time-averaged wave properties at every station and wave texture is shown to be self-similar. Moreover, due to weak variations in the substrate thickness and the sensitivity of the coarsening dynamics to it, the downstream evolution along this self-similar family can be captured by a generic cascade coalescence model for all wave separations. The linear coarsening rate of the average wave period is shown to be roughly (√−1) times the fraction of “excited” waves, which is only a weak function of a modified Froude number G based on the channel inclination angle.

Contribution of Supposed Wave Condition on Long-term Distribution of Wave Induced Load

This study is the second report concerned with statistical analysis on long-term distribution of wave induced load. In the first report, authors examined which factor gives influence by load revel in the long -term distribution, such as significant wave height, average wave period of supposed wave condition and relative angle between ship course and wave direction. The long-term distribution was decomposed into every these factors and a contribution rate analysis method for these factors in each load revel was introduced. Based on the method, it was clarified that the maximum wave induced stress value in the vicinity of the probability of exceedance around 10-8 can be governed by the most sever short-term wave condition which has the largest value of short-term wave induced Raleigh distribution parameter.In this report, the shape of the long-term distribution of the wave induced load for evaluation of fatigue strength is studied. Based on S-N curves and Miner's rule, the relation between the fatigue damage and supposed wave condition to calculate the long-term distribution is examined. The contribution rate analysis method for fatigue damage from supposed wave condition, such as significant wave height, average wave period of supposed wave condition and relative angle between ship course and wave direction, is introduced. It is shown that the most sever short-term wave condition, defined by the former report, also plays the most important role in the fatigue damage. The simple estimation method for long-term distribution described by Weibull distribution from the statistical propaty of the most sever short-term wave condition is introduced. Several examples show the applicability of the estimation method and estimation errors of the maximum value with probability exceedance 10-8 are less than 5% and of the fatigue damage rates are within 1030% large value.

Contribution of Supposed Wave Condition on Long-term Distribution of Wave Induced Load

This report is concerned with statistical analysis on long-term distribution of wave induced load. The relation between the statistical property of supposed wave condition and the long term distribution of wave induced load is studied. For long term distribution, authors examine which factor gives influence by load revel, such as significant wave height, average wave period of supposed wave condition and relative angle between ship course and wave direction. The analysis method is that the long term distribution is decomposed into every these factor and contribution rate of these factor in each load revel is introduced. The method is applied for the long term deck stress data measured by 2 destroyers and for the numerical estimation of long term distributions of double bottom stress of a bulk carrier. As the result, whether wave condition (significant wave height, and average wave period) and the navigation condition decide the distribution shape of the long term distribution can be made clear and whether wave condition and the navigation condition determine the maximum value of the stress in the vicinity of the probability of exceedance 10-8 can be specified by using the proposed analysis method.

A statistical comparison of wind speed, wave height, and wave period derived from satellite altimeters and ocean buoys in the Gulf of Mexico region

The capability of spaceborne altimeters to provide precise measurement of significant wave height and wind speed has been demonstrated repeatedly. It is shown in this paper that in addition to the significant wave height and wind speed, the wave period can be calculated from the semiempirical functions established from earlier wave research. The calculated characteristic wave period using the altimeter‐derived wind speed and wave height are found to be in excellent agreement with the peak wave period and average wave period from the ocean buoy measurements in the Gulf of Mexico. Also, with the long time series of collocated data set, it is possible to compare altimeter output of wind and wave parameters with ocean buoy measurements taking into consideration the spatial lags between the buoy locations and the altimeter footprints, and the temporal lags between the two sensor systems. It is found that when the spatial lags are less than 10 km, the RMS difference of the significant wave height is approximately 0.1 m, which is the digitization resolution of the output from both altimeter and ocean buoy. For the wind speed, the RMS difference approaches 1.2 m/s in the Gulf of Mexico using the empirical algorithms. The wind speed agreement is significantly improved to 0.8 m/s when the tilting effect on the altimeter cross section is accounted for. In contrast to the spatial lags, temporal lags of up to 1 hour do not appear to produce significant difference in the statistics of comparison based on this study.

An Estimation of Ocean Wave Characteristics Based on Measured Ship Motions

It is known that a ship can be regarded as a type of wave measuring device, and under the assumption of linear superposition, wave spectra can thus be estimated from measured spectra of ship motions. Based on this idea, the evaluation of one-dimensional wave spectra, as well as directional wave spectra, has been extensively carried out in recent years. However, when a ship is traveling with an advance speed in following seas, there is a range of encounter frequencies ωe for which cannot be related to the wave frequencies ω by a single-value conversion. Practically, this difficulty has been solved by keeping the lowest frequency solution, however resulting spectra may only a narrow range of wave frequency when a ship navigates with high speed in following seas.In the previous paper, we proposed to determine the wave spectrum by using a nonlinear programming method, in which a standard wave spectrum, such as the ISSC, is selected, and a significant wave height and average wave period are used as design variables. The optimization was carried out in the wave frequency domain.In this paper, we propose to determine the wave spectrum by using a method in which the ordinates of wave spectrum at an arbitrary wave frequency are used as design variables and the optimization has been carried out in the encounter frequency of the ship.The capability of this approach has been confirmed by comparing the wave spectra estimated from the measured motions of container and ore-carrier models, with the ones obtained from the direct measurement of waves in the experimental tank.

An Estimation of Ocean Wave Characteristics Based on Measured Ship Motions

Needless to say, the accumulation of a reliable database of ocean wave characteristics is very important for safe ship design and navigation. Usually, such information has been collected from reports based on shipboard visual observations. On the other hand, a ship can be regarded as a type of wave recorder and, under the assumption of linear superposition, wave spectra can thus be estimated from measured ship motions. Based on this idea, the evaluation of one-dimensional wave spectra, as well as directional wave spectra, has been extensively carried out in recent years. However, when a ship is traveling with an advance speed in following seas, there is a range of the encounter frequency ωe of the ship for which ωe cannot be related to the wave frequency by a single-value transformation. Practically, this difficulty has been addressed by using an approximate method where only one solution ω of the relationship is retained by partitioning the ω-axis. When one keeps the lowest-frequency ω solution, however, resulting spectra tend to be narrower and displaced towards low frequencies.In this study, we propose to design a wave spectrum by using a nonlinear programming method, in which a standard wave spectrum, such as the ISSC, is selected, and a significant wave height and average wave period are used as design parameters. The capability of this approach has been confirmed by comparing its results, based on the full-scale measurements of the motions of a container ship, with those from the so-called SMB method.

A survey of Pc 5 pulsations in the dayside high‐latitude regions observed by Viking

We have examined magnetic and electric field observations acquired with the polar orbiting Viking satellite near its 3 RE apogee and at local times from dawn through noon to dusk. Our objective was to determine the statistical properties of Pc 5 (150–600 s period) pulsations at different dayside local times and their relationship to large‐scale Birkeland currents. The Viking data examined in detail here were acquired from 41 orbits during the period from March 26, 1986, to July 19, 1986. Pulsations could be readily identified on prenoon orbits as evidenced in a series of 10 consecutive orbits in one case and six consecutive orbits in another. The waveforms in the postnoon hours are more complicated than in the morning, and this made it more difficult to identify pulsations in this region. The simultaneous electric and magnetic field measurements from Viking were used to distinguish the magnetic variations associated with large‐scale Birkeland currents from those associated with waves. These observations also made it possible to derive values for Pedersen and wave conductivities and Poynting fluxes for the waves. The average wave period for the 40 cases studied here is 4.8 min (frequency of 3.5 mHz), the average magnetic field amplitude is 30 nT, the average electric field amplitude (for the 11 cases when the electric field observations were available) is 7 mV/m, and the average incident Poynting flux is 85 μW/m2. The principal characteristics of the waves include the following: (1) From morning to noon, the magnetic field pulsations are polarized primarily in the east–west direction, and the associated electric field oscillations lag by 60°–80° and are polarized close to the north–south direction. Consequently, these pulsations are interpreted as the fundamental modes of resonant toroidal magnetic field oscillations. (2) In the afternoon hours, the magnetic field pulsations have a strong north–south component and include higher‐frequency components (possibly the second harmonic). (3) In both the morning and afternoon hours, the pulsations occur 2°–5° equatorward of the interface between the counterflowing region 1 and region 2 Birkeland currents. (4) The average wave periods increase from ∼3 min near 0800 magnetic local time (MLT) to ∼5 min near noon. (5) The average wave amplitudes range from ∼40 nT near 0900–1000 MLT to ∼25 nT near 1300–1600 MLT.

Disturbance effects of stranded kelp on populations of the sandy beach bivalve Donax serra (Röding)

Twelve beaches on the coast west of Cape Agulhas, South Africa, were surveyed to examine the influence of several physical factors, including stranded kelp, on the zonation, density and biomass of populations of the wedge clam Donax serra. Biomass and density of adult clams were significantly higher on beaches with lower cover of stranded kelp; this pattern did not hold for juveniles. Discriminant analysis of beaches with and without Donax classified these beaches 100% correctly — the most important factor being kelp cover followed by average winter temperature, wave height, morphodynamic state, beach length, wave period and beach slope. Beaches with Donax had a significantly lower percentage of the drift line covered by stranded kelp (mean=30%) than beaches without Donax (mean=77%). On two beaches of the southwest coast with similar morphodynamics and temperature regimes but different kelp cover, adult populations were centered in different zones: in the low intertidal to subtidal where kelp cover was higher (mean=42%) and in the mid-intertidal where no kelp was found. A disturbance hypothesis is developed to explain the observed patterns: kelp stranding in varying quantities interferes with Donax feeding and burrowing activities, dislodging animals of increasing size gradually downshore to the saturation and inner surf zones, where adult populations are eventually established. In the presence of extremely high quantities of stranded kelp, both juveniles and adults would be dislodged from the intertidal to the subtidal. The disturbance process may interact with several other physical factors, being magnified when coupled with low temperatures and small waves on reflective pocket beaches with steep slopes and coarse sands. Additionally, kelp gulls predate dislodged animals, explaining the absence of clams in a stretch of 20 m above the swash zone. It is thus concluded that the zonation patterns here observed are the result of a disturbance effect triggered by stranded kelp and mediated by multiple interacting factors. The adaptations of Donax serra that enable it successfully to colonize intertidal and subtidal habitats of the beach ecosystem are discussed.

Bottom Currents And Sediment Transport on San Pedro Shelf, California

ABSTRACT GEOPROBE (Geological Processes Bottom Environmental) tripods were used to measure bottom currents, pressure, and light transmission and scattering and to obtain time-series photographs of the sea floor at depths of 23 m and 67 m on San Pedro shelf between 18 April and 6 June 1978. Winds were light (< 5 m/s) with a mean direction from the southwest throughout the measurement period. Hourly averaged currents 1 m above the bottom never exceeded 21 cm/s; average speeds were about 5 cm/s at the 23-m site and 6.8 cm/s at 67 m, and the strongest currents were produced by the tides. The mean flow of bottom water was less than 3 cm/s at both GEOPROBES and was rather persistently southward (offshelf). Wave-generated bottom currents and bottom-pressure variations were sampled at hourly intervals; average wave period and wave height were 12.8 s and 0.44 m, respectively, at the 23-m site. Wave orbital velocities ranged from about 5 to 30 cm/s at 23 m and from 2 to 8 cm/s at 67 m. Bottom photographs at 67 m show that the relatively sluggish tide-generated and mean currents were below threshold velocity for the silty, very fine sand throughout the observational period. Threshold depth for wave rippling of very fine sand averaged about 28 m with a range from about 12 m to 50 m. Wave-generated currents were the only currents that exceeded threshold levels. The wave currents maintained relatively high concentrations of sediment in suspension near the bottom over the inner shelf (< 25 m), and this material (principally silt and clay) was transported offshore by the weak mean flow. Approximately 50% of this material was deposited as the bottom orbital velocities decreased to subthreshold values ( 10-15 cm/s). The o served movement of fine sediment across the inner shelf can account for a portion of the mud content of the modern silty sands on the central shelf and on the outer shelf. However, it is clear that the sand fractions, which constitute greater than 70% of the central shelf substrate, must be transported during high-energy winter storms.