A background error covariance model of significant wave height employing Monte Carlo simulation

2012 ◽  
Vol 30 (5) ◽  
pp. 814-821 ◽  
Author(s):  
Yanyou Guo ◽  
Yijun Hou ◽  
Chunmei Zhang ◽  
Jie Yang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Wave Height ◽  
Significant Wave Height ◽  
Covariance Model ◽  
Background Error ◽  
Significant Wave ◽  
Background Error Covariance ◽  
Error Covariance

Simulation of Jack-Up Overturning Using the Monte Carlo Method With Artificially Increased Significant Wave Height

2010 ◽  
Author(s):  
Jo̸rgen Juncher Jensen
Keyword(s):  
Monte Carlo ◽  
Wave Height ◽  
Time Domain ◽  
Significant Wave Height ◽  
Reliability Index ◽  
Form Analysis ◽  
Significant Wave ◽  
The Mean ◽  
The Time Domain ◽  
Jack Up

It is well known from linear analyses in stochastic seaway that the mean out-crossing rate of a level r is given through the reliability index, defined as r divided by the standard deviation. Hence, the reliability index becomes inversely proportional to the significant wave height. For non-linear processes the mean out-crossing rate depends non-linearly on the response level r and a good estimate can be found using the First Order Reliability Method (FORM), see e.g. Jensen and Capul (2006). The FORM analysis also shows that the reliability index is strictly inversely proportional to the significant wave height irrespectively of the non-linearity in the system. However, the FORM analysis only gives an approximation to the mean out-crossing rate. A more exact result can be obtained by Monte Carlo simulations, but the necessary length of the time domain simulations for very low out-crossing rates might be prohibitive long. In such cases the property mentioned above for the FORM reliability index can be assumed valid in the Monte Carlo simulations making it possible to increase the out-crossing rates and thus reduced the necessary length of the time domain simulations by applying a larger significant wave height than relevant from a design point-of-view. The mean out-crossing rate thus obtained can then afterwards be scaled down to the actual significant wave height. Some previous results using this property have been presented by Tonguc and So¨ding (1986), albeit in a more empirical way. In the present paper the usefulness of this property to estimate extreme wave loads will be evaluated considering the overturning of a jack-up rig.

A Hybrid Background Error Covariance Model for Assimilating Glider Data into a Coastal Ocean Model

2011 ◽  
Vol 139 (6) ◽  
pp. 1879-1890 ◽  
Author(s):  
Max Yaremchuk ◽  
Dmitri Nechaev ◽  
Chudong Pan
Keyword(s):  
Null Space ◽  
Coastal Ocean ◽  
Ocean Model ◽  
Covariance Operator ◽  
Covariance Model ◽  
Error Statistics ◽  
Background Error ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Coastal Ocean Model

Abstract A hybrid background error covariance (BEC) model for three-dimensional variational data assimilation of glider data into the Navy Coastal Ocean Model (NCOM) is introduced. Similar to existing atmospheric hybrid BEC models, the proposed model combines low-rank ensemble covariances with the heuristic Gaussian-shaped covariances to estimate forecast error statistics. The distinctive features of the proposed BEC model are the following: (i) formulation in terms of inverse error covariances, (ii) adaptive determination of the rank m of with information criterion based on the innovation error statistics, (iii) restriction of the heuristic covariance operator to the null space of , and (iv) definition of the BEC magnitudes through separate analyses of the innovation error statistics in the state space and the null space of . The BEC model is validated by assimilation experiments with simulated and real data obtained during a glider survey of the Monterey Bay in August 2003. It is shown that the proposed hybrid scheme substantially improves the forecast skill of the heuristic covariance model.

scholarly journals A Monte Carlo Background Covariance Localization Method for an Ensemble–Variational Assimilation System

2017 ◽  
Vol 145 (11) ◽  
pp. 4543-4557 ◽  
Author(s):  
Ivo Pasmans ◽  
Alexander L. Kurapov
Keyword(s):  
Monte Carlo ◽  
Data Assimilation ◽  
Compact Support ◽  
Long Distance ◽  
Background Error ◽  
Localization Method ◽  
Background Error Covariance ◽  
Error Covariance ◽  
Sample Covariance ◽  
Grid Points

Spurious long-distance correlations in estimates of the background error covariance can deteriorate the performance of ensemble-based data assimilation methods. In this study, a localization method, called Monte Carlo (MC) localization, is presented to remove these correlations. It is particularly useful for use in high-dimensional ensemble–variational data assimilation systems. In this method, raw ensemble members are truncated by multiplying them with functions having compact support. This creates a larger ensemble, in which points spaced farther apart than the size of the compact support have zero correlation. The localized background error covariance is then estimated as the sample covariance of this larger ensemble. It is hypothesized that this localized background error covariance can be approximated by the MC approximation method using a limited set of the truncated ensemble members. This hypothesis is tested here on a grid with 1001 grid points and assuming a Gaussian true background error covariance. It is found that the mean relative error has an upper bound that scales with the inverse square root of the number of truncated ensemble members. In the case studied the size of the support for which the localized background covariance best approximates the true background covariance increases with increasing number of raw ensemble members and is close to 4 times the standard deviation of the Gaussian when 20 raw ensemble members are used. In the Fourier space the localization manifests itself as a convolution resulting in smoothing of the power spectral density of the ensemble members.

On the Sensitivity of Passive Multistatic Radar Amplitude and Doppler Measurements to Significant Wave Height

2021 ◽  
pp. 1-5
Author(s):  
Jeffrey D. Ouellette ◽  
William T. Bounds ◽  
David J. Dowgiallo ◽  
Jakov V. Toporkov ◽  
Paul A. Hwang
Keyword(s):  
Wave Height ◽  
Significant Wave Height ◽  
Significant Wave ◽  
Multistatic Radar

scholarly journals Estimation of Significant Wave Heights from ASCAT Scatterometer Data via Deep Learning Network

2021 ◽  
Vol 13 (2) ◽  
pp. 195
Author(s):  
He Wang ◽  
Jingsong Yang ◽  
Jianhua Zhu ◽  
Lin Ren ◽  
Yahao Liu ◽  
...  
Keyword(s):  
Deep Learning ◽  
Wave Height ◽  
Significant Wave Height ◽  
Incidence Angle ◽  
Ocean Waves ◽  
Global Scale ◽  
Learning Technology ◽  
Sea State ◽  
Significant Wave ◽  
Wave Heights

Sea state estimation from wide-swath and frequent-revisit scatterometers, which are providing ocean winds in the routine, is an attractive challenge. In this study, state-of-the-art deep learning technology is successfully adopted to develop an algorithm for deriving significant wave height from Advanced Scatterometer (ASCAT) aboard MetOp-A. By collocating three years (2016–2018) of ASCAT measurements and WaveWatch III sea state hindcasts at a global scale, huge amount data points (>8 million) were employed to train the multi-hidden-layer deep learning model, which has been established to map the inputs of thirteen sea state related ASCAT observables into the wave heights. The ASCAT significant wave height estimates were validated against hindcast dataset independent on training, showing good consistency in terms of root mean square error of 0.5 m under moderate sea condition (1.0–5.0 m). Additionally, reasonable agreement is also found between ASCAT derived wave heights and buoy observations from National Data Buoy Center for the proposed algorithm. Results are further discussed with respect to sea state maturity, radar incidence angle along with the limitations of the model. Our work demonstrates the capability of scatterometers for monitoring sea state, thus would advance the use of scatterometers, which were originally designed for winds, in studies of ocean waves.

scholarly journals Physical Modelling of the Effect on the Wave Field of the WaveCat Wave Energy Converter

2021 ◽  
Vol 9 (3) ◽  
pp. 309
Author(s):  
James Allen ◽  
Gregorio Iglesias ◽  
Deborah Greaves ◽  
Jon Miles
Keyword(s):  
Wave Height ◽  
Wave Energy ◽  
Significant Wave Height ◽  
Wedge Angle ◽  
Wave Energy Converter ◽  
Wave Period ◽  
Surface Elevation ◽  
Energy Converter ◽  
Significant Wave ◽  
Model Scale

The WaveCat is a moored Wave Energy Converter design which uses wave overtopping discharge into a variable v-shaped hull, to generate electricity through low head turbines. Physical model tests of WaveCat WEC were carried out to determine the device reflection, transmission, absorption and capture coefficients based on selected wave conditions. The model scale was 1:30, with hulls of 3 m in length, 0.4 m in height and a freeboard of 0.2 m. Wave gauges monitored the surface elevation at discrete points around the experimental area, and level sensors and flowmeters recorded the amount of water captured and released by the model. Random waves of significant wave height between 0.03 m and 0.12 m and peak wave periods of 0.91 s to 2.37 s at model scale were tested. The wedge angle of the device was set to 60°. A reflection analysis was carried out using a revised three probe method and spectral analysis of the surface elevation to determine the incident, reflected and transmitted energy. The results show that the reflection coefficient is highest (0.79) at low significant wave height and low peak wave period, the transmission coefficient is highest (0.98) at low significant wave height and high peak wave period, and absorption coefficient is highest (0.78) when significant wave height is high and peak wave period is low. The model also shows the highest Capture Width Ratio (0.015) at wavelengths on the order of model length. The results have particular implications for wave energy conversion prediction potential using this design of device.

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