Analysis and Applications of Second-Order Models for Maximum Crest Height

2004 ◽  
Vol 126 (1) ◽  
pp. 66-71 ◽  
Author(s):  
Harald E. Krogstad ◽  
Stephen F. Barstow

Expressions for the maximum crest height are reviewed and tested on data from five different sensors in the WACSIS data set. The overall agreement is good and the analysis supports that second-order models give accurate expressions for the distribution of the maximum crest height for varying water depth and wave steepness. In the second part of the paper, the expressions are combined with the existing extreme crest and wave height framework and applied to sets of time series and long term wave data. It is concluded that the second-order models represent a definite improvement over earlier empirical parametrizations.

Author(s):  
Harald E. Krogstad ◽  
Stephen F. Barstow

Expressions for the maximum crest height are reviewed and tested on data from five different sensors in the WACSIS data set. The overall agreement is good and the analysis supports that second order models give accurate expressions for the distribution of the maximum crest height for varying water depth and wave steepness. In the second part of the paper, the expressions are combined with the existing extreme crest and wave height framework and applied to sets of time series and long term wave data. It is concluded that the 2nd order models represent a definite improvement over earlier empirical parametrizations.


Author(s):  
Øistein Hagen ◽  
Jørn Birknes-Berg ◽  
Ida Håøy Grue ◽  
Gunnar Lian ◽  
Kjersti Bruserud ◽  
...  

As offshore reservoirs are depleted, the seabed may subside. Furthermore, the extreme crests estimates are now commonly higher than obtained previously due to improved understanding of statistics of non-linear irregular waves. Consequently, bottom fixed installations which have previously had sufficient clearance between the deck and the sea surface may be in a situation where wave impact with the deck must be considered at relevant probability levels. In the present paper, we investigate the long-term area statistics for maximum crest height under a fixed platform deck for 2nd order short crested and long crested sea based on numerical simulations as a function of platform deck dimension for jackets. The results are for one location in the northern North Sea, but some key results are also reported and verified for a more benign southern North Sea location. Time domain simulations for long crested and short crested waves over a spatial domain with dimension of a platform deck are performed, and relevant statistics for airgap assessment determined. Second order waves are simulated for the different cells in the (Hs, Tp) scatter diagram for Torsethaugen two-peak wave spectrum for long-crested and short-crested sea. A total of 1000 3-hour sea states are generated per cell, and time series generated for 160 spatial points under a platform deck. Short-term and long-term statistics are established for the maximum crest height as function of platform dimension; inline and transverse to the wave direction, and over the area. Results are given for the linear sea and for the second order time series. The annual q-probability estimates for the maximum crest height over area as a function of platform dimension is determined for a location at the Norwegian Continental Shelf by weighting the short-term statistics for the individual cells in the scatter diagram with the long-term probability of occurrence of the sea state. To reduce the number of numerical second order simulations, the effect of excluding cells that have a negligible effect on the long term extreme crest estimate is discussed. The percentiles in the distribution of maximum crest (over area) in design sea states that corresponds to the extreme values obtained from the long-term analysis are determined for long crested and short crested sea. The increase in the extreme crest over an area compared to the point in space estimate is estimated for both linear and second order surface elevation.


2021 ◽  
Author(s):  
Annette Dietmaier ◽  
Thomas Baumann

<p>The European Water Framework Directive (WFD) commits EU member states to achieve a good qualitative and quantitative status of all their water bodies.  WFD provides a list of actions to be taken to achieve the goal of good status.  However, this list disregards the specific conditions under which deep (> 400 m b.g.l.) groundwater aquifers form and exist.  In particular, deep groundwater fluid composition is influenced by interaction with the rock matrix and other geofluids, and may assume a bad status without anthropogenic influences. Thus, a new concept with directions of monitoring and modelling this specific kind of aquifers is needed. Their status evaluation must be based on the effects induced by their exploitation. Here, we analyze long-term real-life production data series to detect changes in the hydrochemical deep groundwater characteristics which might be triggered by balneological and geothermal exploitation. We aim to use these insights to design a set of criteria with which the status of deep groundwater aquifers can be quantitatively and qualitatively determined. Our analysis is based on a unique long-term hydrochemical data set, taken from 8 balneological and geothermal sites in the molasse basin of Lower Bavaria, Germany, and Upper Austria. It is focused on a predefined set of annual hydrochemical concentration values. The data range dates back to 1937. Our methods include developing threshold corridors, within which a good status can be assumed, and developing cluster analyses, correlation, and piper diagram analyses. We observed strong fluctuations in the hydrochemical characteristics of the molasse basin deep groundwater during the last decades. Special interest is put on fluctuations that seem to have a clear start and end date, and to be correlated with other exploitation activities in the region. For example, during the period between 1990 and 2020, bicarbonate and sodium values displayed a clear increase, followed by a distinct dip to below-average values and a subsequent return to average values at site F. During the same time, these values showed striking irregularities at site B. Furthermore, we observed fluctuations in several locations, which come close to disqualifying quality thresholds, commonly used in German balneology. Our preliminary results prove the importance of using long-term (multiple decades) time series analysis to better inform quality and quantity assessments for deep groundwater bodies: most fluctuations would stay undetected within a < 5 year time series window, but become a distinct irregularity when viewed in the context of multiple decades. In the next steps, a quality assessment matrix and threshold corridors will be developed, which take into account methods to identify these fluctuations. This will ultimately aid in assessing the sustainability of deep groundwater exploitation and reservoir management for balneological and geothermal uses.</p>


2018 ◽  
Vol 611 ◽  
pp. A85 ◽  
Author(s):  
R. Silvotti ◽  
S. Schuh ◽  
S.-L. Kim ◽  
R. Lutz ◽  
M. Reed ◽  
...  

V391 Peg (alias HS 2201+2610) is a subdwarf B (sdB) pulsating star that shows both p- and g-modes. By studying the arrival times of the p-mode maxima and minima through the O–C method, in a previous article the presence of a planet was inferred with an orbital period of 3.2 years and a minimum mass of 3.2 MJup. Here we present an updated O–C analysis using a larger data set of 1066 h of photometric time series (~2.5× larger in terms of the number of data points), which covers the period between 1999 and 2012 (compared with 1999–2006 of the previous analysis). Up to the end of 2008, the new O–C diagram of the main pulsation frequency (f1) is compatible with (and improves) the previous two-component solution representing the long-term variation of the pulsation period (parabolic component) and the giant planet (sine wave component). Since 2009, the O–C trend of f1 changes, and the time derivative of the pulsation period (p.) passes from positive to negative; the reason of this change of regime is not clear and could be related to nonlinear interactions between different pulsation modes. With the new data, the O–C diagram of the secondary pulsation frequency (f2) continues to show two components (parabola and sine wave), like in the previous analysis. Various solutions are proposed to fit the O–C diagrams of f1 and f2, but in all of them, the sinusoidal components of f1 and f2 differ or at least agree less well than before. The nice agreement found previously was a coincidence due to various small effects that are carefully analyzed. Now, with a larger dataset, the presence of a planet is more uncertain and would require confirmation with an independent method. The new data allow us to improve the measurement of p. for f1 and f2: using only the data up to the end of 2008, we obtain p.1 = (1.34 ± 0.04) × 10−12 and p.2 = (1.62 ± 0.22) × 10−12. The long-term variation of the two main pulsation periods (and the change of sign of p.1) is visible also in direct measurements made over several years. The absence of peaks near f1 in the Fourier transform and the secondary peak close to f2 confirm a previous identification as l = 0 and l = 1, respectively, and suggest a stellar rotation period of about 40 days. The new data allow constraining the main g-mode pulsation periods of the star.


Author(s):  
Christos N. Stefanakos

In the present work, return periods of various level values of significant wave height in the Gulf of Mexico are given. The predictions are based on a new method for nonstationary extreme-value calculations that have recently been published. This enhanced method exploits efficiently the nonstationary modeling of wind or wave time series and a new definition of return period using the MEan Number of Upcrossings of the level value x* (MENU method). The whole procedure is applied to long-term measurements of wave height in the Gulf of Mexico. Two kinds of data have been used: long-term time series of buoy measurements, and satellite altimeter data. Measured time series are incomplete and a novel procedure for filling in of missing values is applied before proceeding with the extreme-value calculations. Results are compared with several variants of traditional methods, giving more realistic estimates than the traditional predictions. This is in accordance with the results of other methods that take also into account the dependence structure of the examined time series.


Author(s):  
Jule Scharnke ◽  
Janou Hennig

In a recent paper the effect of variations in calibrated wave parameters on wave crest and height distributions was analyzed (OMAE2010-20304, [1]). Theoretical distribution functions were compared to wave measurements with a variation in water depth, wave seed (group spectrum) and location of measurement for the same initial power spectrum. The wave crest distribution of the shallow water waves exceeded both second-order and Rayleigh distribution. Whereas, in intermediate water depth the measured crests followed the second order distribution. The distributions of the measured waves showed that different wave seeds result in the same wave height and crest distributions. Measured wave heights were lower closer to the wave maker. In this paper the results of the continued statistical analysis of basin waves are presented with focus on wave steepness and their influence on wave height and wave crest distributions. Furthermore, the sampling variability of the presented cases is assessed.


Open Physics ◽  
2009 ◽  
Vol 7 (3) ◽  
Author(s):  
Shahriar Shadkhoo ◽  
Fakhteh Ghanbarnejad ◽  
Gholam Jafari ◽  
Mohammad Tabar

AbstractIn this paper, we investigate the statistical and scaling properties of the California earthquakes’ inter-events over a period of the recent 40 years. To detect long-term correlations behavior, we apply detrended fluctuation analysis (DFA), which can systematically detect and overcome nonstationarities in the data set at all time scales. We calculate for various earthquakes with magnitudes larger than a given M. The results indicate that the Hurst exponent decreases with increasing M; characterized by a Hurst exponent, which is given by, H = 0:34 + 1:53/M, indicating that for events with very large magnitudes M, the Hurst exponent decreases to 0:50, which is for independent events.


2007 ◽  
Vol 7 (4) ◽  
pp. 11761-11796 ◽  
Author(s):  
S. Mieruch ◽  
S. Noël ◽  
H. Bovensmann ◽  
J. P. Burrows

Abstract. Global water vapour total column amounts have been retrieved from spectral data provided by the Global Ozone Monitoring Experiment (GOME) flying on ERS-2, which was launched in April 1995, and the SCanning Imaging Absorption spectroMeter for Atmospheric CHartographY (SCIAMACHY) onboard ENVISAT launched in March 2002. For this purpose the Air Mass Corrected Differential Optical Absorption Spectroscopy (AMC-DOAS) approach has been used. The combination of the data from both instruments provides us with a long-term global data set spanning more than 11 years with the potential of extension up to 2020 by GOME-2 data, on Metop. Using linear and non-linear methods from time series analysis and standard statistics the trends of H2O contents and their errors have been calculated. In this study, factors affecting the trend such as the length of the time series, the magnitude of the variability of the noise, and the autocorrelation of the noise are investigated. Special emphasis has been placed on the calculation of the statistical significance of the observed trends, which reveal significant local changes of water vapour columns distributed over the whole globe.


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