Long Term Wave Analysis Quiz

Extreme Value Analysis and Return Period

• The return period is the average time between two exceedances of a certain event, with a 100-year return period having an average annual probability of 1%.
• Extreme value analysis involves determining the extreme value distribution of events, such as storm surges, over time.
• The Generalized Extreme Value distribution is a probabilistic function that combines parameters from various distribution functions like Weibull, Gumbel, and Frechet.
• The probability of non-exceedance of a 100-year return period event in 100 consecutive years is approximately 36.6%, meaning the probability of occurrence is 63.4%.
• The scalar and directional annual extreme distribution of a parameter, like storm surge heights, involves assigning probabilities to annual maximum values and analyzing the probability of non-exceedance over a certain period.
• The return period concept is related to the probability of each year, and it is used to calculate the probability of overcoming a 100-year return period event in 100 years.
• The failure of a marine structure is associated with the exceedance of a certain value of a sea state parameter, and the probability of failure can be calculated using the extreme annual scalar distribution and the Cumulative Distribution Function.
• The lifetime probability of failure for a marine structure can be calculated using the relationship between the annual extreme distribution of a parameter, the lifespan, and the probability of failure.
• The Generalized Extremes function (GEV) is a family of continuous probability distribution functions developed by extreme value theory, combining Gumbel, Fréchet, and Weibull distributions.
• The GEV function is determined by the dimensionless variable T(Hso) = 1 / (1 – FRT(Hso)), where Hso is the calculation value of the sea state parameter.
• The distribution function of the GEV involves parameters like location, scale, and shape, and is used to calculate the return period and probability of failure for extreme wave events.
• The GEV function is used to determine the return period and probability of failure for extreme wave events, and it is crucial for understanding the likelihood and impact of these events over time.

Extreme Value Analysis and Return Period

• The return period is the average time between two exceedances of a certain event, with a 100-year return period having an average annual probability of 1%.
• Extreme value analysis involves determining the extreme value distribution of events, such as storm surges, over time.
• The Generalized Extreme Value distribution is a probabilistic function that combines parameters from various distribution functions like Weibull, Gumbel, and Frechet.
• The probability of non-exceedance of a 100-year return period event in 100 consecutive years is approximately 36.6%, meaning the probability of occurrence is 63.4%.
• The scalar and directional annual extreme distribution of a parameter, like storm surge heights, involves assigning probabilities to annual maximum values and analyzing the probability of non-exceedance over a certain period.
• The return period concept is related to the probability of each year, and it is used to calculate the probability of overcoming a 100-year return period event in 100 years.
• The failure of a marine structure is associated with the exceedance of a certain value of a sea state parameter, and the probability of failure can be calculated using the extreme annual scalar distribution and the Cumulative Distribution Function.
• The lifetime probability of failure for a marine structure can be calculated using the relationship between the annual extreme distribution of a parameter, the lifespan, and the probability of failure.
• The Generalized Extremes function (GEV) is a family of continuous probability distribution functions developed by extreme value theory, combining Gumbel, Fréchet, and Weibull distributions.
• The GEV function is determined by the dimensionless variable T(Hso) = 1 / (1 – FRT(Hso)), where Hso is the calculation value of the sea state parameter.
• The distribution function of the GEV involves parameters like location, scale, and shape, and is used to calculate the return period and probability of failure for extreme wave events.
• The GEV function is used to determine the return period and probability of failure for extreme wave events, and it is crucial for understanding the likelihood and impact of these events over time.

Extreme Value Analysis and Return Period Concept

• Return period is the average time between two exceedances of an event and its inverse is the annual probability of the event being exceeded.
• For independent events, the joint probability of occurrence is the product of individual probabilities.
• The Generalized Extreme Value distribution is a probabilistic function that combines parameters from various distribution functions.
• The probability of non-exceedance for 100 consecutive years of an event with a 100-year return period is 36.6%.
• The scalar and directional annual extreme distribution of significant wave height (Hs) involves selecting N annual maximum values and assigning probabilities to each.
• On average, a storm surge event larger than 120 cm occurs every 100 years.
• The probability of overcoming a 100-year return period event in 100 years is 63.4%.
• The failure probability of a marine structure is associated with the exceedance of a certain value of a sea state parameter.
• The return period of a parameter X is the average time between two exceedances of X, and its probability of exceedance in a year is 1 - FRT(X).
• The lifetime probability of failure, PFV, is calculated as 1- FRT(Hso)V, where Hso is the calculation value.
• The Generalized Extremes function (GEV) is a family of continuous probability distribution functions that combines the Gumbel, Fréchet, and Weibull distributions.
• The distribution function of the GEV involves location, scale, and shape parameters and can be used to calculate return periods and failure probabilities for extreme wave distributions.

Wave Climate System and Extreme Value Analysis

• Wave climate system encompasses characteristics, variability, and statistical distribution of wave parameters such as wave direction, mean wave energy flux, and significant wave height (Hs).
• Long term distributions are used to determine statistical distribution of sea state parameters over a period of time, such as the annual mean distribution of Hs.
• The most commonly used distributions for fitting long term wave distribution are Weibull and Lognormal, represented by probability density function (PDF) and cumulative distribution function (CDF).
• Other representations used for wave climate include mean range, color-coded relative frequency, and percentiles.
• Extreme value analysis is crucial for assessing extreme events and return periods, which quantifies the probability of an event being equaled or exceeded in a certain time interval.
• Return period concept allows quantifying the probability of an event, with the average time between independent events referred to as the "return period".
• For extreme value analysis, it is necessary to define the threshold and analyze the occurrence and duration of storms, which can vary based on coastal locations and meteorological disturbances.
• The concept of return period is illustrated with an example of significant wave height (Hs) and its exceedance probability over a certain time interval.
• Extreme value analysis aids in coastal management, particularly in assessing flooding risks and designing maritime works to withstand extreme events.