Shanshan Tao

Parameter Estimation of the Maximum Entropy Distribution of Significant Wave Height

ABSTRACT Dong, S.; Tao, S.; Lei, S., and Guedes Soares, C., 2013. Parameter estimation of the maximum entropy distribution of significant wave height. This paper compares the estimation of the four parameters of the maximum entropy distribution by different methods and applies them in two test cases with significantly different characteristics of variability. The moment method and the maximum likelihood method for the maximum entropy distribution with four parameters are formulated in the paper. These methods are compared with the moment method for the maximum entropy distribution with three parameters and an empirical curve-fitting method, both of which have been used earlier. These four estimation methods are applied to two test cases. One consists of hindcast wave heights at Weizhoudao hydrological station in the northern area of the South China Sea, which is subject to typhoon type of events. The other data set is hindcast wave heights at a location in the North Atlantic Ocean, which is subject to frequent storm weather. The maximum likelihood and the empirical methods appear to provide the most consistent results.

Estimating storm surge intensity with Poisson bivariate maximum entropy distributions based on copulas

This paper introduces four kinds of novel bivariate maximum entropy distributions based on bivariate normal copula, Gumbel–Hougaard copula, Clayton copula and Frank copula. These joint distributions consist of two marginal univariate maximum entropy distributions. Four types of Poisson bivariate compound maximum entropy distributions are developed, based on the occurrence frequency of typhoons, on these novel bivariate maximum entropy distributions and on bivariate compound extreme value theory. Groups of disaster-induced typhoon processes since 1949–2001 in Qingdao area are selected, and the joint distribution of extreme water level and corresponding significant wave height in the same typhoon processes are established using the above Poisson bivariate compound maximum entropy distributions. The results show that all these four distributions are good enough to fit the original data. A novel grade of disaster-induced typhoon surges intensity is established based on the joint return period of extreme water level and corresponding significant wave height, and the disaster-induced typhoons in Qingdao verify this grade criterion.

Joint occurrence period of wind speed and wave height based on both service term and risk probability

Return periods calculated for different environmental conditions are key parameters for ocean platform design. Many codes for offshore structure design give no consideration about the correlativity among multi-loads and over-estimate design values. This frequently leads to not only higher investment but also distortion of structural reliability analysis. The definition of design return period in existing codes and industry criteria in China are summarized. Then joint return periods of different ocean environmental parameters are determined from the view of service term and danger risk. Based on a bivariate equivalent maximum entropy distribution, joint design parameters are estimated for the concomitant wave height and wind speed at a site in the Bohai Sea. The calculated results show that even if the return period of each environmental factor, such as wave height or wind speed, is small, their combinations can lead to larger joint return periods. Proper design criteria for joint return period associated with concomitant environmental conditions will reduce structural size and lead to lower investment of ocean platforms for the exploitation of marginal oil field.

Joint return probability analysis of wind speed and rainfall intensity in typhoon-affected sea area

Strong wind and rainfall induced by extreme meteorological processes such as typhoons have a serious impact on the safety of bridges and offshore engineering structures. A new bivariate compound extreme value distribution is proposed to describe the probability dependency structure of annual extreme wind speed and concomitant process maximum rainfall intensity in typhoon-affected area. This probability model takes full account of the case that there may be no rainfall in a typhoon process. A case study based on the observation data of typhoon maximum wind speed and maximum rainfall intensity in Shanghai is conducted to testify the efficiency of the model. Weibull distributions with two parameters are applied to fit respective probability margins, and the joint probability distribution is constructed by Gumbel–Hougaard copula. The fitting results and K–S tests show that these models describe the original data well. The joint return periods are calculated by Poisson bivariate compound extreme value distribution we have proposed. They indicate that typhoons with no rain have smaller joint return periods, and wind speed is the main factor which impacts the change of the joint return periods.

Interval Estimation of Return Wave Height for Marine Structural Design

The general procedure is discussed for determining the interval estimation of N-year return period extreme wave height with maximum likelihood method (MLM). The specific interval estimation expressions of the N-year return extreme wave height with MLM are given when the extreme wave height series fits a sort of maximum value distribution, such as Weibull distribution, generalized extreme value distribution and log-normal distribution. This paper also proposes a sign test method (STM) to estimate the interval of return extreme wave height. It is a non-parametric method that does not depend on the type of maximum value distributions. By adopting both MLM and STM, a stochastic simulation of the interval estimation is conducted to estimate the quantiles of the above maximum value distributions. The results indicate that SMT behaves well only when the sample size is sufficiently large (generally above 100), and the advantage of simulation with MLM is apparent if the sample size is smaller. Finally, a case study has been carried out with the extreme wave height measured at Weizhoudao hydrological station in the northern area of South China Sea.© 2011 ASME

Long-term statistics of extreme tsunami height at Crescent City

Historically, Crescent City is one of the most vulnerable communities impacted by tsunamis along the west coast of the United States, largely attributed to its offshore geography. Trans-ocean tsunamis usually produce large wave runup at Crescent Harbor resulting in catastrophic damages, property loss and human death. How to determine the return values of tsunami height using relatively short-term observation data is of great significance to assess the tsunami hazards and improve engineering design along the coast of Crescent City. In the present study, the extreme tsunami heights observed along the coast of Crescent City from 1938 to 2015 are fitted using six different probabilistic distributions, namely, the Gumbel distribution, the Weibull distribution, the maximum entropy distribution, the lognormal distribution, the generalized extreme value distribution and the generalized Pareto distribution. The maximum likelihood method is applied to estimate the parameters of all above distributions. Both Kolmogorov-Smirnov test and root mean square error method are utilized for goodness-of-fit test and the better fitting distribution is selected. Assuming that the occurrence frequency of tsunami in each year follows the Poisson distribution, the Poisson compound extreme value distribution can be used to fit the annual maximum tsunami amplitude, and then the point and interval estimations of return tsunami heights are calculated for structural design. The results show that the Poisson compound extreme value distribution fits tsunami heights very well and is suitable to determine the return tsunami heights for coastal disaster prevention.

Interval Estimations of Return Wave Height Based on Maximum Entropy Distribution

ABSTRACT Dong, S.; Tao, S.; Chen, C., and Soares, C.G., 2014. Interval estimations of return wave height based on maximum entropy distribution. Five different interval estimation methods for extreme wave heights based on maximum entropy distribution are considered and compared. Three are parametric methods: Woodruff, maximum likelihood, and sample quantile asymptotic, and two are nonparametric methods: order statistics and sign test. The extreme significant wave height is fitted by a maximum entropy distribution, which is then used to conduct numerical simulations so as to apply the interval estimation methods to the 100 year return period estimates. These simulation results show that parametric methods have generally better performance than the nonparametric ones. Finally, a case study using the extreme wave height from Weizhou Island in the South China Sea is considered, and it is shown that the maximum likelihood method gives the best interval estimation for the actual data.

Stochastic Model for Estimating Extreme Water Level in Port and Coastal Engineering Design

Extreme water level is an important consideration when designing coastal protection structures. However, frequency analysis recommended by standard codes only considers the annual maximum water level, whereas water levels should actually be regarded as a combination of astronomical tide and storm surge. The two impacting factors are both random variables, and this paper discusses their dependency structures and proposes a new joint probability method to determine extreme design water levels. The lognormal, Gumbel, Weibull, Pearson type 3, traditional maximum entropy, and modified maximum entropy distributions are applied to fit univariate data of astronomical tides and storm surges separately, and the bivariate normal, Gumbel-Hougaard, Frank and Clayton copulas are then utilized to construct their joint probability distributions. To ensure that the new design method is suitable for use with typhoon data, the annual occurrence frequency of typhoon processes is considered and corresponding bivariate compound probability distributions are proposed. Based on maximum water level data obtained from Hengmen hydrological station in the Pearl River Basin, China, these probability models are applied to obtain designs for extreme water levels using the largest sum of the astronomical tide and storm surge obtained under fixed joint return periods. These design values provide an improved approach for determining the necessary height of coastal and offshore structures.

Study on temporal and spatial characteristics of cold waves in Shandong Province of China

Based on daily minimum temperature data during 1979–2013, the frequency of occurrence,the beginning date and ending date and other characteristic values of cold waves at all levels are processed. Then, by using the method of Mann–Kendall method, correlation analysis, empirical orthogonal function and Morlet wavelet analysis, the spatiotemporal distribution and inter-annual variation and other characteristics of cold wave, strong cold wave and ultra-strong cold wave of Shandong Province are analyzed. The tendency of cold waves at all levels in Shandong Province is predicted for the coming years, which might be referable in the prevention of cold wave and storm surge disaster.

Estimation of design sea ice thickness with maximum entropy distribution by particle swarm optimization method

The maximum entropy distribution, which consists of various recognized theoretical distributions, is a better curve to estimate the design thickness of sea ice. Method of moment and empirical curve fitting method are common-used parameter estimation methods for maximum entropy distribution. In this study, we propose to use the particle swarm optimization method as a new parameter estimation method for the maximum entropy distribution, which has the advantage to avoid deviation introduced by simplifications made in other methods. We conducted a case study to fit the hindcasted thickness of the sea ice in the Liaodong Bay of Bohai Sea using these three parameter-estimation methods for the maximum entropy distribution. All methods implemented in this study pass the K-S tests at 0.05 significant level. In terms of the average sum of deviation squares, the empirical curve fitting method provides the best fit for the original data, while the method of moment provides the worst. Among all three methods, the particle swarm optimization method predicts the largest thickness of the sea ice for a same return period. As a result, we recommend using the particle swarm optimization method for the maximum entropy distribution for offshore structures mainly influenced by the sea ice in winter, but using the empirical curve fitting method to reduce the cost in the design of temporary and economic buildings.