Sheng Dong

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.

Long-Term Statistical Analysis of Typhoon Wave Heights With Poisson-Maximum Entropy Distribution

Using the maximum typhoon wave height series observed at Nakagusukuwan Observation Station in Japan, a novel compound distribution, Poisson-maximum entropy distribution, is proposed to calculate typhoon wave height return values. In this paper, both the Annual Maximum method and Peak Over Threshold method are adopted for long-term wave height analysis. Calculation results by Peak Over Threshold method show that the choice of threshold slightly affects the return values of wave height under the same long statistical series. For a relatively short sample by the Peak Over Threshold method, the estimation accuracy is still higher under the condition that the maximum typhoon wave height is included in the statistical sample.© 2009 ASME

The application of a Grey Markov Model to forecasting annual maximum water levels at hydrological stations

Compared with traditional real-time forecasting, this paper proposes a Grey Markov Model (GMM) to forecast the maximum water levels at hydrological stations in the estuary area. The GMM combines the Grey System and Markov theory into a higher precision model. The GMM takes advantage of the Grey System to predict the trend values and uses the Markov theory to forecast fluctuation values, and thus gives forecast results involving two aspects of information. The procedure for forecasting annul maximum water levels with the GMM contains five main steps: 1) establish the GM (1, 1) model based on the data series; 2) estimate the trend values; 3) establish a Markov Model based on relative error series; 4) modify the relative errors caused in step 2, and then obtain the relative errors of the second order estimation; 5) compare the results with measured data and estimate the accuracy. The historical water level records (from 1960 to 1992) at Yuqiao Hydrological Station in the estuary area of the Haihe River near Tianjin, China are utilized to calibrate and verify the proposed model according to the above steps. Every 25 years’ data are regarded as a hydro-sequence. Eight groups of simulated results show reasonable agreement between the predicted values and the measured data. The GMM is also applied to the 10 other hydrological stations in the same estuary. The forecast results for all of the hydrological stations are good or acceptable. The feasibility and effectiveness of this new forecasting model have been proved in this paper.

A storm surge intensity classification based on extreme water level and concomitant wave height

Storm surge is one of the predominant natural threats to coastal communities. Qingdao is located on the southern coast of the Shandong Peninsula in China. The storm surge disaster in Qingdao depends on various influencing factors such as the intensity, duration, and route of the passing typhoon, and thus a comprehensive understanding of natural coastal hazards is essential. In order to make up the defects of merely using the warning water level, this paper presents two statistical distribution models (Poisson Bi-variable Gumbel Logistic Distribution and Poisson Bi-variable Log-normal Distribution) to classify the intensity of storm surge. We emphasize the joint return period of typhoon-induced water levels and wave heights measured in the coastal area of Qingdao since 1949. The present study establishes a new criterion to classify the intensity grade of catastrophic storms using the typhoon surge estimated by the two models. A case study demonstrates that the new criterion is well defined in terms of probability concept, is easy to implement, and fits well the calculation of storm surge intensity. The procedures with the proposed statistical models would be useful for the disaster mitigation in other coastal areas influenced by typhoons.

Return Value Estimation of Significant Wave Heights With Maximum Entropy Distribution

The maximum entropy distribution is proposed to fit the long term and extreme distribution of significant wave heights from which return value estimates are derived. The maximum entropy distribution is applied to data from two sites of different characteristics, namely from Japan characterized by the occurrence of typhoons and from the North Sea with continuous variation of sea state intensity. The compound distribution, Poisson-maximum entropy distribution, is described and adopted to model the data from these two locations. It is shown that in the case of continuous data from the North Sea, this model does not bring any advantage over the direct application of the maximum entropy distribution to adjust the significant wave heights larger than different thresholds. For this case the maximum entropy distribution provides good fits.

Study on Joint Return Period of Wind Speed and Wave Height Considering Lifetime of Platform Structure

Summarize the definition of design return period in existent codes and industry criteria. Joint return periods of different ocean environmental conditions are determined from the view of project life and risk probability. Based on equivalent bivariate maximum entropy distribution, joint design parameters of wave height and wind speed are estimated occurred in some place of Bohai Sea. The calculating results show that even if the return value of each environmental factor, such as wave height or wind speed, is small, their combinations usually lead to larger joint return periods. This will make the investment of ocean platform lower.Copyright

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.

Wind Wave Characteristics and Engineering Environment of the South China Sea

Wave simulation was conducted for the period 1976 to 2005 in the South China Sea (SCS) using the wave model, WAVEWATCH-III. Wave characteristics and engineering environment were studied in the region. The wind input data are from the objective reanalysis wind datasets, which assimilate meteorological data from several sources. Comparisons of significant wave heights between simulation and TOPEX/Poseidon altimeter and buoy data show a good agreement in general. By statistical analysis, the wave characteristics, such as significant wave heights, dominant wave directions, and their seasonal variations, were discussed. The largest significant wave heights are found in winter and the smallest in spring. The annual mean dominant wave direction is northeast (NE) along the southwest (SW)-NE axis, east northeast in the northwest (NW) part of SCS, and north northeast in the southeast (SE) part of SCS. The joint distributions of wave heights and wave periods (directions) were studied. The results show a single peak pattern for joint significant wave heights and periods, and a double peak pattern for joint significant wave heights and mean directions. Furthermore, the main wave extreme parameters and directional extreme values, particularly for the 100-year return period, were also investigated. The main extreme values of significant wave heights are larger in the northern part of SCS than in the southern part, with the maximum value occurring to the southeast of Hainan Island. The direction of large directional extreme Hs values is focus in E in the northern and middle sea areas of SCS, while the direction of those is focus in N in the southeast sea areas of SCS.