Extreme Value Analysis of Metocean Data for Barents Sea

An extreme value analysis of metocean data which include wave, wind, and current data is a prerequisite for the operation and survival of offshore structures. The purpose of this study was to provide information about the return wave, wind, and current values for the Barents Sea using extreme value analysis. Hindcast datasets of the Global Reanalysis of Ocean Waves 2012 (GROW2012) for a waves, winds and currents were obtained from the Oceanweather Inc. The Gumbel distribution, 2 and 3 parameters Weibull distributions and log-normal distribution were used for the extreme value analysis. The least square method was used to estimate the parameters for the extreme value distribution. The return values, including the significant wave height, spectral peak wave period, wind speed and current speed at surface, were calculated and it will be utilized to design offshore structures to be operated in the Barents Sea. Received 15 October 2019, revised 28 January 2020, accepted 14 February 2020 Corresponding author Kwang Hyo Jung: +82-51-510-2343, kjung@pusan.ac. kr c 2020, The Korean Society of Ocean Engineers This is an open access article distributed under the terms of the creative commons attribution non-commercial license (http://creativecommons.org/licenses/by-nc/4.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. Extreme Value Analysis of Metocean Data for Barents Sea 27 the method of moment, maximum likelihood estimation, and least-squares method (DNV, 2014). Jeong et al. (2004) conducted extreme value analyses using Weibull, Gumbel, Log-Pearson type-III, and log-normal distributions using the Hs data of approximately 20 years obtained from 67 ocean stations in South Korea. They provided design wave height information in the deep-sea for the return period of 50 years and suggested that Gumbel distribution was the most suitable method. In addition, they provided the extreme highest tide level information for each return period by conducting an extreme value analysis through generalized extreme value, Gumbel, and Weibull distributions using the extreme highest tide level data of 23 tide stations on the coast of South Korea, and they suggested that Gumbel distribution was the most suitable method (Jeong et al., 2008). Ko et al. (2014) developed a numerical wind speed model that numerically implemented typhoons for four locations on the west coast of the Korean Peninsula (Gunsan, Mokpo, Jeju, and Haemosu No. 1) and presented extreme wind speeds for the four locations by applying the Gumbel distribution and estimating parameters through the probability weighted moment method. EVDs were applied to various metocean data. In the case of wave data, however, Hs and Tp were important design elements for the design of offshore structures. DNVGL (2017) and BV (2015) recommended the use of the inversed first order reliability method (I-FORM), which used the joint distribution of EVDs, to obtain the return values for Hs and Tp. In this study, the metocean data (wave, wind, and current) of the Barents Sea in the Arctic region were collected. In addition, for the extreme value analysis of the wave data, return values were calculated using I-FORM, which used the joint distribution of the marginal probability distribution for Hs (Gumbel distribution and twoand three-parameter Weibull distributions) and the conditional probability distribution of Tp for the given Hs (log-normal distribution) (DNVGL, 2017; BV, 2015; Choi, 2016). For the wind and current speeds, which are single variables, extreme value analysis was conducted through the Gumbel distribution and twoand three-parameter Weibull distributions. The least-squares method was used for parameter estimation, and the Kolmogorov-Smirnov (K-S) test was applied as the goodness-of-fit test. Through these processes, the return values for Hs, Tp, wind speed, and current speed required for the design of offshore structures to be operated in the Barents Sea were derived. 2. Metocean Data Collection and Analysis The project site (Fig. 1) is the Barents Sea of water depth 258 m (latitude: 73N and longitude: 44E), where gas fields were distributed around the site (Fig. 2). For the wave (Hs, Tp, and wave direction), wind (wind speed and wind direction), current (current speed and current direction), and an ice floe thickness data, the hindcast datasets of Global Reanalysis of Ocean Waves 2012 (GROW2012) from Oceanweather Inc. were purchased. In the hindcast datasets of GROW2012, wave and wind models provided by the General Bathymetric Chart of the Oceans and Climate Forecast System Reanalysis were used to estimate the data for waves, wind, current, and ice floe (Oceanweather Inc.). To conduct the extreme value analysis, the consistency, period, and validity of the collected data must be examined first (Van Os et al., 2011). Compared with the measurement data, the hindcast data have no possibility of missing data and generating outliers owing to typhoons or defects in the measuring equipment and can secure a data period irrespective of the installation time of the measuring equipment. The wave and wind data were recorded at one hour intervals for a decade from January 2007 to December 2016, and the current data were recorded in the water depth direction at one day intervals for two decades from January 1993 to December 2012. The ice floe thickness data during the same period as that of the current data were provided, but it was discovered that no ice existed in the project site. Fig. 1 Project site in Barents Sea (Wikipedia, 2019) Fig. 2 Oil and gas filed in Barents Sea (WorldMap, n.d.) 28 Sung Boo Park et al. Fig. 4 Wave rose and wind rose The wave data showed the wave scatter diagram (WSD) for Hs and Tp; the wave rose for the wave direction and Tp, and the wind data showed that the wind rose for the wind direction and wind speed (Ws) (Figs. 3 and 4). The current data represented the current increase for the current direction and current speed (Cs) at the surface and the current profile in the water depth direction (Fig. 5). The WSD showed frequencies at 1 m intervals for Hs and at 1s intervals for Tp, and the total number of data was approximately 87,600. The wave conditions with the highest frequencies in the Fig. 5 Current profile and current rose at surface project site were 1-2 m for Hs and 6-7 s for Tp. The wave, wind, and current directions could be confirmed through the rose diagrams, and the directions were categorized into east (90°), south (180°), and west (270°) in the clockwise direction from the north direction (0°). In the case of the hindcast data purchased from Oceanweather Inc., the wave and current directions were defined as the directions to which the wave and current were moving, while the wind direction was defined as the direction from which the wind was coming. The wave and wind directions with the highest frequencies were East and NorthFig. 3 Wave scatter diagram with Hs and Tp Extreme Value Analysis of Metocean Data for Barents Sea 29 Northwest (Fig. 4). Fig. 5 shows the current speed profile and direction in the water depth direction (z). The current speed profile was nondimensionalized with the water depth of the project site (d). The average and maximum current speeds were the fastest at the surface, and the dominant current direction at the surface was from the West to the East. 3. Extreme Value Analysis For the extreme value analysis of metocean data, data collection, data selection, EVD selection, parameter estimation method selection, goodness-of-fit test, and return value derivation are required (Mathiesen et al., 1994). In this study, a global model that utilizes all of the collected metocean data was selected. In addition, the Gumbel distribution, twoand three-parameter Weibull distributions, and log-normal distribution were used as EVDs. The least-squares method was used to estimate the parameters of the EVDs. As the goodnessof-fit test, the K-S test that uses the maximum distance as a test statistic by comparing the cumulative distribution function (CDF) of metocean data with that of each EVD was used (Jeong et al., 2004; Jeong et al., 2008). Eqs. (1)-(4) show the CDF of each EVD (Coles, 2001; Goda, 2000). Gumbel distribution CDF:   expexp    (1) 2-parameter Weibull distribution CDF:   exp     