A New Approach for Environmental Contour and Multivariate De-Clustering

Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulation s as a part of the stand ard current practice for designing marine structure s to survive extreme sea states. Such environmental contours are characterized by combinations of significant wave height ( ) and energy period ( ) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first - order reliability method (IFORM) i s standard design practice for generating environmental contours. In this paper, the traditional appli cation of the IFORM to generating environmental contours representing extreme sea states is described in detail and its merits and drawbacks are assessed. The application of additional methods for analyzing sea state data including the use of principal component analysis (PCA) to create an uncorrelated representation of the data under consideration is proposed. A reexamination of the components of the IFORM application to the problem at hand including the use of new distribution fitting techniques are shown to contribute to the development of more accurate a nd reasonable representations of extreme sea states for use in survivability analysis for marine struc tures. Keywords: In verse FORM, Principal Component Analysis , Environmental Contours, Extreme Sea State Characteri zation, Wave Energy Converters

Environmental contours based on inverse SORM

Environmental wave contours by inverse FORM and Monte Carlo Simulation with variance reduction techniques

A comparative study of two methods for the generation of the environmental contours is presented investigating the sensitivity of the predicted extreme vessel responses to the type of the contour lines. Two approaches for the generation of environmental contours of the significant wave height and peak period are compared: the Inverse First Order Reliability Method (IFORM) and Constant Probability Density (CPD) approach. Case studies include several global responses of a ship-shaped weather-vaning vessel and a semisubmersible platform. The case studies reveal that the differences between the IFORM and CPD contours are more pronounced in the range of long wave periods. Vessel responses which are less sensitive to long wave periods exhibit less difference (less than 1.0%) in their maximum values between the two types of contours. In contrast, responses which are sensitive to long wave periods show significantly larger differences of up to 7.0%. Uncertainties also exist in the predicted extreme responses where the environmental contour and the response isoline behave tangentially. Differences between the extreme responses produced by the two contours generally decrease with an increase in return period; however exceptions exist due to the tangential behaviour. It is advised that these sensitivities should be taken into consideration when the environmental contours are used in the design.

The environmental contour concept is often applied in marine structural design in conjunction with the Inverse First Order Reliability Method (IFORM). It allows for the great advantage of considering the environmental loads independently of the structural response. In this way, design sea states may be identified along the contour and time consuming response calculations are only needed for a limited set of design sea states. The traditional way of establishing such environmental contour lines is by applying the Rosenblatt transformation and identify the circle (in two dimensions) with radius equal to the reliability index βr The points along this circle are then transformed back to the original environmental space, specifying the closed contour. In this paper, an alternative approach for establishing the environmental contour lines in the original environmental space is proposed, eliminating the need for any transformations. This approach utilizes Monte Carlo simulations of the joint environmental model and is generally found to perform well. Advantages are that it yields a more precise interpretation and allows for more flexible modelling of the environmental parameters. This makes it easier to modify the environmental models to account for effects such as climate change if this is desired. In addition, possible over- or underestimation of failure probabilities due to the Rosenblatt transformation inherent in the traditional approach can be avoided with the proposed method.

Development of environmental contours for first-year ice ridge statistics

A new approach to environmental contours for ocean engineering applications based on direct Monte Carlo simulations

Synthetic aperture radar (SAR) altimeters represent a new method of microwave remote sensing for ocean wave observations. The adoption of SAR technology in the azimuthal direction has the advantage of a high resolution. The Sentinel-3 altimeter is the first radar altimeter to acquire global observations in SAR mode; hence, the data quality needs to be assessed before extensively applying these data. The European Space Agency (ESA) evaluates the Sentinel-3 accuracy on a global scale but has yet to perform a detailed analysis in terms of different offshore distances and different water depths. In this paper, Sentinel-3 and Jason-2 significant wave height (SWH) data are matched in both time and space with buoy data from the United States East and West Coasts and the Central Pacific Ocean. The Sentinel-3 SWH data quality is evaluated according to different offshore distances and water depths in comparison with Jason-2 SWH data. In areas more than 50 km offshore, the Sentinel-3 SWH accuracy is generally high and less affected by the water depth and sea conditions (root-mean-square error of 0.28 m and correlation coefficient of 0.98); in areas less than 50 km offshore, the SWH data accuracy is slightly affected by water depth and sea conditions (especially the former). Compared with Jason-2, the observation ability of the Sentinel-3 altimeter in nearshore areas with water depths of 0 m-500 m is greatly improved, but in some deep water areas with stable sea conditions, the Jason-2 SWH data accuracy is higher than that of Sentinel-3. This work provides a reference for the refined application of Sentinel-3 SWH data in offshore deep water areas and nearshore shallow water areas.

Environmental contours of extreme sea states are often utilized for the purposes of reliability-based offshore design. Many methods have been proposed to estimate environmental contours of extreme sea states, including, but not limited to, the traditional inverse first-order reliability method (I-FORM) and subsequent modifications, copula methods, and Monte Carlo methods. These methods differ in terms of both the methodology selected for defining the joint distribution of sea state parameters and in the method used to construct the environmental contour from the joint distribution. It is often difficult to compare the results of proposed methods to determine which method should be used for a particular application or geographical region. The comparison of the predictions from various contour methods at a single site and across many sites is important to making environmental contours of extreme sea states useful in practice. The goal of this paper is to develop a comparison framework for evaluating methods for developing environmental contours of extreme sea states. This paper develops generalized metrics for comparing the performance of contour methods to one another across a collection of study sites, and applies these metrics and methods to develop conclusions about trends in the wave resource across geographic locations, as demonstrated for a pilot dataset. These proposed metrics and methods are intended to judge the environmental contours themselves relative to other contour methods, and are thus agnostic to a specific device, structure, or field of application. The metrics developed and applied in this paper include measures of predictive accuracy, physical validity, and aggregated temporal performance that can be used to both assess contour methods and provide recommendations for the use of certain methods in various geographical regions. The application and aggregation of the metrics proposed in this paper outline a comparison framework for environmental contour methods that can be applied to support design analysis workflows for offshore structures. This comparison framework could be extended in future work to include additional metrics of interest, potentially including those to address issues pertinent to a specific application area or analysis discipline, such as metrics related to structural response across contour methods or additional physics-based metrics based on wave dynamics.

In the past, the oil industry has used highly simplified design current profiles. The simplification process produces errors which are typically unimportant in shallow water but the errors can be substantial in deeper water where currents are more complex and some design concepts are sensitive to current. We suggest a new method to develop more accurate current profiles without significantly burdening the design engineer. The method consists of two steps. In the first step, we simplify the current data using Empirical Orthogonal Functions (EOF), a method that accurately expresses complex data with just a few energetic modes. To these modes, we then apply the inverse First Order Reliability Method (FORM) to develop a profile with an n-year recurrence. We describe the EOF and FORM methods and provide some examples of how the analysis applies to real data. Introduction Historically the oil industry has based the vertical variation of design current profiles on either simple theoretical formulas or piecewise linear profiles. The latter are usually derived by applying some simplistic vertical averaging to numerical model hindcast results. Figure 1 shows several examples of design profiles given in the codes of API (1993), DOE (1992), and DnV (1991). Note the simple shapes. The magnitudes of the profiles are not important because they reflect local forcing. These simple design profiles are reasonable for shallowwater and more traditional structures like jackets where waves are a more important load factor then currents. For these cases, the extreme loads occur during extreme storms and the current profiles are relatively simple. Errors in the profiles are of little consequence because the waves dominate the load equation. In deeper water the situation can change, especially for newer concepts like spars and subsystems like risers. In these cases, currents can actually dominate the load equation so simplification of the profile can introduce substantial errors. In addition, the currents tend to be much more complex and less constant with depth. The extreme load may indeed occur during a storm but it may be accompanied by a persistent and strong non-storm generated current. A good example of this condition is found west of Shetlands where there is often a strong (I m/s) current which is largely independent of local wind forcing. Figure 2 shows some examples of strong, non-storm current profiles measured in various sites around the world. Note the complex profiles. This paper describes a technique to develop more realistic current profiles with two techniques used in sequence: empirical orthogonal functions (EOF) followed by the inverse First Order Reliability Method (FORM). EOFs are used to reduce a vertical profile into a small number of values, called modes. These are analyzed by the inverse FORM to develop design currents of a specified recurrence interval. Once the EOF procedure has been used to reduce the data to a few characteristic modes, we apply the inverse FORM to the modal components to derive currents at specified recurrence intervals. The inverse FORM is an elegant way to develop loads from multiple inputs that may be statistically dependent In our case, the inputs correspond to the dominantmodes derived from the EOF.

Application of principal component analysis (PCA) and improved joint probability distributions to the inverse first-order reliability method (I-FORM) for predicting extreme sea states

Chinese-French Oceanography Satellite (CFOSAT), the first satellite which can observe global ocean wave and wind synchronously, was successfully launched On 29 October 2018. The CFOSAT carries SWIM that can observe ocean wave on a global scale. Based on National Data Buoy Center (NDBC) buoys and Jason-3 altimeter data, this study evaluated the accuracy of L2 level products of CFOSAT SWIM from August 2019 to September 2020. The results show that the accuracy of the nadir Significant Wave Height (SWH) data of the SWIM wave spectrometer is good. Compared with the data of the NDBC buoys and Jason-3 altimeter, the RMSE of the nadir box SWH were 0.39 and 0.21 m, respectively. The variation trend of SWH were first increasing and then decreasing with the increasing of the wave height. The precision of off-nadir wave spectrum SWH is not better than nadir box SWH data. Accuracy was evaluated for off-nadir data from August 2019 to June 2020 and after June 2020, respectively. After linear regression correction, the accuracy of off-nadir wave spectrum SWH was improved. The data accuracy evaluation and comparison of different time period showed that the off-nadir wave spectrum SWH accuracy was improved after the data version was updated in June 2020, especially for 6° and 8° wave spectrum. The precision of off-nadir wave spectrum SWH decreases with the increasing of wave height. The accuracy of the dominant wave direction of each wave spectrum is also not very good, and the accuracy of the dominant wave direction of 10° wave spectrum is slightly better than the others. In general, the accuracy of SWIM nadir beam SWH data reaches the high data accuracy of traditional altimeter, while the accuracy of off-nadir wave spectrum SWH is less than that of nadir beam SWH data. The off-nadir SWH data accuracy after June 2020 has been greatly improved.

On environmental contours for marine and coastal design

Nonlinear time-domain simulations are often used to predict the structural response at the design stage to ensure the acceptable operation and/or survival of floating structures under extreme conditions. An environmental contour (EC) is commonly employed to identify critical sea states that serve as the input for numerical simulations to assess the safety and performance of marine structures. In many studies, marginal and conditional distributions are defined to construct bivariate joint probability distributions for variables, such as significant wave height and zero-crossing period. Then, ECs can be constructed using the inverse first-order reliability method (IFORM). This study adopts alternative models to describe the generalized dependence structure between environmental variables using copulas and discusses the Nataf transformation as a special case. ECs are constructed using measured wave data from moored buoys. Derived design loads are applied on a semisubmersible platform to assess possible differences. In addition, a linear interpolation scheme is utilized to establish a parametric model using short-term extreme tension distribution parameters and wave data, and the long-term tension response is estimated using Monte Carlo simulation. A 3D IFORM-based approach, in which the short-term extreme response that is ignored in the EC approach is used as the third variable, is proposed to help establish accurate design loads with increased accuracy. Results offer a clear illustration of the extreme responses of floating structures based on different models.

Marine operations are a significant expense for offshore wind farms, representing up to one third of total project costs. An improved understanding of the variation of met-ocean conditions across a wind farm site offers the potential to reduce weather downtime and associated costs. This work employs a machine learning approach utilising a surrogate wave model trained on the relationship between the wave conditions at discrete measurement locations to wave conditions across the entire model domain. The surrogate model can then be run with real-time data inputs from the discrete measurement locations to provide a spatial dataset for waves, without the high computational power needed to run the physics-based wave model itself. This new method enhances the accessibility of met-ocean data to allow more informed decision making for the installation, operation, and maintenance of offshore wind farms. The approach has already proven successful with fixed measurement buoys, and work is ongoing to adapt the modelling framework to use satellite-derived wave data as an input. With freely available global coverage, satellite data is a useful complementary data source to wave buoy data. Several Earth Observation satellite missions host radar altimeters that report significant wave height along the satellite’s ground track. The first step towards utilising radar altimeter data with the machine learning framework is assessing the impact of using only significant wave height data as measurement inputs. This paper compares the model outputs from running the model with wave height, period, and direction data, and with wave height data only. The results show that running the model with wave height data only produces a small reduction in the accuracy of output wave predictions in coastal areas.