Uncertainties in extreme value modelling of wave data in a climate change perspective

J. Ocean Eng. Mar. Energy (2015) 1:339–359 DOI 10.1007/s40722-015-0025-3 RESEARCH ARTICLE Uncertainties in extreme value modelling of wave data in a climate change perspective Erik Vanem1 Received: 13 February 2015 / Accepted: 15 April 2015 / Published online: 8 May 2015 © Springer International Publishing AG 2015 Abstract The extreme values of wave climate data are of great interest in a number of different applications, including the design and operation of ships and offshore structures, marine energy generation, aquaculture and coastal installations. Typically, the return values of certain met-ocean parameters such as significant wave height are of particular importance. In a climate change perspective, projections of such return values to a future climate are of great importance for risk management and adaptation purposes. However, there are various ways of estimating the required return values, which introduce additional uncertainties in extreme weather and climate variables pertaining to both current and future climates. Many of these approaches are investigated in this paper by applying different methods to particular data sets of significant wave height, corresponding to the historic climate and two future projections of the climate assuming different forcing scenarios. In this way, the uncertainty due to the extreme value analysis can also be compared to the uncertainty due to a changing climate. The different approaches that are considered in this paper are the initial distribution approach, the block maxima approach, the peak over threshold approach and the average conditional exceedance rate method. Furthermore, the effect of different modelling choices within each of the approaches will be explored. Thus, a range of different return value estimates for the different data sets is obtained. This exercise reveals that the uncertainty due to the extreme value analysis method is notable and, as expected, the variability of the estimates increases for higher return periods. Moreover, even though the variability due to the extreme value analysis is greater than the climate variability, a shift towards higher extremes in a future wave climate B Erik Vanem 1 DNV-GL Strategic Research and Innovation, Høvik, Norway can clearly be discerned in the particular datasets that have been analysed. Keywords Ocean and coastal engineering · Wave climate · Extreme value analysis · Climate change · Significant wave height · Environmental loads 1 Introduction Extreme value analysis of wave climate parameters is an important part of ocean and coastal engineering where the extreme loads from extreme environmental conditions need to be taken into account. However, there are large uncertainties associated with extreme value analyses, and the uncertainties generally increase for higher return periods. Ideally, time series that are long compared to the desired return periods should be available to reliably extract return values. In practice, however, the opposite is true and return values corresponding to return periods much longer than the length of recorded data are needed. Therefore, there is a need to extrapolate to obtain estimates of the tail behaviour of the underlying statistical distributions. Intuitively, the further away from the data one has to extrapolate, the larger the uncertainties of the resulting estimates will be. As a rule of thumb, for example, the ISO standard ISO 19901-1 (ISO 2005) recommends to not use return periods more than a factor of four beyond the length of the data set when deriving return values for design of offshore structures. Hence, for the datasets analysed in this paper, covering a period of 30 years, the longest return periods that should be investigated are 120 years. Adhering to this rule of thumb, return values for 20- and 100-year return periods will be estimated in this paper. 123 340 There are a number of different approaches to extreme value analysis and return value estimation, which all rely on a set of assumptions. The initial distribution approach fits a statistical model to all the data under the assumption of independent and identically distributed (iid) observations and estimate high return values by extrapolating the fitted distribution to high quantiles corresponding to the desired return periods. However, one fundamental problem with this approach is that most of the data used to fit the model will lie near the mode of the distribution and hence quite remote from the tail area of interest. As a consequence, such models will typically often be able to capture the area close to the mode of the distribution quite well, but may give poor fit to the tail of the distribution. Another source of uncertainty encountered with this approach, as indeed with all statistical model fits, is the fitting procedures. Even after having selected a parametric model to fit to the data, there are several methods to estimate the model parameters, such as the maximum likelihood, the method of moments, the least squares method and other approaches. Some methods for the initial distribution approach will be investigated in this paper and compared to other means of estimating extreme values. Some of the classical approaches to extreme value analysis rely on assumptions on the asymptotic behaviour of the extremes as the number of observations approaches infinity. These methods will typically also assume that the data are iid, i.e. that the observations are realizations from the same stationary process and can be construed as independent samples drawn from the same probability distribution. Two commonly used approaches to extreme value analysis are the block maxima (BM) approach and the peaks over threshold (POT) approach. An obvious drawback with these approaches is that they are wasteful and only exploits a small subset of all the data available. As will be demonstrated in this study, this also significantly increases the statistical uncertainty of the resulting return value estimates. An introduction to these methods, along with a general introduction to the theory behind extreme value analysis, can be found in Coles (2001). Both the block maxima approach and the POT method will be explored in this paper. Recent applications of the POT approach to analyse the extremes of ocean waves are presented in e.g. Caires and Sterl (2005) and Thevasiyani and Perera (2014). A more recent method for extreme value analysis that allows for the assumptions of independence to be relaxed is proposed in Naess and Gaidai (2009), i.e. the average conditional exceedance rate method (ACER). It was initially proposed only for the asymptotic Gumbel case, but was later extended to apply in more general cases (Naess et al. 2013). A further generalization to the bivariate case has also been presented in Naess and Karpa (2013). In the study presented in this paper, the univariate ACER approach will be applied 123 J. Ocean Eng. Mar. Energy (2015) 1:339–359 and compar (...truncated)