Detection of changes in the characteristics of oceanographic time-series using changepoint analysis.

Changepoint analysis is used to detect changes in variability within GOMOS hindcast time-series for significant wave heights of storm peak events across the Gulf of Mexico for the period 1900–2005. To detect a change in variance, the two-step procedure consists of (1) validating model assumptions per geographic location, followed by (2) application of a penalized likelihood changepoint algorithm. Results suggest that the most important changes in time-series variance occur in 1916 and 1933 at small clusters of boundary locations at which, in general, the variance reduces. No post-war changepoints are detected. The changepoint procedure can be readily applied to other environmental time-series

Estimating the parameters of ocean wave spectra

Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when modelling structural response or other engineering concerns. Therefore, accurate and precise recovery of the parameters of such a form, from observed wave records, is important. Current techniques are known to struggle with recovering certain parameters, especially the peak enhancement factor and spectral tail decay. We introduce an approach from the statistical literature, known as the de-biased Whittle likelihood, and address some practical concerns regarding its implementation in the context of wind-generated waves. We demonstrate, through numerical simulation, that the de-biased Whittle likelihood outperforms current techniques, such as least squares fitting, both in terms of accuracy and precision of the recovered parameters. We also provide a method for estimating the uncertainty of parameter estimates. We perform an example analysis on a data-set recorded off the coast of New Zealand, to illustrate some of the extra practical concerns that arise when estimating the parameters of spectra from observed data

A multivariate pseudo-likelihood approach to estimating directional ocean wave models

Ocean buoy data in the form of high frequency multivariate time series are routinely recorded at many locations in the world's oceans. Such data can be used to characterise the ocean wavefield, which is important for numerous socio-economic and scientific reasons. This characterisation is typically achieved by modelling the frequency-direction spectrum, which decomposes spatiotemporal variability by both frequency and direction. State-of-the-art methods for estimating the parameters of such models do not make use of the full spatiotemporal content of the buoy observations due to unnecessary assumptions and smoothing steps. We explain how the multivariate debiased Whittle likelihood can be used to jointly estimate all parameters of such frequency-direction spectra directly from the recorded time series. When applied to North Sea buoy data, debiased Whittle likelihood inference reveals smooth evolution of spectral parameters over time. We discuss challenging practical issues including model misspecification, and provide guidelines for future application of the method

Uncertainties in estimating the effect of climate change on 100-year return value for significant wave height

The process of estimating the effect of a changing climate on the severity of future ocean storms is plagued by large uncertainties; for safe design and operation of offshore structures, it is nevertheless important that best possible estimates of climate effects is made given the available data. We explore the variability in estimates of 100-year return value of significant wave height ( H S ), and changes in estimates over a period of time, for output of WAVEWATCH-III models from 7 representative Coupled Model Intercomparison Project (CMIP) Phase 5 General Circulation Models (GCMs), and the FIO-ESM v2.0 CMIP Phase 6 GCM. Non-stationary extreme value analysis of peaks-over-threshold and block maxima using Bayesian inference provide posterior estimates of return values as a function of time; MATLAB software for the extreme value analysis is provided. Best overall estimates for return values, and changes in return value over the period 1979-2100, are calculated by averaging estimates for individual GCMs. We focus attention on neighbourhoods of locations east of Madagascar and south of Australia where a previous study of CMIP5-derived output reported significant decrease and increase in H S respectively, under Representative Concentration Pathway (RCP) scenarios RCP4.5 and RCP8.5. There is large variation between return value estimates from different GCMs, and with longitude and latitude within each neighbourhood for estimates based on samples corresponding to ≤ 165 years of model output; these sources of uncertainty tend to be larger than those due to typical modelling choices (such as choice of threshold for peaks over threshold, or block length for block maxima). However, we also find that careful threshold choice and block length are critical east of Madagascar, because of the presence of a mixed population of storms there. Nevertheless, there is general evidence supporting the trends reported by others, but these findings are conditional on the choice of 8 GCMs being representative of climate evolution. We use simple randomisation testing to identify “significant” departures from steady climate. The long 700-year pre-industrial control (piControl) output of the CMIP6 GCM offers an excellent opportunity to quantify the apparent inherent variability in return value as a function of time, estimated using a subsample of output corresponding to a continuous time interval of between 20 and 160 years in length, where no climate forcing is present. We find large variation in return value estimates of approximately ± 15 % made from samples corresponding to periods of time of around 50 years drawn from piControl data

Wave instability in finite depths

Waves in finite-depth and shallow water represent an important and challenging research topic, both from practical and academic perspective. Most of practical applications related to the ocean are conducted in coastal areas, but most of research attention has been dedicated to the surface waves in deep water. Shallow areas are effectively a different physical environment, where wave kinematics change, waves become steeper and consequently more nonlinear but less or non-dispersive, and as a result their nonlinear behaviors change dramatically, waves directly interact with the bottom, in a number of different ways, and most importantly release their energy and momentum through intensive and extensive breaking. In the paper, modulational instability in finite depths will be discussed. This mechanism is regarded responsible for rogue waves, and hence extreme wave heights in deep water. Extreme wave heights are a key design criterion for the ocean industry, including shallow environments too. It is believed, however, that wave breaking rather than wave instabilities is the primary mechanism that controls the maximum possible wave height in depth-limited environments. Here, data of the LoWish JIP will be used in order to identify the criteria for transition from modulational instability being active in the deep-water environments to being suppressed in the shallow waters

Statistics of extreme ocean environments: Non-stationary inference for directionality and other covariate effects

Numerous approaches are proposed in the literature for non-stationarity marginal extreme value inference, including different model parameterisations with respect to covariate, and different inference schemes. The objective of this paper is to compare some of these procedures critically. We generate sample realisations from generalised Pareto distributions, the parameters of which are smooth functions of a single smooth periodic covariate, specified to reflect the characteristics of actual samples from the tail of the distribution of significant wave height with direction, considered in the literature in the recent past. We estimate extreme values models (a) using Constant, Fourier, B-spline and Gaussian Process parameterisations for the functional forms of generalised Pareto shape and (adjusted) scale with respect to covariate and (b) maximum likelihood and Bayesian inference procedures. We evaluate the relative quality of inferences by estimating return value distributions for the response corresponding to a time period of 10× the (assumed) period of the original sample, and compare estimated return values distributions with the truth using Kullback–Leibler, Cramer–von Mises and Kolmogorov–Smirnov statistics. We find that Spline and Gaussian Process parameterisations, estimated by Markov chain Monte Carlo inference using the mMALA algorithm, perform equally well in terms of quality of inference and computational efficiency, and generally perform better than alternatives in those respects

On the Functionality of Radar and Laser Ocean Wave Sensors

Ocean wave design criteria are required for the design of offshore platforms and floating systems, which are derived using in situ measurements. However, there is uncertainty regarding the performance of the instruments used for the in situ measurements. The main instruments used by the offshore industry are the Datawell Directional Waverider buoy and Rosemount WaveRadar, with Laser instruments also having been used for specific studies. Recent reports indicate measurements from these three instruments differ in the order of 10% but given the quite disparate nature of the measurements made by these instruments, it is far from clear what the source of this difference is. This paper investigates the wave measurement principles of Radar and Laser instruments using linear wave field simulations to better understand how the instruments perform. The Radar and Laser simulations include modeling electromagnetic signal beam reflections from water surfaces of an area equal to their footprint sizes, considering their beam characteristics and antenna pattern. The study confirms that the Radar underestimates spectral levels at frequencies above 0.5 Hz due to its significantly larger footprint at the water sea surface compared to the Laser (5.25 m vs. 0.15 m). The Laser performs well for almost the entire frequency range for all the cases considered