Kevin Ewans

Propagating waves on the ocean surface can be represented as a stochastic process whose statistics are characterized by a spectrum. This paper reviews methods for measuring the wave spectrum and related quantities. Observations begin by sensing fluid dynamical properties of the sea surface over space and/or time. Visual observations, collected routinely since the mid‐18th century, comprise the longest‐running wave record. Nearshore measurement methods continue to advance, including traditional pressure and acoustic sensing as well as newer technologies like distributed acoustic sensing and LiDAR. Detailed small‐scale wave physics can now be explored with measurement techniques using light, including stereo‐imaging and polarimetry. Reductions in the size, cost, and power consumption of microelectronics have propagated through ocean wave instrumentation, most notably in wave buoys. Global networks of freely drifting miniature wave buoys offer novel observational capabilities. Remote sensing techniques based on radar and LiDAR continue to evolve and are widely deployed from land, ships, aircraft, autonomous vehicles, and satellites. Spaceborne altimeters form one of the most important records of wave height, and new spaceborne sensors now observe directional spectra globally with sampling akin to traditional altimetry. Aircraft and autonomous systems provide strategic sampling capabilities for detailed process studies and access to extreme storm environments. The quality and quantity of ocean wave measurements have never been greater. This review aims to help make sense of it all.

The specification of design wave spectra is based on spectral parameters estimated from available wave data. Measured data allow high-resolution estimates to be made, but they suffer from sampling variability and often do not contain a sufficient number of measurements in extreme sea states. Hindcast data can be used to examine spectral features associated with extreme sea states, but they can be limited by resolution and are dependent on how the physics are incorporated in the source terms of the wave model. We examine and compare the effects of estimating JONSWAP spectrum peak enhancement factor from measured and hindcast data for a range of sea states but particularly those with large significant wave heights. In the case of measured data, we build on earlier work and review effects associated with different methods for processing measured time series data, including the effect of sampling frequency, record length, and smoothing. These are then contrasted with estimates made from typical hindcast data, including the effect of the spectral shape associated with different source terms — in particular the four-wave interaction term. Finally, we provide recommendations on how best to estimate the peak enhancement factor of the JONSWAP spectrum for design purposes.

Offshore wave conditions can be measured using wave buoys, which are generally designed for wind waves. Longer waves (swell or bound second-order waves) are very relevant for certain maritime structures. The accuracy of the instrumentation in a typical wave buoy in long and short waves was therefore studied, and it was investigated if the buoy can be applied in longer waves. A Waverider buoy was placed on a hexapod, which applied regular and irregular prescribed motions in multiple degrees of freedom. The hydrodynamic response of the buoy in waves and the effect of its mooring system were not evaluated; the buoy was assumed to follow the orbital motions of a wave and to rotate with its slope. The tests showed that the buoy sensors measure accelerations and rotations with periods between 1.5 and 35 s very well. Vertical displacements derived from the accelerations by the buoy are accurate for the period range of 2 to 20 s. In longer waves, the motions are significantly underestimated, even though the accelerations are accurately measured. This will not lead to large errors in normal operation, as the energy of such long waves is generally low. This explains why the buoy also performs well when it is subjected to irregular motions (less than 2% error in the significant wave height of a half-hour measurement in realistic irregular sea states with peak periods between 5 and 20 s can be expected). It can be concluded that the buoy accurately measures accelerations. The accuracy of the derived displacements decreases when very long swell wave energy (> 20 s) is present. Review of the internal integration procedure may be considered when there is a specific interest in measuring longer waves.

A spectral description of the wave spectrum is usually required in the design of offshore structures, and a generalised form of the JONSWAP spectrum is often used. The JONSWAP spectrum involves parameters that allow flexibility in the specification of the spectral peak, which is important for the response of both fixed and floating structures, but particularly for the floating structures. The peak of the wave spectrum is also important in nonlinear effects that for example contribute to the probability of a large crest occurring in a sea state time series realisation in a model basin, used to test a design platform. There has been a number of studies focused on the uncertainties of JONSWAP parameter estimates. We review these to establish an overview of the present understanding of the uncertainties, and we undertake further analyses to investigate the sensitivity of the uncertainties to the method of analysis and the types of data typically available for analysis, including both time series and spectral data.

WaveRadar REX (SAAB) instruments are widely used in the offshore oil and gas industry for wave, tide and air gap observations. This study extends the application of WaveRadar REX to the estimation of storm surge and reservoir subsidence from long-term water level measurements. AirGap data from several offshore fixed steel platforms offshore Borneo island (South China Sea) were analysed, yielding waves, astronomical tides, Sea Surface Anomalies (SLAs), which included storm surge and changes to water level due to long-term climate variability. Vertical platform movements, which can be attributed to reservoir subsidence and Vertical Land movements, were also derived. The storm surge estimates were consistent with values reported for the region, with positive storm surge (+0.3m) peaking in November and December, at the onset of winter western North Pacific Monsoon and northeasterly winds; negative storm surges (-0.2m) were recorded from March to July, coinciding with the boreal summer East Asian Summer Monsoon and southwesterly winds. Locations further offshore showed marginally lower storm surge compared to the coastal stations. Along the coast of Borneo, there was a shift in the timing of the positive storm surge arrival offshore Sabah, with establishment of positive storm surge shifted forward by about a month. Lastly, trends of SLAs derived from WaveRadar REX AirGap can be used to monitor long-term Vertical Land Movements and offshore platform subsidence. The comparison of AirGap subsidence estimates against independent dGPS measurements of vertical platform movement showed excellent agreement for several offshore platforms, all results within 0.05m accuracy. The new technique offers a cheap and reliable method of continuous vertical subsidence monitoring of fixed offshore platforms using instrumentation routinely installed offshore, thus offering an alternative to dGPS subsidence monitoring.

Modelling rare or extreme events is critical in many domains, including financial risk, computer security breach, network outage, corrosion and fouling, manufacturing quality and environmental extremes such as floods, snowfalls, heat-waves, seismic hazards and meteorological-oceanographic events like extra-tropical storms, hurricanes and typhoons. Statistical modelling enables us to understand extremes and design mechanisms to prevent their occurrence and manage their impact. Extreme events are challenging to characterise as they are, by definition, rare and unusual even in a big data world. The frequency and extent of extreme events is typically driven by both primary attributes (dependent variables) and secondary attributes (independent variables or covariates). Studies have shown that improved inference can be gained from including covariate effects in predictive models but this inclusion comes at a heavy computation cost. In this paper, we present a framework for risk estimation from extreme events that are non-stationary, i.e., they are dependent on multi-dimensional covariates. The approach is illustrated by estimation of offshore structural design criteria in a storm environment non-stationary with respect to storm direction, season and geographic location. The framework allows consistent assessment of structural reliability with thorough uncertainty quantification. The model facilitates estimation of risk for any combination of covariates, which can be exploited for improved understanding and ultimately optimal marine structural design. The computational burden incurred is large, especially since thorough uncertainty quantification is incorporated, but manageable using slick algorithms for linear algebraic manipulations and high-performance computing.