Waves are the dominant environmental load for most offshore and coastal structures, so engineers need to know how waves are observed, described and predicted. This graduate-level course covers observing, describing and analysing ocean surface waves for offshore and coastal engineering applications. It moves from wave measurements, including point measurements and satellite altimetry, to short-term wave statistics and extremes, then to the variance density spectrum and its practical estimation from sampled records using the fast Fourier transform. It develops linear wave theory, including dispersion, phase and group velocity, pressure and particle kinematics, then explains wind-wave generation, growth limits, standard spectral shapes and swell. Finally, it covers coastal wave transformation through shoaling, refraction, diffraction, reflection and radiation stress, with a worked nearshore example tying the methods together.
Course at a glance: Duration 20 hours · Self-paced online · 9 sections, 31 lessons, a 147-page downloadable course book
What you will learn
- Identify the main methods used to observe ocean waves and explain what each method measures.
- Compute short-term wave statistics, including significant wave height and exceedance probabilities.
- Interpret the variance density spectrum and explain when it provides a complete description of a sea state.
- Estimate and critique a wave spectrum from a sampled surface-elevation record.
- Apply linear wave theory to relate surface elevation to dispersion, pressure and particle motion.
- Explain wind-wave generation, growth limits, standard spectra and swell.
- Evaluate shoaling, refraction, diffraction, reflection and radiation stress for coastal engineering.
Inside the course: a high-level summary, section by section.
Observing ocean waves
The course begins with how waves are measured. Point measurements, such as wave buoys, wave staffs and pressure sensors, record the surface elevation at a single location over time. Satellite altimetry is fundamentally different: rather than resolving individual crests and troughs, it estimates a statistical property of the sea state from the shape of the returned radar pulse, which, through the usual narrow-banded relationship, leads to significant wave height over large areas. Understanding what each instrument measures, and its limitations, is the first step in using wave data responsibly. The section closes by showing how surface-elevation traces are turned into statistical descriptions.
Short-term wave statistics
A short-term sea state, lasting from about twenty minutes to a few hours, is treated as stationary: its statistics are constant even though individual waves are random. Zero-up-crossing analysis defines each wave: the period is the time between successive up-crossings, and the height is the vertical distance from crest to trough between them. The resulting heights form a random sample. For a narrow-banded sea, wave heights follow the Rayleigh distribution, which links the spread of wave heights to the variance of the surface elevation. Significant wave height, historically the mean of the highest third of waves, is related to this variance. Short-term extremes describe the probability that a wave height will exceed a threshold during a specified duration, which is the bridge from wave statistics to design events and structural response.
The wave spectrum
Why use a spectrum? The variance density spectrum describes how the variance of the sea surface, and therefore its energy, is distributed over frequency. It does not just list frequencies; it shows how much of the sea’s variability sits near each frequency. The course defines the spectrum carefully and explains the conditions under which it provides a complete statistical description of a sea state, namely a stationary, Gaussian process. Spectral moments, the integrals of the spectrum weighted by powers of frequency, give characteristic wave heights and periods, and they also predict the rate of zero-crossings and the bandwidth of the sea state.
Estimating a spectrum
Practical spectral analysis begins by digitising a continuous record at a suitable sampling interval. The fast Fourier transform converts the time series into frequency components, with frequency resolution set by record length. Aliasing occurs if sampling is too slow to capture high frequencies, while leakage arises from finite record lengths and can be reduced by windowing. Raw spectral estimates are very noisy, so smoothing by averaging segments or neighbouring frequencies is used, trading resolution for statistical reliability. The course emphasises critical evaluation: knowing when a computed spectrum can be trusted.
Linear wave theory
Linear wave theory linearises the governing equations and boundary conditions by assuming small wave amplitude, giving simple sinusoidal solutions. The dispersion relation links wave frequency, wave number and water depth, showing that longer waves travel faster in deep water and that all waves slow down in shallow water. Phase velocity and group velocity are distinguished, with energy travelling at the group velocity. The theory gives expressions for subsurface pressure and particle kinematics, including orbital velocities and accelerations that decay with depth, which are essential inputs for wave loads on structures. The effects of surface tension at very short wavelengths and the limits of linear theory for steep or extreme waves are also discussed.
Wave generation and spectra
Wind generates waves through energy input at the sea surface, while energy is lost through whitecapping, bottom friction and breaking. Growth limits depend on wind speed, fetch and duration: a sea may be fetch-limited, duration-limited or fully developed. The Pierson-Moskowitz spectrum describes a fully developed sea, while the JONSWAP spectrum represents fetch-limited seas with a sharper peak. Swell, waves that have travelled away from their generation area, has a narrow spectrum and long periods, and the course discusses interactions between wind sea and swell and non-linear transfers of energy between frequencies.
Coastal wave transformation
As waves approach the coast, they change. Shoaling alters wave height as water depth decreases and group velocity changes. Refraction bends wave crests as different parts of a wave travel at different speeds in varying depth, and wave rays track these paths. Diffraction spreads wave energy into sheltered regions behind breakwaters and headlands, while reflection from structures and steep beaches can create partially standing waves. Radiation stress describes the excess momentum flux due to waves, which drives wave set-up, set-down and longshore currents. A worked nearshore example combines these processes into a realistic coastal calculation.
How the topics connect
The course follows a logical chain used in real projects: measure the sea, describe it statistically, represent it spectrally, convert the description into water particle motions and pressures with linear theory, understand how the sea was generated and finally transform it to the site of interest. Each stage relies on assumptions, such as stationarity, narrow bandwidth or small amplitude, and the course helps learners recognise when those assumptions are reasonable and when they need to be questioned.
Why this matters in practice
Design wave conditions affect the size, cost and safety of offshore platforms, ships, breakwaters, ports and coastal defences. Engineers who understand how waves are measured and analysed can specify measurement campaigns, interpret metocean reports, choose appropriate spectra and transformation methods and recognise the limitations of wave data and models.
Key takeaways
You leave able to explain wave observation methods, compute short-term statistics, interpret and estimate wave spectra, apply linear wave theory, understand wave generation and evaluate coastal wave transformation processes.
How you study
The course is delivered fully online and is self-paced, so you can fit roughly 20 hours of study around professional commitments. Lessons combine clear explanation with examples, diagrams and short interactive checks, and the main sections end with graded quizzes (7 in total) so you can confirm you can apply each method before moving on. A 147-page course book can be downloaded and printed for offline reading and later reference.
Course contents
- Observing Ocean Waves: Why Observe Waves?; Point Measurements; Satellite Altimetry; From Traces to Statistics
- Short-Term Wave Statistics: Zero-Crossing Waves; Rayleigh Wave Heights; Significant Wave Height; Short-Term Extremes
- Variance Density Spectrum: Why a Spectrum?; Defining S(f); Complete Description Conditions; Spectral Moments and Crossings
- Spectral Analysis of Records: Digitising the Record; Aliasing and Leakage; Smoothing and Reliability
- Linear Wave Theory: Linearising the Problem; Dispersion and Velocities; Pressure and Kinematics; Surface Tension and Extremes
- Wave Generation and Spectra: Wind Input and Dissipation; Growth Limits; PM and JONSWAP; Swell and Interactions
- Coastal Wave Transformation: Shoaling Effects; Refraction and Wave Rays; Diffraction and Reflection; Radiation Stress; Worked Nearshore Example
- Summary: Key Takeaways
Who this course is for
This graduate-level course is for engineering graduates and practising engineers in offshore, coastal, ocean and naval engineering, metocean specialists and researchers who need a rigorous understanding of ocean waves. A background in engineering mathematics, including calculus and basic statistics, is assumed.
Frequently asked questions
How long does Ocean Waves take?
The course is designed for about 20 hours of study. It is self-paced and fully online, so you can spread it over a few weeks or complete it more quickly.
What is covered?
The course is organised into 9 sections with 31 lessons, moving from foundations to applied methods, as summarised above.
Is there material to keep after the course?
Yes. A downloadable 147-page course book accompanies the lessons for offline reading and later reference.
How is progress checked?
Each main section closes with a graded quiz (7 in total). The quizzes test understanding of the concepts and methods explained in the lessons rather than memorisation, and you can review the relevant lessons before attempting them.
Can I record this study for my own professional development?
Yes. The course notebook includes a self-assessment of the course objectives before and after study, a reflection page and a learning log, which you can use to keep your own record of professional development.
Duration: 20 hours
Related courses: D04 – Physical Oceanography; D05 – Offshore Hydromechanics; D01 – Offshore Engineering Fundamentals; A04 – Project Introduction to Hydromechanics
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Study at your own pace and work through the full course material, worked examples and section quizzes. Enrol in D03 – Ocean Waves →
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