Day: 5 April 2023

Finding maximums part 2: Why using multiple sea state realizations quickly reveals extreme mooring loads

This is part 2 of an article series on maximum dynamic loads in moorings. Start from part 1 here first.

The maximum load in a severe sea state usually drives a mooring design. It’s common to use a dynamic analysis process and a numerical model of a mooring system to resolve the extreme peak loads. In a time-domain analysis, the mooring loads are calculated in a specific realization of a sea state. But what exactly is a sea state realization?

It’s not always flat calm in the ocean

Most places in the ocean at any given time have many different sizes and frequencies of ocean waves. A compact way to express the sea state is with a wave spectrum. A wave spectrum is like a convenient short-hand that describes how much wave height there is at different frequencies. But a wave spectrum isn’t the same thing as an actual sea state. This is where a sea state realization comes in.

A sea state realization is a fully detailed description of the state of the ocean surface. This is in the form of a complete picture of the water surface height in space and time. Thousands of specific sea state realizations have the same wave spectrum, but each realization is unique in that it has its own differences in surface elevation through space and time. The subtle differences in the water surface are vital to revealing extremes in the analysis of floating systems, like the maximum peak load in a mooring system.

Sea state realizations all have the same spectrum, but they are individually different from each other.

How do sea state realizations reveal extreme mooring loads?

The key is in the subtle differences in the time variation in the water surface. A wave spectrum can give an idea of the general characteristics of the sea surface. But it’s not always clear what rare events in the realization will look like. For example, the maximum distance from a wave trough to the next wave crest is one indication of the worst-case wave height in a specific sea state realization. You can’t know what this worst-case wave will be for a sea state realization by looking at the wave spectrum alone. You also won’t know exactly how a floating system will respond to each worst-case wave. A systematic approach is needed to check how a floating system will react in specific sea state realizations and confirm the resulting dynamic mooring loads. But rather than just checking one very long sea state realization, there are good reasons to use several.

One reason to check multiple sea state realizations is because of variations in the intensity of the water surface

In theory, a well-constructed sea state realization will have a perfect match to the characteristics of its matching wave spectrum. Attributes like the significant wave height and peak period should be identical. But the practical reality is that sea state realizations tend to have some variation in these parameters. One sea state realization might have a slightly higher significant wave height, and another might have a slightly lower one.

Significant wave height is an essential driver of motions and mooring loads, so checking multiple sea state realizations ensures you are aware of a single sea state realization that is less severe than you intend. This is a critical facet in using multiple sea state realizations, but there’s also a practical reason to evaluate multiple sea state realizations.

Another key reason to check multiple sea state realizations is that calculations can be computed in parallel

Calculating one long time series of mooring dynamics can take a while, slowing down the design process while you need to wait for the results to get design feedback. Yet it’s trivial to use multicore computers to calculate the mooring response in different sea state realizations in parallel. Often, shorter simulations in various sea state realizations can be computed much faster than one extended analysis, giving more robust design feedback than a single simulation.

While each simulation may be shorter than a storm duration, it still needs to be long enough individually to capture a meaningful number of extreme peak loads. Comparing the extreme peak loads produced by a mooring in each sea state realization gives you confidence that you have a reasonable peak load to base the design on the mooring.

But how much variation can you have between extreme peak loads?

There isn’t a specific number to use and you need to rely on engineering judgment. The extreme loads from each sea state realization will be different every time. However, the spread between the extreme values should not be too severe. If they are too far apart in magnitude, it’s an indication that your simulations are too short or that there may be severe tension shocks in the mooring response, and some changes may be needed in the design. Typically, for oceanographic mooring design, it makes sense to start by looking at least three sea state realizations to get a good picture of the extreme peak loads.

Example time

Let’s look at more data generated by ProteusDS of the Southern Ocean Flux Station full ocean-depth mooring. This mooring response was calculated in a 9m, 13s wave spectrum. The first plot shows the mooring tension from the first sea state realization. The maximum tension is around 32kN.

Another simulation in ProteusDS with a new realization of the same sea state reveals a different time series of dynamic tension. The peak is just under 30kN.

The third realization shows a peak tension of about 28kN. These load cases were all calculated in parallel on a desktop computer much faster than one long individual simulation. It’s encouraging to see similar maximum peak values across the three realizations, building confidence that the maximum is likely in this range of 30kN. A shorter duration of 500 seconds may even be justified but this is driven by the characteristic peak values that have already come out of the analysis.


A sea state realization is a fully detailed representation of the ocean surface. It’s derived from a wave spectrum and includes a time series of the water surface elevation everywhere in space and time. Thousands of sea state realizations may have the same wave spectrum and statistical characteristics, like the significant wave height. But it’s the specific details and time variation that drive floating systems, and sometimes rare events like a sequence of wave troughs and crests, that affect extreme peak loads. While in theory, sea state realizations should be characteristically the same, they often are slightly more or slightly less intense in terms of significant wave height. With low-cost multicore computing readily available, it’s also easy to run numerical models of moorings in different sea state realizations in parallel. These are both good reasons to check the extreme loads in multiple sea states to find the extreme values faster.

Next step

This is the second article in a series of three on finding extremes in mooring analysis. Read the next and final article in the series that focuses on the effect of a repeating sea surface here.