Finding maximums part 3: How a repeating sea surface hides extreme mooring loads

This is part 3 of an article series on maximum dynamic loads in moorings. If you haven’t seen it yet, start from part 1 here first.

Mooring design is often driven by the maximum load in a severe sea state. 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. A critical mistake to avoid is a repeating sea surface in the sea state realization. But what does this mean exactly and how does a repeating sea surface happen?

Southern Ocean Flux Station (SOFS) full ocean depth buoy recovered after over a year at sea in 4km deep water near Tasmania. With an average sea state of 4m significant wave height, often reaching 10m significant wave height and higher, peak loads are important to understand and anticipate. Picture credit: Peter Jansen from CSIRO / IMOS / Marine National Facility

A repeating sea surface what happens when there isn’t enough detail in the sea state realization

In a time domain analysis, this looks like a pattern of water surface that repeats itself over time. How often it repeats depends on how much detail is in the sea state realization. A sea state realization is formed by superimposing a finite number of sinusoidal ocean waves. Each sinusoidal wave segment has its own period with an associated height governed by the representative wave spectrum. The problem with a repeating wave surface is when there aren’t enough wave segments to represent the sea surface. Consider, in the absolute worst case, a sea state realization of a wave spectrum using only a single ocean wave segment: it will have a repeating sea surface after one wave period! The effect of this repetition can mean a disaster for mooring analysis.

The problem is that a repeating sea surface fools you into a false sense of security

A repeating sea surface causes a repeating mooring load response. No matter how long you run the analysis, you still get the same repeating tension. A consequence is that you are missing an accurate representation of the extreme values of the mooring response. You might think you’ve captured a reasonable maximum dynamic mooring history by checking it with a long simulation time and multiple sea state realizations. But in reality, you’ve just been looking at the results of a repeating pattern over and over. You can miss a lot of detail in the system’s dynamics, and there’s a risk you can underestimate the maximum loads. In this way, the repeating sea surface hides the extreme values from you.

How can you tell you have a repeating sea surface?

It’s difficult to tell in a systematic way, but often looking at a time history of the sea surface and the mooring tensions, it can become evident with some experience. If you see a repeating pattern of groups of peaks, there’s a good chance that you may have a repeating sea surface. A repeating pattern may be evident in the motion or mooring tension, too. But how can you avoid the problem of a repeating sea surface?

The key is in having enough detail in your sea state realization. You need enough individual wave segments to have a healthy representation of the sea state spectrum without repetition. Building up experience and visually checking your sea surface and mooring response is essential to look for telltale signs of a repeating signal.

But why not use thousands of wave segments in all sea state realizations?

The practical consideration is that the computational burden increases with wave segments. The sea state surface and water particle velocities and accelerations are all the result of contributions from every wave segment that’s included in the sea state. In turn, these physical parameters are all factors in the forcing of a floating system and its mooring. So with the number of wave segments used, the computational burden goes up, and the analysis speed goes down. A careful balance is needed to get enough detail for a realistic design process without slowing the entire process down too much.

It’s time for an example

Let’s look at more data generated by ProteusDS of the Southern Ocean Flux Station (SOFS) full ocean-depth mooring. This mooring response was calculated in a 9m, 13s wave spectrum. The sea state realization was constructed using a custom sea state with only 10 wave segments with an anticipated energy repetition of 36 seconds.

Looking at a time series of the sea state realization, you can see a repeating wave pattern, but it looks like it repeats around every 100 seconds.

However, the dynamic mooring tension shows something slightly different. The largest peaks show a repeating pattern and similar shape approximately every 36 seconds. While the sea surface looks like it takes longer to repeat, the most dominant energetic wave pattern is driving the mooring tensions with a repetitive tension at this rate.

The big problem is that these repetitive peaks are not representative of what to expect in a realistic sea state – just like you wouldn’t expect the peak loads from a single sinusoidal ocean wave to realistically reconstruct the dynamic loads of a mooring in an irregular sea state. You can’t rely on results from any statistical extrapolations to estimate maximum tensions over a time period longer than your simulation either. The consequence is that you may drastically overestimate or underestimate the maximum tensions in the mooring because of this uncertainty. This is an effect that can show up in any dynamic analysis tool that generates a time series of sea state realizations.

Note that ProteusDS uses a few tricks to avoid a repeating sea surface even when only a few wave segments are specified. While you may not see a repeating sea surface with only a few wave segments, there still may not be enough detail in the sea state realization to get meaningful maximum values – and again you may significantly under- or overestimate maximum tensions. When you’re looking at a new kind of mooring in a particular sea state, sensitivity studies on the detail in the sea state realization and the resulting mooring and motion peaks may help give you an idea of what works for future reference.


A sea state realization is formed from the superposition of many sinusoidal ocean waves. But beware that you can get a repeating sea surface if you don’t use enough of these wave segments. The problem is that once the sea surface starts repeating, you don’t get any new information from the dynamic response of a floating system and its mooring. You could even be significantly underpredicting the maximum loads. You might think you are capturing a lot of detail in a long simulation or in multiple sea state realizations, but you’re missing important information on the true extreme loads in the system.

Next step

Comparison of measured mooring tensions to dynamic analysis results is always an important validation exercise. The comparison of SOFS mooring measured tensions with ProteusDS results factors in multiple sea state realizations, long-duration simulations, and many wave segments to ensure reliable results. Read more on the detailed comparison of measured peak mooring loads on the SOFS mooring compared to ProteusDS calculations in the oceanographic validation report here.