September 28 2019 0Comment

Pandora’s box: Hs & Tp

Let me start this post with the statement that I’m not an oceanographer nor a meteorologist. I’m an engineer with a background in hydrodynamics, who rely strongly on input from the ocean side. So I might cut a few corners here and there. In this post I would look like to bring up what is being overlooked due to the way we look at waves in offshore operations for decision making.

It is common to describe a sea state with a significant wave height (Hs), peak period (Tp) and main direction. Weather forecasts present these parameters, often split into a wind and swell component. Forecasts are used to determine if an operation may be performed within set limits to ensure safe execution, so implicitly a forecast addresses the expected motions of the vessel in said waves. Hence these parameters play an important role in any offshore or shipping operation.

The wave parameters are derived from the underlying 2D wave spectra and only give a rough estimate of the actual conditions. The models that forecasting companies use produce 2D wave spectra as raw output. In the figure below an example is given of an actual sea state. You can see two wave systems, a wind and swell sea.

The main advantage of working with a limited set of wave parameters is that it is simple. The significant wave height can be validated by looking out the window, and the peak period can be estimated by counting the waves. However, there are also significant drawbacks.

First of all, it may be too simple. Ships can be very sensitive to certain wave periods. For example, the roll motions for a 1m wave (RAO) at various periods is given below for beam seas. At a wave period of 7s we expect 1 degree of roll, but in 11s waves we can expect almost 13 degrees of roll. There might be a swell with a very low significant wave height left out of the forecast, that is causing such high roll motions that operations cannot commence. Often engineering does not consider multiple wave systems due to the increasing number of load cases. So there simply are no limits for combined sea states.

The wave parameters from a forecast do not consider the spreading of energy. For a wind driven sea energy can be spread up to 180 degrees in a developing sea state. In the example figure, the wind sea is spread over 150 degrees. This has a significant effect on ship motions. Below in the right figure, the difference between a unidirectional spectrum and a spectrum with wave spreading is shown by comparing the heave response for both cases. Sometimes the motion is 25% higher or lower. This is a big difference. Same for a one second difference in the peak period, which can also lead up to significant differences in response. And we haven’t touched the occurrence of multiple wave systems yet, nor a different spectral shape than the assumed JONSWAP (or other parameterized spectra).

There has been a lot of work perfomed into improving forecasting of the significant wave height. However, forecasting (and measuring) of the peak period can be very tricky. This can be seen in the validation performed by ECMWF below (link). On the left the significant wave height measured with a buoy is shown to model output. I believe it’s the nowcast data. In the figure to the right the peak period validation is shown. It is immediately clear that the trend is much less defined here. When we compare that to how sensitive a vessel is for peak periods, this is not what we would like to see.

Further, it is not straight forward to measure the ocean surface. Often one of two methods is applied: a wave buoy or radar. They don’t always agree with each other, which means that getting actual observations can be difficult. It’s much more straight forward to measure the vessel motions with one or more MRUs.

To get a better understanding of the expected behavior of the vessel, it is much better to relate vessel motions with 2D spectra, instead of having an additional step of simplifying the data to wave parameters. For many operations it is possible to forecast the ship response directly with 2D spectra. The spreading in wave energy, spectral shape and various wave systems are all automatically included. Furthermore, monitoring is simpler as well. There’s no need to deploy a buoy because the accuracy of available vessel MRUs is very good.

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