Question:

How many samples should I use?

Answer:

The number of wave samples depends on the shape of the wave spectrum that you are sampling and the sampling method that you choose to invoke.
The default sampling setting used by SEA is 15 constant-variance samples. This is equivalent to:

SEA /SAMP: 15

Constant variance sampling means each sample captures an equivalent amount of energy of the overall spectrum. The total energy, or variance, of the spectrum is simply the total "area" under the spectral curve. A spectrum with a larger variance represents a seaway with a higher total energy.

When using constant variance sampling, wave samples near the spectral peak will be closer together and samples further from the peak will be more widely spaced. This ensures that the area, or variance, associated with each sample is equivalent, hence the term constant variance. For this reason, constant variance sampling will always create more wave samples near areas of high energy.

Constant variance sampling is very efficient when sampling spectra that have very narrow and/or large peaks. This means you can usually use fewer samples and still effectively sample around the peak of a spectrum. The drawback to constant variance sampling is that it tends to truncate the samples near the low- and high-frequency regions of a spectrum, which are generally of lower energy. Low energy areas are more sparsely sampled when using constant variance sampling.

Alternatively, SEA offers a constant bandwith/frequency range sampling method, where the desired number of samples are evenly spaced (hence constant bandwidth) over a specified frequency range. Invoking this sampling method with 30 samples over a range of 0.1 to 1.5 rad/s looks like:

SEA /SAMP: 30, 0.1, 1.5

Constant bandwidth/frequency range sampling is advantageous when you require control over the sampling range, or need to sample high- or low-frequency areas more densely. However, because constant bandwith sampling places samples at constant intervals, it may not adequately sample narrow peaks. Generally, constant bandwidth sampling requires a larger number of samples.

When choosing a sampling method, use the following guidelines:

Is the spectrum relatively low energy?
If so, consider using the constant bandwidth/frequency range sampling method. If not, consider using the constant variance method.
Does the spectrum have a very narrow or very tall peak?
If so, consider using the constant variance sampling method.
Do you care about the low- or high-frequency wave content?
If yes, consider using a frequency range sampling method to capture all wave frequencies of interest.
Do you want RAOs that span the entire range of wave frequencies?
If yes, consider using a frequency range sampling method over a range of 0.1 to 2.0 rad/s (for example) to ensure all RAOs span a wide frequency range.
Are you using a data file to define the wave spectrum?
If so, sampling is irrelevant! SEA will use each sample from the data file explicitly without resampling.

When selecting the number of samples, use the following guidelines:

Is the spectrum defined using significant wave height?
If so, compare the numerical significant wave height given in the wave components tables to the entered value. If the values match closely, then the spectrum is likely adequately sampled. If not, increase the number of samples and recompute.
Look at the wave spectrum plot in the report file.
The red square data points indicate the discrete wave samples. Imagine these points connected with straight lines: does the straight line representation compare well to the spectrum curve? If the two representations match closely, then the spectrum is likely adequately sampled. If not, increase the number of samples and re-evaluate.
Perform a convergence study on the numerically derived spectrum variance.
The numerically derived spectrum variance is given in the wave components table. As the number of wave samples is increased, the spectrum variance should converge. If increasing the number of wave samples significantly changes the spectrum variance, the number of samples is likely too low. If increasing the number of samples does not result in a significant change, the spectrum is likely adequately sampled.

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