I trying to find a computing algorithm for the Significant wave height $H_{1/3}$, or $H_\text{s}$ or $H_\text{sig}$ in the time domain. This is defined as the average height of the one-third part of the measured waves—which are $N$ in number—having the largest wave heights:

$$ H_{1/3} = \frac{1}{\frac13 N} \sum_{m=1}^{\frac13 N} H_m $$

For an example set consider $\{100,300,400,400, ..\}$ of height values $H_m$.

| cite | improve this question | | | | |
  • $\begingroup$ Hi, welcome on SciComp. If I understand your question, you just have to evaluate your formula, provided that the set $\{H_m\}$ is ordered for decreasing $H_m$, i.e $H_1 \geq H_2 \geq H_3 \geq \ldots \geq H_N$. $\endgroup$ – Stefano M Sep 6 '13 at 22:14

Significant wave height, $H_{1/3}$, defined as the average height of the highest one-third of all waves, is historical. In the early days, the wave state was observed visually, which resulted in this definition of $H_{1/3}$. This quantity is not necessarily equal to the contemporary notion of significant wave height, $H_{s}$, which is defined as:

$$ H_{s} = 4 \sqrt{m_0}, $$ where $m_{0}$ is the zero-order moment of the wave variance spectrum:

$$ m_0 = \int{F(f)}\ df = <\!\eta^2\!\!>. $$

$\eta$ is the surface elevation, and $<\!\eta^2\!\!>$ is the time average of the surface elevation variance.

Though $H_{s} \ne H_{1/3}$, Phillips (1977) shows that $H_{s} \approx H_{1/3}$ for a narrow wave variance spectrum $F(f)$. See Dynamics of The Upper Ocean by Phillips, 1977, Cambridge University Press.

If you have time series of $\eta$, you can then calculate $H_{s}$ from $m_0$ in a straightforward fashion. Keep in mind that $H_{s}$ as an integrated quantity only makes sense for linear (small slope) waves that are quasi-uniform in space and time, i.e. $F(f)$ and $H_s$ are changing over a significantly longer time scale than that of $\eta$.

| cite | improve this answer | | | | |
  • $\begingroup$ Hi @IRO-bot, I'm getting Sea Level values every 10 secs and I want get Hs, H/3 and H/10 every one hour, I was thinking calculate m0 on this way: vitutor.co.uk/estadistica/descriptiva/images/26.gif $\endgroup$ – Goku Sep 9 '13 at 20:52
  • $\begingroup$ Yes, you can calculate $m_0$ that way. The obvious question is over how many samples to average? This depends on your application. To capture the longest swell (i.e. Pacific ocean), 1 minute should suffice. If your data is from the field and not from the lab/tank, I would average over 10 minutes even, as $H_{s}$ typically changes on much longer time scales. $\endgroup$ – milancurcic Sep 9 '13 at 21:37

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.