Water particle velocity in storm sea states

I am looking for a formula to help estimate the water particle velocity in irregular waves specified by Hs and Tp instead of H and T. As a catch, these are 100-year storm waves which are high and steep. I will use the relative velocity to calculate drag on a piling. Can you point me to a reference or common rule of thumb for the water particle velocity?

 

There are two different things going on in your question, one is the spectral development of an irregular seaway and the second is order statistics.
The first can be worked out from any spectral development (Bretschneirer, JONSWAP, Pierson-Moskowitz, etc.) but I would use an Ochi-Hubble 6 parameter development because it more correctly represents a real seaway.
Once you have the spectral development you can then use the wave theory of you choice (I'd use 2nd order Stokes) to develop a spectral density for the velocity you are looking for (x, z, or orbital) at the depth of water you are in.
Once you have the first 5 moments (0 through 4) of that spectra you can then use order statistics to give you the velocity associated with the confidence factor (i.e. 90% of waves do not exceed, 95%, 99%, 99.5%, etc.) for the time period you are considering.
I think I answered a similar question several years ago, so a thread search might be in order.