Dear all,
After years of comparing buoy, model and satellite data, it seems that we need to clarify the WMO definition. ECMWF has this: https://confluence.ecmwf.int/display/WLW/Significant+height+of+combined+wind+waves+and+swell
“Better known as the Significant Wave Height. The significant wave height is defined as 4 times the square root of the integral over all directions and all frequencies of the two-dimensional wave spectrum. The integration is performed over all frequencies up to infinity.” which applies to model and is not even correct: what is the lower bound of the integral? Also, a model can provide a completely local value at t=0 and x=0 of Hs, but how does that relate to measurements in which we use 4 times the standard deviation of the surface elevation? Any measurement will contain group-related fluctuations, which I think must be filtered to make the height “significant”. I touched on this here: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2023JC020832 but I’d be curious to get more opinions and how we may talk to WMO / ECMWF and others for updates in definitions. One detail: should we include IG waves in Hs (I tend to think yes, just like we have wind sea and swell in Hs, and I don’t mind if we also have ship wakes and other transients in there … but we certainly do not want to include time scales to infinity and have the tides in Hs!)
Lower bound for frequency. I have always assumed that Hs is related to wind generated waves, so, I agree with excluding tides. Infra- gravity waves are unclear, but I think I would also exclude them. Would the energy in such waves make much difference to Hs?
Groups. The wave record would show these as modulations of the wave amplitude. So, my initial feeling is that they are part of the wind-wave system and therefore should be included.
However, Hs is a construct, so could be defined in various ways. Agree however, a debate is required.
Ian
Thank you Ian. Agreeing on a lower bound (frequency for time series, wavenumber for spatial sampling) should be relatively easy and a matter of convention.
For frequency/periods:
if we exclude the main peak of the IG waves we can choose anywere between 28 s and 40-50s, with 30 s being a nice and round number, or 0.03 Hz, close to it. That would make things easier.
including IG waves would push this to 200 s or 300 s beyond the usual main IG peak around 100 s… that would also include short tsunamis.
having said that, including IG waves in Hs may be natural for the nearshore, where IG waves actually break. Keeping IG in Hs will only add 1 cm at most in deep water, but right on the beach it can dominate the signal, and not having IG would be like only considering wind sea when swell can be present. Any views from nearshore folks?
I can’t resist sharing this picture from Sheremet et al. (2014, https://doi.org/10.1002/2013GL058880) showing the sea level across a very special surf zone (on a cliff) with the “offshore” sensor in blue and the “nearshore one” in red, they are separated by 30 m horizontally and 6 m vertically.
Hello, for nearshore comparison, we prefere to compare modelled and observed spectra and if we want to look at integrated values, we separate IG from short waves, with a separation at fp(offhore)/2. But the best is to check the spectrum to find the best compromise (spectra that must be calculated for pressure sensors and phase-resolved waves with the same reconstruction method, burst time, etc). And sometimes, Hs from IG are really non negligible !
Héloïse
I was just speaking to someone who was describing the challenge of estimating Hs from along-track measurements, where groups can cause some bias. I believe there may be a corollary in this discussion to the conventions for atmospheric turbulent flux calculation from time series analysis, but I am not aware of similar methods in elevation time (or space) analysis.
For example, in convective conditions, shorter intervals may suffice for flux calculation given the dominance of higher frequency motions driving the flux. In thermal stable conditions, low frequency motion may contribute significantly, but this can be missed or aliased if using a short, discrete averaging window. Anecdotally, I have seen cases akin to the de Carlo & Ardhuin 2023 Figure 3 example, but from a time series analysis perspective. In the flux analysis, we use the covariance ogive and cumulative summation to test, amongst other things, the suitability of the a priori selected time window for spectral averaging. In the aircraft literature, Zhang et al. 2008 (in BLM) and French et al. 2007 (JAS) provide an example of this kind of analysis.
Is there a way to inspect a sample of wave elevations to test what length of averaging interval (time or space) is appropriate to the local state and wave height contributions? From my naive perspective, I think that wind wave groups would want to be included in the calculation of significant wave height, since their generation and scale is locally relevant.
I don’t think it will be feasible to re-define H_S (too historical). It’s poorly defined as is, so trying to define it further would add to the confusion.
For wind-waves, I think we are mostly concerned with the lower frequency bound. Higher bound yields diminishing returns, so it can be assumed +\infty, unless we’re in a model that has a hard f_{max}.
There could be many different height definitions that would be interesting to different people (swell, windsea, all wind waves, IG, tides, all of the above, etc.).
It seems to me that, rather than introducing a new definition, there should be a notation to allow being very specific about what we mean.
This could be, e.g. H_{0.04-\infty} for wind-waves, H_{0.003-0.03} for IG (don’t quote me on the exact bound values), and similar. But it allows you to use any bounds you need. It’s verbose, but being specific usually comes with verbosity. It may very well be that people have already used this in papers; I can’t think of any from the top of my head though.
Thanks Milan, that is indeed a nice proposition. Some people have been using H_10 (how do you type equations in here ?) for f < 0.1 Hz, so that is a nice generalization.
Now, about the group-resolving or not: should we take the fluctuations of “SWH” as part of the variations of the significant wave height, or should we consider that these are random fluctuations around a true significant wave height?
My take is that in this plot the significant wave height is Hs = 2a , and the fluctuating measurements (here from 0.1 to 1.6 Hs) are some approximation of it.
Thanks for bringing this up Fabrice, really interesting discussion. I think we can and should have it both ways. The WMO should use a definition with specific integral bounds, and enforce this as a standard for operational oceanography. For research purposes, we should instead adopt Milan’s notation that specifies the bounds. And colloquially, we all still talking about Significant Wave Height.
This discussion brought to mind a related discrepancy in the literature on short term statistics. In some papers, individual wave heights are normalized by H1/3 and in others Hm0 (from the spectral integral). There is typically 5% difference between these two definitions (e.g. Longuet-Higgins, 1980).
Hs (from standard deviation of time series) is usually very similar to Hm0, but there can be differences. When you window a time series you rescale the spectra accounting for the missing variance. If the stats of the time series in the window do not exactly match the stats of the bulk of the time series, then rescaling might not match the variance of the time series. Even with stationary data small, random differences occur because of finite length records. If data are not stationary for the length considered, then of course the difference will be larger. And at some point we are violating the terms and conditions of spectral analysis.
Not sure about the question of groups and Hs. I think you already approached it the right way in the paper, by thinking about what are the measurements for. If we want to understand how our phase-averge model is performing, then maybe we don’t want to include the group contribution. If there is a platform, and we want to know whether or not to evacuate, I would think the group modulations are important to include.
ref.
Longuet‐Higgins, M.S., 1980. On the distribution of the heights of sea waves: Some effects of nonlinearity and finite band width. Journal of Geophysical Research: Oceans, 85(C3), pp.1519-1523.
Great. From now on I’ll use the Hs notation as suggested by Milan.
For the groups, yes, one side of the issue is the validation / comparison / assimilation in phase-averaged models. I would also like to get some feedback for people that do statistics: if you do not smooth out the groups , and try to predict a Hmax , does the max of all the Hmax gets bigger ? (I do not know if I make sense … )
We use this to encode our original grib1 parameters of the significant wave height between a set of period bands (10-12, 12-14, 14-17, 17-21, 21-25, 25-30 and above 10s).
I suppose with the grib2 template it can be generalised to any period intervals that is of interest to users.
