Rogue Waves: What risks ?. Michel Olagnon IFREMER Brest, France. Outline. Statistics: What is a rogue wave ? Definition Examples Occurrence probabilities Reliability: What are the associated risks ? Small ships Large ships Offshore platforms
A wave of unexpected
severity given the
prevailing sea conditions at the time it occurs
Some say a wave that is more than twice the significant wave height, but that may not be a reliable definition.
A good excuse when crew failed to install port hole storm covers ?
A 15° roll of the camera angle ?
Just something that happens ?
The famous “Draupner wave”
Reconstructed water surface elevations over a 1000 m span, from T-30s (blue) to T (red) for the New Year Wave.
Georg tells us (Lindgren, 1970) that if it comes from the normal gaussian process, it is a wave that looks in retrospect like the autocorrelation function of the water surface elevation signal.
Sverre (Haver, 2000) states that it is a freak wave if it represents an outlier when seen in view of the population of events generated by a piecewise stationary and homogeneous second order model of the sea surface process, otherwise “only” rogue.
Miguel and Al (Onorato & Osborne, 2005) tell us that according to the Schrödinger equation, it sucks energy from its neighbors and thus it is a freak invader from an outer statistical population.
...For various reasons, a much nicer ability would be that of being successful when speculating that approaching waves are not rogue waves, or even that they are.
‘‘ When a woman at a party asks me what I do, I invariably say «I ’m just a speculator.» The encounter ’s over. The only worse conversation stopper is «I ’m just a statistician.» ’’
Victor Niederhoffer, The Education of a Speculator, Wiley, 1997
A wave is coming.
In order to predict its rogueness, should we use quasi-deterministically the non-linear Schrödinger equation or merely rely on the statistics derived from, for instance, Slepian processes ?
1. Do we have more high waves than our conventional long-term statistical models predict ?
2. When we do have high waves, do other characteristics of the whole storm, of the sea state, or of the few previous waves look different from those of other storms, sea states, or sets of a few consecutive waves ?
3. Especially, do characteristics related to theoretical deterministic constructions of rogue waves exhibit statistical evidence of predictive power ?
20 years of data available from Frigg QP platform in the North Sea
1979-1989: mostly 3-hourly measurements, many time-series available.
1991-1999: mostly 20-minute statistics, only reduced parameters
Hmax and H1/3 retrieved preferably from the time-series when available (7%), from the statistics elsewhen.
For storms, missing zero-crossing period information was derived from T1/3 (9.4%) and drawn from the empirical H1/3-Tz distribution when no information at all was available (1.7%).
The final database consists of 265147 statistical records, it is thus equivalent to nearly 9 years of continuous measurements.
Laser measurements at the time of the ”Varg incident”
We (Olagnon & Prevosto, 2005, Olagnon & Magnusson, 2004) tried to investigate the widest time-scale: the whole storm.
Especially, the maximum wave expected in a storm is a more useful forecast to seafarers than the maximum wave in some particular 1- or 3-hour duration sea state of that storm.
It may thus appear natural to relate the maximum wave in a storm to the maximum predicted H1/3 in that whole storm rather than to the prevailing H1/3 at the precise instant of Hmax.
Storms are defined as durations > 12 hours with H1/3> 5m
For each of the 187 identified storms, 1000 random simulations were made using the database statistical parameters and a Jonswap wave spectrum with gamma=3. Second order correction was then applied to all computed Hmax values.
Freakiness of a storm is defined as the quantile rank of that storm’s observed Hmax/ H1/3max in the corresponding distribution over the 187 actual storms (empirical) and over the 187000 simulated storms (2nd order theory).
QQ-plot of Hmax/ H1/3max = blue dots.
H1/3 = green dots
Hmax = red dots
Apart from a very few ones, storms are less “freaky” than 2nd order theory would predict.
QQ-plot of Hmax/ H1/3max = blue dots.
Mean storm BFI = red dots
Benjamin-Feir instability at the time-scale of a storm can only be very weakly related to its “freakiness”.
Expectations based on experience rather than theory would be definitely too low: An explanation for so many freak waves reported ?
Nerzic & Prevosto (98) proposed a Weibull-Stokes model for the distribution of maximum waves Hmax in a sea state, conditional to H1/3 and Tz of the sea state.
They used a 7% subset of the Frigg database, without any special emphasis on extremes, to derive their model.
We use the full database to study how the model performs with long-term extremes.
No underestimation by model !
Again, an appropriate transformation, limited to taking into account standard non-linearities up to second order, is sufficient to explain the observed extremes
Comparison of empirical distribution of Hmax with Nerzic & Prevosto model for H1/3>5 m.
“When a similarity connection is achieved between two objects to 20 decimal places, the greater will move to the lesser”
A.E. Van Vogt, The World of Null-A, 1945
Even though conventional Hmax models seem acceptable for long-term distributions, it might be possible to predict when the extremes in the distribution are most likely to occur : at those times, the similarity between the actual world and the theoretical deterministic world of non-linear Schrödinger equation may be such that we can apply the rules of the latter for some limited time-space window. In that latter world, extremes are governed by Benjamin-Feir instability.
Benjamin-Feir instability, i.e. the ratio of steepness to bandwidth, and signal kurtosis are strongly related (Mori & Janssen 2005)...
… but are kurtosis (BFI) excursions away from regular values the cause of freak waves, or a mere consequence of their observation ?
In other words, is kurtosis (BFI) a predictor or only a detector ?
a clear relationship to kurtosis...
…but if “kurtosis” is computed with removal of the largest wave’s time-duration, the relationship can no longer be seen.
Difficult to assess how good the chosen omens are.
Difficult to find volunteers to go into the worst areas of storms and validate the forecasts...
Instantaneous Benjamin-Feir instability index: nothing.
( # of crests / # up zero crossings ): nothing.
Steepness: let’s have a closer look.
NOTHING AGAIN !
On one hand, 10000 years from
now, the North Sea may well be a
desert, on the other hand, risks
associated with waves are at
least one order of magnitude lower
than those of blast, fire, human
The idea is to keepthe metocean
risk at that relative level.How the offshore industry deals with the risk.
for a while, because of the possibility
of some phenomenon different from
the ones that had been used to derive
the theories that led to design values.
Experience and studies have shown
that there was no problem with those
theories onto the 10-4 limit.
To some extent, the shipping industry
uses a similar approach, but less openly.
To the shipowner, the risk of a rogue
wave is an acceptable one, as we would
say for the risk of a car accident when
driving to work.How the offshore industry deals with the risk.
to be seen on the real estate near the
beaches, that they could be washed
away by a tsunami at any moment.
Yet, if a tsunami occurs in Hawaii,
there will be loss of property, but
likely no loss of lives: those subject
to the risk are properly trained, know
the ominous tokens and what to do
Rogue waves can be considered in
the same fashion: they may happen,
one should just train not to be caught
unprepared in that case.The tsunami analogy
Complex, multiple low pressure meteorological systems
Pressure lows traveling at the same speed as the waves they create (“running fetch”)
A sea state easier to handle than could have been expected from the wind’s strength
The time when the storm’s maximum is close ahead
The time when a cold front is close aheadThe 3 Rules for survival: Training, training and training
Forecast (the priority):No automatic rules, but … it may not be impossible to train super-expert meteorologists to estimate the risks with good chances of success.NOT A MET’OFFICE ACCEPTED PRACTICE HOWEVER !Perspectives
The death of Aeschylus was not of his own will; […]. Having come out of the place where he lived in Sicily, he sat under the sun. An eagle carrying a tortoise happened to fly above him. Mistaken by the whiteness of his bald head, it let the tortoise fall on to it, as it would have done to a stone, in order to break it and eat its flesh. The blow took his life away from the poet who first gave the most perfect form to tragedy.
Valerius Maximus, Factorum ac dictorum memorabilium, IX 12, ca. 30 AD
THAT’S LIFE !