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Michel Olagnon IFREMER Brest, France

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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

- Humanity: How should we deal with those risks ?
- The offshore industry method
- The tsunami analogy
- Perspectives

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.

- If significant wave height was constant and equal to 10 meters, one would encounter a wave of:
- 18.5 m every 3 hours
- 21.5 m every day
- 25.0 m every month
- 27.5 m every year
- 30.0 m every 20 years
- 31.5 m every 100 years
- 33.1 m every 1000 years
- 34.8 m every 10000 years

- Twice the significant wave height is thus by no means abnormal

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.

EKOFISK, operated by ConocoPhillips

Laser measurements at the time of the ”Varg incident”

Norway

North Sea

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 ?

Hmax/ H1/3exhibits

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.

Mostly based on Benjamin-Feir instability, and we just saw not conclusive.

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.

H

H1/3

BFI Index

Irregularity factor

( # of crests / # up zero crossings ): nothing.

H

H1/3

Irr. Fact.

Steepness: let’s have a closer look.

H

H1/3

Steepness

Crest

H1/3

Steepness

H

H1/3

Steepness

NOTHING AGAIN !

- Extreme waves are not found more frequently than conventional long-term distribution models predict.
- When extremes are observed, no abnormal characteristic can be found in non-directional parameters at the time scale of the whole storm, of the sea state or of a set of a few consecutive waves. There is nothing more in rogue waves than what we can see in the statistics.

A small ship usually climbs up the wave...

…but may get rolled over or caught from the back.

Flooding of the bridge or control room

Get green water in addition to white on the foredeck...

…and water weighs a lot !

“for a while until they got it squared away, we launched them sailing backwards…”

Breaking of the structure due to sagging or hogging, in the trough or on the crest.

Only areas where there are more ships at risk...

Except if you are named Hosukai, of course...

Cannot avoid bad weather areas.

The deck has to

be high enough

to let the waves

pass by in the

“transparent”

part.

Reliability targets of 10-4 yearly.

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

errors, etc.

The idea is to keepthe metocean

risk at that relative level.

Design methods were questioned

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.

When you go to Hawaii, there is no sign,

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

then.

Rogue waves can be considered in

the same fashion: they may happen,

one should just train not to be caught

unprepared in that case.

What should you watch for ?

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 ahead

Design:Rogue waves understanding is now far from being a priority, but they do occur (as statistically expected), and should not be neglected.

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 !

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 !

Thank you.