The “Design Wave Philosophy’’ Calculation of the design wave

Trondheim Tekniske Fagskole

The “Design Wave Philosophy’’Calculation of the design waveWave forces on semi-submersible platformsWave forces and bending moments in FPSO-shipsPlatform movements in large wavesExamples of heavy weather damage

***** What is a Rogue Wave ? *****Why, where and when ?Shall we design against Rogue and Freak Waves ?What can a platform master do against Rogue and Freak Waves ?Remote-sensing of sea conditionsSearch And Rescue and emergency operationsDecision making in an emergency

What is a Rogue Wave ?


What is a rogue wave ?



• The various definitions

• What are the problems for design ?

• What are the problems for operations ?

• What are researchers working on ?



Let’s start with “What is a Wave ?”



In practice, you know it was a rogue wave once you saw it.



A good excuse when crew failed to install port hole storm covers ?



A 15° roll of the camera angle ?



Just something that happens ?



In physics and/or statistics, there are several definitions:



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

The maximum in one day is also the maximum in the 20 minutes or 3 hours surrounding it, so twice the significant wave height is by no means abnormal: it happens every day !



One of those waves in a [large] set of a given height that make the set more numerous than it should be from conventional theory.



From the figures above, theory states that there should be 500 waves above 2Hs in a year. If one measures 1000 of them, they are rogue waves: about 500 freak and 500 normal extremes and of course we can’t distinguish easily which are which.



A wave of unexpectedseverity given the prevailing sea conditions at the time it occurs



A wave of unexpected severity given the prevailing sea conditions at the time it occurs.

Unexpected: A good deal of damage can be avoided if those exposed are fully aware there and then.

Severity: Steepness, Front steepness and other characteristics may be more damaging than mere height.



Reconstructed water surface elevations over a 1000 m span, from T-30s (blue) to T (red) for the New Year Wave.

The famous “Draupner wave”


Where does it come from ?

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.


It is nice to be able to recognize a Freak or Rogue Wave in the statistics after it occurred...

...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


Where does research stand with regards to rogue waves : recent studies.

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 ?


Discriminating questions:

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 ?


Database:

20 years of data available from Frigg QP platform in the North Sea


Database:

1979-1989: mostly 3-hourly measurements, many time-series available.

1991-1999: mostly 20-minute statistics, only reduced parameters


Database:

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”

North Sea

Norway


Storm “freakiness”

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 ?


Medium term: the sea state time scaleFreaky sea states ?

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.


Distribution of maximum wave heights

Comparison of empirical distribution of Hmax with Nerzic & Prevosto model for H1/3>5 m.

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


Kurtosis and Benjamin-Feir instability

“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.


Kurtosis and 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 ?


Kurtosis and Hmax

Hmax/ H1/3 exhibitsa clear relationship to kurtosis...


Kurtosis and Hmax

…but if “kurtosis” is computed with removal of the largest wave’s time-duration, the relationship can no longer be seen.


What value in Met’Offices warnings ?

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...


What is there to be seen a few waves ahead ?

Instantaneous Benjamin-Feir instability index: nothing.

HH1/3BFI Index



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

HH1/3Irr. Fact.



Steepness: let’s have a closer look.

HH1/3Steepness



HH1/3Steepness

CrestH1/3Steepness

NOTHING AGAIN !


Conclusions so far

• 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.


Associated risks

A small ship usually climbs up the wave...


Risks for small ships

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


Risks for small ships

Flooding of the bridge or control room


Risks for larger ships

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


Risk for larger ships

…and water weighs a lot !“for a while until they got it squared away, we launched them sailing

backwards…”


Risks for larger ships

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


Risky areas where not to sail ?


Risky areas ?

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


The wrong place at the wrong time

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


Offshore platforms

Cannot avoid bad weather areas.

The deck has to

be high enough

to let the waves

pass by in the

“transparent”

part.


How the offshore industry deals with the risk.

Reliability targets of 10-4 yearly.On one hand, 10000 years fromnow, the North Sea may well be adesert, on the other hand, risksassociated with waves are atleast one order of magnitude lowerthan those of blast, fire, human errors, etc.The idea is to keep the metoceanrisk at that relative level.


How the offshore industry deals with the risk.

Design methods were questionedfor a while, because of the possibilityof some phenomenon different fromthe ones that had been used to derivethe theories that led to design values.Experience and studies have shownthat there was no problem with thosetheories onto the 10-4 limit.To some extent, the shipping industryuses a similar approach, but less openly.To the shipowner, the risk of a roguewave is an acceptable one, as we wouldsay for the risk of a car accident whendriving to work.


The tsunami analogy

When you go to Hawaii, there is no sign,to be seen on the real estate near thebeaches, that they could be washedaway by a tsunami at any moment.Yet, if a tsunami occurs in Hawaii, there will be loss of property, butlikely no loss of lives: those subjectto the risk are properly trained, knowthe ominous tokens and what to dothen.Rogue waves can be considered inthe same fashion: they may happen,one should just train not to be caughtunprepared in that case.


The 3 Rules for survival: Training, training and training

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


Perspectives

• 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 !


Freak events do happen

THAT’S LIFE !Thank you.

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

Documents

The “Design Wave Philosophy’’ Calculation of the design wave