Freak Waves: Clues for Prediction in Ship Accidents?

Abstract

Description of freak waves is not only important for design work but also for operational purposes it would be of benefit if warnings could be given to mariners. Meteo-centers already provide wave forecast based on spectral wave model. Although a spectrum gives some average description of the sea-state, it might contain additional information indicating an increased probability of occurrence of exceptional waves. To this end a database with 650 ship accidents was extracted from Lloyd's Marine Information Service database. Their study may help in identifying the ocean areas more prone to bad weather in general and abnormal waves in particular.

Full text

Freak Waves: Clues for Prediction in Ship Accidents?
Alessandro Toffoli
Burgerlijke Bouwkunde
K.U.Leuven
Leuven, Belgium
Jean Michel Lefevre
Div. Marine et
Oceanographie
Meteo-France
Toulouse, Cedex, France
Jaak Monbaliu
Burgerlijke Bouwkunde
K.U.Leuven
Leuven, Belgium
Henri Savina
Div. Marine et
Oceanographie
Meteo-France
Toulouse, Cedex, France
Elzbieta Bitner-
Gregersen
Dept. for Strategic
Research
DNV
Høvik, Norway
ABSTRACT
Description of freak waves is not only important for design work but
also for operational purposes it would be of benefit if warnings could
be given to mariners. Meteo-centers already provide wave forecast
based on spectral wave model. Although a spectrum gives some
average description of the sea-state, it might contain additional
information indicating an increased probability of occurrence of
exceptional waves. To this end a database with 650 ship accidents was
extracted from Lloyd’s Marine Information Service database. Their
study may help in identifying the ocean areas more prone to bad
weather in general and abnormal waves in particular.
KEY WORDS: Freak waves; ship accidents.
INTRODUCTION
Air travel may be the fastest growing transport mode. However ships
are two orders more efficient than air freight (in terms of cost per tonne
mile) and hence continue to carry around 95% of the international
freight (Faulkner, 2002). Owing to the increasing demands from
developing countries, it is also expected that shipping freight may
double in the next years and even more attention needs to be given to
safety at sea. It is therefore necessary that warning can be given to
avoid these cargos to encounter dangerous seas.
Although the forecasts are accurate, abnormal sea phenomena may
appear suddenly. On September 28th 2000 the passenger ship “Oriana”
was hit by a 17-meters wave (Howard, 2000). As reported by the
Captain, the ship was handling the weather very well before an
abnormal wave struck it. The incident ended without losses, but quite
frequently the economic, human and environmental consequences are
enormous.
Although several can be the causes of ship accidents, approximately
80% of shipping casualties are due to human errors in all phases of the
process, i.e. design, constructions and operation (e.g. Gaarder et al,
1997). Nevertheless, accidents might occur due to unexpected sea
conditions that might cause the unability to keep the ship under proper
control. It is assumed that dangerous unexpected conditions will only
occur if sea conditions are fairly rough. Looking at ship accidents
reported as due to heavy sea conditions might therefore give us some
clues as to why they could happen, which in turn may lead to possible
warnings for mariners.
The objective of this study is to examine information related to the
reported ship accidents that occurred in the last years due to heavy
weather. This information concerns data about the ship themselves, but
also other abut shipping density and sea-state.
The paper first presents a more detailed description of the ship
accidents. The location of the area more prone to these events will be
related to the shipping density. In the second part of the paper, the sea-
state conditions that were obtained from numerical wave model
analyses during the casualties are investigated.
The work is aimed by the need to find some common features or
thresholds that might lead to a clear definition of risk – defined herein
as probability of occurrence – for the encounter of abnormal sea-
phenomena in general and “freak” wave in particular. In other words,
the correlation between ship accidents and sea-state parameters is
investigated to search for common features in the sea conditions during
the selected casualties.
SHIP ACCIDENTS
Ships have greatly increased in size in the last five decades and quite
often these cargo consist of hazardous materials, for which a safe
handling and a safe navigation is required to prevent accidents leading
to increase risk to life, property and environment. The memory of
37000-ton oil tanker “Erika” is still alive (December 8th 1999), when
the “Prestige” accident happens. Sailing in monotonous seas the
Erika’s hull cracked and water was being taken on board. The next
morning the Erika broke in two and started to sink. Thousands of tons
of oil leaked from her cargo tanks. The huge blanket of oil drifted
towards the Brittany coastline and one of the biggest environment
disasters had started (Mangold, 2000). However, it is not just the
environment, which causes concern. Because the vast majority of the
Proceedings of The Thirteenth (2003) International Offshore and Polar Engineering Conference
Honolulu, Hawaii, USA, May 25–30, 2003
Copyright © 2003 by The International Society of Offshore and Polar Engineers
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23

world’s trade is carried by sea, it is the total loss of ships, their valued
cargo and lives as well as the collateral damage that is unacceptable.
Presently accidents still occur with severe and often less than severe
weather conditions even though the forecasts are good and accurate.
For this reason, it is also of concern to several meteo-centers to include
the sea-state in marine weather forecast when it exceeds some
threshold. Unfortunately some events occur in sea-states where the
prevision of classical parameters does not reflect its. Also it does not
give information about some specific and potentially dangerous
phenomena such as the increase of the steepness in case of opposite
wave direction to current flow or of cross seas, or abnormal waves.
Within the last decades some large ships have been lost, and in many
cases the cause is believed to be a “freak” wave, which is individual
wave of exceptional wave height or abnormal shape (Rosenthal 2002).
The notation of “freak” waves was introduced to address single waves
that are extremely unlikely as reported by the Rayleigh distribution of
wave height (Dean, 1990). Precisely it is assumed that the wave height
(from crest to trough) exceeds the significant wave height by a factor of
2 (Ochi, 1998).
There are several reasons why these wave phenomena may occur.
Often extreme events can be explained by the presence of ocean
currents (e.g. Agulhas current) or bottom topography that may cause
focusing of wave energy in a small area. On the other hand, it is
believed that in the open ocean – away from non-uniform currents or
bathymetry – these waves can be produced by nonlinear self
modulation of a slowly varying wave train (Janssen, 2002).
The European research program “MaxWave” aims at investigating the
occurrence and properties of rogue waves, demonstrating impact of
rogue waves on current design structures for ship and offshore
structures and developing improved forecast product including
warnings for extreme waves. The present investigation is expected to
contribute mainly to the latter.
MEANS OF INVESTIGATION
Five years (1995 – 1999) of ship accidents due to bad weather,
collected from the Lloyd’s Marine Information Service (LMIS) and
Lloyd’s casualty reports have been studied. The location of ship
damages as well as losses due to severe weather are shown in figure 1.
Although only a few accidents are categorized as being caused by freak
waves (e.g. Gunson et al, 2001), it does not mean that other ship
accidents under severe weather were not due to freak waves. Therefore
all accidents under severe weather were considered when wave and
wind fields were retrieved from the ECMWF-archive.
Figure 1. Worldwide ship accidents (1995-1999) due to severe weather. Source:
Lloyd’s Marine Information Service (LMIS) casualty database.
The study of the ship accidents in heavy weather can help in
identifying the ocean area more prone to bad weather conditions in
general and to abnormal waves in particular. However, due to the
complexity of the sea-state, the analysis done addresses not only the
classical wave parameters (from the wave energy spectrum), but also
the geographical and technical parameters (i.e. ship characteristics).
TECHNICAL DATA SETS
Ship Accidents Database
The data covers all reported serious casualties due to bad weather
including total losses to all propelled sea-going merchant ships in the
world of about 100 gross tonnage and above. It should be noted that the
category “bad weather” applies to the first event that occurred, and
does not record other consequences that may have occurred in the same
accident. The Lloyd’s database is recognized as the most reliable one
among the existing databases. It was developed in 1979 in response to
the shipping community’s growing need for more detailed information
on reported casualties and demolitions. The database is continuously
updated based on reports received daily from Lloyd’s Agents and
Lloyd’s Register Surveyors, situated in over one hundred and thirty
countries all over the world. All information received from the
surveyors is accuracy checked (Bitner-Gregersen & Eknes, 2001).
Ship Density
Whenever a ship is using a radio transmission outside harbors, the
location (in space and time) is recorded as well as the so-called “call
sign’. The call sign is a name used by ships for radio transmission and
it is better than the ship’s name because a call sign is always the same
while a ship’s name can include spaces, lower cases/upper cases and
can slightly differ depending upon who indicates the ship’s name.
Although ships can change names and also call signs, most of the time
the same call sign is used for a long time by a given ship. Therefore it
can be addressed as a ship’s indicator.
As the call sign is a unique name, it can be used to define the ship
density that represents a geographic index of usage. The ship density is
defined as an index of 100 if 8 call signs can be counted in an area of
500 X 500 km2 per day.
The ship density data set covers the period 2000 – 2001 (ship track data
were made available by JCOMMOPS). The index was calculated as an
average over the month and it refers to a single MAR zone, which is an
area of 10°X10° (Fig.2). The MAR zone defines an area that differs
from the ship density definitions. Therefore a adjustment factor was
applied.
Note that the ship density includes all ships and is thus not consistent
with the accident database, which contains ships of 100 gross tonnage
and above. The information we have at this moment does not permit us
to make this consistent.
Sea-State Parameters
In order to construct the sea-state during each of the ship accidents, the
ECMWF data set, see Persson (2002), has been queried. The wave
model that is used to produce ocean wave analysis at ECMWF is the
WAM model, which describes the rate of change of the wave spectrum
due to advection, wind input, dissipation due to white capping and non
linear wave - wave interaction.
24

Data were collected for a specified space and time window. When the
casualties’ location was known, an area of 3° X 3° was defined. When
the location was not known exactly, the entire MAR zone (in which the
accident took place) was investigated. On the other hand, the time
window covered a total period of three days: the two days before the
event and the day of the casualty.
The data set that was available contained the full 2D wave spectra and
some integrated parameters such as the significant wave height, mean
period, mean direction (all of them for wind sea and swell), the peak
period, etc… from the wave model analysis. The data availability was
at 12 GMT for casualties that occurred before June 28th 1998, while
after this date, the data were available at 0, 6, 12 and 18 GMT.
Ship D ensit y
Value
High : 1713.77
Low : 0.0 87 Ship Density Index: Jan 2000
-
Figure 2. Ship Density Index: the distribution is representing the month of
January 2000.
ANALYSIS OF CASUALTIES
Accident Types
The main causes of ship losses over the last two decades are due to
“operational” causes (60%) and “design and maintenance” causes
(40%), see Faulkner (2002).
In conditions of heavy sea, accidents may occur as a combination
of different events (e.g. took water, capsized and sank). They can be
classified as follow:
- Foundered 36%
- Water ingress 25%
- Severe hull damages 16%
- Capsize of intact ship 8%
- Others 15%
Geographical Distribution
The ship accidents geographical distribution follows the ship density.
In other words, a high number of accidents were recorded in those
areas of high ship transit. More precisely, the casualties occurred in the
North Sea, along the North American coast and both in the East and
South China Sea.
Figure 3 shows the density of the casualties. This density was defined
addressing index 1 for each accident that occurred in an area of 500 X
500 km2.
It is not a surprise that only 6% of the casualties were recorded in the
Southern Hemisphere.
Seasonal Distribution
Due to generally more severe weather in winter compared to the other
parts of the year, extreme phenomena occur as expected more often in
the winter period. The seasonal distribution extracted by the ship
accident database confirms this assumption. Figure 4 shows the time
distribution histogram. It only contains the casualties that occurred in
the Northern Hemisphere. However, the same conclusion may be
derived from the Southern Hemisphere’s casualties.
The winter season (from December to February) is characterized by
35% of the events, and more than 60% of them are placed in the period
between October and March. Nevertheless it is remarkable to mention
that about 16% of the cases are recorded between June and July (early
summer).
Ship Acc. Density
Value
High : 8 .78
Low : 0.2 0 Ship Accidents Density (1995-1999)
-
Figure 3. Geographical distribution: ship accidents per MAR zone – period
1995-1999.
Ship Accident - Seasonal Distribution
0
10
20
30
40
50
60
70
80
90
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Figure 4. Seasonal distribution of ship accidents – period 1995-1999.
25

Geographical Density of Risk
Nowadays the forecasts are quite accurate and often they also include
warnings concerning the sea-state. It is therefore believed that shipping
routes avoid more dangerous areas. With this in mind, the ship density
index was put forward as a normalizing factor to provide a first
evaluation for the risk of occurrence of ship accidents. More precisely,
the risk density was described by the ratio between the ship accident
density and the ship density. This definition should not be seen as the
ultimate definition for risk since only one parameter – the ship density
– is considered. Figure 5 reports this distribution.
The analysis indicates that the Southern Hemisphere seems to be more
prone to casualties than the Northern one. Nonetheless, the risk density
is remarkable in all-South Asia regions, and part of the Mediterranean
Sea. On the other hand, the North Atlantic appears less severe. The
high number of accidents in the North Atlantic was balanced by
intensive shipping activities.
Risk De ns ity
Value
High : 0.996
Low : 0 .001 Risk to encounter heavy sea
-
Figure 5. Risk to encounter ship accidents due to heavy sea. The risk concerns
only the casualties and the shipping densities. Its values were normalized by
means of the highest one.
ANALYSIS OF THE SEA-STATE
Parameters
The two parameters most widely used to describe the sea-state are the
significant wave height and the mean wave period (WMO, 1998).
These two classical values are not conclusive to evaluate the risk of
extreme events. However, they might lead to interesting results
together with other possible parameters if combined with real
casualties.
The list of potentially important parameters is long. The analysis is
limited to the ones give in Table 1.
Table 1: Wave parameters considered in the analysis
Parameter Formula Reference
Significant Wave
Height 0
4mH S=(Ochi 1998)
Spectral Peak
Period
{}
)(max
2
ωω
π
S
TP=(WMO, 1998)
Spectral Mean
Period 0
1
1m
m
Tm−
−=(WMO, 1998)
Average Wave
Steepness 2
2
P
s
PgT
H
S
π
=(WMO 1998)
Mean Directional
Spread
()
1
12 r−=
σ
(Bidlot, 2001)
Spectral
Bandwidth 1
2
1
02 −=
m
mm
ν
(Longuet-
Higgins, 1983)
In the formulas above of Table 1, mn is the nth-order moment of the
spectrum (WMO, 1998), ω is the angular frequency, g the acceleration
due to gravity (m/s2), and r1 is the first-order centred Fourier
coefficient.
In addition the 10-m wind speed was also considered. It is essential for
defining the surface stress, which is the basic force that leads to ocean
waves.
Sea-State
One Set of Parameter per Day
The sea-state parameters were analyzed in correlation with 250 ship
accidents (40% of the available casualties). The values were observed
at 12 GMT the day of the accident. Although the time of the accidents
was not known, it was assumed that this sea-state is representative for
the time of the accident. Therefore rapid changes on the day or before
the day of the accidents cannot be observed. The wave parameters were
evaluated from a full 2D wave spectrum. Table 2 reports exceedance
levels found by the investigation.
Table 2: Accidents exceeding a given threshold – Parameters at 12 GMT.
Parameter Threshold Accidents
Significant Wave Height < 5 m87%
Spectral Peak Period 8 s < Tp < 18 s63%
Spectral Mean Period 4s < TP < 12 s77%
Average Wave Steepness < 0.03 79%
Mean Directional Spread 0.5 < σ < 0.75 60%
Spectral Bandwidth 0.3 < ν < 0.4 80%
10 m Wind Speed < 10 m/s 53%
Figures 6 to 8 show the histogram-plots for the significant wave height,
the average wave steepness and the 10 m wind speed.
An encounter with a steep wave condition can be disastrous, even for a
large ship. An example is given by the FPSO “Schiehallion”. The ship
(80000 tons) was located 60°21’ N and 4°4’ E when it sustained heavy
weather damage above the waterline around 22 GMT on November 9th
1998. The reported damage was not caused by a wave of extreme
26

height, but by a wave of exceptional steepness. Wave model hindcast
results showed steepness values of about 0.04 (Gunson et al, 2001).
Note that average wave steepness extracted from the Pierson-
Moskowitz spectral formulation (Pierson-Moskowitz, 1964) is
characterized by a constant value SP equal to 0.0295.
The propagation characteristics of an ocean wave field can be obtained
from the circular standard deviation of the directional distribution
function, and it is usually referred to as the directional spread (σ). The
parameter is a function of the first-order centred Fourier coefficient of
the directional distribution (r1), and it takes values between 0 and 2,
where the value of 0 corresponds to unidirectional spectrum and the
value of 2 to uniform spectrum (Bidlot, 2001).
The spectral width (bandwidth) parameter can be used as a measure of
the irregularity of the sea-state (WMO, 1998). Irregular wave patterns
may be observed if ν ≈ 1, while ν<<1 is indication of regular waves
(narrow spectrum).
It is hard to define a real threshold above which one can assume
warnings for shipping, as nowadays ships are designed to sail in
extreme seas. Nevertheless, the present study shows that a high number
of casualties occurred in a low sea-state condition. Note again that the
sea-state parameters calculated refer to the 12 GMT the day of the
accident.
0246810 12 14 16
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Significant Wave Height
Hs [m]
Normalized Number of Ships
Figure 6. Significant wave height histogram. Data referred at 12 GMT. The
normalization of the y-axes lead to an area under the histogram equal to 1.
00.01 0.02 0.03 0.04 0.05 0.06
0
5
10
15
20
25
30
35
Average Wave Steep ness
Sp
Normalized Number of Ships
Figure 7. Average wave steepness histogram. Data referred at 12 GMT. The
normalization of the y-axes lead to an area under the histogram equal to 1.
0 5 10 15 20 25 30 35 40
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
10-m Win d Speed
U10 [m/s]
Normalized Number of Ships
Figure 8. 10-m wind speed histogram. Data referred at 12 GMT. The
normalization of the y-axes lead to an area under the histogram equal 1.
Four Sets of Parameters per Day
About 40 accidents of the 250 analyzed cases (16%) occurred in the
period after June 28th 1998. For them, the data were recorded every six
hours, and hence “rapid” changes in the parameters can be observed.
The analysis of these 40 accidents covered two days before and the day
of a casualty. In this period a sharp increase of the significant wave
height, average wave steepness, and wind speed was observed in the
last 24 hours (e.g. Fig. 9 shows the significant wave height for an event
that occurred off Nova Scotia). None the less, the sea-state appeared
again to be rather low. However, an average wave steepness equal to
0.03 was overcome in 46% of the cases, which represents more than
double the quantity observed at 12 GMT.More detailed research has to
be done to sea whether next to having values for certain parameters of
the sea-state also an indication of the gradient (in time and in space) is
needed.
On the other side, a flat line was usually observed for the mean
directional spread and the bandwidth parameter. However, for several
cases a sharp peak was observed for the bandwidth parameter.
050
0
2
4
Time [h]
Hs [m]
Significant Wave Height - 1998/09/28 - Nova Scotia
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
050
0
2
4
Figure 9. Evolution in time of the significant wave height. It reports the
parameter in the retrieval grid points (mesh of 1°X1°). The casualties can be
located between the four middle plots.
27

050
0
0.02
0.04
Time [h]
Sp
Average Wave Steepness - 1998/09/28 - Nova Scotia
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
050
0
0.02
0.04
Figure 10: Evolution in time of the average wave steepness. It reports the
parameter in the retrieval grid points (mesh of 1°X1°). The casualties can be
located between the four middle plots.
050
0
5
10
15
Time [h]
U10 [m/s]
10-m Wind Speed - 1998/09/28 - Nova Scotia
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
050
0
5
10
15
Figure 11: Evolution in time of the 10-m wind speed. It reports the parameter in
the retrieval grid points (mesh of 1°X1°). The casualties can be located between
the four middle plots.
Wind Sea and Swell Separation
The wave parameters discussed before do not take into account the
directions of wind sea and swell. Under this consideration, the mean
direction for wind sea and swell were observed on the day of the
accidents (wind sea and swell separation had been performed by
ECMWF’s WAM model). The Cartesian plane was divided in four
sectors: “following sea” between 315° and 45°, “cross-sea” between
45° and 135°, and between 225° and 315°. Also the “opposite sea”
between 135° and 225° was detected. This distinction gives the
following results:
- Following Sea: 53% of the cases;
- Cross Sea: 38% of the cases;
- Opposite Sea: 9% of the cases.
The definition above covers quite a large directional range. It was
intended to categorize each entry of the entire data set.
If the directional range for a particular category changed from 90 to 45
degrees (e.g. cross-sea between 67.5 and 112.5 degrees and between
247.5 and 292.5 degrees), the number of cross-sea cases also decreases
to half. In other words only 19% of the cases then satisfy the condition
of cross-sea. However, the analysis for the entire three-days data set
shows that very often the condition of cross-sea changes to the
condition of opposite sea when approaching the day of the events.
Since conditions of cross-sea and opposite sea are believed to be
dangerous for ships, it is remarkable that only about 50% of the cases
were reported in such conditions.
One clear example of cross-sea is shown in Figure 12. The swell that
was coming from South South-West crossed the wind sea coming from
West with an angle of approximately 90°.
We noted that about 60% of the cases of cross-sea are located in those
areas where a high risk to encounter ship accidents were detected (see
Fig. 5).
Bathymetry
Value
High : - 1
Low : -9956
Wind Sea & Swell
Swell
²0.00
²0.01 - 0.70
²0.71 - 1.40
²
1.41 - 1.96
Wind Sea
²0.00
²0.01 - 0.70
²0.71 - 1.40
²1.41 - 1.96
-
Figure 12. Wind Sea and Swell mean direction – Cross Sea condition. The
length of the arrows is made proportional to the significant wave height.
28

CONCLUSIONS
Ships that founder represent a great disaster both from an economical
and a human point of view. Moreover the environmental collateral
damages may be enormous. Therefore it would be of great benefit if
warning might be given to mariners.
Data on ship density as well as wave and wind field data (retrieved
from the ECMWF-archive) were used in the analysis of ship accidents
due to heavy weather. About 250 accidents were consequently looked
at.
The combination of the shipping density and the density of ship
accidents allows to define those locations in which there is an increased
risk (probability of occurrence) worth. Nevertheless, the density cannot
be assumed as the only parameter for consideration and hence the sea-
state conditions were added. Surprisingly, the investigation showed that
in most of the cases the casualties occurred in rather low sea-state
(according to wave model analysis). This can be caused by the fact that
data are referred to a fixed time (12 GMT). The present analysis has
several limitations and therefore the results should be used with care.
Further investigations are necessary in order to reach a firm conclusion.
A cross-check of model data with altimeter data (Topex-Poseidon
campaign) will for example be done.
The study indicates that the classical spectral parameters (HS and TP)
are not sufficient to point at possibly extreme wave phenomena.
However processes that form huge waves such as interaction between
waves and currents (e.g. Agulhas Current) are usually not adequately
represented in operational forecast products.
Cross, opposing or following seas may play a role, but the current
results do not allow to draw firm conclusions.
There are indications that rapidly changing conditions can create
dangerous situations. An adequate time resolution of wave parameters
is therefore needed to understand the importance of gradient
information in developing warning criteria for operational purposes.
Important to remark in that respect is that all ships react differently to a
certain sea-state and that an interpretation of wave forecast will be
needed for type of ship and possibly for each individual ship.
ACKNOWLEDGMENTS
This work was carried out in the framework of the European project
MAXWAVE (project no. evk: 3-2000-00544). The authors would like
to thank the Joint WMO/IOC Technical Commission for Oceanography
and Marine Meteorology In Situ Observing Platform Support Center
(JCOMMOPS) for the ship tracks data.
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