In this paper, a numerical simulation of sea wave characteristics and operation downtimes of offshore structures is presented. The simulation was based on available wind data and seawater temperature recorded by an oceanography buoy installed in the Caspian Sea. Wave characteristics were simulated for deepwater parts of the Caspian Sea by applying the Bretschneider spectrum and equations using following recorded data: wind velocity, wind duration, fetch length, and water/air temperature differences. Since recorded wave data were only available for a one-year period, they were solely used for validation of the simulation results with recorded data but for not the simulation itself. Some practically established thresholds for wave velocity, wave period, and wind velocity were considered as constrains, limiting the operation of offshore installations. The numerical simulation model revealed that it is possible to operate offshore installations for 250 days per year in the southern parts of the Caspian Sea. A worst-case scenario showed that the maximum waiting time for restarting the offshore installations is 17 days. Considering the swell parameter, it was concluded that the annual downtime period of offshore installation operations in southern parts of the Caspian Sea is about one third of a year and the maximum waiting time for this operation is about two third of a month.

1. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
A Numerical Simulation for Predicting Sea Waves
Characteristics and Downtime for Marine and Offshore
Structures Installation Operations
Kabir Sadeghi1
Girne American University, Department of Electrical and Electronic Engineering,
TRNC
Abstract
In this paper, a numerical simulation of sea wave characteristics and operation
downtimes of offshore structures is presented. The simulation was based on available
wind data and seawater temperature recorded by an oceanography buoy installed in
the Caspian Sea. Wave characteristics were simulated for deepwater parts of the
Caspian Sea by applying the Bretschneider spectrum and equations using following
recorded data: wind velocity, wind duration, fetch length, and water/air temperature
differences. Since recorded wave data were only available for a one-year period, they
were solely used for validation of the simulation results with recorded data but for
not the simulation itself. Some practically established thresholds for wave velocity,
wave period, and wind velocity were considered as constrains, limiting the operation
of offshore installations. The numerical simulation model revealed that it is possible
to operate offshore installations for 250 days per year in the southern parts of the
Caspian Sea. A worst-case scenario showed that the maximum waiting time for
restarting the offshore installations is 17 days. Considering the swell parameter, it
was concluded that the annual downtime period of offshore installation operations in
southern parts of the Caspian Sea is about one third of a year and the maximum
waiting time for this operation is about two third of a month.
Keywords: Simulation, Bretschneider, Wave Height/Period, Caspian Sea, Marine
Introduction
In order to design, calculate, construct, and install coastal, port, marine, and
offshore structures, environmental data are needed, in particular wave and wind
data. To determine wave data, simulation models, measuring devices, and remote
sensing by satellites are used. Obtaining valuable and long-term environmental
data by measuring devices or satellites is time consuming and very expensive. In
addition, these types of data are not available for all regions.
1
ksadeghi@gau.edu.tr
1

2. Wave Characteristics and Downtimes of Offshore Structures
Because of the above-mentioned drawbacks of the direct measuring methods,
simulation models are widely used in establishing environmental data. They are
easy to use and are applicable for every geographical area, provided valid
equations and spectrums are chosen, calibrated, and well adapted to the specific
situation. To predict the wave characteristics in lakes, gulfs, seas, and oceans, the
equations and spectrums of Sverdrup-Munk-Bretschneider (S.M.B), Bretschneider,
Pierson-Moskowitz, and JONSWAP (Joint North Sea Wave Project) are mainly
used. These models can be adapted to every point in any water depth in the sea
waters (Sadeghi 2001).
To evaluate the validity of the Bretschneider spectrum, a case study was carried out
by the author for the Caspian Sea. The Bretschneider spectrum was selected for this
study because its equations and spectrums consider the very important parameter of
water/air temperature differences.
The Caspian Sea was chosen as study area, since sufficient wave characteristics
data are not available for some parts of the Caspian Sea allowing the evaluation of
sensitive operations such as installations of offshore petroleum platforms and the
like. Simulation of wave characteristics was carried out based on available wind
data recorded by Khazar Oceanography Buoy (KEPCO 2001). This buoy is located
in the south-eastern part of Caspian Sea, 30 km from Neka Harbour at a water
depth of 35 m and operated by KEPCO (Iranian Company for Exploration of Oil in
Caspian Sea).
Wave characteristics were simulated for deep water parts of the Caspian Sea based
on recorded wind data using the Bretschneider spectrum (Bhattacharyya 1972,
Cold Bay Study [CBS] 1999) and various modeling equations (U.S. Army Coastal
Engineering Research Center 1980, Sadeghi 1989, 2001). Wind duration, wind
velocity, fetch length, and water/air temperature differences were considered in the
simulation. Some constrains for wave velocity, wave period and wind velocity
were used as limitation criteria for offshore installation operations. It is important
to mention that only one-year wave data were available for the study area. Thus,
these data have only local validity and are not valid for other points of the Caspian
Sea, particularly for deep-water areas. Therefore, the recorded wave data were only
used for comparison purpose and were not applied in the simulation.
Information and data used
General information on environmental conditions (wave, wind, current, etc.)
obtained from literature were used for general consideration and overall
engineering judgments (U.S. Army Coastal Engineering Research Center 1980,
Sadeghi 1989, 2001). The data used in the wave characteristic simulations were
taken from KEPCO (2001).
2

3. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
Formulas used in this study
The Bretschneider equations and spectrum were applied to predict forecasting the
wave characteristics (U.S. Army Coastal Engineering Research Center 1980, Sadeghi
1989, 2001, CBS 1999). The Bretschneider equations take the effects of wind
blowing duration, wind velocity, air-sea temperature difference, and fetch length
into account.
Summary of assumptions and analysis approach
The analysis is based on one-year environmental data recorded in the Caspian Sea,
and Bretschneider equations and Rayliegh distributions for prediction of wave
characteristics (Bhattacharyya 1972, U.S. Army Coastal Engineering Research Center
1980, Sadeghi 1989, 2001, 2004, DNV Classification Notes, 2000).
Following assumptions and analysis steps were applied:
a. Since there is lack of wind data for all points in south Caspian Sea, the
wind data recorded in the location of the above-mentioned buoy were
used for all points of the south Caspian Sea considering different fetch
lengths. Comparing the wind data for different parts of the south
Caspian Sea presented in literature (Kosarev & Yablonskaya 1994)
showed that this assumption could be considered as a valid.
b. A summary of used formulas based on the Bretschneider spectrum is
presented.
c. Data on seawater temperature, wind velocity, direction of wind, wind
duration, and air temperature were taken from KEPCO Engineering
Department measured by the KEPCO buoy (KEPCO 2001) and were
used for the numerical simulation of wave characteristics of the south
Caspian Sea. It is to be underlined that the available one-year data
covers only a certain period (1988/1989).
d. In the available data (KEPCO 2001), the period of each set of record
is three hours. It is important to note that this 3-hour period is not
necessarily the wind blowing duration. Therefore following criteria
were used for evaluating the wind duration:
If the directions of wind for two consecutive sets of recorded data
were different, the wind duration is considered as 1.5 × 3 hours
(because of difference between measuring period and real wind
duration by considering minimum probable duration of 4.5 hours).
3

4. Wave Characteristics and Downtimes of Offshore Structures
If the differences among wind directions between every two
consecutive periods of recorded data were less than 7 degrees, the
consecutive accumulated wind measuring duration were
considered as wind blowing duration (t). In this case the average
wind velocity was also used.
e. With regard to wind velocity and blowing duration, the required
related minimum fetch was calculated from the Bretschneider
equation which should be less than maximum effective fetch existing
in the south Caspian Sea (i.e. 450 km).
f. Based on the Bretschneider spectrum, the ratio of maximum wave
height over significant wave height is normally bigger than two. In
this study the Rayliegh ratio for Hmax/Hs was used for the benefit of
simplicity (i.e. Hmax/Hs = 1.85) (DNV Classification Notes 2000,
Sadeghi 2001).
g. Significant wave height, significant wave period, and peak period
were calculated based on the Bretschneider equation considering the
air-sea water temperature difference.
h. Constraints for the limitation of installation operation were defined as
follows:
Maximum wind velocity equal to 20 Knots
Maximum wave height equal to 2 meters
Maximum wave period equal to 8 seconds
Installation operation duration equal to 5 days (This duration is
considered for mooring and installation operation of the IranAlborz semi-submersible drilling platform in water depth of 970
m in the Caspian Sea).
Wave characteristics simulation results
Comparison of simulated and recorded wave characteristics
Simulated wave height and period for the south Caspian Sea were compared with
recorded wave height and period for a distinct point in this sea (30 km from Neka
Harbour, at 35 m water depth). It is important to note that the results of simulated
values were different from that of existing recorded values at that certain point. The
reason is that the reference point in this study was located at the south-east corner
4

5. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
of Caspian Sea and thus, the fetch will be different from other points at southern
basin of Caspian Sea.
Figures 1, 2, 3, and 4 present the maximum wave height (Hmax in meters) versus
time (sets of 3 hours registered data). In the horizontal axis of these figures, 40
means 40 × 3 hours that equals to five days and 720 means 720 × 3 hours
equaling three months.
Figures 5, 6, 7 and 8 show the recorded values of Hmax. As it can be seen from these
figures the simulated values are generally well adopted with the recorded values
but a little bigger than them due to longer fetches.
8.0
Hmax (Simulated)
7.0
Non Operational Days = 17
Maximum Wave Height (m)
6.0
5.0
Non Operational Days = 7
Non Operational Days = 2
4.0
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
Time (Number of Registration 3 hours period)
Figure 1. Simulated maximum wave height for months 11, 12, year 1988 and month
1, year 1989.
As shown in figures 7 and 8 for an about two-month periods, the wave heights
were not recorded, but for the time period, the wave heights were simulated and are
presented in figures 3 and 4.
Figures 9, 10, 11 and 12 show the simulated peak period (Tm) versus time (sets of 3
hours registered data).
On the above-mentioned figures, the limitation criteria are shown by full block
lines and also the non-operational days are presented. It is to be mentioned that the
recorded and simulated wave periods were moderately different. This is mainly due
to the swell effect that has not been considered in Bretschneider formula and as a
result of the numerical simulation.
5

6. Wave Characteristics and Downtimes of Offshore Structures
8.0
Hmax (Simulated)
7.0
Maximum Wave Height (m)
6.0
Non Operational Days = 7
5.0
N. Op. D. = 1
N. Op. D. = 1
N. Op. D. = 1
N. Op. D. = 1
4.0
N. Op. D. = 1
N. Op. D. = 1
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
Time (Number of Registration 3 hours period)
Figure 2. Simulated maximum wave height for months 2, 3 and 4, year 1989.
8.0
Hmax (Simulated)
7.0
Maximum Wave Height (m)
6.0
Non Operational Days = 12
5.0
N. Op. D. = 1
N. Op. D. = 9
N. Op. D. = 3
4.0
N. Op. D. = 1
3.0
Limit Line (Criteria)
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
721
Time (Number of Registration 3 hours period)
Figure 3. Simulated maximum wave height for months 5, 6 and 7, year 1989.
6

7. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
8.0
Hmax (Simulated)
7.0
Maximum Wave Height (m)
6.0
N. Op. D. = 7
Non Operational Days = 12
5.0
N. Op. D. = 1
N. Op. D. = 2
4.0
N. Op. D. = 1
N. Op. D. = 1
N. Op. D. = 1
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
721
761
Time (Number of Registration 3 hours period)
Figure 4. Simulated maximum wave height for months 8, 9, 10 and 11, year 1989.
8.0
Hmax (Recorded)
7.0
Non Operational Days = 13
Maximum Wave Height (m)
6.0
5.0
N. Op. D. = 2
N. Op. D. = 8
4.0
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
Time (Number of Registration 3 hours period)
Figure 5. Recorded maximum wave height for months 11, 12, year 1988 and month 1,
year 1989
7

8. Wave Characteristics and Downtimes of Offshore Structures
8.0
Hmax (Recorded)
7.0
Maximum Wave Height (m)
6.0
Non Operational Days = 6
5.0
N. Op. D. = 1
N. Op. D. = 1
N. Op. D. = 1
4.0
N. Op. D. = 1
N. Op. D. = 4
N. Op. D. = 1
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
Time (Number of Registration 3 hours period)
Figure 6. Recorded maximum wave height for months 2, 3 and 4, year 1989.
8.0
Hmax (Recorded)
7.0
Maximum Wave Height (m)
6.0
5.0
Not Recorded
N. Op. D. = 1
4.0
Non Operational Days = 3
3.0
Limit Line as per Criteria
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
Time (Number of Registration 3 hours period)
Figure 7. Recorded maximum wave height for months 5, 6 and 7, year 1989.
8
681
721

9. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
8.0
Hmax (Recorded)
7.0
N. Op. D. = 1
Maximum Wave Height (m)
6.0
N. Op. D. = 3
Non Operational Days = 11
5.0
N. Op. D. = 4
N. Op. D. = 1
4.0
N. Op. D. = 5
3.0
Limit Line (Criteria)
2.0
1.0
0.0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
721
761
Time (Number of Registration 3 hours period)
Figure 8. Recorded maximum wave height for months 8, 9, 10 and 11, year 1989.
15
14
Tm (Simulated)
13
12
11
Peak Period (s)
10
9
Limit Line as per Criteria
8
7
6
5
4
3
2
1
0
1
41
81
121
161
201
241
281
321
361
401
441
481
Time (Number of Registration 3 hours period)
Figure 9. Simulated peak period for months 11, 12, year 1988 and month 1, year 1989.
9

10. Wave Characteristics and Downtimes of Offshore Structures
15
14
Tm (Simulated)
13
12
11
Peak Period (s)
10
9
Limit Line as per Criteria
8
7
6
5
4
3
2
1
0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
Time (Number of Registration 3 hours period)
Figure 10. Simulated peak period for months 2, 3 and 4, year 1989.
15
14
Tm (Simulated)
13
12
11
Peak Period (s)
10
9
Limit Line as per Criteria
8
7
6
5
4
3
2
1
0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
Time (Number of Registration 3 hours period)
Figure 11. Simulated peak period for months 5, 6 and 7, year 1989.
10
561
601
641
681
721

11. K. Sadeghi, GAU J. Soc. & Appl. Sci., 3(5), 1-12, 2007
15
14
Tm (Simulated)
13
12
11
Peak Period (s)
10
9
Limit Line as per Criteria
8
7
6
5
4
3
2
1
0
1
41
81
121
161
201
241
281
321
361
401
441
481
521
561
601
641
681
721
761
Time (Number of Registration 3 hours period)
Figure 12. Simulated peak period for months 8, 9, 10 and 11, year 1989.
Conclusion
Due to the limitation of the existing recorded data (only one year available data for
a certain point near the shoreline), this simulation can be considered only as a
guide for evaluation of situations and can be used only for preliminary estimations.
Considering the operational constraints (Hmax = 2 m, Tm = 8 s and gust velocity =
20 Knots) used for numerical simulation, an installation operation of 250 days per
year is possible. The maximum waiting time for restarting the installation operation
is estimated to last 17 days.
As only the seas are simulated and due to lack of data and information for swell, it
can be in general concluded that the installation operation is possible for 2/3 of the
year and the maximum waiting time for this operation is about 2/3 of months.
References
Bhattacharyya R, 1972. Dynamics of marine vehicles.
Cold Bay Study [CBS], 1999. Section IV (Climatology).
11

12. Wave Characteristics and Downtimes of Offshore Structures
DNV Classification Notes, 2000. Environmental conditions and environmental
loads, No. 30.5, March 2000.
KEPCO Engineering Department, 2001. "Work Report on data obtained from
Khazar oceanography buoy and related CD electronic file", winter of 2001.
Kosarev AN, Yablonskaya EA, 1994. The Caspian Sea, translated from Russia by
Winstin AK, published by SPB Academic Publishing, The Hague.
Sadeghi K, 1989. Design and analysis of marine structures. Published by Khajeh
Nasirroddin Toosi University of Technology, Tehran, Iran, 1989, 456 pp.
Sadeghi K, 2001. Coasts, ports and offshore structures engineering. Published by
Power and Water University of Technology, Tehran, Iran, 501 pp [ISBN: 96493442-0-9]
Sadeghi K, 2004. An analytical approach to predict downtime in Caspian Sea for
installation operations. 6th International Conference on Ports, Coasts and Marine
Structures (ICOPMAS 2004), Tehran, Iran, Dec. 2004.
U.S. Army Coastal Engineering Research Center, 1980. Shore protection manual,
Vol. 1 & 2, 4th edition.
12