Document no.: Contract no./project no.: Filing no.:
TNE MTO PTM MGE RA 55
Classification: Distribution:
Internal Internal
Distribution date: Rev. date: Rev. no.: Copy no.:
2010-01-16 2010-01-16 1
Author(s)/Source(s):
Martin Mathiesen, Polytec Foundation
Subjects:
Wind, waves, current, temperature and salinity
Remarks:
Valid from: Updated:
Responsible publisher: Authority to approve deviations:
Techn. responsible: Name: Date/Signature:
Responsible: Name: Date/Signature:
TNE MTO PTM MMG MGE Einar Nygaard
Recommended: Name: Date/Signature:
TNE MTO PTM MSR STAV Sverre K. Haver
Approved: Name: Date/Signature:
TNE MTO PTM MMG MGE Eelco van Raaij
Table of contents
1 Introduction... 5
1.1 Katla Field... 5
1.2 Codes, regulations and design premises... 5
1.3 Conventions and definitions... 6
1.3.1 Units... 6
1.3.2 Directions ... 6
1.3.3 Seasons... 6
1.3.4 Extremes... 6
1.3.5 Use of extreme values ... 7
1.4 Climate change... 7
2 Wind ... 8
2.1 Wind data ... 8
2.2 Long-term wind statistics... 20
2.3 Wind profile and gust... 24
2.4 Wind spectra ... 27
2.5 Operational data ... 29
3 Waves ... 33
3.1 Wave data... 33
3.2 Long-term wave statistics ... 35
3.3 Short-term sea states ... 48
3.3.1 Wave spectra ... 48
3.3.2 Directional wave spectra ... 52
3.3.3 Wave-induced bottom currents ... 52
3.4 Individual waves ... 54
3.5 Operational data ... 61
4 Currents ... 67
4.1 Current data... 67
4.2 Long-term current statistics... 67
5 Water level ... 68
5.1 Tidal elevations ... 68
5.2 Storm surge ... 68
5.3 Total water level... 69
5.4 Sea level rise ... 69
6 Splash zone... 70
7 Marine growth... 71
8 Snow and icing... 72
8.1 General requirements ... 72
8.2 Snow ... 72
8.3 Icing ... 72
9.1 Sea temperatures ... 73
9.2 Air temperature ... 75
10 Salinity ... 79
11 References ... 81
1 Introduction
1.1 Katla Field
The Katla Field is located (at 60.30º N, 02.53º E) in the Northern North Sea as shown in Figure 1.1. The water depth is about 110 m. The Katla MDB is also representative for the Oseberg Field.
Figure 1.1 Map showing location of the Katla Field in the Northern North Sea.
1.2 Codes, regulations and design premises
The design of facilities in the petroleum industry is governed by Regulations relating to design and outfitting of facilities etc. in the petroleum activities [1] issued by the Norwegian Petroleum Directorate (presently: Petroleum Safety Authority Norway). Section 10 of the guidelines to these regulations [2]
stipulates that in order to fulfil the requirements to loads, load effects, resistance and combinations of loads the following standards should be used:
• For load bearing structures: NORSOK N-001 [3], N-003 [4] and N-004 [5] for steel structures and NS 3473 [7] for concrete structures.
• For pipeline systems: ISO 13623 [9] Chapter 6 and DNV OS-F101 [10] Sections 3,4 and 5 for steel lines, DNV OS F-201 [11] Sections 3,4 and 5 for catenary metallic risers and API 17J [13]
Chapter 5 for flexible pipeline systems.
For structures where both the structural behaviour and the load process are of a linear nature, a long term stochastic response analysis is recommended (by Statoil). This is also the case for slightly non- linear structural systems if some sort of linearization is expected to yield results of sufficient accuracy.
For structures dominated by drag induced non-linearities, the design wave concept together with a proper dynamic amplification factor is recommended. If the structure essentially behaves quasi-
statically, the design wave concept can be adequate. If dynamics (or for other reasons lower waves) are important, the structural behaviour during a specified design storm can be simulated. In this case, the contour line concept, see e.g. [4] and [21], is recommended, e.g. the 10-2 – probability (annual
probability of exceedance) design storm is taken as the most unfavourable sea state along the 10-2 – probability contour line. The duration of the sea state is taken to be 3 hours, and as an estimate of the 10-2 response, the 90% fractile of the 3-hour extreme value distribution is recommended.
1.3 Conventions and definitions
1.3.1 Units
Parameters and data values are (with some exceptions) given in the International System of Units (SI).
Current, wind and wave directions are given in degrees (º) measured clockwise from north.
1.3.2 Directions Current
The current direction, measured in degrees clockwise from north, is the direction towards which the current is flowing. Currents of direction 90º are towards the east.
Wind
The wind direction, measured in degrees clockwise from north, is the direction from which the wind is blowing. Winds of direction 90º are coming from the east.
Waves
The wave direction, measured in degrees clockwise from north, is the direction from which the waves are coming. Waves of direction 90º are coming from the east.
1.3.3 Seasons
Seasonal variations are given on a monthly basis.
1.3.4 Extremes
Extreme values are, in NORSOK Standard N-003 [4], defined through their annual probabilities of exceedance referred to as q - probability values. A q - probability value is the value corresponding to an
and return period, R, is given by:
⎟⎠
⎜ ⎞
⎝⎛−
−
= R
q 1 exp T (1.1)
where T = 1 year.
It is seen that q = 0.63 for R = 1 year and that q is approximately 10-1 and 10-2 for R = 10 and 100 years, respectively.
1.3.5 Use of extreme values
When predicting extreme structural response using directional weather extremes it shall be verified that the obtained extreme response is in agreement with overall requirements regarding annual exceedance probabilities.
1.4 Climate change
The report “Klima i Norge 2100” [20] gives a description of the expected change in climate in Norway and surrounding waters through the 21st century.
The climate models predict little or no change in mean wind speed. The frequency of higher wind speeds is expected to increase, but this is uncertain.
The climate models predict no change in the wave climate in the Northern North Sea [20, Figure 5.4.4].
2 Wind
2.1 Wind data
Wind data are available from the Wam10 hindcast model operated by the Norwegian Meteorological Institute. The data chosen for analysis are from the grid point at 60.31º N, 02.50º E and cover the period 1958 – 2008 (51 years). The sample interval is 3 hours.
The Wam10 wind data are found to be of good quality for wind speeds up to about 15 m/s. Wind speeds higher than this are found to be too low. Consequently, wind speeds higher than 15 m/s have been adjusted (corrected) prior to analysis. The corrected wind speed, UCor, is computed from:
[
1 ( Min)]
Cor U pU U
U = + − for U ≥UMin (2.1)
where U is (the Wam10) wind speed, p = 0.01 (m/s)-1 and UMin = 15.0 m/s.
Figure 2.1 shows the (all-year) wind rose from the Katla Field for the period 1958 – 2008. The wind rose shows the percentage of observations within each 30° sector. Figure 2.2 and Figure 2.3 show wind roses for each month separately.
0
30
60
90
120
150 180
210 240
270 300
330
0% 5% 10% 15%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30
Katla Field - Year
Figure 2.1 All-year wind rose for the Katla Field for the period 1958 – 2008.
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - January
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - February
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - March
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - April
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - May
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - June
Figure 2.2 Wind roses for the Katla Field for the months of January – June.
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - July
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - August
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - September
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - October
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - November
0
30
60
90
120
150 180
210 240 270
300 330
0% 5% 10% 15% 20%
Wind speed (m/s)
>0 - 5
>5 - 10
>10 - 15
>15 - 20
>20 - 25
>25 - 30
>30 Katla Field - December
Figure 2.3 Wind roses for the Katla Field for the months of July – December.
Table 2.1 shows the annual direction sample distribution of non-exceedance of 1-hour average wind speed at the Katla Field. Table 2.2 - Table 2.4 show the monthly sample distributions.
Table 2.5 shows the monthly sample distribution of non-exceedance of wind speed.
Table 2.1 Annual direction sample distribution of non-exceedance (%) of 1-hour average wind speed 10 m above sea level at the Katla Field.
Wind
(m/s) 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° Omni
< 2 0.24 0.26 0.27 0.28 0.26 0.25 0.27 0.26 0.27 0.25 0.24 0.29 3.14
< 4 1.17 1.16 0.98 0.96 1.00 1.09 1.07 1.02 1.03 1.02 1.04 1.17 12.70
< 6 2.79 2.49 1.86 1.77 2.09 2.51 2.63 2.44 2.37 2.30 2.40 2.70 28.36
< 8 4.76 3.71 2.42 2.29 3.03 4.12 4.79 4.29 4.04 3.81 3.79 4.45 45.50
< 10 6.90 4.74 2.67 2.55 3.76 5.86 7.22 6.15 5.78 5.22 5.08 6.04 61.97
< 12 8.78 5.49 2.78 2.70 4.29 7.49 9.37 7.76 7.36 6.36 6.02 7.42 75.80
< 14 10.12 5.99 2.83 2.79 4.70 9.02 11.04 8.93 8.49 7.23 6.59 8.34 86.08
< 16 10.83 6.24 2.86 2.83 4.94 10.21 12.18 9.67 9.23 7.77 6.93 8.91 92.60
< 18 11.13 6.34 2.86 2.84 5.04 11.14 12.91 10.06 9.61 8.07 7.12 9.22 96.35
< 20 11.27 6.36 2.86 2.84 5.10 11.72 13.30 10.25 9.76 8.22 7.22 9.39 98.31
< 22 11.33 6.37 2.86 2.84 5.13 12.10 13.48 10.32 9.85 8.27 7.27 9.47 99.30
< 24 11.37 6.37 5.14 12.30 13.54 10.35 9.88 8.30 7.30 9.50 99.75
< 26 11.37 6.37 5.15 12.40 13.56 10.36 9.89 8.31 7.30 9.51 99.92
< 28 11.38 5.15 12.44 13.57 10.36 9.89 8.31 7.30 9.51 99.98
< 30 11.38 12.45 13.57 9.89 8.31 7.30 9.51 99.99
< 32 11.38 12.45 9.89 7.31 9.52 100.00
Total 11.38 6.37 2.86 2.84 5.15 12.45 13.57 10.36 9.89 8.31 7.31 9.52 100.00
Mean 9.0 7.5 5.3 5.6 7.7 10.9 10.0 9.2 9.3 8.9 8.3 8.8 9.0 Maximum 31.5 24.1 20.3 21.0 26.3 31.1 29.8 27.8 31.5 28.0 30.9 30.9 31.5
Table 2.2 Direction sample distribution of non-exceedance (%) of 1-hour average wind speed 10 m above sea level for the months January – April at the Katla Field.
Wind
(m/s) 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° Omni January
< 5 1.08 1.25 1.14 0.94 1.03 1.13 0.98 0.94 0.99 1.03 1.08 0.97 12.56
< 10 3.98 3.46 2.27 2.05 2.66 3.72 3.99 4.74 4.69 4.30 4.14 3.80 43.81
< 15 6.90 5.09 2.55 2.48 4.03 8.10 9.72 9.81 9.06 7.59 6.33 6.64 78.30
< 20 7.75 5.37 2.56 2.49 4.41 12.13 13.28 11.86 10.93 9.22 7.12 7.61 94.73
< 25 7.87 5.40 4.52 14.05 13.99 12.27 11.46 9.60 7.31 7.89 99.42
< 30 7.89 4.53 14.34 14.10 12.29 11.53 9.61 7.32 7.91 99.98 Total 7.89 5.40 2.56 2.49 4.53 14.35 14.10 12.29 11.54 9.61 7.32 7.91 100.00 Mean 10.1 8.5 6.0 6.6 9.2 13.9 12.6 11.5 11.4 11.1 9.9 10.5 11.1 Maximum 26.3 21.9 16.4 15.5 26.3 31.1 29.8 27.8 31.5 26.7 25.5 25.6 31.5 February
< 5 1.07 1.57 1.65 1.09 1.17 1.35 1.25 1.28 1.26 1.33 0.96 1.12 15.09
< 10 3.48 4.49 2.96 2.07 2.97 4.59 5.33 6.13 5.10 5.08 3.73 3.98 49.91
< 15 5.63 5.88 3.19 2.27 4.28 9.01 10.81 10.67 9.84 8.41 5.91 6.84 82.74
< 20 6.46 5.99 3.22 2.33 4.68 12.59 13.78 12.49 11.39 9.55 6.71 7.82 97.02
< 25 6.65 4.75 13.66 14.26 12.69 11.63 9.78 6.79 8.07 99.84
< 30 6.67 13.77 14.28 8.08 99.99
Total 6.67 5.99 3.22 2.33 4.75 13.78 14.28 12.69 11.63 9.78 6.79 8.08 100.00 Mean 10.1 7.7 5.5 5.9 8.9 12.6 11.7 10.5 10.7 10.0 9.8 10.4 10.3 Maximum 26.7 18.8 17.1 17.8 23.3 30.2 26.2 23.2 23.2 24.5 23.7 26.0 30.2 March
< 5 1.22 1.40 1.48 1.31 1.55 1.81 1.48 1.25 1.29 1.19 1.08 1.11 16.17
< 10 4.57 3.86 2.50 2.43 3.95 5.69 6.89 5.56 5.28 4.22 3.70 3.78 52.44
< 15 6.93 4.96 2.66 2.75 5.69 10.75 13.04 9.67 9.29 7.04 5.66 6.87 85.31
< 20 7.47 5.10 2.66 2.77 6.02 14.01 15.88 10.69 10.53 8.07 6.39 8.03 97.62
< 25 7.64 5.11 2.78 6.04 15.07 16.33 10.75 10.69 8.14 6.50 8.16 99.87
< 30 15.18 16.36 100.00
Total 7.64 5.11 2.66 2.78 6.04 15.18 16.36 10.75 10.69 8.14 6.50 8.16 100.00 Mean 9.4 7.5 5.2 5.8 8.4 12.0 11.2 9.9 10.2 10.0 9.6 10.5 10.0 Maximum 24.7 23.2 14.5 20.8 22.4 28.3 27.1 22.4 23.5 24.5 23.9 24.3 28.3 April
< 5 2.17 2.46 2.27 1.94 2.06 1.96 2.33 1.76 1.73 1.52 1.56 1.90 23.67
< 10 7.56 6.67 4.09 3.67 4.79 6.23 8.48 6.27 5.89 4.44 4.27 5.51 67.89
< 15 11.28 9.58 4.27 3.95 5.58 10.13 12.69 8.55 8.11 6.09 5.42 8.43 94.07
< 20 12.27 10.12 3.95 5.69 11.43 13.62 8.75 8.26 6.25 5.69 9.23 99.53
< 25 12.38 11.61 13.65 6.27 5.69 9.33 99.98
< 30 11.63 100.00
Total 12.38 10.12 4.27 3.95 5.69 11.63 13.65 8.75 8.26 6.27 5.69 9.33 100.00 Mean 9.1 8.3 5.3 5.4 6.7 9.8 9.0 8.0 8.0 8.0 7.8 9.2 8.3 Maximum 22.0 19.6 14.4 15.5 17.7 26.2 23.3 17.8 17.6 23.0 20.3 23.3 26.2
Table 2.3 Direction sample distribution of non-exceedance (%) of 1-hour average wind speed 10 m above sea level for the months May - August at the Katla Field.
Wind
(m/s) 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° Omni May
< 5 3.23 2.98 1.86 2.21 2.71 2.44 2.17 2.17 1.93 1.93 2.21 2.79 28.64
< 10 12.30 7.35 3.34 3.72 5.60 8.40 8.02 6.10 5.08 4.33 5.07 7.63 76.94
< 15 18.05 9.34 3.55 3.83 6.41 12.43 10.65 7.16 6.23 4.99 5.90 9.18 97.71
< 20 18.47 9.49 3.56 6.51 13.13 10.91 7.26 6.36 5.07 5.95 9.38 99.91
< 25 6.53 13.16 5.08 5.98 9.38 100.00
< 30
Total 18.47 9.49 3.56 3.83 6.53 13.16 10.91 7.26 6.36 5.08 5.98 9.38 100.00 Mean 8.5 7.3 5.3 4.8 6.4 8.7 8.0 6.9 7.1 6.5 6.5 7.0 7.4 Maximum 18.8 18.8 17.1 14.6 20.4 22.8 17.1 17.1 19.3 21.1 21.5 20.5 22.8 June
< 5 3.14 2.52 1.70 1.94 2.47 2.87 2.83 2.53 2.43 2.39 2.74 3.15 30.72
< 10 12.10 5.78 2.73 2.70 4.56 7.58 9.34 6.68 5.84 6.02 6.66 9.62 79.62
< 15 18.91 6.99 2.79 2.75 4.86 9.45 11.49 7.54 7.35 7.08 7.64 11.75 98.60
< 20 19.58 7.10 4.87 9.60 11.58 7.59 7.44 7.17 7.66 11.83 99.97
< 25 19.59 11.58 7.60 7.45 100.00
< 30
Total 19.59 7.10 2.79 2.75 4.87 9.60 11.58 7.60 7.45 7.17 7.66 11.83 100.00 Mean 8.9 6.8 4.5 4.0 5.4 7.3 7.4 6.5 7.0 6.7 6.3 7.2 7.1 Maximum 20.0 19.2 14.4 12.0 15.4 18.3 20.0 23.3 22.0 18.3 18.3 16.3 23.3 July
< 5 3.15 2.70 1.49 1.54 1.76 2.44 2.83 2.66 2.83 2.93 3.18 3.87 31.37
< 10 10.46 5.69 2.39 2.42 3.37 7.03 10.01 7.38 7.60 7.41 8.70 11.10 83.55
< 15 15.43 6.35 2.43 2.54 3.56 8.97 11.83 8.06 8.63 8.37 9.62 13.51 99.30
< 20 15.70 3.57 9.08 11.86 8.06 8.69 8.43 9.69 13.60 100.00
< 25
< 30
Total 15.70 6.35 2.43 2.54 3.57 9.08 11.86 8.06 8.69 8.43 9.69 13.60 100.00 Mean 8.3 5.9 4.7 4.7 5.3 7.4 7.1 6.3 6.6 6.4 6.5 7.1 6.8 Maximum 17.8 15.0 13.7 13.3 17.5 19.6 19.6 15.1 16.4 19.3 18.7 17.9 19.6 August
< 5 3.55 2.55 1.65 1.44 1.68 2.59 2.70 2.59 2.55 2.66 3.24 3.72 30.91
< 10 10.78 5.01 2.74 2.32 3.83 7.58 9.39 7.33 7.61 7.08 7.75 9.58 81.00
< 15 14.33 5.76 2.85 2.47 4.44 10.26 12.38 8.66 9.10 8.02 8.57 11.84 98.69
< 20 14.58 5.78 2.86 4.48 10.57 12.55 8.74 9.23 8.07 8.63 11.98 99.94
< 25 14.60 12.56 9.25 100.00
< 30
Total 14.60 5.78 2.86 2.47 4.48 10.57 12.56 8.74 9.25 8.07 8.63 11.98 100.00 Mean 7.8 6.0 4.9 4.8 6.5 7.8 7.8 6.9 7.1 6.6 6.3 7.0 7.0 Maximum 21.4 15.9 15.9 14.8 17.6 18.1 20.1 17.5 21.3 16.6 17.8 18.1 21.4
Table 2.4 Direction sample distribution of non-exceedance (%) of 1-hour average wind speed 10 m above sea level for the months September - December at the Katla Field.
Wind
(m/s) 0° 30° 60° 90° 120° 150° 180° 210° 240° 270° 300° 330° Omni September
< 5 1.87 1.55 1.63 1.54 1.70 1.50 1.95 1.91 1.80 1.39 1.53 1.76 20.12
< 10 6.73 4.08 2.73 2.82 4.22 5.96 8.28 7.01 6.83 6.05 5.66 6.16 66.52
< 15 9.38 4.66 2.79 2.99 5.11 10.51 13.10 10.57 10.13 8.78 7.67 8.56 94.26
< 20 9.93 4.75 3.00 5.26 12.16 13.86 11.02 10.65 9.17 7.95 8.84 99.39
< 25 9.99 4.76 3.01 5.29 12.30 13.91 11.12 10.69 9.23 8.02 8.85 99.96
< 30 10.69 9.24 8.03 99.98
Total 9.99 4.76 2.79 3.01 5.29 12.30 13.91 11.12 10.69 9.24 8.05 8.85 100.00 Mean 8.6 6.8 4.8 5.3 7.2 10.4 9.3 8.8 8.8 8.8 8.5 8.3 8.6 Maximum 22.9 22.1 13.9 21.0 23.8 22.9 23.0 23.2 26.3 28.0 30.9 21.9 30.9 October
< 5 1.04 1.14 1.08 1.05 1.15 1.57 1.31 1.29 1.27 1.42 1.05 1.19 14.56
< 10 3.55 3.76 2.05 2.29 3.57 6.11 8.33 6.58 5.80 5.04 3.91 3.83 54.81
< 15 5.76 5.12 2.25 2.77 5.01 11.60 14.82 11.21 10.02 7.95 5.82 6.28 88.61
< 20 6.54 5.42 2.29 2.79 5.42 14.50 16.68 12.18 10.90 8.72 6.23 6.83 98.51
< 25 6.72 5.45 2.30 5.50 14.99 16.84 12.28 10.97 8.75 6.36 6.93 99.90
< 30 6.74 15.05 12.29 10.98 99.99
Total 6.75 5.45 2.30 2.79 5.50 15.05 16.84 12.29 10.98 8.75 6.36 6.93 100.00 Mean 10.0 8.5 5.7 6.7 8.9 11.4 10.3 9.9 9.8 9.3 9.2 9.5 9.7 Maximum 31.5 21.0 20.3 15.8 24.3 26.8 23.2 25.6 28.6 21.6 23.4 23.8 31.5 November
< 5 1.08 1.13 1.11 1.01 1.17 1.18 1.23 1.23 1.30 1.03 1.10 1.00 13.57
< 10 4.11 3.86 2.16 2.10 3.13 4.29 5.52 5.54 5.57 4.97 4.17 3.99 49.41
< 15 7.06 5.40 2.46 2.48 5.06 8.37 11.05 10.07 9.65 8.17 6.63 7.00 83.41
< 20 8.27 5.79 2.48 2.55 5.54 11.54 13.71 11.45 10.80 9.29 7.21 8.56 97.19
< 25 8.47 5.60 12.62 14.20 11.67 10.94 9.35 7.32 8.81 99.80
< 30 12.73 14.22 8.86 99.98
Total 8.47 5.79 2.48 2.55 5.60 12.73 14.22 11.67 10.94 9.35 7.32 8.87 100.00 Mean 10.4 8.5 6.1 6.7 9.2 12.6 11.6 10.4 10.1 10.0 9.4 11.0 10.4 Maximum 24.7 18.8 15.8 18.1 24.6 30.0 27.1 24.6 24.8 23.5 23.0 30.5 30.5
December
< 5 1.19 1.20 1.07 1.05 1.04 1.11 1.12 1.05 0.96 1.14 1.16 1.19 13.28
< 10 4.10 3.38 2.30 2.11 2.74 3.99 4.51 5.67 5.16 4.44 3.78 4.22 46.39
< 15 7.02 4.86 2.46 2.53 4.16 7.12 9.40 10.97 10.18 8.27 6.55 7.46 80.97
< 20 7.96 5.12 2.47 2.56 4.78 9.90 11.94 13.01 12.07 9.73 7.39 8.90 95.84
< 25 8.10 5.16 4.90 11.69 12.54 13.20 12.32 9.95 7.61 9.12 99.65
< 30 8.12 11.95 12.56 13.21 12.33 9.96 7.62 9.15 99.99 Total 8.12 5.16 2.47 2.56 4.90 11.95 12.56 13.21 12.33 9.96 7.62 9.16 100.00 Mean 10.1 8.5 5.9 6.7 9.6 13.4 11.9 11.0 11.0 10.7 10.2 10.7 10.8 Maximum 27.6 24.1 16.0 16.4 24.1 28.7 26.6 25.8 25.9 26.8 25.6 30.9 30.9
Table 2.5 Monthly and annual sample distribution of non-exceedance (%) of 1-hour average wind speed 10 m above sea level at the Katla Field.
Wind
(m/s) Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec Year
< 2 1.84 2.08 2.25 3.24 4.48 5.29 4.47 5.22 2.79 2.22 1.83 1.95 3.14
< 4 7.36 9.43 9.41 14.37 17.44 18.68 18.67 19.47 12.14 9.01 8.21 8.00 12.70
< 6 17.29 20.36 21.97 31.99 38.58 40.42 42.87 41.30 27.25 20.26 19.02 18.42 28.36
< 8 29.89 33.80 36.14 50.29 59.33 61.72 65.40 63.13 45.98 35.68 32.78 31.14 45.50
< 10 43.15 49.07 51.64 67.10 76.18 78.92 82.81 80.27 65.57 53.98 48.57 45.58 61.97
< 12 57.47 64.19 66.61 80.92 88.10 90.54 93.61 91.90 80.47 70.61 63.95 60.64 75.80
< 14 71.41 77.10 79.61 90.52 95.49 97.04 98.36 97.26 90.72 83.34 77.34 74.29 86.08
< 16 82.69 86.59 88.82 95.89 98.68 99.27 99.71 99.34 96.08 91.51 87.41 84.98 92.60
< 18 89.93 93.42 94.67 98.48 99.67 99.80 99.94 99.87 98.45 96.27 93.84 91.75 96.35
< 20 94.73 97.02 97.62 99.53 99.91 99.97 100.00 99.94 99.39 98.51 97.19 95.84 98.31
< 22 97.65 98.82 99.07 99.88 99.99 99.98 100.00 99.75 99.45 98.86 98.15 99.30
< 24 99.01 99.72 99.68 99.96 100.00 100.00 99.94 99.81 99.58 99.28 99.75
< 26 99.64 99.89 99.94 99.98 99.97 99.93 99.88 99.85 99.92
< 28 99.91 99.98 99.99 100.00 99.98 99.98 99.95 99.97 99.98
< 30 99.98 99.99 100.00 99.98 99.99 99.98 99.99 99.99
< 32 100.00 100.00 100.00 100.00 100.00 100.00 100.00 Total 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00 100.00
Mean 11.1 10.3 10.0 8.3 7.4 7.1 6.8 7.0 8.6 9.7 10.4 10.8 9.0 Maximum 31.5 30.2 28.3 26.2 22.8 23.3 19.6 21.4 30.9 31.5 30.5 30.9 31.5
2.2 Long-term wind statistics
The long-term distribution of wind speed is modelled in terms of a Weibull distribution:
⎪⎭
⎪⎬
⎫
⎪⎩
⎪⎨
⎧
⎥⎦
⎢ ⎤
⎣
−⎡ −
−
=
γ
β α u u
F( ) 1 exp (2.2)
where:
u Wind speed, 1-hour average α Location parameter β Scale parameter γ Shape parameter
Extreme values, uR, corresponding to a return period, R, are obtained by inverting Equation (2.2) for a cumulative probability F = 1 – τ/pR, i.e.:
τ γ
β α
/ 1
ln ⎥
⎦
⎢ ⎤
⎣
⎡ ⎟⎟⎠
⎜⎜ ⎞
⎝
− ⎛ +
= pR
uR
(2.3)
where
τ Duration of event (= 1 hour for mean wind speed)
p Sector or monthly probability (=1/12 for monthly omni-directional distributions) R Return period
The annual probability of exceedance, q, is given by:
⎟⎠
⎜ ⎞
⎝⎛−
−
= R
q 1 exp T (2.4)
where T = 1 year. It is seen that q = 0.63 for R = 1 year and that q is approximately 10-1 and 10-2 for R = 10 and 100 years, respectively.
Figure 2.4 shows the observed and fitted distributions of wind speed at the Katla Field.
Figure 2.4 Observed (green dots) and fitted (red line) distributions of 1-hour average wind speed at the Katla Field.
In the analyses of directional and monthly extremes the data are smoothed prior to computations. This is done by adding 50 % of the data from the two adjacent sectors (months) to the central sector (month).
The probability for each sector (month) is kept unchanged. The directional (monthly) extremes for the most severe direction (150º) and month (January) are adjusted to the omni-directional (all-year) extremes. No adjustment is performed for the other directions (months).
Figure 2.5 and Table 2.6 show directional Weibull parameters and corresponding extremes of 1-hour average wind speed at the Katla Field. Figure 2.6 and Table 2.7 show monthly Weibull parameters and corresponding extremes.
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
0º 30º 60º 90º 120º 150º 180º 210º 240º 270º 300º 330º
Wind speed ‐m/s
Katla Field
q = 0.63 q = 0.10 q = 0.01
Figure 2.5 Direction variation of 1-hour average wind speed of annual probability of exceedance of 0.63, 10-1 and 10-2 10 m above sea level at the Katla Field.
Table 2.6 Directional Weibull parameters and corresponding extreme values for 1-hour average wind speed 10 m above sea level at the Katla Field. Duration of event is 1 hour.
Weibull parameters Annual probability of exceedance Direction Sector
prob. Shape Scale Location 0.63 10-1 10-2
% - m/s m/s m/s m/s m/s
0º 11.38 2.100 9.64 0.13 24 28 31
30º 6.37 2.000 8.89 0.00 22 26 29
60º 2.86 1.741 6.61 0.37 18 22 25
90º 2.84 1.520 6.14 0.73 20 25 29
120º 5.15 1.950 10.06 0.00 26 30 34
150º 12.45 2.155 11.47 0.00 28 32 36
180º 13.57 2.243 11.26 0.01 27 31 34
210º 10.36 2.200 10.62 0.00 25 29 32
240º 9.89 2.200 10.29 0.00 25 28 31
270º 8.31 2.050 9.79 0.14 25 29 32
300º 7.31 1.930 9.08 0.48 24 28 32
330º 9.52 2.000 9.38 0.40 25 29 32
0º - 360º 100.00 2.048 9.96 0.08 29 33 36
0.0 5.0 10.0 15.0 20.0 25.0 30.0 35.0 40.0
Jan Feb Mar Apr May Jun Jul Aug Sept Oct Nov Dec
Wind speed ‐m/s
Katla Field
q = 0.63 q = 0.10 q = 0.01
Figure 2.6 Monthly variation of 1-hour average wind speed of annual probability of exceedance of 0.63, 10-1 and 10-2 10 m above sea level at the Katla Field.
Table 2.7 Monthly and annual Weibull parameters and corresponding extreme values for 1-hour average wind speed 10 m above sea level at the Katla Field. Duration of event is 1 hour.
Weibull parameters Annual probability of exceedance Month Annual
prob. Shape Scale Location 0.63 10-1 10-2
% - m/s m/s m/s m/s m/s
Jan 8.33 2.245 12.19 0.00 28 32 36
Feb 8.33 2.237 11.75 0.00 27 31 35
Mar 8.33 2.173 10.86 0.00 26 30 33
Apr 8.33 2.097 9.56 0.00 24 27 30
May 8.33 2.129 8.47 0.00 21 24 26
Jun 8.33 2.185 7.97 0.00 19 22 24
Jul 8.33 2.226 7.78 0.00 18 21 23
Aug 8.33 2.142 8.15 0.08 20 23 25
Sept 8.33 2.178 9.46 0.05 23 26 29
Oct 8.33 2.299 10.81 0.00 25 28 31
Nov 8.33 2.307 11.60 0.00 26 30 33
Dec 8.33 2.282 12.10 0.00 28 32 35
Year 100.00 2.048 9.96 0.08 29 33 36
2.3 Wind profile and gust
According to the NORSOK Standard N-003 [4, Section 6.3.2] the wind speed U(z,t) at height z (m) above sea level and corresponding averaging period t (s) less than or equal to t0 = 3600 s may be calculated as:
⎥⎦
⎢ ⎤
⎣
⎡
⎟⎟⎠
⎜⎜ ⎞
⎝
⋅ ⎛
⋅
−
⋅
=
0
ln ) ( 41 . 0 1 ) ( ) ,
( t
z t I z
U t z
u u (2.5)
where the 1-hour mean wind speed U(z) (m/s) is given by:
⎥⎦
⎢ ⎤
⎣
⎡ ⎟
⎠
⎜ ⎞
⎝
⋅ ⎛ +
⋅
= 1 ln 10
)
( 0 z
C U
z
U (2.6)
[
0]
122 1 0.15 10
73 .
5 U
C = ⋅ − ⋅ + ⋅ (2.7)
where the turbulence intensity Iu(z) is given by:
[
0]
0.22043 10 . 0 1 06 . 0
−
⎟⎠
⎜ ⎞
⎝
⋅⎛
⋅ +
⋅
= z
U
Iu (2.8)
where Uo (m/s) is the 1 hour average wind speed at z = 10 m.
Figure 2.7 and Table 2.8 show (scaled) wind profiles for wind speeds from 5 to 35 m/s at z = 10 m.
Figure 2.8 and Table 2.9 show (scaled) wind profiles for various averaging times when U0 = 36.0 m/s corresponding to an annual probability of exceedance of 10-2.
Structures or structural components that are not sensitive to wind gusts may be calculated by
considering the wind action as static. In the case of structures or structural parts where the maximum dimension is less than approximately 50 m, 3 s wind gusts shall be used when calculating static wind actions. In the case of structures or structural parts where the maximum length is greater than 50 m, the length of averaging for wind may be increased to 15 s. When design actions due to wind need to be combined with extreme actions due to waves and current and actions due to waves and/or currents are governing, wind speed averaged over a 1 min period can be used. A longer averaging period may be used if properly documented; NORSOK Standard N-003 [4, Section 6.3.3].
0 10 20 30 40 50 60 70 80 90 100
0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.30 1.40
Height above sea level ‐m
Relative wind speed
Wind Profiles
u10=5 m/s u10=10 m/s u10=15 m/s u10=20 m/s u10=25 m/s u10=30 m/s u10=35 m/s
Figure 2.7 Wind profiles for various values of wind, u10, 10 m above sea level.
Table 2.8 Wind profiles: Wind speed at height z relative to wind speed at z = 10 m.
Wind speed (m/s) at z = 10 m above sea level Height
above sea
level (m) 5 10 15 20 25 30 35
100 1.17 1.21 1.24 1.26 1.29 1.31 1.33 90 1.17 1.20 1.23 1.25 1.27 1.30 1.31 80 1.16 1.19 1.21 1.24 1.26 1.28 1.30 70 1.15 1.18 1.20 1.22 1.24 1.26 1.28 60 1.14 1.16 1.19 1.21 1.22 1.24 1.26 50 1.12 1.15 1.17 1.18 1.20 1.22 1.23 40 1.11 1.13 1.14 1.16 1.17 1.19 1.20 30 1.08 1.10 1.11 1.13 1.14 1.15 1.16 20 1.05 1.06 1.07 1.08 1.09 1.09 1.10 10 1.00 1.00 1.00 1.00 1.00 1.00 1.00
8 0.98 0.98 0.98 0.97 0.97 0.97 0.97
6 0.96 0.95 0.95 0.94 0.94 0.93 0.93
4 0.93 0.92 0.91 0.89 0.89 0.88 0.87
2 0.88 0.85 0.83 0.82 0.80 0.78 0.77
1 0.83 0.79 0.76 0.74 0.71 0.69 0.67
0 20 40 60 80 100 120 140 160
1.00 1.10 1.20 1.30 1.40 1.50 1.60 1.70 1.80
Height above sea level ‐m
Relative wind speed
Wind profiles
1 hour 10 minutes 1 minute 15 seconds 3 seconds
Figure 2.8 Wind profiles for various averaging times when U0 = 36.0 m/s.
Table 2.9 Wind speed at height z relative to wind speed at z = 10 m for various averaging times when U0 = 36.0 m/s corresponding to annual probability of exceedance of 10-2.
Averaging time Height
(m) 1 hour 10 minutes 1 minute 15 seconds 3 seconds
10 1.00 1.11 1.26 1.34 1.44
20 1.10 1.21 1.34 1.43 1.52
30 1.16 1.26 1.39 1.47 1.56
40 1.20 1.30 1.43 1.51 1.59
50 1.23 1.33 1.46 1.53 1.62
60 1.26 1.36 1.48 1.55 1.64
70 1.28 1.38 1.50 1.57 1.65
80 1.30 1.39 1.51 1.58 1.67
90 1.32 1.41 1.53 1.60 1.68
100 1.33 1.42 1.54 1.61 1.69
110 1.35 1.44 1.55 1.62 1.70
120 1.36 1.45 1.56 1.63 1.71
130 1.37 1.46 1.57 1.64 1.72
140 1.38 1.47 1.58 1.65 1.73
150 1.39 1.48 1.59 1.66 1.73
2.4 Wind spectra
For structures and structural elements for which the dynamic wind behaviour is of importance, the following 1-point wind spectrum shall be used for the spectral density of the longitudinal wind speed fluctuations [4, Section 6.3.2], Andersen and Løvseth [17]:
(
f n)
nU z f
S
3 5
45 . 2 0
0
1 ~
10 320 10
) (
+
⎟⎠
⎜ ⎞
⎝
⋅⎛
⎟⎠
⎜ ⎞
⎝
⋅⎛
= (2.9)
where n = 0.468, and
75 . 0 3 0
2
10 172 10
~ −
⎟⎠
⎜ ⎞
⎝
⋅⎛
⎟⎠
⎜ ⎞
⎝
⋅⎛
⋅
= z U
f
f (2.10)
where
S(f) (m2s-2/Hz) Spectral density at frequency f (Hz) z (m) Height above sea level
U0 (m/s) 1- hour mean wind speed 10 m above sea level
The wind profile description Equations (2.5) - (2.8) and the spectral description Equations (2.9) - (2.10) are valid both for moderate and strong (extreme) wind speed conditions. However, for moderate
conditions (U0 < 15 – 20 m/s) and non-neutral stability conditions both the wind profile and the wind spectrum may deviate significantly from the above neutral descriptions. For the non-neutral wind profile reference is made to Plate [24] and for the wind spectrum to Andersen and Løvseth [18].
The squared correlation between the spectral densities, Equation (2.9), of the longitudinal wind speed fluctuations of frequency f between two points is described in terms of the two-point coherence spectrum.
The recommended coherence spectrum between two points at:
• levels z1 and z2
• across-wind positions y1 and y2
• along-wind positions x1 and x2 is given by:
⎥⎥
⎥
⎦
⎤
⎢⎢
⎢
⎣
⎡
⎟⎠
⎜ ⎞
⎝
⋅⎛
−
=
∑
= 2 1 3
1 2 0
exp 1 ) (
i
Ai
f U
Coh (2.11)
where
i i
i p
g q
i r i
i f z
A =α ⋅ ⋅Δ ⋅ − (2.12)
( )
10
2 1 2
1 z
zg z ⋅
= (2.13)
where the coefficients αi, pi, qi, ri and the separations Δi are given in Table 2.10.
Table 2.10 Coefficients and separation for the 3-D (i = 1, 2, 3) coherence spectrum. Separations are given by absolute values.
i Δ qi pi ri αi
1 |x2 – x1| 1.00 0.4 0.92 2.9
2 |y2 - y1| 1.00 0.4 0.92 45.0
3 |z2 - z1| 1.25 0.5 0.85 13.0
2.5 Operational data
Marine operations may be delayed due to wind speeds exceeding prescribed operational levels (limits) leading to a possible increase in the duration of the operations. Marine operations which must be completed without break are called critical. Otherwise they are termed non-critical. The duration statistics presented in the present report is restricted to critical operations, only. Figure 2.9 illustrates how the duration of a critical operation is defined.
Figure 2.9 Example of a critical operation limited by wind speed 10 m/s and needing 12 hours of work to be completed. Work starts as wind speed becomes lower than 10 m/s and is completed before the wind speed exceeds 10 m/s. The duration of the operation is the time from arrival at time t = 0 to completion. The initial window is too short to be used.
Figure 2.10 - Figure 2.15 show expected duration of operations limited by wind speeds of 10 and 15 m/s for 12, 24 and 48 hours. The figures show the expected mean duration and 10, 50 and 90 percentiles.
The figures show duration characteristics for completing a critical operation including waiting time.
Duration is measured from the day the operation is ready for launching. The day of launching is assumed to be an arbitrary day within the relevant month.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean 2.9 2.3 2.0 1.1 0.9 0.9 0.8 0.8 1.3 1.9 2.0 2.4
P10 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
P50 1.6 1.3 1.1 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.2 1.4
P90 7.1 5.5 4.7 2.5 2.0 1.8 1.6 1.7 3.0 4.4 4.7 5.6
0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0
Duration -days
U < 10 m/s for 12 hours
Mean P10 P50 P90
Figure 2.10 Expected duration, including waiting time, in order to perform operations limited by a wind speed (U) of 10 m/s for 12 hours.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean 0.9 0.8 0.7 0.6 0.5 0.5 0.5 0.5 0.6 0.7 0.8 0.8
P10 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
P50 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
P90 1.9 1.6 1.4 0.7 0.5 0.5 0.5 0.5 0.7 1.2 1.5 1.6
0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0
Duration -days
U < 15 m/s for 12 hours
Mean P10 P50 P90
Figure 2.11 Expected duration, including waiting time, in order to perform operations limited by a wind speed (U) of 15 m/s for 12 hours.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean 6.0 4.9 4.6 2.4 1.8 1.7 1.6 1.7 2.9 4.3 5.0 6.0
P10 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
P50 3.8 2.8 2.7 1.5 1.0 1.0 1.0 1.0 1.7 2.6 3.1 3.5
P90 14.1 10.7 11.1 4.9 3.6 3.2 3.0 3.4 6.2 10.3 11.7 14.4 0.0
2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0
Duration -days
U < 10 m/s for 24 hours
Mean P10 P50 P90
Figure 2.12 Expected duration, including waiting time, in order to perform operations limited by a wind speed (U) of 10 m/s for 24 hours.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
Mean 2.0 1.7 1.5 1.2 1.1 1.0 1.0 1.0 1.2 1.4 1.6 1.8
P10 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
P50 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
P90 4.1 3.3 2.8 1.7 1.0 1.0 1.0 1.0 1.8 2.4 3.0 3.4
0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5
Duration -days
U < 15 m/s for 24 hours
Mean P10 P50 P90
Figure 2.13 Expected duration, including waiting time, in order to perform operations limited by a wind speed (U) of 15 m/s for 24 hours.
