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A Monte Carlo approach to joint probability of wave, tide and surge in extreme water level calculations

Prepared by PhysE Limited for the Health and Safety Executive 2009

RR740

Research Report

Health and Safety Executive

A Monte Carlo approach to joint probability of wave, tide and surge in extreme water level calculations

Joseph P Fox MPhys PhD PhysE Limited The Harbour Offices The Quay Yarmouth Isle of Wight PO41 0NT

Extreme Water Level is the total level of the water arising from wave crest, storm surge and tidal level acting in combination with each other throughout an extreme event. Individually, each of these components is relatively well understood. However, the combination of these components is not straightforward and depends on the conditions of the location in question. This study addresses the behaviour of the individual components, their interaction, and their joint probability, leading to the development of a Monte Carlo based approach to the estimation of Extreme Water Level. The study concludes with a review of latest ISO guidance on estimating extreme water levels and a comparison between extreme water level results derived using existing methods, ISO guidance and Monte Carlo simulations. This report and the work it describes were funded by the Health and Safety Executive (HSE). Its contents, including any opinions and/or conclusions expressed, are those of the author alone and do not necessarily reflect HSE policy.

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TABLE OF CONTENTS

EXECUTIVE SUMMARY ................................................................................... 7

1. BACKGROUND ........................................................................................ 1

2. DATA ........................................................................................................ 4

2.1 MEASURED DATA.................................................................................................... 4

2.2 MODEL DATA .......................................................................................................... 4

2.3 OVERVIEW OF MAXIMA AND ASSOCIATED VALUES .................................................... 5

3. WAVE CREST........................................................................................... 6

3.1 KROGSTAD/BORGMAN INTEGRAL ............................................................................. 7

3.2 TROMANS & VANDERSCHUREN METHOD .................................................................. 9

4. TIDES...................................................................................................... 12

4.1 INFLUENCE OF TIDE ON SURGE AND WAVES ........................................................... 13

5. STORMS ................................................................................................. 21

6. RELATIONSHIP BETWEEN SURGE AND WAVE HEIGHT ................... 29

7. MONTE CARLO SIMULATIONS............................................................. 31

7.1 THE PROCESS....................................................................................................... 31

7.1.1 Wave heights ............................................................................................................ 31

7.1.2 Tidal heights............................................................................................................. 33

7.1.3 Surge heights............................................................................................................ 33

7.2 MONTE CARLO OUTPUT STATISTICS ...................................................................... 35

8. RESULTS................................................................................................ 36

8.1 100 YEAR RETURN PERIOD EXTREME WATER LEVELS ........................................... 36

8.2 10,000 YEAR RETURN PERIOD EXTREME WATER LEVELS ...................................... 37

8.3 COMMENTS ON 100 AND 1,000 YEAR EXTREME WATER LEVELS ............................. 38

8.4 MEASURED EXTREME WATER LEVELS.................................................................... 39

8.5 CALIBRATING THE SIMULATION .............................................................................. 40

8.6 100 AND 10,000 YEAR RETURN PERIOD EXTREME WATER LEVELS......................... 41

9. CONCLUSIONS ...................................................................................... 43

10. APPENDIX: SOFTWARE TESTING..................................................... 44

10.1 SOFTWARE TESTING.......................................................................................... 44

10.1.1 Input Data............................................................................................................. 44

10.1.2 Hs ......................................................................................................................... 45

10.1.3 Surges ................................................................................................................... 45

10.1.4 Tides ..................................................................................................................... 48

10.1.5 Still water level ..................................................................................................... 48

10.1.6 Summary ............................................................................................................... 51

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FIGURES

Figure 1 Figure 2 Figure 3 Figure 4 Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 Figure 18 Figure 19 Figure 20 Figure 21 Figure 22 Figure 23 Figure 24 Figure 25 Figure 26 Figure 27 Figure 28 Figure 29 Figure 30 Figure 31 Figure 32 Figure 33

Figure 34 Figure 35 Figure 36 Figure 37 Figure 38 Figure 39 Figure 40 Figure 41 Figure 42 Figure 43

Location of measured data sources used in this study........................................................................ 4

Exceedence Distribution of Extreme Crest Elevation .......................................................................... 8

Illustration of mean excess plot............................................................................................................. 10

Probability of occurrence of measured tidal level (m) at Auk, K13 and Euro. Relative to MSL ... 12

K13 measured: Probability of occurrence of maximum surge and maximum wave height relative

to high water.......................................................................................................................................... 14

K13 Model: Probability of occurrence of maximum surge and maximum wave height relative to

high water. ............................................................................................................................................. 14

Euro Measured: Probability of occurrence of maximum surge and maximum wave height

relative to high water............................................................................................................................ 15

Euro model: Probability of occurrence of maximum surge and maximum wave height relative to

high water. ............................................................................................................................................. 15

Auk Measured: Probability of occurrence of maximum surge and maximum wave height relative

to high water. Based on measured Auk data .................................................................................. 16

Auk Model: Probability of occurrence of maximum surge and maximum wave height relative to

high water. ............................................................................................................................................. 16

Auk Measured: Maximum Hs and SWL throughout the positive tide. ............................................. 18

Auk Model: Maximum Hs and SWL throughout the positive tide. .................................................... 18

K13 Measured: Maximum Hs and SWL throughout the positive tide. ............................................. 19

K13 Model: Maximum Hs and SWL throughout the positive tide..................................................... 19

Euro Measured: Maximum Hs and SWL throughout the positive tide............................................. 20

Euro Model: Maximum Hs and SWL throughout the positive tide.................................................... 20

Auk Measured: Surge duration analysis .............................................................................................. 22

Auk Model: Surge duration analysis..................................................................................................... 22

K13 Measured: Surge duration analysis.............................................................................................. 23

K13 Model: Surge duration analysis based on model K13 data ...................................................... 23

Euro Measured: Surge duration analysis ............................................................................................ 24

Euro Model: Surge duration analysis ................................................................................................... 24

Auk Measured: Time series plots of largest 5 surges........................................................................ 25

K13 Measured: Time series plots of largest 5 surges........................................................................ 26

Euro Measured: Time series plots of largest 5 surges ..................................................................... 27

Auk Measured: Hs-Surge (positive only) scatter plot......................................................................... 30

K13 Measured: Hs-Surge (positive only) scatter plot ........................................................................ 30

Euro Measured: Hs-Surge (positive only) scatter plot ....................................................................... 30

Monte Carlo: Input Specifications for Significant Wave Height ........................................................ 32

Monte Carlo: Input Specifications for Tidal level ................................................................................ 33

Monte Carlo: Input Specifications for Surge........................................................................................ 34

Monte Carlo: Identification of the Surge `Scaling factor'.................................................................... 35

Variation of 20 year EWL with decreasing scaling factor. The red dashed line represents the

measured 20 year extreme water level at K13................................................................................. 40

Comparison between simulated and theoretical 100 year Hs values.............................................. 45

Distribution of surges associated with the maximum crest+surge. .................................................. 46

Distribution of surges associated with the maximum crest+surge. .................................................. 46

Distribution of surges associated with the maximum crest+surge ................................................... 47

Distribution of surges associated with the maximum crest+surge. .................................................. 47

Distribution of tides associated with the maximum crest+tide. ......................................................... 48

Distribution of SWL associated with the maximum crest+tide+surge.............................................. 49

Distribution of SWL associated with the maximum crest+tide+surge.............................................. 49

Distribution of SWL associated with the maximum crest+tide+surge.............................................. 50

Distribution of SWL associated with the maximum crest+tide+surge.............................................. 50

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