Estimating extreme water level probabilities: A comparison of the direct methods and recommendations for best practise

Coastal Engineering

Volumn 81, Issue , 2013, Pages 51-66

  Arns, A ^a   Wahl, T ^a   Haigh, I D ^b,c   Jensen, J ^a   Pattiaratchi, C ^c  

^a UNIVERSITY OF SIEGEN   (Germany)

^b UNIVERSITY OF SOUTHAMPTON   (United Kingdom)

^c UNIVERSITY OF WESTERN AUSTRALIA   (Australia)

Author keywords

Coastal flooding; Extreme value distribution; Extreme water levels; German Bight; Return levels and periods

Indexed keywords

COASTAL FLOODING; EXTREME VALUE DISTRIBUTIONS; EXTREME VALUE STATISTICS; GERMAN BIGHT; LEVELS OF PROTECTIONS; OBJECTIVE APPROACHES; PEAKS-OVER-THRESHOLD METHOD; RETURN LEVEL;

ESTIMATION; PROBABILITY; SEA LEVEL;

WATER LEVELS;

COASTAL ENGINEERING; COASTAL PROTECTION; COMPARATIVE STUDY; DATA SET; FLOODING; PARAMETERIZATION; PROBABILITY; WATER LEVEL;

ATLANTIC OCEAN; AUSTRALIA; GERMAN BIGHT; NORTH SEA; UNITED KINGDOM;

EID: 84881248638     PISSN: 03783839     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.coastaleng.2013.07.003     Document Type: Article

References (74)

1. Acero F.J., García J.A., Gallego M.C. Peaks-over-threshold study of trends in extreme rainfall over the Iberian Peninsula. Journal of Climate 2011, 24:1089-1105.
2. AghaKouchak A., Easterling D., Hsu K., Schubert S., Sorooshian S. Extremes in a changing climate. Detection, Analysis and Technology 2013, Springer.
3. Aguilar E., Auer I., Brunet M., Peterson T., Wieringa J. Guidelines on climate metadata and homogenization. World meteorological organization 2003, Secretariat of the World Meteorological Organization.
4. Allamano P., Laio F., Claps P. Effects of disregarding seasonality on the distribution of hydrological extremes. Hydrology and Earth System Sciences 2011, 15:3207-3215.
5. Arns A., Wahl T., Haigh I., Jensen J. Determining extreme water return levels at un-gauged sites: a case study of the Schleswig-Holsteins coastline and Islands in north-west Germany. Proceedings of the Coastal Dynamics conference 2013 2013.
6. Batstone C., Lawless M., Tawn J., Horsburgh K., Blackman D., McMillan A., Worth D., Laegers S., Hunt T. A UK best-practice approach for extreme sea-level analysis along complex topographic coastlines. Ocean Engineering 2013, (in press). ISSN 0029-8018. http://dx.doi.org/10.1016/j.oceaneng.2013.02.003.
7. Brabson B.B., Palutikof J.P. Tests of the generalized Pareto distribution for predicting extreme wind speeds. Journal of Applied Meteorology 2000, 39:1627-1640.
8. Choulakian V., Stephens M.A. Goodness-of-fit tests for the generalized Pareto distribution. Technometrics 2001, 43:478-484.
9. Church J.A., White N.J., Coleman R., Lambeck K., Mitrovica J.X. Estimates of the regional distribution of sea level rise over the 1950-2000 period. Journal of Climate 2004, 17:2609-2625.
10. Coles S. An Introduction to Statistical Modeling of Extreme Values 2001, Springer Verlag, London.
11. Cunnane C. A particular comparison of annual maxima and partial duration series methods of flood frequency prediction. Journal of Hydrology 1973, 18:257-271.
12. Davison A.C., Smith R.L. Models for Exceedances over High Thresholds 1990, 52:393-442.
13. De M. A new unbiased plotting position formula for Gumbel distribution. Stochastic Environmental Research and Risk Assessment 2000, 14:1436-3240.
14. Dixon M.J., Tawn J.A. Extreme sea-levels at the UK A-class sites: site-by-site analyses. Proudman Oceanographic Laboratory Internal Document No. 65 1994.
15. Dixon M.J., Tawn J.A. A semi-parametric model for multivariate extreme values. Statistics and Computing 1995, 5(3):215-252.
16. Dixon M.J., Tawn J.A. Estimation of extreme sea conditions. Final report 1997, Ministry of Agriculture, Fisheries and Food.
17. Dixon M.J., Tawn J.A. The effect of non-stationarity on extreme sea-level estimation. Journal of the Royal Statistical Society: Series C: Applied Statistics 1999, 48:135-151.
18. Douglas B.C. Global sea level rise. Journal of Geophysical Research 1991, 96:6981-6992.
19. Dupuis D.J. Exceedances over high thresholds: a guide to threshold selection. Extremes 1998, 1:251-261.
20. Environment Agency Coastal flood boundary conditions for UK mainland and islands. Project: SC060064/TR2: Design sea-levels 2011, Environment Agency of England and Wales.
21. Ferro Ch.A.T., Segers J. Inference for clusters of extreme values. Journal of the Royal Statistical Society: Series B 2003, 65:545-556.
22. Gönnert G., Müller O., Gerkensmeier B. Development of extreme storm surge events - results of the XtremRisK project. Research for policy and practice 2013, F. Klijn, T. Schwecckendiek (Eds.).
23. Grabemann I., Weisse R. Climate change impact on extreme wave conditions in the North Sea: an ensemble study. Ocean Dynamics 2008, 58:199-212.
24. Haigh I.D., Nicholls R., Wells N. A comparison of the main methods for estimating probabilities of extreme still water levels. Coastal Engineering 2010, 57:838-849.
25. Haigh I., Nicholls R., Wells N. Assessing changes in extreme sea levels: application to the English Channel, 1900-2006. Continental Shelf Research 2010, 30:1042-1055.
26. Haigh I.D., Wijeratne E.M.S., MacPherson L.R., Pattiaratchi C.B., George S. Estimating present day extreme total water level exceedance probabilities around the coastline of Australia: tides, extra-tropical storm surges and mean sea level. Climate Dynamics 2013, (in press-a). http://dx.doi.org/10.1007/s00382-012-1652-1.
27. Haigh I.D., MacPherson L.R., Mason M.S., Wijeratne E.M.S., Pattiaratchi C.B., Crompton R.P., George S. Estimating present day extreme total water level exceedance probabilities around the coastline of Australia: tropical cyclone induced storm surges. Climate Dynamics 2013, (in press-b). http://dx.doi.org/10.1007/s00382-012-1653-0.
28. Hawkes P.J., Gonzalez-Marco D., Sánchez-Arcilla A., Prinos P. Best practice for the estimation of extremes: a review. Journal of Hydraulic Research 2008, 46:324-332.
29. Hirsch R.M., Helsel D.R., Cohn T.A., Gilroy E.J. Statistical analysis of hydrological data. Handbook of Hydrology 1992, D.R. Maidment (Ed.).
30. Hosking J.R.M., Wallis J.R. Parameter and quantile estimation for the generalized Pareto distribution. Technometrics 1987, 29:339-349.
31. Hosking J.R.M., Wallis J.R. Regional Frequency Analysis 1997, Cambridge University Press, Cambridge.
32. Jensen J. Änderungen der mittleren Tidewasserstände an der Nordseeküste. Mitteilungen Leichtweiß-Institut der TU Braunschweig, Heft 83 1984.
33. Jensen J. Über instationäre Entwicklungen der Wasserstände an der deutschen Nordseeküste. Mitteilungen Leichtweiß-Institut der TU Braunschweig, Heft 88 1985.
34. Jensen J., Müller-Navarra S. Storm surges on the German Coast. Die Küste, Heft 74 2008, 92-125.
35. Jensen J., Mügge H.-E., Schönfeld W. Analyse der Wasserstandsentwicklung und Tidedynamik in der Deutschen Bucht. Die Küste, Heft 53 1992.
36. Katz R.W., Parlange M.B., Naveau P. Statistics of extremes in hydrology. Advances in Water Resources 2002, 25:1287-1304.
37. Kuncheva L.I. A stability index for feature selection. Proceedings of the 25th IASTED International Multi-Conference: artificial intelligence and applications 2007, 390-395.
38. Lang M., Ouarda T.B.M.J., Bobée B. Towards operational guidelines for over-threshold modeling. Journal of Hydrology 1999, 225:103-117.
39. LKN (Landesbetrieb für Küstenschutz, Nationalpark und Meeresschutz Schleswig-Holstein) Generalplan Küstenschutz der Landes Schleswig-Holstein, Fortschreibung 2012. Entwurf für die Anhörung der Verbände 2012.
40. Mathiesen M., Goda Y., Hawkes P.J., Mansard E., Martín M.J., Peltier E., Thompson E.F., Van Vledder G. Recommended practice for extreme wave analysis 1994, 32(6):803-814.
41. Méndez F.J., Menéndez M., Luceño A., Losada I.J. Analyzing monthly extreme sea levels with a time-dependent GEV model. Journal of Atmospheric and Oceanic Technology 2007, 24:894-911.
42. Middleton, Thompson Return periods of extreme sea levels from short records. Journal of Geophysical Research 1986, 91:11,707.
43. Morton I.D., Bowers J. Extreme value analysis in a multivariate offshore environment. Applied Ocean research 1996, 18:303-317.
44. Mudersbach C., Jensen J. Nonstationary extreme value analysis of annual maximum water levels for designing coastal structures on the German north sea coastline. Journal Flood Risk Management 2010, 3(1):52-62. 10.1111/j.1753-318X.2009.01054.x.
45. Mudersbach C., Wahl T., Haigh I.D., Jensen J. Trends in extreme high sea levels along the German north sea coastline compared to regional mean sea level changes. Continental Shelf Research 2013, (in press). ISSN 0278-4343. http://dx.doi.org/10.1016/j.csr.2013.06.016.
46. Naveau P., Nogaj M., Ammann C., Yiou P., Cooley D., Jomelli V. Statistical methods for the analysis of climate extremes. Comptes Rendus Geosciences 2005, 1013-1022.
47. Nicholls R.J. Planning for the impacts of sea level rise. Oceanography 2011, 24(2):144-157. 10.5670/oceanog.2011.34.
48. Nicholls R.J., Wong P.P., Burkett V.R., Codignotto J.O., Hay J.E., McLean R.F., Ragoonaden S., Woodroffe C.D. Coastal systems and low-lying areas. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change 2007, 315-356. Cambridge University Press, Cambridge, UK. M.L. Parry, O.F. Canziani, J.P. Palutikof, P.J. van der Linden, C.E. Hanson (Eds.).
49. Nicholls R.J., Hanson S., Herweijer C., Patmore N., Hallegatte S., Corfee-Morlot J., Château J., Muir-Wood R. Ranking port cities with high exposure and vulnerability to climate extremes: exposure estimates. OECD Environment Working Papers, No. 1 2008, OECD Publishing. 10.1787/011766488208.
50. Niedersächsischer Landesbetrieb für Wasserwirtschaft, Küsten- und Naturschutz (NLWKN) Generalplan Küstenschutz Niedersachsen/Bremen-Festland 2007.
51. Pawlowicz R., Beardsley B., Lentz S. Classical tidal harmonic analysis including error estimates in MATLAB using T_TIDE. Computers & Geosciences 2002, 28(8):929-937.
52. Pirazzoli P.A., Costa S., Dornbusch U., Tomasin A. Recent evolution of surge-related events and assessment of coastal flooding risk on the eastern coasts of the English Channel. Ocean Dynamics 2006, 56:498-512.
53. Pugh D.J. Tides, Surges and Mean Sea-Level. A Handbook for Engineers and Scientists 1987, 472. Wiley, Chichester.
54. Pugh D., Vassie Extreme sea levels from tide and surge probability. Proceedings of the sixteenth Coastal Engineering Conference 1979, 1:911-930.
55. Pugh D., Vassie Applications of the joint probability method for extreme sea level computations. Proceedings of the Institution of Civil Engineers 1980, 69:959-975.
56. Rao A.R., Hamed K.H. Flood Frequency Analysis 2000, CRC Press, Boca Raton.
57. Rosbjerg D., Madsen H., Rasmussen P.F. Prediction in partial duration series with generalized Pareto-distributed exceedances. Water Resources Research 1992, 28:3001-3010.
58. Sachs L. Angewandte Statistik. Anwendung Statistischer Methoden 1997, Springer Verlag, Berlin, Heidelberg, New York.
59. Seneviratne S.I., Nicholls N., Easterling D., Goodess C.M., Kanae S., Kossin J., Luo Y., Marengo J., McInnes K., Rahimi M., Reichstein M., Sorteberg A., Vera C., Zhang X. Changes in climate extremes and their impacts on the natural physical environment. A Special Report of Working Groups I and II of the Intergovernmental Panel on Climate Change 2012, 109-230. Cambridge University Press, Cambridge, UK, and New York, NY, USA.
60. r largest annual events. Journal of Hydrology 1986, 86:27-43.
61. Smith R.L., Weissman I. Estimating the extremal index. Journal of the Royal Statistical Society: Series B: Methodological 1994, 56:515-528.
62. Soares G., Scotto M.G. Application of the r largest-order statistics for long-term predictions of significant wave height. Coastal Engineering 2004, 51:387-394.
63. s-design values S. The Open Ocean Engineering Journal 2011, 4:34-43.
64. Stedinger J.R., Vogel R.M., Foufoula-Georgiou E. Frequency analysis of extreme events. Handbook of Hydrology 1992, D.R. Maidment (Ed.).
65. Tawn J.A. Bivariate extreme value theory: models and estimation. Biometrika 1988, 75:397-415.
66. Tawn J.A. Estimating probabilities of extreme sea-levels. Journal of the Royal Statistical Society: Series C: Applied Statistics 1992, 41:77-93.
67. Tawn J.A., Vassie J.M. Extreme sea levels: the joint probabilities method revisited and revised. Proceedings of the Institution of Civil Engineers 1989, 87:42-442.
68. Thompson K.R., Bernier N.B., Chan P. Extreme sea levels, coastal flooding and climate change with a focus on Atlantic Canada. Natural Hazards 2009, 51:139-150.
69. Wahl T., Jensen J., Frank T., Haigh I.D. Improved estimates of mean sea level changes in the German Bight over the last 166years. Ocean Dynamics 2011, 61:701-715.
70. Walden A.T., Prescott P., Webber N.B. An alternative approach to the joint probability method for extreme high sea level computations. Coastal Engineering 1982, 6:71-82.
71. Wang W., Van Gelder P.H.A.J.M., Vrijling J.K. Trend and stationarity analysis for stareamflow processes of rivers in western Europe in the 20th century. IWA International Conference on Water Econimics, Statistics, and Finance 2005, 451-461.
72. Woodworth P.L., Blackman D.L. Evidence for systematic changes in extreme high waters since the mid-1970s. Journal of Climate 2004, 17:1190-1197.
73. Zachary S., Feld G., Ward G., Wolfram J. Multivariate extrapolation in the offshore environment. Applied Ocean research 1998, 20(5):273-295.
74. Zhang X., Ge W. A new method to choose the threshold in the POT model. Proceedings to the 1st International Conference on Information Science and, Engineering (ICISE2009) 2009.