A NEW APPROACH TO CALCULATE EXTREME STORM SURGES

IRRIGATION AND DRAINAGE

Irrig. and Drain. 60 (Suppl. 1): 91–98 (2011)

Published online in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/ird.681

A NEW APPROACH TO CALCULATE EXTREME STORM SURGES†

GABRIELE GÖNNERT* and KRISTINA SOSSIDI

Free and Hanseatic City of Hamburg, Agency of Roads, Bridges and Waters, Hamburg, Germany

ABSTRACT

Climate change and its consequences, for example for sea level, will have serious effects on the safety of people and economicassets in coastal areas. The uncertainties inherent in climate change necessitate new concepts of coastal protection and riskmanagement. In the project Xtrem Risk, the ‘source pathway receptor’ concept will be used as a basis for risk analysis andthe development of new strategies.

The objective of this paper is to determine relevant extreme events. The paper will give an overview of findings from theanalyses which were conducted and the method which was developed for calculating extreme storm surge events at differenttidal gauges. These extreme scenarios are necessary for risk analyses and can also be used for design levels.

Here a deterministic method will be used which takes the physics of storm surges into account. The most relevant contributionsto a storm surge are spring tide, wind surge and sometimes an external surge that enters the North Sea from the Atlantic. With themethod that has been developed, these three components will be analysed and their development and non-linear interaction overthe last 100 years will be assessed. Since the storm surge curve is necessary for analysis, the curve and its components are alsoanalyzed. Copyright © 2011 John Wiley & Sons, Ltd.

key words: design level; physics of storm surges; risk analysis

RÉSUMÉ

La mer du Nord est sérieusement menacée par les tempêtes. Le changement climatique et ses conséquences par exemple pour leniveau de la mer aura des effets graves sur la sécurité des personnes et des biens économiques dans les régions côtières. Les incer-titudes inhérentes au changement climatique nécessiteront de nouveaux concepts de protection du littoral et la gestion des risques.

XtremRisK––acronyme en allemand pour cotes extrêmes sur les côtes ouvertes et les zones estuariennes: évaluation etatténuation des risques sous condition de changements climatiques––est un projet de recherche conjoint, financé par legouvernement fédéral allemand, conçu pour aider à relever ce défi. Le concept de ‘source-chemin-récepteur’ sera utilisécomme base pour l’analyse des risques et le développement de nouvelles stratégies.

L’objectif de cet article est pertinent pour déterminer les événements extrêmes. Dans le cadre du projet XtremRisK, lesméthodes seront développées pour évaluer les événements extrêmes dans les conditions prévalant aujourd’hui. Ensuite, lesévénements extrêmes seront évalués sur la base des conditions qui reflètent les scénarios de changement climatique. Laprésentation donnera un aperçu de la méthode qui a été développée pour le calcul des cotes extrêmes à différentes échellesde marée et présentera des résultats des analyses qui ont été menées. Ces scénarios extrêmes sont nécessaires pour lesanalyses de risque et peuvent également être utilisés pour la conception.

Il existe plusieurs méthodes, souvent de nature statistique, pour calculer une cote extrême. La méthode utilisée ici est uneméthode déterministe qui prend en compte la physique des ondes de tempête. Les contributions les plus pertinentes pourune cote de tempête sont la marée, le vent et parfois une surcote due à une poussée extérieure qui pénètre, de l’Atlantique, dansla mer du Nord. Avec la méthode qui a été développée, ces trois composantes seront analysées, et leur évolution ainsi que leursinteractions non linéaires au cours des 100 dernières années seront évaluées. Dès lors que la courbe de l’évènement est nécessairepour l’analyse, les courbes des composantes seront analysées et la courbe de cote de tempête est également prise en compte.

mots clés: conception; la physique des ondes de tempête; l’analyse des risque; cote de tempête; surcôte

* Correspondence to: Gabriele Gönnert, Free and Hanseatic City of Hamburg, Agency of Roads, Bridges and Waters, Hamburg, Germany. E-mail: [email protected]†Une nouvelle approche pour le calcul de cotes extrêmes de tempête.

Copyright © 2011 John Wiley & Sons, Ltd.

92 G. GÖNNERT AND K. SOSSIDI

INTRODUCTION

Most of the world’s coastal areas are affected by stormsurges. Along the coast of the North Sea, storm surgesconstitute the major geophysical risk (Gönnert et al.,2001). At the same time, coastal regions are preferred settle-ment and industrial areas with a high density of populationand highly valuable properties. As a consequence, the costof flood damage on the coast can be very high.

Climate change and its consequences for sea level risewill increase the risk of floods and may have serious conse-quences for the safety of people and assets in coastal areas.This means that new concepts are needed to meet thechallenge of the future. The project ‘XtremRisK–– ExtremeStorm Surges on Open Coastlines and Estuarine Areas, RiskAssessment and Mitigation under Climate Change Aspects’,funded by the German Federal Ministry of Education andResearch (BMBF), will help us to face this challenge. The‘source pathway receptor’ concept will be used as a basisfor risk analysis and the development of new managementstrategies (Oumeraci et al., 2009).

To evaluate the consequences of climate change, it is firstnecessary to assess extreme storm surge events underclimatic and hydrological conditions prevailing today. In asecond step, scenarios of potential sea level rise are identi-fied and investigated to evaluate future extreme eventscenarios.

These extreme scenarios are necessary for risk analysesand can also be used for design water levels. Based on thesescenarios, it will be possible to determine the risk forspecific locations and to develop mitigation strategies.

The main driving force behind a storm surge is windvelocity, which causes the wind surge. The wind surge can

Figure 1. Location of the pilot


be strengthened further by a coinciding high spring tide, asoccurred on 31 January and 1 February 1953 (Flather,1984; Wolf, 2008), and by an external surge of the typewhich occurred during the storm surge event on 16 February1962 (Laucht, 1968). Accordingly, this paper illustrates adeterministic approach to calculate extreme storm surgeswhich are physically possible. Using this method, the threemain components of a storm surge–– tide, wind surge andexternal surge–– will be analysed and their developmentover time will be assessed.

The focus lies on the analysis of: (i) the highest observedoccurrence of each component and (ii) the interaction be-tween tide and wind surge and the interaction between stormsurge and external surge. This detailed analysis is neededbecause the components do not interact linearly. Investiga-tion of the hydrodynamics and physics of storm surges hasshown that the components have to be added non-linearly(e.g. Tang et al., 1996; Horsburgh and Wilson, 2007; Jonesand Davies, 2007), which leads to a lower water level thanin the case of linear superposition. An extreme event basedon the maximum components can be calculated with thisknowledge. The result is a realistic extreme scenario undercurrent climate conditions.

PILOT SITES

The analyses are conducted for one location on the opencoast (island of Sylt) and another which is situated in anestuarine area (city of Hamburg). These different areas(Figure 1) were chosen mainly for the following reasons:

• different spatial development of extreme storm surgelevels and effect of the morphology;

sites Hamburg and Sylt


93A NEW APPROACH TO CALCULATE EXTREME STORM SURGES

• different socio-economic patterns that determined thevulnerability of the areas at risk;

• different opportunities to react to changing storm surgerisks.

The study sites were chosen to allow for transferability ofthe developed methods to other coastal or estuarine areas.The transferability of the findings is an essential aim of theproject.

The city of Hamburg is the second largest in Germany.Around 1.8 million people live in this metropolitan areawhich is a centre for trade, transport and services and animportant location for industry. Furthermore, the port ofHamburg is the largest seaport in Germany.

The island of Sylt is the biggest of the North FrisianIslands. With 40 km of beach on its western side, it is oneof the most popular places in Germany for tourists. Due toits exposed position in the North Sea it is vulnerable tosevere erosion during storm surges.

A lengthy, consistent time series of water level observa-tions is needed if the storm surges are to be characterised.Consequently, the extreme storm surge for the city ofHamburg will be determined at tidal gauge at Cuxhavenand its propagation upstream to Hamburg will subsequentlybe calculated by numerical modelling. The storm surge forSylt will be determined at the tidal gauge at Hörnum(Figure 1).

The approach to the analysis of extreme storm surges andthe individual components will be presented below. It wasdeveloped at the tidal gauge of Cuxhaven because this isthe best-evaluated tidal gauge in Germany with a continuoustime series that stretches back to 1900.

THE METHODOLOGICAL APPROACH

The chosen approach is based on a deterministic procedurethat takes into account the hydrodynamic interactions ofthe storm surge components as well as their meteorologicalcontext.

For the construction of extreme storm surge events it isessential to consider the highest observed occurrence ofeach component. Since these extreme values appearedduring different storm surge events, they must be combinedin order to generate a new extreme storm surge. If a resultthat corresponds to physical law is to be achieved, thenon-linear interaction of the storm surge components mustbe taken into account (Figure 2). In consideration of this,the calculated extreme storm surge is a feasible event in fact.

Before combining the components to form a new stormsurge, it is necessary to examine the physical possibility ofthe components’ observed maximum values coinciding.This involves examining the possibility of a simultaneous


occurrence of a high spring high tide, external surges andhigh wind surge at the tidal gauge at Cuxhaven.

In the course of a comprehensive analysis the componentsare firstly scrutinised separately and secondly their interac-tion is investigated using empirical, statistical and numericalmethods (Figure 2). The consistency of the results of thedifferent methods allows us to optimally ascertain thephysical context and validate the methods used. Thenon-linear interaction is worked out. Finally, the highestobserved values for each component are added non-linearlyin line with natural law to bring about an extreme stormsurge event.

The components of a storm surge

The wind is the main reason for the formation of a stormsurge. It pushes the water against the coast, causing waterlevels higher than the ordinary sea level which is influencedby the tides. The tidal range reaches its maximum at springtide so that during spring tides, high waters rise to an excep-tional level. The water level on the North Sea coast can alsobe raised by external surges that are generated by cyclonesover the north-eastern Atlantic and propagate into the NorthSea (Lundbak, 1955; Timmerman, 1975), pushing additionalwater masses into the basin. The coincidence of wind surge,spring high tide and external surge leads to extreme stormsurge levels along the coast (Figure 3).

In the project, storm surges from 1843 for individualevents and continuously from 1901 to 2008 at the tidalgauge at Cuxhaven, and from 1936 to 2008 at the tidalgauge at Hörnum for Sylt, were analysed and decomposedinto wind surge, external surge and astronomical tide. Thesethree components will be outlined in the followingparagraphs.

Wind surge. A wind surge is caused by a wind-induced onshore surface current. The wind direction thatproduces the highest wind surge at the tidal gauge atCuxhaven is 295� (westerly to north-westerly winds). Atthe tidal gauge at Hörnum it is 267� (westerly winds).The wind causes a rise in the water near the coast andhence a tilt of the North Sea’s water surface from the deepwater area towards the coast. The height of the wind surgedepends on wind speed and wind direction.

A formula for calculating wind surge as a function ofwind speed and wind direction exists only for few tidalgauges on the German North Sea coast. Therefore a windsurge is generally calculated by subtracting the astronomicaltide (or the mean tide) from the observed tide. Either way,the wind surge also contains other factors that are not causedby the wind, such as the effect of local air pressure or theexternal surge. Before further analyses were conducted, anexamination was therefore carried out to ascertain which


Figure 2. Methods to estimate the non-linear effects

Figure 3. The components of a storm surge


of the storm surges since 1901 occurred simultaneously withan external surge.

The analyses of the data showed that the wind surgemaximum can occur in all tidal phases, but mostly occursaround tidal low water. The highest wind surge maxima alsooccurred around tidal low water. This confirms earlierstudies which indicated that the maximum wind surge tendsnot to coincide with high tide (e.g. Keers, 1968; Siefert,1968; Gönnert, 2003; Horsburgh and Wilson, 2007).


The highest wind surge event at the tidal gauge atCuxhaven which was not influenced by an external surgereached a height of 4.15m. This occurred in January 1976around low tide. The highest wind surge event at the tidalgauge at Hörnum was 3.50m. It occurred in January 1990around low tide.

Spring tide. Tide is caused by the gravitational forces ofthe sun and moon. At new and full moon the tidal powers of



moon and sun amplify each other. This leads to increasedhigh tides and reduced low tides which are called springtides. At half moon the attraction forces reduce each other,resulting in a smaller tidal amplitude which is called aneap tide.

The mean tidal curve is the arithmetical average observedtidal curve at a specific gauge of a certain time period. In thisprocess, tidal curves of different moon phases are averagedso that the differences of spring and neap tide are indeter-minable. The past analyses of storm surges were based onthe mean tide for pragmatic reasons: the mean tide is astatistical term which requires only a relatively shortcalculation period (Siefert, 1968). In the past it wasmathematically difficult and time-consuming to calculatethe astronomical tide for any one day. Nowadays mostcomputers have the required processing power. The Agencyof Roads, Bridges and Waters enhanced two existingprograms for calculating the astronomical tide (Thummand Gönnert, 2008) with the help of the Federal Maritimeand Hydrographic Agency. Thus it is possible to dividethe stochastic process from astronomical effects and toanalyse the tide–surge interaction.

The highest values of spring high tide at the tidal gaugeswere ascertained by subtracting the mean high tide fromastronomical high tide. In Cuxhaven it was 60 cm and inHörnum it was 63 cm.

External surge. External surges are generated in thenorth-eastern Atlantic as a result of air pressure variationsgenerated by fast-passing cyclones. These produce observ-able waves on the water surface as well as internal wavesin the water body. The propagation of an external surge intothe North Sea takes place primarily when the track of thecausative cyclone leads from the sea areas between Irelandand Iceland to mid-Norway (Schmitz et al., 1988). It propa-gates through the North Sea in a manner similar to a tidalwave, but independent of tide phase and any periodicregularity, and travels through the North Sea in ananticlockwise direction.

External surges are calculated using observed tide data atthe tidal gauges at Aberdeen, Immingham and Cuxhaventhat were recorded by the Federal Maritime and Hydro-graphic Agency. Gönnert (2003) defined a collective ofexternal surges. Their height is calculated by subtractingthe astronomical tide, wind surge and the effect of local airpressure from the observed low and high waters. Thecalculated values may still contain components besides theexternal surge. These are seiches, effects of air pressureand air pressure variations over the North Sea, effects ofwater temperature and temperature difference between airand water. This variety of potential causes of an increasein the water level reveals the necessity of a precise definitionof external surges. So residual surges are defined as external


surges only if they can also be identified at the tidal gaugesat Aberdeen and Immingham on the British coast and reacha minimum level there to rule out local wind effects. Theremust also be a special cyclone track over the Atlantic fordeveloping a North Sea external surge (Gönnert et al., 2003).

The maximum height of an external surge recognised atCuxhaven was 1.09m. This external surge reached 1.08min Aberdeen. It did not coincide with a storm surge. Thehighest external surge that coincided with a storm surgereached a peak level of 1.00m at Cuxhaven. One-fifth toone-sixth of storm surges at the tidal gauge at Cuxhavenoccurred at the same time as an external surge (Gönnert, 2003).

No records of external surges exist for the tidal gauge atHörnum. Since external surges travel through the NorthSea in a manner similar to the tide (Banner et al., 1979;Pugh, 2004), the external surges ascertained at the tidalgauge at Cuxhaven are shifted to Hörnum with the observedtide to estimate the time of occurrence at that tidal gauge.For the time periods ascertained, the height of externalsurges at the tidal gauge at Hörnum will be calculated byapplying the method used at the tidal gauge at Cuxhaven.

Investigations of the non-linear interaction

When calculating the height of an extreme storm surge, itmust be taken into account that the components of a stormsurge do not superimpose linearly. Due to the hydrostaticequilibrium, their interaction is non-linear and depends onthe water depth. The wind-induced onshore surface currentgenerates an offshore-directed bottom return current. Thisreturn current increases with rising water level near the coastwhich in turn leads to a decrease in the water level. Conse-quently, taking this into account when calculating stormsurge events leads to lower storm surge levels than linearsuperposition.

A comprehensive analysis of non-linear interactionsbetween the storm surge components is carried out bycombining empirical, statistical and numerical methods(Figure 2). Using this analysis, the effect of non-linear inter-action when combining the maximum values of the compo-nents can be determined in order to ascertain the extremestorm surge’s curve and peak water level at high tide. Thisapproach is presented with the example of Cuxhaven. Theresults are given for both tidal gauges analysed.

Non-linear interaction between tide and windsurge. To ascertain the highest observed wind surge,the wind surge curve was calculated for each of the stormsurge events. The wind surge curve was calculated bysubtracting the astronomical tide from the observed tide,as well as by subtracting the mean tide from the observedtide. The mean tide shows the general tidal situation at aspecial gauge, while the astronomical tide shows the



variations. The effect of the astronomical dissimilarity onthe wind surge can be identified by means of these twowind surge curves.

The calculation of the wind surge curve for the wholestorm surge period makes it possible to determine amaximum wind surge peak regardless of tide phase for eachstorm surge. The highest observed wind surge values occuraround low water. Since there is no cohesion between tidephase and wind, the maximum force of wind can also occurat other tide phases such as high water. The data show thatthe height of wind surge is less around high water, however.

To determine the ratio of wind surge height around lowwater to its height around high water, the relations betweenwind surge, the respective wind speed and tide are analysed.The effective wind is calculated on the basis of the winddirections that produce the highest wind surge at therespective tidal gauge (see above). It describes the windspeed converted to the wind direction that produces thehighest wind surge. The analysis of wind surge dependingon effective wind in each tide phase showed the relationbetween the height of the wind surge around high tide andaround low tide. At the tidal gauge at Cuxhaven, the windsurge at high tide accounts for 82–94% of the wind surgearound low tide. At the tidal gauge at Hörnum, thecorresponding value is 85–95%. The extent of the remainingwind surge increases along with the effective wind speed.These values can be adapted to calculate the effects of thespring tide on storm surge levels (see below).

This ratio makes it possible to detect the highest windsurge around high tide by shifting the observed wind surgeevents to high tide and reducing their height as appropriate.The precondition for this shifting is that the effective windin question acts over an extended period of time.

The highest wind surge event around high water at thetidal gauge at Cuxhaven that is not influenced by an externalsurge measured 3.70m. It occurred in January 1976 aroundhigh tide and does not have to be shifted. During this stormsurge event the wind surge reached 4.15m around theprevious low tide. The wind did not change during that time,so the observed wind surge values are equivalent to areduction of 89%.

At the tidal gauge at Hörnum the highest wind surgereached a height of 3.50m at low tide. The wind surge curvefrom this event is very steep and does not correspond to thetypical wind surge curve on an island (Gönnert, 2003). Thehighest wind surge event with a flatter wind surge curvearose in November 1981 around high tide and measured3.19m.

When wind surge coincides with spring high water, aninvestigation must be carried out to ascertain the contributionof this spring tide to the effective increase in the storm surgewater level. Three different methods are used to conduct thisinvestigation:


• statistical analysis of the correlation between effectivewind and wind surge determined from astronomicaltide and mean tidal curve;

• analysis of numerical modelling studies;• calculation of the spring tide’s influence on an extremeevent.

The investigations of spring tide are based on the cal-culation of astronomical tide curves using a non-harmonicmethod. The cross-correlation shows the minor effect ofthe astronomically induced deflection of water level on thewind surge curve and peak. The analysis of the relationbetween the height of wind surge around high tide andaround low tide clarified the increasing relevance of thewind as wind speed increases. It can be assigned to theastronomical dissimilarity. Hence the extent of the reductionin wind surge caused by shifting from low water to highwater can be adapted to determine the reduction in theeffects of spring tide on storm surge water levels. Becausethere is a connection between the overall water level andits reduction, the calculation of the decrease in theastronomical dissimilarity has to include wind surge.

For Cuxhaven, the astronomical dissimilarity in combina-tion with the wind surge of 3.70m is reduced to 0.10m. Thisresult matches the results of numerical modelling studies byDick (2000) which showed that the effect of the astronomi-cal dissimilarity decreases as the wind surge increases.

At the tidal gauge at Hörnum the amount of spring tide isreduced to about 0.44m when it coincides with a wind surgeof 3.19m.

Non-linear interaction between storm surge andexternal surge. The cyclone that causes an external surgein the Atlantic Ocean has negligible to substantial effects onthe water level in the North Sea, depending on the cyclone’strack. The investigation of the development of the externalsurges from Aberdeen to Cuxhaven via Immingham showedthat most of the external surges increased in height on theirway from Aberdeen to Immingham and decreased again onthe way to Cuxhaven. When the development in the heightof each external surge is seen in connection with the respec-tive meteorological situation, it shows that:

• external surges will increase if the cyclone trackssouthwards and influences the water body of the NorthSea (and sometimes produces a storm surge);

• external surges decrease (or stay more or less at thesame level) if the cyclone tracks northwards and has norelevant influence on the water body of the North Sea.

When the cyclone features a southern track the waterlevel in the North Sea can be affected by, for example,effects of air pressure and air pressure variations over the



sea as well as additional wind. To prevent a situation wherethe peak of the external surge combined with the extremestorm surge contains changes in the water level due to theseinfluences, only the external surges that occurred without acoinciding storm surge are taken into account. The averagedecrease in these external surges between Aberdeen andCuxhaven is about 30%. Between Cuxhaven and Hörnumit is about 40%.

The highest observed external surge reached 1.08m at thetidal gauge at Aberdeen. When reduced by 30% on its wayto Cuxhaven, it arrives there with a peak of about 0.80m.This equates to the peak of the external surge that wasobserved during the storm surge of 1962. In Hörnum theexternal surge arrives with a peak of about 0.46m.

Calculation of an extreme storm surge event

The extreme storm surge is calculated by adding the highestobserved values of each storm surge component with dueregard to their non-linear interaction investigated in thisstudy and by adding the resulting value to the meanhigh tide.

The wind surge curve that is a constituent of theconstructed storm surge curve is characteristic of a severestorm surge event at the respective tidal gauge. The stormsurge curve consists of the wind surge curve, the externalsurge curve and an astronomical tide curve that reflects themean tide condition plus the ascertained effect of the astro-nomical dissimilarity. Figures 4 and 5 show the constructedextreme storm surges at the two tidal gauges at Cuxhavenand Hörnum.

Figure 4. The extreme storm surge and its com


To ascertain the storm surge curve at the tidal gauge at StPauli in Hamburg, the propagation of the extreme stormsurge determined at the tidal gauge at Cuxhaven upstreamto Hamburg will be calculated by numerical modelling.

SUMMARY

This paper presents an empirical approach to determiningextreme storm surges at different tidal gauges. Statisticaland numerical methods are brought in to validate theempirical methods. The approach takes account of the stormsurge components wind surge, tide and external surge. Itfocuses on (i) the analysis of the highest event of eachcomponent and (ii) the analysis of the interaction betweentide and surge and the interaction between surge andexternal surge to (iii) calculate an extreme storm surgeevent based on the result of the analyses. The considerationof the non-linear effects between the storm surge componentsleads to a lower water level than in case of linear superposition.

Since the resulting value is added to the mean high tide,climate change can be taken into account by adding thepotential sea level rise to the mean tide.

The approach presented here is developed at the tidalgauge at Cuxhaven because of its continuous timeline thatstretches back to 1900 as a full series and to 1843 for furtherindividual events. It is then transferred to the tidal gauge atHörnum. The implementation at this second tidal gaugeshowed that–– assuming the availability of an adequatedata series–– the approach can be transferred to otherstudy areas.

ponents at the tidal gauge at Cuxhaven


Figure 5. The extreme storm surge and its components at the tidal gauge at Hörnum


CONFLICTS OF INTEREST

None of the authors have any conflicts of interest to declare.

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A NEW APPROACH TO CALCULATE EXTREME STORM SURGES