G E O M A T I C A

WATER MODELER: A COMPONENT OF ACOASTAL ZONE DECISION SUPPORT SYSTEMTO GENERATE FLOOD-RISK MAPS FROMSTORM SURGE EVENTS AND SEA-LEVEL RISE

Tim L. Webster and Roger Mosher, Applied Geomatics Research GroupCentre of Geographic Sciences, Nova Scotia Community College, Middleton, Nova Scotia

Mike Pearson, GeoNet Technologies Inc., Central Badeque, Prince Edward Island

This paper outlines a new software tool, Water Modeler, which is a component of a Coastal Zone DecisionSupport System. The Water Modeler can analyze a time series of water-level records (tide gauge observations)to determine the risk associated with a high water level from a storm surge event or long-term sea-level rise.The new tool has been applied in two case studies in Nova Scotia, Canada, where coastal flood-risk mapshave been derived from high-resolution LiDAR digital elevation models. The first case study is for AnnapolisRoyal on the Bay of Fundy side of the province, while the second looks at the Kingsburg area of LunenburgCounty on the Atlantic shore. The Saint John, New Brunswick, and Halifax tide gauge records were used forAnnapolis Royal and Kingsburg, respectively, in the Water Modeler to examine the risks of coastal flooding.The Groundhog Day storm of 1976, which caused coastal flooding around the Bay of Fundy, was used as abenchmark for Annapolis Royal. At current rates of sea-level rise, 22 cm/century, the average return period ofthis water level is 43 years (65 percent probability) and there is a very high probability (99 percent) that it willreoccur within 121 years. If relative sea-level rise rates increase to 80 cm/century from climate change, thenthe average return period reduces to 23 years, and there is a 99 percent probability of reoccurrence within 55years. The benchmark storm used from the Halifax water record was Hurricane Juan, which occurred inSeptember 2003. The cumulative flood-level probabilities were calculated for this water level and a returnperiod of 95 years was determined, with an average return period of 52 years (65 percent probability) undercurrent sea-level conditions. The combination of geomatics tools, such as high-resolution LiDAR digital ele-vation models (DEMs) for coastal flood inundation and the Water Modeler to estimate the associated risk,allows coastal communities to better plan for the future.

GEOMATICA Vol. 62, No. 4, 2008, pp. 393 to 406

Cet article décrit un nouvel outil logiciel, le Water Modeler, qui est une composante d’un système d’aideà la décision pour les zones côtières. Cet outil peut analyser une série chronologique d’enregistrements duniveau des eaux (observations de marégraphes) pour déterminer les risques associés à un niveau élevé de l’eaurésultant d’une onde de tempête ou d’une élévation du niveau de la mer à long terme. Le nouvel outil a étéutilisé pour deux études de cas en Nouvelle-Écosse, au Canada, où des cartes de risques d’inondationscôtières ont été dérivées de modèles numériques d’élévation dérivés de LiDAR à haute résolution. La premièreétude de cas est celle d’Annapolis Royal, sur la côte de la Baie de Fundy, alors que la seconde examine lesecteur de Kingsburg du comté de Lunenburg, sur la côte atlantique. Les enregistrements du marégraphe deSaint John, au Nouveau-Brunswick, et les enregistrements du marégraphe de Halifax, ont été utilisés par l’outildans le cas d’Annapolis Royal et de Kingsburg, respectivement, pour examiner les risques d’inondationcôtière. La tempête du jour de la marmotte de 1976 qui a causé une inondation côtière autour de la baie a étéutilisée comme étalon pour Annapolis Royal. Au taux actuel d’élévation du niveau de la mer de 22 cm parsiècle, la période moyenne de récurrence de ce niveau de l’eau est de 43 ans (probabilité de 65 p. cent) et ilexiste une probabilité très élevée (99 p. cent) qu’elle se reproduise d’ici 121 ans. Si le taux relatif d’élévationdu niveau de la mer augmente à 80 cm par siècle en raison des changements climatiques, la période moyennede récurrence est alors réduite à 23 ans et il existe une probabilité de l’ordre de 99 p. cent d’une nouvelleoccurrence d’ici 55 ans. La tempête étalon utilisée pour les enregistrements du marégraphe de Halifax étaitl’ouragan Juan qui s’est produit en septembre 2003. Les probabilités cumulatives du niveau d’inondationont été calculées pour ce niveau de l’eau et une période de récurrence de 95 ans a été déterminée avec unepériode moyenne de récurrence de 52 ans (probabilité de 65 p. cent) selon les conditions actuelles du niveaude la mer. La combinaison des outils de géomatique tels que les modèles numérique d’élévation de LiDARà haute résolution pour les inondations côtières et du Water Modeler pour évaluer les risques connexes per-mettent aux collectivités côtières de mieux planifier pour l’avenir.

Roger Mosher

Mike Pearson

Tim L. Webster

G E O M A T I C A

1. IntroductionCoastlines all over the world are becoming

more developed and populated, regardless of thethreat of coastal flooding. Susceptibility to coastalflooding from storm surges is expected to becomeworse in the future, with increased sea-levelsresulting from climate change [Church et al. 2001].The east coast of Canada is vulnerable to stormsurges and coastal flooding [Shaw et al. 1994;Parkes et al. 1997]. There have been several stud-ies in the Maritimes to examine the potential flood-risk from climate change [McCulloch et al. 2002;Daigle et al. 2006]. Light Detection and Ranging(LiDAR) has been used to build digital elevationmodels (DEMs) of the terrestrial coastal regionsand produce flood inundation maps associated withhigh water levels from storm surges and long-termsea-level rise [Webster et al. 2004, 2006; Websterand Forbes 2006]. The risk associated with a givenwater level in the form of return periods or proba-bilities of occurrence for these past projects hasbeen supplied by researchers in the OceanographyDepartment at Dalhousie University [Thompson etal. 2002; Bernier 2005; Bernier et al. 2006]. Thepast climate change studies in the region involvedlarge teams of scientists from several governmentagencies and academic institutions. The PrinceEdward Island (PEI) study [McCulloch et al. 2002]was meant to serve as a template of which skillsand tools were required to analyze the problem of

coastal vulnerability. This project identified theneed for new geomatics-based software tools tobetter facilitate the mapping of risk associated withclimate change in coastal areas.

As a result, the requirements identified in theP.E.I. project were used as the basis for an AtlanticInnovation Fund (AIF) grant from the AtlanticCanada Opportunities Agency (ACOA) to theApplied Geomatics Research Group (AGRG) of theNova Scotia Community College (NSCC), alongwith private-sector partners GeoNet TechnologiesInc. and CARIS to develop a Coastal Zone DecisionSupport System (DSS). In general terms, the coastaldecision-support system (DSS) enhances the effec-tiveness of long-term planning for climate changethrough the analysis of the extent and severity ofimpacts arising from coastal processes and extremeevents. The intended potential end-user for the DSSis the geomatics professional or, potentially, amunicipal land-use planner. This paper outlines anew software tool that is part of the DSS. The WaterModeler is used to determine the risk associated withhigher coastal water levels from storm surge eventsand long-term sea-level rise. Pugh [2004] outlinesseveral methods to determine risk for extreme sea-levels. Coles [2001] provides a basic theoreticalframework for extreme value modelling, whileshowing how these techniques can be applied inpractice. He discusses classical models, as well asthreshold and point process approaches, and issuesrelated to dependency, stationarity and multi-variatesituations. Kamphius [2000] provides a practicalintroduction to coastal engineering, in which he dis-cusses the use of extreme value methods for predic-tion of extreme wind events. These same techniquescan be applied to extreme water level events withgood results. The two most common methods todetermine the probability of an extreme water levelare the annual maximum and joint probability meth-ods, which have been used in several coastal studies[Dixon and Tawn 1999; D’Onofrio et al. 1999;Suursaar and Sooaar 2007]. The Water Modeler tooldraws on these past studies to calculate the risk of agiven water level occurring, based on the time seriesof tide-gauge data.

The Water Modeler tool has been applied intwo case studies in Nova Scotia, where coastalflood-risk maps have been derived from high-reso-lution LiDAR DEMs. The first case study is forAnnapolis Royal on the Bay of Fundy side of theprovince (Figure 1). Although Shaw et al. [1994]do not highlight this region to be highly vulnerableto storm surge flooding—in part, because of thelarge tidal range and the requirement for a stormsurge to coincide with high tide to cause damage—past storm events, such as the 1976 Groundhog

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Figure 1: Case study location areas in southwest Nova Scotia, AnnapolisRoyal and Kingsburg (white rectangles). The closest tide gauge locations atHalifax and Saint John, New Brunswick, (solid triangles) are also indicated.Background image represents a shaded relief elevation model, with mergedRADARSAT-1 data for Nova Scotia. Inset map in the top right corner showsthe study area within Maritime Canada.

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Day storm, prove that this area is susceptible toflooding [Belbin and Clyburn 1998; Abraham et al.1999; Desplanque and Mossman 1999, 2004;MacDonald 2006]. A very large storm surge knownas the Saxby Gale also devastated the region onOctober 5, 1869 [Abraham et al. 1999].Unfortunately, very few details exist on the exactwater levels and flood inundation area that wasassociated with that storm. The second case study isthe Kingsburg area of Lunenburg County on theAtlantic shore, approximately 90 km southwest ofHalifax (Figure 1). Post-tropical storm Noel in2007 caused higher than usual sea-levels, and asso-ciated coastal flooding and erosion along the coast-line of the Kingsburg area. Hurricane Juan causedhigh water levels to the east in the Halifax area inSeptember 2003, and has been used as a benchmarkstorm to calculate return periods.

2. MethodsThe methods used in this study can be divided

into two broad categories: coastal flood inundationmapping using LiDAR-based geomatics tools; andthe prediction of return periods or probabilitiesassociated with given flood inundation water levelsunder current conditions and into the future, con-sidering rising sea-levels.

2.1 LiDAR Elevation Modeling The east coast of Canada periodically experi-

ences storm surges, which are caused by high windsand low air-pressure systems [Parkes et al. 1997].Surges in this region typically do not exceed 2 m andthus require high-precision mapping techniques toaccurately predict areas of coastal inundation. Mostof the rural coastal areas in the Maritimes aremapped at a scale of 1:10,000, with elevations hav-ing an associated vertical accuracy of 2.5 m (NovaScotia Geographic Information Standards). It is clearthat regional elevation data are not sufficient to accu-rately predict flood inundation from storm surges.

Airborne LiDAR has emerged in the last fiveto ten years as the most accurate means of elevationmapping of large areas. The Annapolis RoyalLiDAR data were collected using the Mark II sen-sor from Terra Remote Sensing Inc. in April of2004. This is a 30 kHz sensor capable of recordingthe first and last laser return, with an averageground point spacing of 1 m. Independent GPS val-idation indicated the LiDAR DEM has a mean off-set of 10 cm, with a standard deviation of 12 cm.The Kingsburg LiDAR data were flown by theApplied Geomatics Research Group in April 2005,

utilizing their Optech ALTM 3100 sensor, whichwas operated at 70 kHz; and recorded the first andlast returns with an average point spacing of 0.5 m.Independent GPS validation indicated the LiDARDEM has a mean offset of 35 cm, with a standarddeviation of 9 cm. The LiDAR surfaces for bothstudy sites were adjusted by the mean offset valueto the GPS validation points.

The result of a LiDAR survey is a dense set ofelevation points (on the order of cm or m spacing)that include the Earth’s surface, as well as featuressuch as trees and buildings. The points are projectedinto the UTM NAD83 coordinate system and areseparated into those representing the Earth’s surface,known as ‘ground’ points; and all others, known as‘non-ground,’ using specialized software [Terrasolid2008]. The points are then brought into a geograph-ic information system (GIS) and used to build twostandard surfaces: a DEM representing the baldEarth topography from the ground points only; and aDigital Surface Model (DSM) that represents all ofthe features on the terrain (includes trees and build-ings). Since the survey aircraft position is calculatedbased on GPS, the LiDAR point heights and associ-ated surface values are referenced to the WGS84 ref-erence system. For coastal flooding applications, theLiDAR surfaces are translated to reference theCanadian Geodetic Vertical Datum of 1928(CGVD28), which approximates mean sea-level(MSL) using the HTv2 geoid–ellipsoid separationmodel [Veronneau et al. 2006].

2.2 Flood Inundation Mapping andSea-Level Rise

The method to generate still-water, flood-inun-dation maps ensuring the flooding of only thoselow-lying areas connected to the ocean has beendescribed by Webster et al. [2004], and some of theunique hydrologic challenges presented by the highresolution of LiDAR are described in Webster et al.[2006]. An ArcGIS application has been built toautomate the still-water, flood-inundation process,and is described in Webster and Stiff [2008].

Relative sea level for a region is a combinationof three factors: global sea-level; crustal motion(uplift or subsidence); and tidal range. Global sealevel is expected to increase in the next 100 years,according to the Intergovernmental Panel on ClimateChange Third Assessment Report [Church et al.2001], which gives a range between 9 and 88 cm ofsea-level rise by 2100, with a central value of 48 cm.For this study, we use the central value of 0.5 m toestimate the global sea-level contribution to theregion over the next 100 years. The major influenceon crustal motion for this region is related to the last

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An ArcGISapplication

has beenbuilt to auto-

mate thestill-water,

flood-inundationprocess…

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glaciation that ended ca. 10,000 years ago. The areaswhere the ice was thickest were depressed the mostand peripheral regions were actually uplifted, termedthe “peripheral bulge.” The Maritimes represent partof the peripheral bulge and the crust in the regions ofsouthern New Brunswick and Nova Scotia are sub-siding. Subsidence rates vary across the region, withthe Fundy region of Nova Scotia sinking at a rate of20 cm per century [Peltier 2004]. The subsidence ofthe crust is important for coastal communities, inthat it compounds the problem of local sea-level riseand must be considered when projecting future floodrisk. The Bay of Fundy tidal range is expected toincrease by 10 cm over the next century withincreasing sea-levels [Godin 1992]. When all ofthese factors are combined—global sea-level rise,crustal subsidence and tidal amplitude—a potentialincrease in relative sea-level of 80 cm in the nextcentury is probable for the Bay of Fundy region. Inthe Kingsburg study area, a more conservative esti-mate of 48 cm of relative sea-level rise over the nextcentury was used.

2.3 Water Modeler—CalculatingWater-Level Probabilities andReturn Periods

Coastal flooding statistics for return periods orprobability of occurrence can be generated by exam-ining long-term, water level records. For coastalareas in Canada, these records are derived fromtide-gauge records, which are under the jurisdictionof the Canadian Hydrographic Service (CHS) of theDepartment of Fisheries and Oceans (DFO). Thecoastal water level records are available from DFO’sMarine Environmental Data Service (MEDS) on theInternet. These water level records are referenced tolocal harbours and chart datum. A storm surge repre-sents the difference between the predicted waterlevel and the observed, also known as the residual.

Without specialized statistical software, endusers such as land-use planners would obtain infor-mation about the return period of a high water levelfrom a set of return period graphs, if available forthe area of interest. These graphs are typically plot-ted on a log-normal scale, with years on the log Xaxis, and water level or storm surge on the normalY axis. As part of the coastal zone decision-supportsystem, AGRG has developed a new software pro-gram, known as “Water Modeler,” to analyze a timeseries of water level records and generate statisticsfrom them [Mosher 2007].

The Water Modeler is a set of software toolsdesigned to be used for the management of hourlywater level and related meteorological data for thepurposes of estimating current rates of sea-level

rise, and future probabilities of still-water stormsurge. Atmospheric pressure and wind data are notrequired by Water Modeler to estimate long-termstill-water, storm-surge probabilities. However,they are useful for visualization and for water levelinference.

The Water Modeler uses the MySQL databasemanagement system for storing most of the data itworks with. Based on the historical water-levelrecord, the software is able to estimate the proba-bility of a water level being met or exceeded with-in the next so many years, taking various sea-levelrise scenarios into account.

In order to do this, a number of tasks areundertaken:

1. Determine annual means from the historicalwater level record.

2. Determine the current rate of sea-level rise.3. Determine de-trended annual maximum water

levels.4. Construct annual probabilities for these maxi-

mums as (1-CDF) Cumulative DistributionFunction.

5. Create a model which represents current annu-al probabilities:(a) for water levels less than the minimum

annual maximum, the annual probabilitywill be 1; and

(b) for water levels greater than the minimumannual maximum, annual probabilities aremodelled using the Gumbel distributionwith the Gringorten estimate [NationalInstitute of Standards and Technology2006].

6. For given scenarios, propagate annual probabil-ities into the future to estimate probabilities ofreoccurrence for intervening years, taking intoaccount sea-level rise amounts and rates and

7. Considering the results of a number of scenarioevaluations, determine ranges of plausibleprobabilities and expected reoccurrences.

2.3.1 Removing Current Sea-Level Rise Trends Since the reporting unit of interest is the year,

annual probabilities are of concern. Furthermore, itis desirable to remove the effects of current sea-level rise to de-trend the data. When projectingprobabilities into the future, sea-level rise will bere-inserted according to the specifications of thescenarios being evaluated, and it would not serve tohave hidden sea-level rise expressed in the proba-bilities that are to be projected.

2.3.2 The Historical Water Level Record The historical hourly water level record should

be sufficiently long to provide enough data to allow396

Coastalflooding sta-tistics…canbe generatedby examininglong-term,water-levelrecords.

G E O M A T I C A

for plausible conclusions [Pugh 2004]. Thirty yearsis probably a lower limit; a short record may not berepresentative. For example, the public water levelrecord for Shediac, New Brunswick, ran for about20 years, from the 1970s into the early 1990s.There was steady but uncharacteristic decline inannual means through the early to mid-1980s.Calculations of sea-level rise rates based on theShediac tide gauge were too low compared to othergauges in the region, and had to be corrected.Furthermore, storms occurred before and after thisperiod (one in the 1960s (inferred) and one in2000), which resulted in water levels significantlygreater than any found in the record.

2.3.3 De-trending Annual Maximums The hourly water level record was traversed

and yearly means and maximums were calculated(Equation 1). A linear regression on the annualmeans was used to determine a yearly rate of rela-tive sea-level rise (rate). The point at which theregression line crossed mean sea-level was used todetermine a reference year (yearreference).

At various points in the process where de-trended water level (wldetrended) values wererequired, the relative sea-level rise rate (rate) andthe reference year (yearreference) were used to flattenthe water level record, removing current sea-levelrise effects. The current year of observation(yearcurrent) is used in the de-trending process. Inparticular, water levels (wl) before the referenceyear were raised, and water levels after the refer-ence year were lowered:

wldetrended = wl - (yearreference - yearcurrent) * rate (1)

2.3.4 Constructing Probabilities for theAnnual Maximums

In order to assign probabilities (P) to the de-trended annual maximums (Equations 2, 3), theywere sorted from lowest to highest. It is a simplematter to progress through the list, value by value,counting the number of values that went before(Countprevious). Whenever a new value in the list isencountered, we can easily determine the probabil-ity that a lesser value (P (val < cur)) might havebeen encountered by the ratio of the count of theprevious value (Countprevious) and the total numberof annual maximums (Total):

P (val < cur) = Countprevious /Total (2)

and therefore, the probability of the current value(P(val > cur)) being met or exceeded is simply:

P(val > cur) = 1- P(val < cur) (3)

2.3.5 Modelling Water Level Probabilities A simple approach might involve counting the

number of times the level was met or exceeded anddividing by the number of years. The problem withthe simple approach is that it does not account for theclustering of extreme readings around rare events.Suppose a certain high level was met or exceeded 8times within the time span of 2 particularly fiercestorms that occurred 15 years apart. Suppose that thelevel was not otherwise met or exceeded within the30 years of the record. The simple method would saythat the annual probability is 8/30 or 0.267, whichhas a return period of 30/8 or 3.75 years. In truth, theevent which fathered the exceedances only happenedtwice in the 30-year period and the true annual prob-ability is 2/30 or 0.067, with a return period of 15years. A more reasonable way to determine annualprobabilities is to count up the number of years anevent was met or exceeded (2) and divide by thenumber of years in the record (30). Because there areonly 30 years in the record, in the example, there areonly 30 possible probability levels. Empirical annu-al probabilities are too coarse to be used to build amodel of annual probabilities directly, but may beused to check the plausibility of such a model.

The lowest maximum—that is, the minimumannual maximum—is of special interest since anywater level which is less than, or equal to, this mini-mum annual maximum must have a probability of 1.Such a water level will be met or exceeded everyyear. For water levels greater than the minimumannual maximum, the Gumbel distribution (Figure 2)with the Gringorten estimation was found to provide

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Figure 2: Example of a Gumbel extreme value distribution.

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a reasonable fit. The software allows one to gener-ate a diagnostic graph to compare the modelledextreme values to the observed extreme values(Figure 3). The use of annual maxima could be crit-icized because this approach provides relativelyfew data points on which to build a model. Thislower resolution tends to increase the variance andlower the degree of confidence in the results (i.e.confidence intervals are greater). However, while itis possible to create models using more data points(finer resolution), the generalization of these resultsto the annual introduces the assumption thatextreme events are distributed evenly across theyears. This is clearly not the case; rather, extremeevents tend to cluster.

2.4 Projecting Annual Probabilities 2.4.1 Methodological Preliminaries

A given water level was either exceeded or notexceeded in any given year, heads or tails. TheBinomial Distribution is an appropriate distributionto use when reasoning about such occurrences.

2.4.1.1 Accounting for Sea-Level Rise When tossing coins or throwing dice, the prob-

abilities remain constant from one trial to the nexttrial. Because of sea-level rise, the probabilitieschange from trial to trial, year to year. It would beinteresting and useful, though perhaps not practical,

to provide site-specific models of these changes inprobability—based not only on sea-level rise ratesand expectations, but also the effects of localtopography and changes to local topography; not tomention local variations of regional climaticchange. Instead, the software implements the fol-lowing simplification (Equation 4): the currentannual probability of a water level (P (wl)) beingmet or exceeded is modified in subsequent years byassuming that the probability after n years (P (wl)n)will be the probability of some lesser water level (P(wl - sealevelrise)0), namely:

P (wl)n=P (wl - sealevelrise)0 (4)

2.4.1.2 Accounting for Acceleration of theSea-Level Rise Rate

For a given scenario, the user is asked to supplythe expected amount of sea-level rise (Risetotal(n))over some period (e.g., 100 years), and the currentrates of relative sea-level rise (Riselocal(n)) for thesite and global sea-level rise (Riseglobal(n)) (Equation5). As well, the user specifies a curve that representstheir estimation of the rate of acceleration of futureglobal sea-level rise. Current rates are assumed to belinear [Church et al. 2001].

The steepness curve is a designer curve, and isnot intended to have any physical meaning.However, if the current rate of global (eustatic) sea-level rise (Riseglobal(n)) is half or a third of the rateneeded to create projected amounts of sea-level rise,some assumptions about how that rate is going tochange are required. The steepness parameter allowsthe user to look at different acceleration curves. Theglobal sea-level rise (Riseglobal(n)) in the future iscalculated by considering the current rate of globalsea-level rise (CurrentGlobalRiseRate) and theanticipated additional global sea-level contribution(AdditionalRise), which is controlled by the user-defined sea-level curve (Ratio (n)) (Equation 6). The(AdditionalRise) is calculated by considering thetotal global sea-level rise (TotalGlobalRise), theglobal rise rate (CurrentGlobalRiseRate) and thetime period of interest (RisePeriod) (Equation 7).The effect of non-linear, sea-level rise in the future isconsidered by examining the user-defined curve(Equation 8), where the total number of years(totalYears) and the steepness of the sea-level curve(steeepness) is considered. The local sea-level rise(Riselocal(n)) is calculated by using the local crustalsubsidence rate (LocalSubsidenceRate) and thenumber of years (n) (Equation 9). The local crustalsubsidence rate (LocalSubsidenceRate) is the differ-ence between the local relative sea-level rise rate

398

Figure 3: Diagnostic quantile plot showing the Halifax water level model witha 95% confidence interval of +/- 0.06 metres. The diagnostic plots de-trendedannual maxima water level (m) against values predicted by the model. Theoriginal diagram is produced in colour, with the outer lines in red representingthe confidence interval, as noted in the text in the lower right corner.

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(RelativeSLR) and the current global sea-level riserate (CurrentGlobalRiseRate) (Equation 10).

With these parameters in hand:

Risetotal(n) = Riseglobal(n) + Riselocal(n) (5)

where :

Riseglobal(n) = AdditionalRise * Ratio(n) + n *CurrentGlobalRiseRate (6)

AdditionalRise = TotalGlobalRise - (RisePeriod *CurrentGlobalRiseRate) (7)

Ratio(n) = exp((n - totalYears)/steepness) -(1- n/totalYears) * exp(totalYears/steepness)

(8) and where

Riselocal(n) = n * LocalSubsidenceRate (9)

LocalSubsidenceRate =RelativeSLR - CurrentGlobalRiseRate (10)

The ability to express sea-level rise as a set ofindependent components allows the software toshow cumulative probabilities of exceedance with-out respect to any sea-level rise; with respect tolocal components only; and with respect to all com-ponents, including global sea-level rise.

2.4.2 Expected Return Period The expected return period is understood as the

number of years during which there will have beenat least one occurrence of a water level event onaverage. This is calculated as the mean of a bino-mial distribution in which the probabilities changefrom year to year. Whereas the mean of a normaldistribution is about the middle of the distribution,the mean of this distribution, accounting for sea-level rise, tends to occur with probabilities around0.63 to 0.66.

The mean of a binomial distribution (E(X))(Equation 11) is calculated as:

E(X) = np (11)

where (n) is the number of trials and (p) is the prob-ability of the event happening.

The probabilities change from year to year inresponse to sea-level rise, and therefore we simplyadd up the probabilities as they increase from yearto year (p0, p1, p2, …). When the sum of theseprobabilities reaches 1, we indicate the expectedreturn period (E(x)) (Equation 12). That is,

E(x) = p0 + p1 + p2… (12)

where the probability associated with a water level(P) after so many years is determined by Equation 13.

P = exp(-exp(-(waterlevel – location) / scale))(13)

Following the Gumbel distribution of water lev-els (waterlevel). Location (location) and scale (scale)are parameters of the Gumbel distribution, wherelocation is similar to the mean and scale is similar tothe standard deviation of a normal distribution.

2.4.3 Projecting Probabilities into the Future For any given water level and for any given year,

either the water level was met or exceeded, or it wasnot. Heads (H) or tails (T), except that the proba-bilities are neither equal nor constant. Suppose thatthe probability of heads is 0.1 and the probability oftails is 0.9. After 2 years, there are 4 possibilities:

The probability of at least one head in twoyears is 1 — the probability of only tails (i.e. 1-0.81= 0.19 = 0.01+0.09+0.09). The probability of tails(P(tails)) in both years is the probability of tails inany one year, squared. Generalizing to any numberof years, Equation 13 is used to calculate the prob-ability of heads (Pn(heads):

Pn(heads) = 1 - ∏ [1..n]P (tails) (13)

In short, it is easier to propagate the probabili-ty of the event not happening over the years, andthen calculate the probability of at least one eventfrom it, as shown in Equation 13, above.

The probabilities change from year to year, asindicated in Equation 4, and they are implementedin the software code as follows:

tailProb = 1.0;

// accumulate the probability of never//being met or exceeded//---------------------------------------for (year=0; year<nYears; year++) {

seaLevelRise = GetSLR(year);reverseProb = 1 – GetAnnualProb(waterLervel-slr,year);tailprob = tailProb * reverseProb;

}

//probability of having been met at least once399

Year 1 H H T TYear 2 H T H TProbabilities 0.01 0.09 0.09 0.81

Table 1: Cumulative Probabilities.

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3. Case Study Results Two case study areas were used to construct

flood-risk maps using LiDAR DEMs and the WaterModeler. The Saint John, New Brunswick, tidegauge was used in the Annapolis Royal study, andthe Halifax tide gauge was used for the Kingsburgstudy (Figure 1).

3.1 Annapolis Royal

Annapolis Royal was flooded as a result of astorm surge and high waves during the GroundhogDay storm on February 2, 1976. The Nova ScotiaDepartment of Agriculture, Land and WaterEngineering Division, which maintains NovaScotia’s 375 km of dykes, recorded the damagerepair costs to the dykes as a result of the storm tohave been $208,500 in Annapolis County and$314,063 in Digby County. The closest tide gaugein the area—Saint John, New Brunswick—wasoperating, and the hourly data have been used tocompare observed water levels with predicted inorder to determine the storm surge water levels.From these data, a storm surge of approximately1.3 m was observed in Saint John during this peri-od. This value is close to what was reported byDesplanque and Mossman [1999], who determinedthe storm surge in Saint John was 1.46 m; andPublic Safety and Emergency Preparedness Canadastates a 1.6 m storm surge occurred within the Bayof Fundy. To estimate the water level for this eventat Annapolis Royal, the predicted high-tide levelhas been determined and an additional 1.5 m stormsurge and wave setup [upper estimate, Desplanqueand Mossman 1999] has been added in order toinundate the areas described by eye-witnesses andnewspaper reports [February 4 and 11, 1976,Annapolis County Spectator]. The predicted high-tide water level of 8.5 m above Chart Datum (CD),4.1 m orthometric (using Digby CGVD28-CD off-set of 4.39 m) with an estimated storm surge of 1.5m provides the maximum water level of 5.6 m(CGVD28) for flooding. A colour-shaded reliefmodel was constructed from the LiDAR digital sur-face model and used to depict the results of theflood inundation mapping for this storm event(Figure 4). The perspective views were generatedusing the PCI Geomatica suite of software.

In order to estimate the risk of this storm event,hourly water level records for Saint John, NewBrunswick, for the dates between 1966-2006 wereused for the analysis with Water Modeler. To deter-mine the orthometric height of the water level inSaint John during this storm, the observed high-water level 9.14 m CD was subtracted from 4.19 m,the difference between CD and CGVD28 for SaintJohn [Charles O’Reilly, CHS, per comm.]; thus a9.14 m CD water level is equal to a 4.95 m ortho-metric height (CGVD28).

The Water Modeler software calculated a 0.22cm/yr RSL based on the Saint John water levelrecord, which is in agreement with Bernier [2005].However, Desplanque and Mossman [1999] reportRSL at 0.36 cm/yr. The potential climate change

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Figure 4: LiDAR digital surface model (DSM) view ofAnnapolis Royal. Top view DSM with 5.6 m waterlevel, image is approximately 8 km across. Middleperspective view of DSM looking southeast at low tide(-4 m CGVD28). Lower perspective view of DSMlooking southeast at maximum flooding (5.6 mCGVD28) of the Groundhog Day storm.

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induced RSL for the Bay of Fundy is estimated at0.80 cm/yr. Table 2 represents the return period(years) of the Groundhog Day storm for Saint John,based on the current observed relative sea-level(RSL) rate of 22 and 36 cm per century, and theexpected RSL of 80 cm in the next century due toclimate change impacts. The cumulative floodprobabilities were plotted for the Groundhog Daystorm in Saint John (4.95 m orthometric) using the22 cm and 80 cm/century values of relative sea-level (RSL) rise rates. At the current rate of RSL(22 cm/century), the average return period (65 per-cent probability) of the Groundhog Day water levelis 43 years and with a high probability (99 percent)within 121 years. If the projected rate of RSL of 80cm/century is used, the average return period of thiswater level drops to 23 years, with a high probabil-ity within 55 years. The return period was alsographed with the sea-level rise rate of 22 cm percentury (Figure 5) and the expected rate of 80 cmper century due to climate change impacts.

From this type of graph, and using differentsea-level rise rates, the water levels for storm-return periods of 50-, 100-, 150- and 200-yearevents were calculated and rounded to the nearestdecimeter (Table 2).

The Kingsburg area of Lunenburg County wasalso used as a case study site [Mosher and Brydon2007]. The hourly water level record from the clos-est tide gauge, Halifax, was used for the datesbetween 1960 and 2005. The sea-level rise rate forthis area was based on local crustal subsidence of 4cm and eustatic sea-level rise of 18 cm during thepast century. The additional sea-level rise from cli-mate change was estimated at 26 cm during thenext century, thus projecting a total sea-level rise of48 cm during the next century. The benchmarkstorm used from the Halifax water record wasHurricane Juan, which occurred in September2003. The water level associated with Juan was1.92 m (CGVD28) from the 15-minute water-levelrecord. The cumulative flood-level probabilitieswere calculated for this water level (Figure 6). Thereturn period of this storm is close to 95 years, withan average return period of 52 years (probability of0.65). The water levels and return periods (0.99probability) of storms were also plotted using thesame sea-level rise conditions (Figure 7).

From these types of outputs from WaterModeler, a series of observations can be made. Astorm surge water level of 0.55 metres above hightide (1.5 metres above MSL) is to be expected with-in 7 years. This level will almost certainly be metwithin the next 25 years. This result seems to hold,regardless of the sea-level rise curve chosen. Astorm surge water level of 0.8 metres above high

tide (1.75 metres above MSL) will probably occurwithin 19 to 23 years. There is a 10 percent proba-bility that the level will be reached in less than 4years, and it will almost certainly be met within 55years. A storm surge water level of 1.05 metresabove high tide (2.0 metres above MSL) is to beexpected within about 40 to 55 years. HurricaneJuan was 1.95 metres above MSL. There is a 10percent probability that this level will be seen inabout 15-17 years; a very high probability that itwill occur within 75 years, and certainly within 100years. A storm surge water level of 1.55 metresabove high tide (2.5 metres above MSL) is to beexpected in about 90 to 125 years, with a 10 percentchance in 60 to 80 years.

A sea-level rise rate of 39 cm in the next centu-ry was used to examine the probabilities associated

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Figure 5: Water level return periods for Saint John, N.B., using the observedsea-level rise rate of 22 cm per century. The return period in years is on theX axis and the water level (m) relative to CGVD28 is on the Y axis.

Return Period RSL = 0.22 cm/year RSL = 0.36 cm/year RSL = 0.80(Years) (Observed rate) (Desplanque and cm/year

Mossman, 1999) (Climate change)

50 4.7 m 4.7 m 4.9 m

100 4.8 m 4.9 m 5.3 m

150 5.0 m 5.1 m 5.7 m

200 5.1 m 5.3 m 5.8 m

Table 2: Water levels in metres above CGVD28 for Saint John, N.B., forreturn period of 50, 100, 150, and 200 years under different relative sea-levelrise (RSL) rates.

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with different water levels and were related to theinundation maps in a GIS environment (Figure 8).With this approach, the spatial distribution of inun-dation can be visualized against the risk or proba-bility of such an event occurring.

4. Discussion

Pugh [2004] discusses different methods forcalculating risk of extreme water levels. For all ofthe methods Pugh [2004] describes, mean sea-levelrise trends have been removed before the statisticalanalysis of the water level time-series is performed.This technique has been implemented in the WaterModeler, where the time series is de-trended of sea-level rise. The use of the annual maxima from a timeseries of water level records, as in this study, isdescribed by Pugh [2004], although he notes thatthe method has the disadvantage of wasting someof the data in the time series, since only the maxi-ma are used for each year. He describes the jointtide-surge probability method, where the surgelevel is separated from the tide level and probabili-ties determined. Dixon and Tawn [1999] studied theeffect of non-stationarity on extreme sea-level esti-mation, where they compared the annual maximum(AM) and the joint probability (JP) methods. Theyconcluded that when the tidal variations are large,relative to the surges variations, the AM methodunderestimates the long (> 100 years) return periodlevels compared to the JP method for sites aroundthe United Kingdom. However, they warn that the JPmethod requires high-quality data and careful statis-tical analysis, and that for some applications the tra-ditional AM method may still be the better choice.D’Onofrio et al. [1999] also compare the returnperiods calculated using the JP and the AM fitted toa Gumbel function methods for the coast ofArgentina, and found the resultant return-periodwater levels to be similar. Suursarr and Sooaar[2007] used the Gumbel distribution to fit the annu-al maximum and minimum values of water levelsand found that some significant storm-surge eventsrepresented outliers from the distribution because ofthe decadal variations in climate and water levelsrelated to the North Atlantic Oscillation. They pointout that variable climatic oscillations are not fac-tored into any of the extreme value statisticalapproaches. Pugh [2004] also describes the peak-over-threshold, where the number of times a waterlevel exceeds some level is calculated from the timeseries. He suggests the peak-over-threshold methodshould be applied to surge residual values only, andnot to total water levels, to avoid the natural varia-tions in the 18.6-year tidal cycle.

These different methods (AM, JP and peak-over-threshold) were investigated as part of thisstudy, and the annual maximum (AM) approachwas selected for implementation in the WaterModeler because the other methods assume an evendistribution of extreme events over the years when

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Figure 6: Cumulative flood-level probability graph for Hurricane Juanwater level. The black dot represents the average expected return period ofthis water level (0.65 probability). The original diagram is produced incolour, with the lower section in red, middle in blue and upper in black, asnoted in the text in the upper-left corner.

Figure 7: Water level return period graph for Halifax with a total sea-levelrise of 48 cm during the next century. The original diagram is produced incolour with the lower section in red, middle in blue and upper in black, asnoted in the text in the upper-left corner.

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they are calculating probabilities based on hourlyrecords instead of annual records. Both Kamphius[2000] and Coles [2001] note the importance ofusing annual, rather than hourly, data when calcu-lating annual probabilities. Indeed, inconsistencieswith the application of the approaches, compared toempirically calculated annual probabilities, led usto the use of the annual maxima method for theWater Modeler.

At the regional level, Thompson et al. [2002],Bernier [2005] and Bernier et al. [2006] have pro-vided estimates of return periods for storm surgelevels at different sites around Maritime Canada.Bernier [2005] tested the “skill” of the Dalhousiestorm surge model by comparing model outputsbased on atmospheric wind and pressure fields withthe observed water level records for several stations(36 sites) around the North Atlantic coast. Based onher analysis, the largest observed magnitude of theannual maximum surge at Saint John is approxi-mately 0.7 m. This is only about one-half of thestorm surge that was recorded during the 1976Groundhog Day storm at Saint John. The differencein the annual maximum surge level is a result of theaggregation and smoothing procedures (low-passfilter) that have been applied by Bernier [2005] inorder to compare observed water levels with modeloutputs that were limited by their temporal resolu-tion (six hours) of the forcing fields (i.e. AES40winds and inferred pressure). The six-hour timestep is too coarse to be able to resolve all fast-mov-ing storms, including some hurricanes, and themethod underestimates these events. Thus, thereturn periods and associated storm surge waterlevels reported in Bernier [2005] represent a con-servative calculation of past events where theeffects of some short-lived events, such as hurri-canes, have been filtered out.

Based on Bernier’s Figure 4.6 [Bernier 2005;p. 112] (surge plus tide), the 100-year return periodtotal water level for Saint John is approximately4.75 m above MSL using the maximum likelihoodline of best fit through the observed data. The waterlevel calculated from the Water Modeler for the100-year storm using the observed sea-level riserate of 22 cm/century is 4.8 m. The return period ofthe Groundhog Day storm water level (4.95 m) inSaint John calculated by the Water Modeler is 121years, using this sea-level rise rate. The resultsfrom the Water Modeler are consistent with thefindings of Bernier [2005], especially consideringthe differences in methodologies used.

In addition to generating flood-level returnperiods with the Water Modeler, the CoastalDecision Support System (DSS) consists of robustmethods to analyze and communicate risks due to

coastal processes and the potential effectiveness ofspecific mitigation and adaptation measures. Ananimated 3-D rendered generation of an advancingcoastal flood on a LiDAR representation of the ter-rain, complete with topographic features, is oneexample of such methods. A counter displaying ris-ing water level against diminishing probability(from the Water Modeler) informs and supportsdecision-making by planners, politicians and civilsociety. A “what-if” scenario can be presented, forinstance, in the form of shore protection infrastruc-ture, and the demonstration of its predicted role inmitigating coastal flooding can be displayed in asimilar visual animation fashion.

Using data from the Water Modeler, integratedwith topographic and socio-economic / demograph-ic data, the Coastal DSS enables the construction offlood-risk maps, flood-depth maps, and economicimpact assessments and recommendations forcoastal areas (Figure 9). Applying these processesresults in an understanding of coastal zone changesor events that pose a threat, and identification of thevarious steps that can be taken to avoid or mitigatethe effects of such changes or events. The coastalDSS, therefore, is an integrated solution designed toaddress the need for coastal impact risk-assessmentand management for the insurance, real estate, finan-cial and professional sectors, as well as for govern-ments and their associated agencies and others toeffectively manage their vulnerable land assets.

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Figure 8: Inundated coastline for the Kingsburg area, with inset graphshowing the probability and flood-water levels. Inundation level is 3.2 mabove MSL, which exceeds the level that was observed from HurricaneJuan at Halifax (1.92 m). As can be seen from the graph, there is a very lowprobability of the 3.2 m level being reached. The map is approximately 3km across.

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5. Conclusions

The Applied Geomatics Research Group(AGRG) and its project partners have developed aCoastal Decision Support System. The systemexamines erosion and flood-risk using a modularapproach. As part of the system, Water Modeler hasbeen developed, which allows the estimation offlood-level probabilities based on long-term, hourlywater level records and estimates as to future sea-level rise. Several methods are described in the liter-ature to calculate the return periods of extremeevents; however, the annual maxima method wasdetermined to be the most suitable for this applica-tion. The tool provides ballpark estimates which arecompared on a project-by-project basis against exist-ing studies, where possible (as in the case of SaintJohn), and against consistency with known facts andreasonable expectations where not (as in the case ofKingsburg). The work of development, refinementand validation continues. The tool will be utilized infuture storm surge studies at the AGRG and by ourindustry partners, GeoNet Technologies Inc. andCARIS, which has incorporated a version of the soft-ware in their Flood Modeler software. We haveshared our results with the local planning authoritiesfor the two communities, Annapolis Royal andKingsburg, and they are now more aware of the riskof coastal flooding.

The combination of geomatics tools—such ashigh-resolution LiDAR DEMs for coastal floodinundation and the Water Modeler, to estimate theassociated risk—allows coastal communities tobetter plan for the future.

6. Acknowledgements

We are grateful to the following people fortheir contribution to this work: Angela Templin,formally with AGRG, now with the LandInformation Centre Access Nova Scotia whoworked on the Annapolis Royal flood inundationmapping; and Jeff Parkes of Birch HillGeoSolutions and Tamera Hill, for securing thefunding and administering the Annapolis Royal cli-mate change study. Environment Canada for fund-ing the Annapolis Royal climate change study. TheOdell House, Andy Sharpe of the Clean AnnapolisRiver Project, and the citizens of Annapolis Royalfor providing historical information on past storms.Hank Kolstee of the Nova Scotia Department ofAgriculture, for providing damage-cost informa-tion from past storms around Annapolis Royal.Charles Hanna and Charles O’Reilly of Departmentof Fisheries and Oceans, for advice related to theBay of Fundy sea-level conditions. KeithThompson and Natasha Bernier, for their sharingand cooperation related to her Ph.D. thesis. TheAGRG LiDAR system and the Annapolis RoyalLiDAR survey were funded through a grant fromthe Canada Foundation for Innovation. The CoastalZone Decision Support System development andcase studies were funded by a grant from theAtlantic Canada Opportunities Agency’s AtlanticInnovation Fund. Carl Brydon and MarietteHachey of GeoNet Technolgies Inc. for their workon the Kingsburg study.

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Webster, T. and D. Stiff. 2008. The prediction and map-ping of flood risk associated with storm-surgeevents and long term sea level changes. In RiskAnalysis VI Simulations and Harzard Mitigation.WIT Press. Edited by Brebbia, C.A. and E. Beriatos,pp. 129-139.

AuthorsDr. Tim Webster is a Research Scientist with

the Applied Geomatics Research Group at the NovaScotia Community College. He obtained his Ph.D.from Dalhousie University in the Earth ScienceDepartment. Areas of research include the applica-tion of elevation models to landscape evolution andgeoscience, coastal flood-risk mapping and changedetection. Previously, he taught in the RemoteSensing and GIS programs at the Centre ofGeographic Sciences (COGS) since 1991. He has aM.Sc. from Acadia University, an AdvancedDiploma in Remote Sensing from COGS, and aB.Sc. in Geology and Physics from University ofNew Brunswick (UNB).

Roger Mosher, Software Engineer withAGRG, is responsible for project management andtechnical research on the development of a coastalzone decision-support system for disaster manage-ment, as well as teaching responsibilities in theGeomatics Programming program.

Mike Pearson received his Bachelor’s andMaster’s of Science degrees in SurveyingEngineering from UNB, and Post GraduateDiploma in Land Information Management fromthe same institution. He served as Director of theSurveys and Mapping Division for the MaritimeProvinces for five years, and is a past councillor forthe Canadian Institute of Surveying and Mapping.Mike is a member of the Association ofProfessional Engineers of Prince Edward Islandand on the Board of Directors of the GeomaticsIndustry Association of Canada. For the past 14years he has been the CEO and Director ofMarketing for GeoNet Technologies in P.E.I.,where he resides with his wife Nancy and two sons,Matthew and Ben. o

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