Modeling storm surge flooding of an urban area with particular reference to modeling uncertainties: A case study of Canvey Island, United Kingdom

Modeling storm surge flooding of an urban area

with particular reference to modeling uncertainties:

A case study of Canvey Island, United Kingdom

James D. Brown,1,2 Tom Spencer,3 and Iris Moeller3

Received 17 September 2005; revised 8 December 2006; accepted 9 February 2007; published 7 June 2007.

[1] A coupled storm surge and overland flow model is used to simulate extreme coastalflooding of Canvey Island, a dense urban area located at the mouth of the Thames Estuary,U.K. The flood model is based on a shock-capturing numerical scheme and resolves theterrain and buildings of the study area with high-resolution topographic data. Repeatsimulation is used to propagate uncertainties in model inputs and parameters through touncertainties in model outputs, and the main sources of uncertainties are described. Thegreatest uncertainties originate from the forcing inputs to the flood model, includingcoastal water levels and sea defense failures, rather than its internal boundaries, such as themodel terrain and bottom friction. This is consistent with studies in rural andsemideveloped floodplains and reflects a combination of high sensitivity to, anduncertainty in, the forcing inputs. However, other numerical and physical variablesintroduce significant uncertainties, of which many are specific to, or altered by, the urbanfloodplain. In particular, model predictions are sensitive to the spatial resolution (Ds) ofthe numerical grid. This includes the effects of Ds on boundary features (walls, hedges,etc.), which are described in the bed friction coefficient, and on the representation ofbuildings, which are described in the model terrain. Finally, model predictions areintegrated across multiple combinations of breach width and location to explore the‘‘relative’’ hazards (i.e., spatial and temporal variations in hazard) associated with thefloodplain geography.

Citation: Brown, J. D., T. Spencer, and I. Moeller (2007), Modeling storm surge flooding of an urban area with particular reference

to modeling uncertainties: A case study of Canvey Island, United Kingdom, Water Resour. Res., 43, W06402, doi:10.1029/

2005WR004597.

1. Introduction

[2] Human occupation of low-lying coastal areas exposespeople and property to flooding. Tsunamis and storm surgescan result in substantial economic and social impacts,including loss of life, damage to property, and disruptionof essential services [Gram-Jensen, 1991; Tsuchiya andShuto, 1995; Danard et al., 2003] (see also F. M. Lawet al., at http://www.dundee.ac.uk/geography/cbhe). Stormsurges, which are generated by extreme wind stress actingon shallow, continental shelf seas can lead to severe coastalfloods, particularly when they coincide with a high tide andresult in overtopping and breaching of sea defenses [Pugh,1987]. For example, the North Sea storm surge of 31 Januaryto 1 February 1953 caused �1800 deaths in the Nether-lands and �300 deaths in the United Kingdom alone[Rossiter, 1954; Welander, 1961; Pollard, 1978; McRobieet al., 2005]. More recently, Hurricane Katrina caused

extensive damage and at least 1800 deaths on the U.S.Gulf Coast in August 2005 [Wilkinson, 2006]. Many ofthese deaths occurred in New Orleans, where failures inthe sea defenses caused rapid flooding of approximately80% of the city [Wilkinson, 2006].[3] An understanding of the nature and degrees of expo-

sure to coastal flooding is important for reducing its impactson people and property. This may be developed throughfield observations, modeling studies, or some combinationof the two. However, extreme flood events, and henceobservations of these events, are rare, by definition. Whenobservations are available, they may be difficult to extrap-olate in space or time due to variations in floodplainconditions, or to use in modeling studies, as the observa-tions are frequently too coarse or uncertain [Giarrusso andDodd, 1997; Haider et al., 2003]. Also, extreme eventswill typically alter floodplain conditions, both directlyand by prompting changes in floodplain management,further hampering the ‘‘validation’’ of flood models withhistoric observations (as far as predicting future events isconcerned). Thus observations cannot be used routinely toevaluate coastal flood events. Furthermore, as floods areunique occurrences, hazards are best explored for multipleevents and related to the prevailing storm and floodplainconditions. This should lead to an understanding of whichareas are most at risk and why. In the absence of field

1Hydrologic Ensemble Prediction Group, NOAA Office of HydrologicDevelopment, Silver Spring, Maryland, USA.

2Formerly at Physical Geography, Institute for Biodiversity andEcosystem Dynamics, University of Amsterdam, Amsterdam, Netherlands.

3Cambridge Coastal Research Unit, Department of Geography, Uni-versity of Cambridge, Cambridge, UK.

Copyright 2007 by the American Geophysical Union.0043-1397/07/2005WR004597

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WATER RESOURCES RESEARCH, VOL. 43, W06402, doi:10.1029/2005WR004597, 2007

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observations, physically based computer models may beused to explore extreme flood hazards, but the associateduncertainties should be explicitly incorporated into modelpredictions.[4] In recent years, advances in flood propagation algo-

rithms [Alcrudo, 2002] and in the collection and processingof flood data [Marks and Bates, 2000] have supported thewidespread application of hydraulic models to flood pre-diction [Bates and Anderson, 1993; Stelling et al., 1998;Bates et al., 1996; Bates and Hervouet, 1999; Makhanov etal., 1999; Beffa and Connell, 2001]. Most of these appli-cations have focused on rural or semideveloped floodplains,where isolated structures may be modeled [Tayefi et al.,2007], but larger groups of buildings are otherwise ignoredor parameterized as surface friction. This cannot properlyaccount for the blocking effects of buildings on flow [Yuand Lane, 2006a, 2006b]. Studies of flooding within urbanareas have received much less attention. This can beattributed, in part, to the technical difficulties of modelingflow through urban areas, including the need for stable,accurate, and precise solutions of the flow equations. Forsmall-scale (i.e., low-resolution) applications, the blockingand frictional effects of buildings may be represented in asub-grid-scale model [Braschi and Gallatti, 1989; Hervouetet al., 2000; Yu and Lane, 2006b]. This avoids some of thetechnical difficulties of grid-scale modeling. For example,in a study of the Kyrkosjarvi dam break with TELEMAC-2D,Hervouet et al. [2000] used a wall drag coefficient andan effective porosity to model the effects of buildings oninundation extent. Unlike roughness coefficients, whichallow a residual flow at arbitrarily high friction values, aporosity coefficient will allow complete or partial blockingof flow by structures [Lane, 2005]. Using this method,Hervouet et al. [2000] found that buildings had a significantimpact on flooding, leading to a substantial increase in floodextent when compared with an undeveloped floodplain.[5] Following recent advances in the numerical solution

of the flow equations [Molinaro and Natale, 1994], severalexamples of grid-scale modeling of urban areas are begin-ning to appear in the literature [Haider et al., 2003; Mignotet al., 2004; Lin et al., 2006]. These include applications ofthe two-dimensional (2-D) diffusion equation to floodingfrom storm drains [Hsu et al., 2000], and applications of thefull Saint-Venant equations to coastal flooding [Brown,2004] and riverine flooding [Mignot et al., 2006]. Notwith-standing these recent contributions, relatively little is knownabout the necessary complexity of flood models for differenttypes and severities of urban flooding. However, it isunlikely that experiences from rural catchments will trans-late directly into urban areas. On the one hand, many of thekey sensitivities and uncertainties are likely to be the same,with forcing inputs and surface friction contributing most ofthe uncertainty, and model terrain largely determining floodpatterns [Bates et al., 2004; Hall et al., 2005]. On the otherhand, the sources and sinks of floodwater, as well as thetypes of flow, can be substantially different in urban areas,placing different demands on modelling [Mark et al., 2004;Hilden, 2005]. For example, sources of floodwater aretypically more localized in urban areas (defense failures,storm drains etc.), possibly increasing the significance oflocal discretization [Aronica and Lanza, 2005]. Further-more, extreme floods involve both deep and fast flowing

water, which increases the significance of the inertial termsin the flow equations [e.g., Huang et al., 2002]. In order tobetter understand these sensitivities, we conduct high-resolution, grid-scale, modeling of a dense urban area inwhich various scenarios of extreme flooding are explored.[6] Aside from the technical difficulties of modeling flow

around buildings, the accuracy and representativeness offorcing inputs is a major source of uncertainty for extremeevents. Indeed, process controls may be qualitatively dif-ferent under extreme conditions, leading to problems inestimating return periods [Van den Brink et al., 2003;Powell et al., 2003], and even the most basic forcing inputs,such as storm strength and flood defense failures, remaininherently uncertain. For example, it is impossible to predict(with useful accuracy) the location, timing, and subsequentevolution of a breach in masonry defenses [Macdonald andLangridge-Monopolis, 1984; Zoppou and Roberts, 1999;Morris, 2000; Wahl, 2001; Morris and Hassan, 2002]. Forthe few cases in which flooding from overtopping andbreaching has been observed [e.g., Giarrusso and Dodd,1997], the limited accuracy of these observations, togetherwith the lack of simultaneous measurements of overtoppingand breaching volumes, has hampered their ability to‘‘validate’’ flood models or distinguish between competingmodels in field conditions.[7] In the absence of field observations, probabilistic

assessments of uncertainty can be difficult. However, sen-sitivity analyses, and more rudimentary forms of uncertaintyanalysis, may help to identify the key sources and magni-tude of uncertainty in model predictions, respectively. Thisis important for improving flood models and for using theirpredictions in decision-making, as the value of scientificadvice to a policy-maker or manager will depend on howwell its validity and relative importance can be assessed[Handmer et al., 2001; Aronica et al., 2002; Brown andDamery, 2002].[8] Accordingly, this paper employs an in-depth case

study to (1) demonstrate the application of a 2-D hydraulicmodel to flooding within an urban area; (2) identify keysensitivities in model outputs to the specification of inputsand parameters; (3) evaluate and illustrate the propagationof uncertainties from model inputs, including forcing andboundary conditions, to model outputs; and (4) consider thevalue of physically based models for assessing urban floodhazards on Canvey Island and more generally, given theuncertainties in forcing inputs and boundary conditions.This study is a first attempt to model storm surge floodingof an urban area with a 2-D hydraulic model and to explorethe uncertainties associated with model predictions.

2. Canvey Island: A Case Study

[9] Canvey Island lies at the mouth of the ThamesEstuary in southeast England (Figure 1). It is formed onan extremely flat and low-lying alluvial fan, which has anaverage height of �1 m below mean high water [Marsland,1986]. Intertidal mudflats surround Canvey Island to theeast, with extensive areas of salt marsh along the northernand eastern banks and around Two Tree Island [Institute ofEstuarine and Coastal Studies (IECS), 1996]. CanveyIsland itself is characterized by a complex network of tidalcreeks and open drains, passing through residential areas tothe north and east and into a central lake.

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W06402 BROWN ET AL.: MODELING STORM SURGE FLOODING OF AN URBAN AREA W06402

[10] Canvey Island has a long history of devastatingstorm surges, including one on 18 January 1881, whichdestroyed 4.83 km (3 miles) of sea wall on the RiverThames frontage [Environment Agency (EA), 2001]. Morerecently, Canvey Island sustained some of the worst damageand the most casualties of any location on the east coast ofEngland during the storm surge of 31 January to 1 February1953, when 58 people died there [Grieve, 1959; Pollard,1978; Summers, 1978; McRobie et al., 2005].

[11] Storm surges in the Thames Estuary originate fromwind action over the Continental Shelf to the northwest ofScotland, and from pressure gradients acting on the deepwaters of the North Atlantic [Pugh, 1987]. These ‘‘externalsurges’’ may combine with ‘‘internal surges, ’’ produced bywinds acting directly on the North Sea, and then travelsouthward with the semidiurnal tide along the coasts ofScotland and England into the southern North Sea. Theouter reaches of the Thames Estuary are exposed to wind

Figure 1. The location of Canvey Island, UK, along with the flood model boundaries.

W06402 BROWN ET AL.: MODELING STORM SURGE FLOODING OF AN URBAN AREA

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waves generated in the southern North Sea, leading to anopen-ended wave probability distribution [IECS, 1996].Although much of the deepwater wave energy is likely tohave dissipated before reaching Canvey Island [IECS,1996], the wind wave climate of the inner estuary remainsunclear, with no readily available data on wave heights[IECS, 1996; J. Pinder, Port of London Authority, personalcommunication, 2001].[12] Canvey Island is protected against flooding by a

network of sea defenses, comprising reinforced concretewalls and supporting structures along the waterfront, and asecondary line of earthen embankments positioned �500 minland in the north and east (Figure 1). The defenses wereconstructed in the 1980s and extend over 14.2 km from theEasthaven Barrier in the southwest to the Benfleet Barrier inthe northwest (Figure 1). The integrity of the scheme reliesupon the closure of these barriers during a major stormsurge, as the defenses along the western section of CanveyIsland were not improved during the 1980s. The floodwallsvary in height from 6.35 m above Ordnance Datum Newlyn(ODN; which approximates to mean sea level) to 7.15 mODN and in width from 0.4 to 0.6 m. The heights of the seadefenses were based on a statistical analysis of 140 years oftidal data by Suthons [1963], which incorporated a nowuntenable stationary increase in mean sea level to the year2030. Furthermore, the tidal record does not include anydirect observations of a ‘‘1:1000 year’’ water level. Thuswhile the residual risks of flooding remain unknown, theycannot be ignored. Indeed, the social and economic impactsof a major flood event would be severe. In summary, thecombination of high potential losses and a relatively small(self-contained) floodplain makes Canvey Island both aninteresting and practical case study for detailed numericalmodeling.

3. Materials and Methods

3.1. Model Structure

[13] Spatially distributed (2-D) hydraulic models areessential for predicting overland flow across rough terrain[Bates et al., 1998a, 1998b], as 1-D models cannot ade-quately capture an irregular flood boundary. While flowaround buildings, and flooding more generally, has asignificant vertical component, the benefits of 3-D modelingare less clear [Alcrudo, 2002; Haider et al., 2003].[14] The Delft Flooding System (Delft-FLS) was used to

simulate overland flow in this study. Delft-FLS solves the2-D Saint-Venant equations on a rectangular, staggered gridwith a finite difference numerical scheme [Stelling et al.,1998; Mynett, 1999; Hesselink et al., 2003]. The modelemploys a shock-capturing numerical scheme and is there-fore suitable for modeling rapidly varying flows over roughterrain, including flow through defense breaches andaround buildings. Although water depths are guaranteedpositive in Delft-FLS, a minimum depth of 0.01 m wasused to distinguish between ‘‘dry’’ and ‘‘flooded’’ cells in aconsistent way. A detailed description of the technicalspecifications of Delft-FLS is given by WLjDelft hydraulics[2000] and Stelling et al. [1998].

3.2. Flow Boundary Conditions

[15] Raster layers of terrain height and bottom frictionwere generated for input to Delft-FLS. The terrain data

comprised sixteen 2-km2 tiles of light detection and ranging(lidar) data, provided by the UK Environment Agency (seeAshkenazi et al. [1999] for details). The original lidar datawere collected at irregularly spaced intervals of 1.5–5 m andinterpolated to a regular grid or digital elevation model(DEM) of 2 � 2 m cells.[16] Buildings were temporarily removed from the DEM,

as the sampling frequency of the lidar instrument (1–5 m)was insufficient to capture these features adequately. Theywere replaced with data from the UK Ordnance Survey(OS) 1:1250 SuperplanTM maps. Default values wereapplied to the building heights, as overtopping of buildingswas not considered here. The buildings were removed fromthe DEM by constructing a mask with the OS SuperplanTM

data. Similarly, vehicles and vegetation were removed fromthe DEM. Vegetation was incorporated in the bottomfriction coefficient, but vehicles were not included in theflood model. These objects were eliminated through acombination of manual editing and semiautomatic filteringbased on local variations in slope and elevation. Thisinvolved computing the differences in height or slopebetween a central pixel and the mean of the surroundingpixels in a 3 � 3 moving window. Successive thresholdswere tested against 1: 4,000 black-and-white aerial photog-raphy (also supplied by the EA), and obvious filtering errorswere reversed through manual editing. Fully automaticfiltering was not possible, as the lidar data comprised onlya single sensor return, rather than a dual pulse to whichheight differencing can be applied [Marks and Bates, 2000;Cobby et al., 2003]. The sea defenses were also removedfrom the lidar data. They were added back to the DEMusing the 1:1250 SuperplanTM data for position and theoriginal engineering drawings for height. Figure 2 showsthe discretization of buildings by comparing the unpro-cessed and processed lidar data at a grid resolution of 0.5 m.[17] A Leica SR530 differential GPS (dGPS) was used to

assess the vertical accuracy of the lidar DEM at fixed surveypoints. Uncertainty about the ‘‘true’’ heights in the DEMoriginates from the limited size and accuracy of the errorsample. The dGPS was employed in real-time kinematic(RTK) mode with a single base station and a roving receiverto collect the sample data. The base station was tied to theOS Active Network, ensuring the dGPS samples wereunbiased following postprocessing. The coordinates werethen converted from WGS84 to OSGB36 for comparisonwith the lidar data. The upper limit for detecting a signif-icant vertical error in the DEM depends jointly on theuncertainty of the dGPS instrument and the uncertainty ofthe coordinate conversion. These uncertainties were unbi-ased, normally distributed, and statistically independent, withstandard deviations of 0.058 and 0.06 m, respectively. Thusthe propagated uncertainty resulting from their linear com-bination is

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

0:05822 þ 0:062p

¼ 0:084 m [see Taylor, 1997].[18] Since the spatial resolution of the elevation data

(1.4–4 m) greatly exceeded the quoted horizontal precisionof the lidar system (±0.108–0.145 m [Ashkenazi et al.,1999]), horizontal errors were not considered in the dGPSsurvey. Vertical errors were assessed at 1160 survey pointsusing a stratified sampling design, due to problems ofaccess in residential areas. The errors in the DEM wereapproximately normally distributed, with a mean error(bias) of –0.151 m and a standard deviation of 0.089 m.

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The errors were not significantly different in areas that werefiltered and interpolated. This falls at the lower end of theroot-mean-square error (RMSE) reported by Ashkenazi etal. [1999] (±0.11–0.25 m), notwithstanding the bias of�0.151 m.[19] In order to account for the ‘‘sub-grid-scale’’ rough-

ness of the terrain, a friction map was generated using threesources of land cover data, namely, the Landcover Map ofGreat Britain (LCMGB), the OS SuperplanTM data, and the1:4000 black-and-white aerial photography. The LCMGBwas derived from a supervised maximum likelihood classi-fication of Landsat Thematic Mapper (TM) data [Fuller etal., 1994]. The aerial photography and Superplan data wereused to augment the LCMGB in urban/residential areaswhere the LCMGB pixel resolution was too coarse.

[20] In the light of experimental evidence and modelingstudies involving turbulent flows [e.g., Clifford et al., 1993],the horizontal components of the bottom shear stresses, tb,are typically described with a quadratic drag law:

tb ¼ rg

C22D

Uj j; ð1Þ

where j U j is the depth-averaged horizontal velocity andC2D2 is the 2-D Chezy coefficient. As indicated above,

bottom friction is an effective quantity in flood modelingsince it accounts for ‘‘sub-grid-scale’’ roughness of theterrain [see Lane, 2005]. Furthermore, it may represent thelumped effects of several missing processes followingcalibration (e.g., turbulence, vertical dispersion of the

Figure 2. Buildings in the (top) original versus (bottom) filtered lidar data.


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horizontal velocities). Initial values of C2D2 can be derived

from a number of semiempirical equations, includingManning’s formulation, which relates C2D

2 to water depth Hvia the Manning coefficient, n:

C22D ¼

6 ffiffiffiffi

Hp

n: ð2Þ

[21] Using previous studies of bottom friction, Cb, fordifferent surface types [Chow, 1959; Aldridge and Garrett,1973; Arcement and Schneider, 1989; Gilley et al., 1992],13 friction classes were derived from the 22 land coverclasses in the LCMGB (Table 1). Manning’s formulation ofC2D2 was used here because (1) values of n are available for

a wide range of cover types and (2) the dependence ofC2D2 on

flow depth allows an increase in friction during the initialstages of flooding and a reduction during the ‘‘basin filling’’stage, when obstacles become inundated. However, asC2D2 increases exponentially with declining water depth

(equation (2)), a limiting value of n = 0.05 was imposedbelow H = 0.02 m. The ranges of n reflect the precision ofthe land cover classes from which n was derived and lead touncertainties in C2D

2 . Winter ranges were assumed for thevegetation classes because storm surges invariably occur inwinter months. While the values of n in Table 1 are based onexperiments or field observations at the ‘‘point support,’’flood models operate at a much larger (areal) support.Consequently, these values should be aggregated to the gridresolution of the flow model. Typically, this is achieved bycalibrating the flow model for n, although initial values maybe obtained from physical measurements of sub-grid-scalefeatures, such as vegetation [Cobby et al., 2003]. In theabsence of flood data, calibration of n was not possible.Physical measurements were also problematic, due to thevariable nature of the land cover in residential areas and thelikely removal of material during an extreme event. Hereobjects with very different frictional properties appeared in asingle grid cell (e.g., trees, walls, fences, concrete paths,ponds, grass, etc., all appear in gardens). Many of theseobjects are inherently ill defined in a lumped roughnesscoefficient. Thus point-based values of n were used in the

flood model, but sensitivities were explored for a widerange of n.

3.3. Forcing Inputs

[22] A storm surge model of the North West EuropeanContinental Shelf, the southern North Sea, and the ThamesEstuary was used to predict water levels at Canvey Islandfor different scenarios of meteorological and tidal forcing[Brown, 2004]. The largest-scale model was based on theDutch Continental Shelf Model, which is used for opera-tional forecasting of storm surges in the Netherlands[Gerritsen et al., 1995]. Using a simple description of thegeometry of a cyclone, together with observations of surfacepressure from large historic storms, a parametric model wasused to generate meteorological forcing for the flood model[see also Bijl, 1997]. The model parameters were varied togenerate more severe storms than those recorded in the tidalrecords, but storms that were physically plausible givenhistoric meteorological observations [Lamb, 1991]. Theresults from two storm scenarios are presented [see alsoBrown, 2004], namely, a �6.2-m surge tide, comprising a�4-m surge, and a �8.5-m surge tide, comprising an �8-msurge. Although extreme, the �8.5-m surge tide allowedovertopping to be considered alongside breaching of the seadefenses (the sea defenses vary from 6.35 to 7.5 m, ODN).[23] The Simulating Waves Nearshore (SWAN) model of

Holthuijsen et al. [1993] was used to assess the geographicexposure of Canvey Island to overtopping from windwaves. As indicated by IECS [1996], much of the deepwaterwave energy was dissipated on the sandbanks of the outerestuary. Although locally generated wind waves were po-tentially significant along the southern bank of CanveyIsland, further analysis was hampered by wave breakingalong the slopes of a deepwater channel, the YantletDredged Channel, located immediately adjacent to the seadefenses, and by the limitations of SWAN around coastalstructures [Brown, 2004].

3.4. Coupling the Storm Surge and Flood Models

[24] The storm surge model and flood models werecoupled through a bidirectional open boundary in the floodmodel, whereby flow was allowed into and out of the floodmodel, but feedbacks from the flood model to the stormsurge model were not considered. Specifically, the stormsurge model was used to generate a water level curve at theopen boundary of the flood model, which allowed water topass through freely, in either direction, depending on theprevailing hydraulic gradient (i.e., onshore during flood tideand offshore during ebb tide). Given the difficulties insimulating water velocities around the sea defences, andtheir role in ‘‘decoupling’’ the onshore and offshore flows, awater level boundary was preferred to a flux boundary. Inorder to allow the free movement of water through thisboundary, a nonreflective boundary condition was used [seeStelling et al., 1998].[25] Because of the computational effort of simulating

offshore areas, the open boundary was initially placed at thesea defenses. However, the impacts of breaching on off-shore water levels, and thus onshore levels, were alsoexamined by comparing model predictions for an ‘‘offshoreboundary’’ in the flood model, placed well beyond theinfluence of the breach, with an ‘‘onshore boundary,’’

Table 1. Friction Classes With Corresponding Values for

Manning’s n

ID Description Range of n Area, %

A bare ground �0.01 (bare soil) 2.59B tilled land 0.03–0.04 (cultivated land, no crop) 2.28C bare/sparse vegetation �0.01–0.02 (sparse vegetation) 2.37D mowed grass (winter) 0.025–0.03 (grass channel) 3.55E short vegetation 0.03–0.035 (pasture, short grass) 42.17F tall vegetation 0.035–0.05 (pasture, high grass) 3.67G gardens 0.03–0.035 (short grass),

0.013–0.016 (asphalt),0.05–0.06 (light brush and trees)

10.13

H small trees/bushes 0.05–0.06 (light brush and trees) 2.56I concrete, asphalt 0.013 (smooth asphalt),

0.016 (rough asphalt),0.014–0.016 (concrete pavement)

11.76

J drainage channels 0.013–0.017 (concrete, no finish) 2.02K linear boundaries 0.05–0.06 (light brush and trees),

0.25–0.75? (fences and walls)8.61

L sea defenses 0.012–0.014 (monolithic concrete) 0.37M reeds in central lake 0.045–0.06 (reeds in irregular channel) 0.27

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placed directly at the sea defenses. The differences in floodinundation extent (IE) and volume (V) between the onshoreand offshore boundaries were substantial. For example, theoffshore boundary led to a �10–20% increase in IE and a�20–40% increase in Vas water was ‘‘sucked through’’ thebreach via a hydraulic gradient that extended offshore. Thusan offshore boundary was used in the flood model. Thisallowed the impacts of breaching on offshore water levels tobe included without dynamically coupling the storm surgeand flood models. In order to eliminate any disturbancesoriginating from the mismatch between initial and forcingconditions, one full tidal cycle was simulated before breach-ing or overtopping was modeled. At the sea defenses, thewater levels predicted by the storm surge model wereidentical to those predicted by the flood model with theoffshore boundary.

3.5. Modeling Strategy

[26] The aims of the modeling strategy were (1) toestablish the key sources of variability in model predictionsand (2) to identify the impacts of uncertainty in specific(groups of) variables on the overall uncertainties in modelpredictions. The uncertainties in forcing inputs from thestorm surge model are not detailed here [see Brown, 2004],but their impacts on flood prediction are illustrated for themost significant uncertainties.[27] In order to assess the different sources of variability

and uncertainty in model predictions, while minimizing thecomputational overheads of this analysis, a hierarchy offlood models was developed. Thus a ‘‘full-scale’’ model,covering the entire case study site, was used to simulateflooding, by overtopping and breaching, at a fixed spatialresolution of 6 m (‘‘Canvey-Overall’’), while a series of‘‘small-scale’’ models were used to explore the initialpropagation of the flood wave from breaching alone (i.e.,the �6.2-m surge tide) at a variable spatial resolution of upto 2 m (Figure 1).[28] When extensive meteorological and wind wave

observations are available, overtopping of sea defenses ispotentially tractable to probabilistic analysis. In contrast,breaching of masonry defenses is currently intractable toprobabilistic modeling because of the wide range of param-eters involved and their lack of identifiability [Morris,2000]. However, simulations of flooding for differentbreaching scenarios, i.e., a scenario analysis, may providesome valuable insights into the patterns of exposure toflooding that emerge from multiple variables interactingwithin a complex flood model. A scenario analysis was usedhere to explore the impacts of floodplain geography on thespatial distribution of hazard parameters by implementingthe flood model for a wide range of breach locations (themain control on exposure) and a few scenarios of breachwidth.

4. Results and Analysis

4.1. Sensitivity to Space-Time Resolution

[29] Sensitivity to space-time resolution was explored by(1) varying the temporal resolution of the flood model, Dt,at fixed spatial resolutions,Ds, which reflects the impacts ofDt on the precision of the numerical solution, and (2) vary-ing Ds while maintaining a constant ‘‘effective’’ time stepfor a given Ds, as indexed by the Courant number, Cr (the

minimum wavelength resolved by the model). This reflectsthe impacts of Ds on flow via the discretization of themodel terrain and bottom friction.[30] In terms of point 1, the space-time resolution of the

flood model was explored by varying Dt at grid resolutionsof 2 m and 6 m for breaching and overtopping scenarios inthe small- and large-scale models, respectively. In varyingDt, an automatic time step estimator was used to limit theCourant number, Cr, experienced in any given simulation[Stelling et al., 1998]. Model sensitivities were alsoexplored for a fixed absolute Dt, using the same breachingand overtopping scenarios. Simulations were conducted witha limiting Cr of 1, 5, 10, 15, 20, and 50 and for absolutetime steps of 1, 2, 3, 4, and 5 s in the small-scale models andfor a limiting Cr of 1, 5, and 10 and absolute time steps of 1, 2,3, 4, and 5 s in the Canvey-Overall model. In the small-scalemodels, an instantaneous breach of�4 m in depth and 150 min width was applied at peak high water on a �6.2-m surgetide (�4-m surge). The Canvey-Overall model was appliedwith a surge tide of �9 m.[31] Figure 3 (top) plots the full time series of V for each

Cr in the Canvey-Overall model, and Figure 3 (bottom)shows the corresponding results for Canvey-North (resultswere similar for the other small-scale models).[32] As indicated in Figures 3 (top and bottom), the

greatest decline in flooding occurred between Cr = 1 andCr = 5. While a reduction in Dt from 1 s to 4 s did notgreatly affect V in Canvey-Overall (Figure 3, top) orCanvey-North (Figure 3, bottom), a decline from 4 to 5 sled to a substantial increase in IE (�20%) and in V (�25%).The cause of this erratic behavior is unclear, but a time stepof 5 s, or even >> 0.5 s, is not suitable for modeling rapidlyvarying flows at a grid resolution of 2 m. While the Courantcondition (Cr < 1) is not required for stability in implicitnumerical schemes, such as that used in Delft-FLS, it isgenerally recommended for numerical accuracy [Abbott andBasco, 1989] and appears to be necessary for the high flowdepths and velocities (>5 m s�1) experienced here.[33] Model sensitivities to Ds originate from the resolu-

tion of the model grid, and hence flow calculations, andfrom the resolution of the boundary data, including thetopographic data [Horritt and Bates, 2001] and bottomfriction. In addition, the boundary data may be filtered bythe flow grid [e.g., Bates et al., 1996], which may introducecartographic errors and a further loss of precision. Forexample, buildings may be merged or displaced within aregular grid, leading to changes in the overall volume andgeometry of the floodplain, as well as localized shifts interrain. Furthermore, model sensitivities to Ds may beexaggerated in flat terrain, as a small change in Ds canlead to a large relative change in the model terrain, even ifthe absolute changes in terrain height are small. While theseeffects are well documented in undeveloped floodplains[e.g., Bates et al., 1996; Horritt and Bates, 2001], theymay be exaggerated in urban areas where buildings imposedifferent requirements on modeling.[34] The terrain and land cover data were aggregated with

a mean average and a modal average of their input values,respectively. The data were aggregated to spatial resolutionsof 2, 4, 6, 8, and 10 m and applied in the flood model at afixed resolution of 2 m. This allowed buildings to berepresented consistently between models, and their effects


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on flood prediction to be explored separately from the widereffects of Ds on the elevation data (see below).[35] In order to establish model sensitivities to the precise

configuration of topography and land use in the study area,the Canvey-North, -South, and -East models were allapplied with the aggregated data. An instantaneous breachof �4 m in depth and 150 m in width was applied at peakhigh water on a �6.2-m surge tide.[36] Table 2 shows the flood IE, V, and mean current

velocity (C m s�1) for each model and Ds at the time ofmaximum IE, just before boundary contact, i.e., at t0+0.45 hours in Canvey-North and Canvey-South and t0+0.6 hours in Canvey-East.[37] The impacts of varying Ds for the model terrain and

land-use data (bottom friction) were both highly variablebetween locations and with declining Ds. For example, theresolution of the DEM had no significant impact on IE or Vin Canvey-East but led to �6% reduction in IE and Vbetween Ds = 6 m and Ds = 8 m in Canvey-North. This isreadily explained by the topography of Canvey-North. Inparticular, several earthen embankments, together with a

gradual increase in slope between the pre-1953 sea defensesand the current hard-engineered defenses, trap floodwaterand lead to a reduction in volume entering the model, aswell as increased sensitivity to Ds. The large changes in IEand V with declining Ds in the land cover data originatefrom the effects of Ds on localized features with high Cb,such as boundary hedges (Table 1). These occur around thebreach sites in Canvey-South and Canvey-East but are notpresent in Canvey-North, where sensitivities to the resolu-tion of Cb are consequently lower.

4.2. Sensitivity to the Discretization of Buildings

[38] In order to represent buildings in a flood model, anumber of physical and numerical assumptions are required.Physical assumptions include the capacity for inundation ofbuildings, and the possibility of structural damage during anextreme flood. Overall, the effects of buildings on flowmight include (1) blocking of flow by buildings, (2) fric-tional resistance of the floodwater by buildings, (3) inun-dation of buildings by floodwater, (4) loss of floodplain

Figure 3. (top) Time series of V for each Cr in Canvey-Overall. (bottom) Time series of V for each Cr inCanvey-North.

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volume, (5) changes in infiltration rates and pathways, and(6) destruction of buildings during extreme events.[39] Numerical assumptions include the structure of the

computational grid and the choice of grid resolution, Ds(see above also). For example, rectangular grids are wellsuited to modeling complex flows [Stelling et al., 1998] butare poorly suited to modeling discrete objects. Whilestructural damage to, and failure of, buildings might beanticipated for the depths and velocities of flooding identi-fied here [Kelman, 2003], model sensitivities to buildingfailure were not considered, as they cannot be exploredadequately with only a few simulations. Rather, a first-orderanalysis was conducted on the effects of inundation ofbuildings, as they have not been reported elsewhere, butmay significantly alter flood patterns in urban areas. In

terms of numerical parameters, the effects of Ds wereexplored by varying the resolution of the numerical grid,which included the effects of Ds on buildings (unlike theresults in section 4.1). However, as this also included theeffects ofDs on the wider terrain and bottom friction, a finalscenario explored the effects of Ds on the buildings alone.Here the buildings were aggregated separately from thewider DEM and reintegrated at a fixed Ds of 2 m (seebelow). Figure 4 plots the area occupied by buildings inCanvey Island against Ds and shows an increasing sensi-tivity to Ds for grid resolutions below 10 m. The impacts onflooding of the orientation of the model grid are not reportedhere, as they were found to be negligible [Brown, 2004].[40] In order to explore the effects of inundation of

buildings, the Canvey-North, Canvey-East, and Canvey-South models were discretized with solid buildings, whereno loss of flood volume or routing through buildings wasallowed, and hollow buildings, where inundation and rout-ing was allowed through every building (the most likelyscenario for an extreme flood). Since the grid resolution ofthe flood models (2 m) was too coarse to adequatelyreproduce the cavity space of smaller buildings, the wallsof these buildings were shifted to the center of the buildingoutlines, increasing the internal volume of the buildings by1 m on each perimeter. In order to allow for comparisonsbetween the ‘‘solid’’ and ‘‘hollow’’ models, the terrain withsolid buildings was also modified to increase the size of thebuildings. Finally, entrances were assigned to buildings inthe hollow DEM, where two entrances (each of one grid-cell width) were assigned to every building occupying lessthan 200 m2 (10,800 mainly residential or small commercialbuildings) and one entrance was allocated to every 10-msection of buildings occupying more than 200 m2 (564public or industrial buildings). Three scenarios of bottomfriction were considered (the maximum, minimum, andmean Cb from Table 1).[41] Table 3 shows the flood IE and V at maximum IE

(i.e., just before boundary contact) in each model, togetherwith the percent differences in IE and V between models.The areas inundated in only one scenario are also providedin Table 3 (‘‘Area’’ column), as the spatial patterns of

Table 2. IE, V, and C for the Aggregated Terrain and Land Cover

(Buildings Not Aggregated)

Ds, m

Terrain Only Terrain and Friction

IE,km2

V �103 m3

m C,m s�1

IE,km2

V �103 m3

m C,m s�1

Canvey-North Model2 1.79 249.31 1.05 1.79 249.31 1.054 1.74 241.45 1.05 1.86 243.32 1.066 1.84 253.43 1.04 1.93 247.86 1.058 1.73 237.75 1.05 1.96 243.15 1.0710 1.82 248.32 1.04 1.92 235.60 1.08

Canvey-East Model2 1.19 303.46 0.91 1.19 303.46 0.914 1.19 304.08 0.91 1.39 337.56 1.046 1.19 303.63 0.9 1.47 348.79 1.058 1.19 302.84 0.9 1.68 364.79 1.110 1.20 303.81 0.9 1.69 365.64 1.1

Canvey-South Model2 2.35 309.45 1.13 2.35 309.45 1.134 2.38 309.96 1.11 2.55 312.83 1.126 2.40 313.05 1.1 2.57 309.35 1.198 2.37 305.82 1.1 2.94 349.99 1.2210 2.40 308.48 1.09 2.94 346.58 1.19

Figure 4. Area occupied by buildings in the digital elevation model for different Ds.


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inundation varied in some cases without a change in IE. Thedifferences in IE and V between the solid and hollowscenarios were small but nonnegligible, across all modelsand Cb, with an average decline of �2% in IE and �3% inV following complete inundation. The areas inundated inonly one model were consistently larger than the differencesin IE between models, indicating a shift in the pattern offlooding not registered in IE, but the differences were smallin absolute terms.[42] In order to explore the overall effects of Ds on the

boundary data, including the buildings, as well as theprecision of the flow calculations, the model grid wasimplemented with resolutions of 2, 4, 6, 8, and 10 m.Simulations were conducted with Canvey-North, Canvey-East, and Canvey-South. An instantaneous breach of �4 min depth and 150 m in width was applied at peak high wateron a �6.2-m surge tide (�4-m surge). The model time step,Dt, was varied for each Ds, using an automatic time stepestimator and a maximum allowable Cr of 1. In addition,simulations were conducted with a Ds of 2 m, whileprogressively reducing the resolution of buildings in theDEM. Here the buildings were aggregated to resolutions of4–20 m (in 2-m increments) and then returned to the 2-mDEM, while maintaining the coarser representation there.[43] Table 4 shows the flood IE, V, and C at maximum

inundation extent for each Ds in Canvey-North, Canvey-East, and Canvey-South. Figure 5 plots the time series of IEfor each Ds in Canvey-East, where the greatest sensitivitiesto Ds were observed. For comparison, Figure 5 also showsthe IE for each Ds when buildings were removed from theDEM (the boundaries of Canvey-East were extended tosupport the greater IE observed there). Figure 6 shows theeffects of aggregating the buildings alone (i.e., separatelyfrom the DEM or flow grid) on the time series of flood IE inCanvey-East. In computing IE, the area occupied by build-ings was normalized to the Ds = 2 m scenario, as thisprevented ‘‘apparent’’ changes in IE as Ds increased.[44] The impacts of increasing Ds varied substantially

between models, with the greatest effects observed inCanvey-East, where an increase in Ds from 2 to 10 mresulted in a 65% increase in IE and a 22% increase in flood

volume at maximum IE (Table 4). Smaller sensitivities wereobserved in Canvey-North, which experienced a 14% in-crease in IE as Ds increased from 2 to 10 m. As indicated inFigure 5, the scenarios without buildings experienced sim-ilar increases in IE and V. Thus the greatest effects ofDs arenot related to the discretization of buildings. Rather, they areexplained by the effects of Ds on surface friction andspecifically, on boundary features. These include walls,fences, and hedges, which are characterized by high Cb

but are not well represented in a lumped friction coefficient.They appear throughout Canvey-East and to a lesser extent,Canvey-South, but particularly along these sea defenses(unlike Canvey-North), where sensitivities to Cb are greatestin the context of breaching. As indicated in Figure 5, theeffects of Ds increased through time with IE (both inabsolute and relative terms, as the area susceptible to Dsincreases through time) and were therefore greater in thescenarios without buildings. While the direct effects ofaggregating the buildings were small in comparison withthe effects of Ds on Cb, an increase in Ds from 2 to 20 mwas significant, both in terms of the representation ofbuildings in the DEM (Figure 5) and in terms of its impactson flooding (Figure 6). For example, an increase in Ds from2 to 14 m resulted in a 12.4% increase in IE at Dt = 0.6 inCanvey-East, which included a 3% increase between Ds =2 m and Ds = 6 m.

4.3. Uncertainties in Model Terrain and BottomFriction

[45] Uncertainties in terrain heights can be assessedthrough geostatistical simulation and aggregation[Lantuejoul, 2002]. In practice, however, this remainscomputationally prohibitive for large data sets and modelsand was beyond the scope of this study. Rather, the GPSdata were used to estimate the mean error or bias of the lidardata (�0.15 m) and to establish scenarios for the residualerrors, allowing sensitivity testing within this range.[46] Given the constant spatial resolution of the lidar data,

the greatest uncertainties in the interpolated DEM willcoincide with the steepest gradients in the interpolated

Table 3. IE and V for Solid and Hollow Buildings at Maximum

IE

Friction, Cb

Solid Buildings Hollow Buildings Differences, %

IE, km2 V � 103 m3 IE, km2 V � 103 m3 IE Areaa V

Canvey-North ModelMinimum 1.80 244.47 1.78 238.81 1.2 3.1 2.3Mean 1.75 247.75 1.69 237.58 3.5 4.7 4.1Maximum 1.62 237.17 1.60 231.94 1.3 3.8 2.2

Canvey-East ModelMinimum 1.17 302.66 1.14 293.37 2.6 2.8 3.1Mean 1.04 274.31 1.02 266.29 2.1 2.4 2.9Maximum 0.97 253.77 0.95 244.99 1.8 2.1 3.5

Canvey-South ModelMinimum 2.40 309.86 2.33 294.24 2.9 3.0 5.0Mean 2.19 289.35 2.15 280.40 1.9 2.1 3.1Maximum 2.13 290.89 2.09 281.87 1.9 2.4 3.1

aAreas that were flooded in only one simulation (as a percent of the areainundated in the solid scenario).

Table 4. IE, V, and C for the Aggregated Terrain and Land Cover

(Buildings Aggregated)

Ds, m IE, km2 V � 103 m3 m C, m s�1

Canvey-North Model2 1.79 249.31 1.054 1.83 240.28 1.126 1.91 241.57 1.18 2.03 246.8 1.0910 2.04 243.8 1.08

Canvey-East Model2 1.19 303.46 0.914 1.37 337.57 1.096 1.42 342.92 1.078 1.77 363.62 1.0910 1.96 370.09 1.07

Canvey-South Model2 2.35 309.45 1.134 2.46 308.0 1.196 2.58 320.3 1.28 2.7 327.98 1.2110 2.71 328.3 1.19

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coverage. Similarly, in varying the spatial resolution of theDEM, the greatest errors in the aggregated coverage willcoincide with the steepest gradients in the DEM. In bothcases, the greatest underpredictions and overpredictions willoccur in steep terrain, and those areas most susceptible tointerpolation or aggregation can be inferred from each other.Here scenarios for uncertainty in the interpolated DEM wereobtained by varying Ds until the residuals (aggregatedminus original coverage) were roughly equivalent to theerrors revealed by the GPS survey. Six scenarios weregenerated, namely, a ‘‘high estimate’’ of terrain error, wherethe terrain was aggregated from 2 to 6 m, returned to anominal resolution of 2 m, and then subtracted from theoriginal 2m DTM (roughly corresponding to the 0.25-mRMSE of the EA lidar data at this time, as reported byAshkenazi et al. [1999]), an ‘‘intermediate’’ estimate, wherethe terrain was aggregated to 4 m (roughly corresponding tothe GPS-derived RMSE), a ‘‘baseline estimate, ’’ where the

terrain was left unchanged, and the same scenarios with anadditional bias of �0.15 m. Figure 7 compares the vario-grams for the ‘‘unbiased terrain scenarios’’ with the GPSerror variance.[47] Friction scenarios were generated by varying Cb in

fixed percentage increments within the ranges identified inTable 1. In principle, a detailed analysis of the uncertaintiesin Cb should distinguish between (1) the classification ofland use and (2) the translation of land use into surfacefriction, or friction classes. In practice, the classificationerrors in translating ground-based or remote sensing surveysto land-use classes are small in comparison to the aggrega-tion of land-use classes into friction classes and the identi-fication of friction intervals for those classes. Thus theimpacts of uncertainty in land cover classification werenot considered. Rather, friction scenarios were developedfrom the range of Cb in Table 1 and focused on systematicchanges in Cb (bias across all classes), rather than random or

Figure 5. The effects of aggregating the flow grid resolution on IE.

Figure 6. The effects of aggregating the buildings alone on IE.


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correlated variability, as Cb influences flood prediction in asystematic way, allowing bounding of the propagateduncertainties for fixed increments of Cb. In order to reflectthe different ranges of uncertainty in each friction class,these changes were referenced to the mean (0%), maximum(+100%), and minimum (�100%) values within each class,so that a 50% increase in friction corresponded to a 50%increase in every class, or one quarter of the overallmaximum Cb. Scenarios were derived for increments of25% and sampled with the terrain scenarios for each small-scale model, leading to 54 scenarios for each model(27 unbiased scenarios and 27 biased scenarios).[48] Figure 8 (top and middle) shows the flood volume at

maximum IE for the unbiased terrain models in Canvey-North and Canvey-South, respectively. Figure 8 (bottom)shows the corresponding results for the biased terrain modelsin Canvey-South. Table 5 summarizes the flood IE and V forthe unbiased and biased terrain at mean Cb in each model.[49] The flood IE increased systematically with declining

n (increasing Cb) for all scenarios of terrain uncertainty ineach model. However, the greatest changes occurred inCanvey-East and Canvey-South. For example, the floodextent at maximum IE increased from 0.98 km2 at n =�100% to 1.22 km2 at n = +100% (24.5%) in Canvey-Eastwith zero terrain uncertainty. The flood V also declinedsystematically with increasing Cb in Canvey-East andCanvey-South, but was relatively unaffected by Cb inCanvey-North (Figure 8, top). This is consistent with theresponse observed on aggregating Cb (section 4.1) andreflects the importance of localized features with high Cb

near to the breach sites in Canvey-East and Canvey-South.[50] In general, model predictions of IE and V were more

sensitive to bias in the DEMs than correlated variability. Forexample, while IE and V were not significantly affected bythe unbiased terrain scenarios in Canvey-East and Canvey-South, IE declined by �10% in Canvey-East with terrainbias and V increased by �10% in Canvey-South (Table 5).However, these effects varied substantially in space andtime, with the different models, and with the output variableconsidered. For example, while IE and V increased withterrain bias in Canvey-North and Canvey-South, they

declined with terrain bias in Canvey-East. The greatesteffects of terrain bias occurred in Canvey-East and Canvey-South (contrary to the unbiased scenarios) where thedifferences between scenarios also increased systematicallythrough time. However, the implied magnitude and patternof uncertainty, including the direction of change, variedwith the choice of flood parameter. For example, V declinedmore than IE in Canvey-North and Canvey-South, whereasIE increased more than V in Canvey-East, reflecting thedifferences in terrain and friction between models. Asindicated in Figure 8 (middle and bottom), the preciseimpacts of terrain bias also varied with Cb. For example,in Canvey-South, V declined by �10% as Cb increasedfrom Cb�25% to Cb+0% in the ‘unbiased’ terrain scenario(Figure 8, middle), whereas a similar decline in V isobserved between Cb+0% and Cb+25% in the biased terrainscenario. Consequently, the effects of terrain bias weregreatest at Cb+ 0% in Canvey-South.

4.4. Uncertainties Generated by Flood DefenseBreaches

[51] In order to explore the impacts of floodplain geog-raphy on the spatial distribution of flooding from seadefense breaches, the Canvey-Overall model was imple-mented for a wide range of breaching locations and a fewscenarios of breach width. The aim here was not to providea comprehensive description of the flood hazards on CanveyIsland but to show how a collection of breaching scenarios(i.e., a scenario analysis) can help in exploring thesehazards. Scenarios were derived for breaching of the flooddefenses between the Easthaven and Benfleet Barriers(Figure 1). Each scenario involved a single defense breach,with breaches positioned at regular intervals of 250 m alongthe defense line. A systematic placement of breaches waspreferred as complete coverage was impractical, and ran-dom placement was inefficient. The 250-m samples wereobtained in two groups of 500 m, as this allowed an analysisof model sensitivities to the precise location and frequencyof breaches. The breaches involved instantaneous failures of(multiples of) the concrete panels from which the seadefenses were constructed [Brown, 2004]. Three scenarios

Figure 7. Semivariograms for three scenarios of terrain uncertainty (unbiased).

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Figure 8. (top) V in Canvey-North at maximum IE for different terrain and friction. (middle) V inCanvey-South at maximum IE for different terrain and friction. (bottom) V in Canvey-South at maximumIE for biased/aggregated terrain and friction.


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of breach width were considered, namely, instantaneousfailures of 1, 5, and 10 panels (7.7, 38.5, and 77 m, witha sub-grid-scale formulation on boundary pixels [seeStelling et al., 1998]). This resulted in 171 breachingscenarios, with 57 scenarios of breach location for eachscenario of breach width. The breaches were applied at peakhigh water on a �6.2-m surge tide. In order to maintain aconstant flood volume at the point of entry through the seadefenses, the depth of breaching was fixed at 2 m ODN andthe surrounding embankments (in a �10-m-wide strip) werelowered to 2 m ODN.[52] Figure 9 plots the maximum IE for each failure

location and breach width with distance from the EasthavenBarrier, illustrating the dependence of flooding on theposition of the breach site. Figure 10 plots the mean and5th to 95th percentiles of V over time for the five-panelbreach scenario with different breach samples.[53] The maximum instantaneous values of flood depth

(H) and current velocity (C) were recorded at every grid cellin Canvey-Overall and used to derive maps of flooding foreach failure location and breach width. The location-aver-

aged values of H and C were computed from each sample ofbreach locations and for a range of summary statistics,including the mean, standard deviation, and 5th to 95thpercentiles of H and C, together with the frequency ofinundation of each grid cell (percent of breaching locationsfrom which a grid cell was flooded). In addition, H � C wastaken as a simple measure of the hydrodynamic forceexerted by the floodwater, where momentum = (mass �C) = (density � volume � C) = (density � flood horizontalarea � H � C) = (H � C), since the water density and floodhorizontal area are constant for any given H. The maximumvalues of H � C were computed from the maximuminstantaneous values of H � C for each realization. Thisensured that each H � C occurred in at least one realization.[54] Figure 11 (top, middle, and bottom) shows the

mean H, mean C, and 5–95th percentiles of H for thefive-panel breach scenario, respectively. Figure 12 (top andbottom) shows the frequency of flooding for breaches ofone and 10 panels, respectively. Figure 13 shows thestandard deviation of H as a percentage of the mean valuefor the 10-panel breach scenario. Finally, Figure 14 showsthe maximum instantaneous values of H � C (m2s�1) forthe 10-panel breach scenario.[55] As indicated in Figure 9, the main controls on the

spatial distribution and severity of flooding were the loca-tion and width of breaching. These two parameters wereclosely connected, since the geography of the breach sitealso determines the volume of water that can enter themodel over the forcing period. In some cases, this led tosubstantial differences in IE and V between adjacent breachsites (Figure 9). In particular, the dense network of tidalcreeks and drains was important during the initial stages offlooding and caused the local maximum in IE and V at6.25 km from the Easthaven Barrier, where a large systemof tidal creeks can be found. In general, the temporalvariability of IE and V was more systematic, and predict-able, than the spatial variability of IE and V with breachlocation. In terms of the temporal variability, the impacts ofbreach location became increasingly apparent as the floodwave moved away from the breach site (flatter gradient,more sensitive to local terrain) and increased systematically

Table 5. IE and V for the Biased Terrain Models With Mean Cb at

Maximum IE

Terrain Bias

Original TerrainFour-MeterTerrain

Six-MeterTerrain

IE,km2

V �103m3

IE,km2

V �103 m3

IE,km2

V �103 m3

Canvey-North ModelUnbiased 1.74 243.01 1.69 235.34 1.79 247.01Biased 1.73 236.97 1.67 226.40 1.71 232.11

Canvey-East ModelUnbiased 1.07 274.51 1.08 275.09 1.08 274.72Biased 1.16 288.22 1.16 288.38 1.17 288.47

Canvey-South ModelUnbiased 2.31 304.75 2.33 305.22 2.36 308.22Biased 2.20 274.54 2.22 275.02 2.23 274.83

Figure 9. Maximum IE with distance from Easthaven for different breach widths.

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with IE. For example, Figure 10 shows a divergence of the5th and 95th percentiles of V between t + 0 hours and t +�3 hours, where the effects of breach location are greatest,but the rate of change in s is smallest (boundary forcing isnegative at +2.7 m ODN, as the water levels inland exceed0.7 m). Here tidal forcing rather than floodplain geographyimposes an upper limit on IE, and the effects of breachlocation on IE, because flooding persists for many hours ofnegative tidal forcing. For example, in the five-panel breachscenario, IE increases from 5.35 km2 at t + 3 hours to6.52 km2 at t + 5 hours (22%), while the flood volumedeclines from 329.43 � 103 m3 at t + 3 hours to 325.97 �103 m3 at t + 5 hours.[56] As indicated in Figure 10, the mean (m) of IE and V

were not sensitive to the precise location and density ofbreach sites. For example, the greatest difference in IE was0.03 km2 in the one-panel breach scenario, 0.04 km2 in thefive-panel breach scenario, and 0 km2 in the 10-panelbreach scenario. Similarly, a spatial comparison of thedifferences between m in the two groups of 500-m samples(n1 = n2 = 31) revealed significant differences (at a = 0.05)in less than 0.1% of the flooded grid cells for all scenariosof breach width. While the 5th and 95th percentiles of IEand V were understandably more sensitive to breach loca-tion and density than m, similar estimates were obtainedfrom the two sets of 500-m samples (Figure 10), implyingthat the 250-m sample frequency was sufficient to estimatethese (spatially lumped) parameters.[57] As shown in Figures 11–14, some clear spatial

patterns emerge when integrating flood predictions acrossmany different breach scenarios. For all scenarios of breachwidth, the mean water depth is highest around the tidalcreeks and drains, where terrain elevation is low and flood-ing occurs most frequently, and around the sea defenses,where flooding occurs less frequently, but local breachesresult in extreme H. However, while the highest floodfrequencies occur in the center and south of Canvey Islandin the five- and 10-panel breach scenarios (Figure 12,bottom), they are concentrated along the sea defenses inthe one-panel breach scenarios, and particularly in the northwhere locally high terrain leads to a north-south divide in

flood frequencies (Figure 12, top). This is also apparent inthe high average variability of H in the north (Figure 13),which indicates that floodwaters are either trapped insidethe enclosed areas or blocked from entering them, depend-ing on the breach location. In general, the highest watervelocities occur in residential areas, where the streets act asfunnels, routing water away from a breach (Figure 11,middle) and leading to high C in central areas where H ismuch lower.[58] The coincidence of low flood frequencies and high,

and variable, flood depths is also apparent in the east ofCanvey Island, which is geographically isolated for adifferent reason. Here the combination of a narrow flood-plain (< 500 m) and locally high terrain (�2 m ODN) leadsto a reduction in flood frequency at all breach widths, butthe narrow floodplain also traps floodwater, increasing theseverity of the hazard when inundation does occur. Forexample, the highest values of H � C were found in thesoutheast of Canvey Island (Figure 14), with values of up to30 m2 s�1. The west of Canvey Island is much less exposedto flooding than the east (e.g., Figure 12, bottom), partlybecause the sea defenses were left intact there (they areprotected by barriers) and also because the north-southarterial road and the industrial facilities in the southwestlie on raised ground. Despite the low flood frequency at allbreach widths, the mean and 5–95th percentile range of Hare high in the five- and 10-panel scenarios because theaverage terrain elevation is low (�1 m ODN) and a series oftidal creeks and drains connect the agricultural plots in thewest. In summary therefore, the interaction of breach sizeand location with floodplain boundary conditions leads todistinct patterns in the type (e.g., high depth versus highvelocity) and severity of exposure to flooding.

4.5. Uncertainties in Forcing Inputs From the StormSurge Model

[59] In order to illustrate the propagation of uncertaintyfrom the storm surge model to the flood model, the Canvey-Overall model was implemented for eight scenarios ofuncertainty in wind forcing for two parametric storms[Brown, 2004]. The forcing scenarios comprised four per-

Figure 10. Mean, 5th percentile, and 95th percentile of IE for different breaches and five-panel width.


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Figure 11. (top) Mean H (m) for different breach samples: five-panel breach. (middle) Mean C (m s�1)for different breach samples: five-panel breach. (bottom) Fifth to 95th range of H (m) for different breachsamples: five-panel breach.

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turbations of the wind speed, W10, by W10 + 5%, +10%,+15%, and +20%, and two scenarios of the surface dragcoefficient, C10, derived from calibration runs of the surgemodel for two historic storms. The parametric stormscomprised a �6.2-m surge tide and a �9-m surge tide. Inboth cases, sea defense breaches of 10 and 20 panels wereimposed at peak high water in the north of Canvey Island(near the 1953 breach sites). Figure 15 (top and bottom)plots V for the 10-panel breach scenario with low and highestimates of C10, respectively. Figure 16 (top and bottom)plots the corresponding results for the 20-panel breachscenario.[60] Forcing inputs to the flood model originate from

breaching alone at wind speeds of W10 + 5% to W10 + 15%in the lower scenario of C10 and W10 + 5% to W10 + 10% inthe higher scenario of C10. At higher wind speeds, forcinginputs to the flood model originate from a combination ofbreaching and overtopping, with substantial inputs fromovertopping in the high scenario of C10 at W10 + 20%.Overtopping leads to a rapid increase in IE and V during the

initial stages of flooding, and places the breaching volumeon a much higher trajectory during the later stages offlooding, where the floodplain friction is reduced (by theincreased water depths, Figure 15 (bottom) and Figure 16(bottom)). For example, at t + 0.2 hours in the high scenarioof C10, V increases twentyfold from W10 + 5% to W10 +20% and at t + 4 hours V is 3.5 times larger in W10 + 20%(in both scenarios of breach width). In the absence ofovertopping, increases in W10 and C10 produce consistentincreases in IE and V (Figure 15 (top) and Figure 16 (top)).For example, in the low scenario of C10, V increases linearlythrough time at each W10 and by �15% with each 5%increase in W10 (in both scenarios of breach width and at alltime steps).

5. Discussion and Conclusions

[61] Storm surge flooding is the product of a wide rangeof interacting processes: the development of a long wavefrom atmospheric and tidal forcing of the ocean; its

Figure 12. (top) Flood frequency (%) for different breach samples: one-panel breach. (bottom) Floodfrequency (%) for different breach samples: 10-panel breach.


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modulation by surge tide interactions in shallow water;short wave growth and propagation in coastal areas;overtopping and breaching of sea defenses; and blockingof flow by buildings and routing through drainage channelsinland. Similarly, large modeling uncertainties can originatefrom a wide range of physical processes, and at a widerange of space-time scales.[62] In this study, a storm surge model was coupled to a

2-D flood model and used to simulate flooding of a denseurban area. The models were coupled through a bidirec-tional open-boundary, whereby flow was allowed into andout of the flood model, but feedbacks from the flood modelto the storm surge model were not considered. The impor-tance of these feedbacks will depend on the fraction of thesurge tide volume ‘‘lost’’ to flooding but will decline as theconnecting boundary is placed farther offshore. Indeed, asshown here, the boundary must be sufficiently remote to

allow the immediate effects of breaching and overtopping(which extend offshore) to be included in the model. Forexample, in placing the open boundary along the seadefenses, the flood IE and V were initially underestimatedby up to 20% and 40%, respectively.[63] Uncertainties in model predictions originate from

inadequate sampling of model inputs, poorly constrainedparameter values, and simplified representations of complexenvironmental processes, among others. Here the greatestuncertainties originated from the forcing inputs to the floodmodel, including coastal water levels and sea defense fail-ures, rather than its internal boundaries, such as the modelterrain and bottom friction. This is consistent with studies inrural and semideveloped floodplains [Bates and Anderson,1996; Hall et al., 2005] and reflects a combination of highsensitivity to, and uncertainty in, the forcing inputs. How-ever, notable errors and uncertainties originate from other

Figure 13. Standard deviation of H as a percent of the mean H: 10-panel breach.

Figure 14. Maximum instantaneous values of H � C (m2 s�1): 10-panel breach.

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numerical and physical parameters, of which many werespecific to, or altered by, the urban floodplain.[64] In terms of numerical parameters, an automatic time

step estimator was used to limit the Cr experienced in anygiven simulation. Despite the possibility of stable solutionsat Cr > 1, numerical accuracy was compromised at Cr >> 1.Since the highest water depths and velocities were localizedaround the sea defense failures, this was both computation-ally demanding and inefficient. In future, this might beaddressed by partitioning the model a priori into zones ofsimilar flow [e.g., WLjDelft Hydraulics, 2000].[65] In general, however, model predictions were more

sensitive to spatial discretization than temporal resolution.In particular, they were sensitive to the spatial resolution ofthe flow model, which acts as a filter on the model terrain,including the buildings, and Cb. These effects have beenobserved elsewhere [see Bates et al., 1998a; Yu and Lane,2006a], but were modulated here by (1) the complex sub-grid-scale terrain, including the high density of walls,

fences, and hedges in residential areas, which were inade-quately represented in Cb, (2) the presence of bias in theDEM, and (3) the sensitivity of the buildings to Ds.[66] In terms of point 1, model predictions of IE and V

increased systematically with Ds, as boundary features(walls, hedges, etc.) were progressively lost from thesurface roughness. These features are inherently ill definedin a friction coefficient, and highlight the need for improvedmodeling of sub-grid-scale roughness in urban areas [seealso Lane, 2005]. In future, this might involve a compositeblocking or ‘‘porosity’’ coefficient, derived from a sum ofobjects at sub-grid-scales. While maintaining a single pa-rameter, the disaggregation of objects with very differentporosities would be more physically based and more easilycalibrated through small-scale laboratory and modelingstudies (unlike Cb, which is inherently difficult to aggregate).[67] In terms of point 2, terrain bias was a notable source

of uncertainty in model predictions. This is consistent withthe work of Bates et al. [1998a], who found significant and

Figure 15. (top) V for the 10-panel breach scenario with the low estimate of C10. (bottom) V for the 10-panel breach scenario with the high estimate of C10.


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irregular changes in flood IE with terrain bias in a 2-Dhydraulic model and attributed this to the extreme nonlin-earity of the underlying equations. However, unlike Bates etal. [1998a], these results demonstrate the potential forsignificant differences between two closely related outputparameters, flood IE and V, and suggest that any interpre-tation of model predictions should consider more than oneoutput parameter. The results were also sensitive to param-eter interactions, as the impacts of terrain bias were sensi-tively dependent on Cb in some cases (e.g., Canvey-South,which may also explain the irregular response). In summary,these results emphasize the need to consider bias in lidardata, which are typically very precise but may be inaccuratedue to errors in filtering and georeferencing.[68] In terms of the sensitivity of buildings to Ds, the

flood IE and V increased systematically as Ds increasedfrom 2 to 14 m, with more erratic changes in bothparameters for Ds > 14 m. Grid resolutions above 10 mwere unable to capture the smaller (mainly residential)

buildings on Canvey Island. However, notwithstandingother sensitivities to Ds, a grid resolution of �10 m isarguably sufficient for capturing the main effects of build-ings on flow. Indeed, the effects of Ds were small incomparison with the overall effects of buildings, whichreduced the flood IE and V by �50% compared with anundeveloped floodplain. The effects of inundation of build-ings were also explored and found to be small, but non-negligible, with an average decline of �2% in IE and �3%in V following complete inundation. This was comparableto the effects of aggregating the buildings from 2 to 6 m inCanvey-East (but opposite in direction). In future, theeffects of inundation of buildings could be represented ina sub-grid-scale model, whereby mass is removed at theflood infiltration rate [see Kelman, 2003]. However, thiswould probably only be justified for large buildings.[69] Given the uncertainties associated with extreme

coastal flooding, the extent to which hydraulic modelingis useful for assessing absolute flood hazards on Canvey

Figure 16. (top) V for the 20-panel breach scenario with the low estimate of C10. (bottom) V for the 20-panel breach scenario with the high estimate of C10.

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Island, and for urban areas more generally, should bequestioned. For example, tidal observations cannot be usedto accurately estimate the surge heights of storm events witha return period much longer than a century [McRobie et al.,2005]. Similarly, breaches in masonry flood defense cannotbe modeled reliably [Morris, 2000]. Despite these problems,hydraulic models may be useful for assessing the relativehazards (spatial and temporal variations in hazard) thatappear when forcing inputs and floodplain boundariesinteract across a wide range of forcing scenarios. Thisinformation should help to manage the residual risks asso-ciated with flooding in urban areas [Brown and Damery,2002].[70] In this study, model predictions of flooding were

integrated over different combinations of breach width andlocation. The results from these simulations emphasize theimportance of local geography on the outcomes of breach-ing, even in apparently flat terrain, where the configurationof streets, buildings, and drainage channels led to patterns offlooding that were highly differentiated in space and time(and varied for different flood parameters, such as H, V, IE,and C). Hazard assessments with much simpler, or lessresolved, models may not adequately capture this space-time variability. Of course, the ability to reproduce highspace-time variability does not imply the model predictionsare reliable. Rather, they must be explained in terms of thestructure of the model (terrain configuration, etc.) and giventhe uncertainties in its forcing inputs and boundary con-ditions. Such questions are well posed in an uncertaintyframework, because an increase in model complexity will bereflected in the uncertainties associated with its predictions.[71] In terms of the process complexity used here, no

attempt was made to account for infiltration, either throughstorm drains or natural surfaces, or to model flood routingthrough narrow (< 2 m wide) drainage channels, for which acombined 1-D/2-D modeling approach would be useful[WLjDelft Hydraulics, 2000; Sole and Zuccaro, 2005].Another area for improvement concerns the modeling ofovertopping flows from wind waves [Hubbard and Dodd,2002], as the hazards associated with overtopping, orcombined overtopping and breaching may be different fromthose associated with breaching alone.

[72] Acknowledgments. This research was funded by Halifax Gen-eral Insurance Services Ltd. as part of a Ph.D. grant for the first author. Adifferential GPS was provided by the UK Natural Environment ResearchCouncil. The UK Environment Agency provided lidar data and aerialphotography, together with engineering drawings for the sea defenses onCanvey Island.

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Documents

Modeling storm surge flooding of an urban area with particular reference to modeling uncertainties: A case study of Canvey Island, United Kingdom