Advances in Water Resources 32 (2009) 1323–1335

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Advances in Water Resources

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Two-dimensional, high-resolution modeling of urban dam-break flooding:A case study of Baldwin Hills, California

Humberto A. Gallegos a, Jochen E. Schubert b, Brett F. Sanders a,*

a Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697-2175, USAb IESSG, The University of Nottingham, Nottingham NG7 2RD, UK

a r t i c l e i n f o

Article history:Received 9 March 2009Received in revised form 17 May 2009Accepted 19 May 2009Available online 28 May 2009

Keywords:Urban hydrologyFlood inundation modelingShallow-water equationsDam-breakFinite volume methodDTMHigh resolutionLiDARNational Elevation DataShuttle Radar Topography Mission

0309-1708/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.advwatres.2009.05.008

* Corresponding author. Tel.: +1 949 824 4327; faxE-mail address: bsanders@uci.edu (B.F. Sanders).URL: http://sanders.eng.uci.edu (B.F. Sanders).

a b s t r a c t

Modeling of dam-break flooding in an urban residential area in southern California is presented. Model-ing is performed using BreZo, an unstructured grid, Godunov-type, finite volume model that solves theshallow-water equations. The model uses terrain data from a 1.5 m Light Detection and Ranging (LiDAR)Digital Terrain Model (DTM) and contour data depicting the reservoir and breach geometry. A spatiallydistributed Manning coefficient based on a landcover classification derived from digital orthophotosand vector data (e.g., parcel outlines) is also used, and the interception of flow by storm drains is modeledwith sink terms in the 2D continuity equation. The model is validated with flood extent and stream flowmeasurements, and a sensitivity analysis is completed to identify the necessary level of data and modelcomplexity for accuracy purposes. Results show street depressions in the land surface should be resolvedby the computational mesh for flood extent and stream flow accuracy. A ca. 5 m resolution mesh thatspans streets by approximately 3 cells achieves a good balance between accuracy and computationaleffort. Results also show that heterogeneous resistance is important for stream flow accuracy, and theinterception of overland flow by storm sewers is important for flood extent accuracy. The sensitivity ofpredictions to several additional factors such as the reservoir level, breach geometry and DTM source(LiDAR, National Elevation Data, Shuttle Radar Topography Mission Data) is also reported.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Urban flooding is becoming more frequent as a consequence ofseveral factors including continued watershed development withimpervious surfaces [15], population growth which places increas-ing pressure on communities to develop in flood prone areas[6,22], climate change which has magnified the intensity of rainfall[19], sea level rise which threatens coastal developments, anddecaying or poorly engineered flood control infrastructure suchas the levee system of California’s Sacramento-San Joaquin riverdelta [37]. Furthermore, the consequences of flooding are greaterin urban versus rural sites due to the relative economic valueand population density [22,33]. To manage the risk of flooding,damage assessments are needed and should consider not only eco-nomic but also social and environmental factors [41]. This can beaccomplished by first applying hydraulic models to predict thedepth and velocity distribution of probable floods, and then over-laying these data upon assets of an economic, social and environ-mental nature to quantify probable damages.

ll rights reserved.

: +1 949 824 3672.

Government at all levels is increasingly investing in Geograph-ical Information Systems (GIS) to organize and efficiently utilizegeospatial data for a diverse number of management and opera-tional objectives. In Los Angeles County, for example, a consortiumof public agencies known as the Los Angeles Area Imagery Acquisi-tion Consortium (LAR-IAC) jointly funded the acquisition of severalcounty-wide, high-resolution data sets including Light Detectionand Ranging (LiDAR) terrain data, digital orthophotos, and obliqueaerial photos. These data make it possible to resolve landscapegeometry and surface features with a spatial resolution (ca. 1 m)and vertical accuracy (e.g., <10 cm RMSE) that is ideal for floodinundation modeling (FIM) [1,2,29]. Damage estimates can subse-quently be integrated in GIS.

High-resolution modeling of urban flooding from a dam failureis the focus of this study. A two-dimensional (2D) flood inundationmodel based on the shallow-water equations is applied andparameterized using LiDAR terrain data, digital orthophotos andother supporting data, and predictions of flood extent and streamflow are compared to observations for validation purposes.

A number of 2D urban FIM studies have recently appeared inthe literature. Researchers have addressed questions such as thenecessary grid resolution [44,6,33], resistance parameterization[26,6,22], role of sub-surface storm drains [15], tradeoffs between

1324 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

shallow-water and diffusive wave routing schemes [17], and mod-els for the impact of buildings on flood dynamics [44,6,20,33,27]including use of porosity methods [44,45,12,25,34,31]. These stud-ies have shown that urban flood flows manifest as a combination ofsub- and super-critical flow along streets and between buildings,depending on street slopes and flood dynamics, and 2D modelsare poised to resolve these dynamics when important flow pathssuch as streets and gaps between buildings are resolved. Thismay require a grid resolution of 2 m or less [6,17] using structuredgrids or a variable resolution unstructured mesh that is con-strained by building walls [33].

There remains a need for more urban FIM validation studies, todevelop a sound understanding of good modeling practice (e.g.,model formulation, data requirements, mesh resolution) and as-sess the overall predictability of urban flooding, particularly inthe context of dam failures. Mignot et al. [26] simulated two floodevents in Nimes, France where water is channeled along citystreets. The model was found to accurately depict flood extent,as the site was bounded by steep topography, but relatively largeroot-mean-square (rms) errors in flood depth, ca. 50 cm or 50%,were reported despite efforts to calibrate model parameters. Nealet al. [27] modeled fluvial flooding of Carlisle, England using a con-siderably coarser resolution (25 m) than other urban flood model-ing studies have suggested is necessary for resolving street flowsand depicting building effects [6,17,33]. After extensive calibration,model predictions of flood depth yielded smaller rms errors (ca.30 cm) than the Mignot et al. study [26]. Valiani et al. [42] vali-dated a 2D shallow-water model prediction of the Malpassetdam-break flood in France in 1959, but modeling was focused onthe basin scale so smaller scale features germane to urban centerswere not examined. Similarly, Begnudelli and Sanders [4] validateda 2D shallow-water model prediction of the St. Francis dam-breakflood, but the flood zone was exclusively rural and the scale of pre-dictions was relatively large compared to recent high-resolutionstudies of urban flooding (e.g., [26,6,20,17,33]). Notwithstandingthese differences in scale, the Malpasset and St. Francis applica-tions show that Godunov-type finite volume shallow-water mod-els perform well in practical applications, readily accommodatingthe challenge of transcritical over natural terrain with wettingand drying. This has motivated use of similar models in otherFIM studies [43,33,30].

Here, we present a high-resolution 2D FIM study of an urbandam-break flood that occurred in 1963 in the Baldwin Hills regionof Los Angeles, California. Several key datasets have been obtainedto support FIM including a LiDAR Digital Terrain Model (DTM), dig-ital orthophotos of the study site, and post-disaster reports on thereservoir, its hydraulic infrastructure and the failure sequence[36,38]. Two types of field data have been obtained for validationpurposes: (1) a survey of flood extent completed by the US ArmyCorps of Engineers (USACE) [38], and (2) stream flow data for themain channel below the flood zone, Ballona Creek [38]. To theknowledge of the authors, this represents the first attempt tovalidate a 2D urban dam-break flooding model that utilizes high-resolution data including LiDAR, aerial imagery and other miscella-neous vector data.

The remainder of the paper is organized as follows,

� Section 2 describes the hydrodynamic routing methodologyincluding mesh generation, terrain and resistance parameteriza-tion, treatment of sub-surface storm drains, dam breach model-ing, and model initialization.

� Validation of the model is presented in Section 3.1, followed by asensitivity analysis in Section 3.2 to identify the most importantfactors relative to model accuracy.

� Section 4 provides a discussion of results, followed by conclu-sions in Section 5.

2. Materials and methods

2.1. Site description

Baldwin Hills Reservoir was placed into service in 1951 by theLos Angeles Department of Water and Power (LADWP) for watersupply purposes. The reservoir was situated on the north slopesof Baldwin Hills, approximately 3.2 km (2 miles) south of Interstate10 and 4 km (2.5 miles) east of Interstate 405 as shown in Fig. 1.The topography of Baldwin Hills was ideal for water supply pur-poses, having sufficient elevation near the service area, though itwas close to the Inglewood fault which at that time was one ofthe most active in California [36]. The reservoir capacity was1,110,000 m3 (897 acre-ft) and the surface area was estimated at79,200 m2 (20 acre) at the spillway crest, elevation 145.5 m(477.5 ft). The reservoir was rectangular in shape and encircledby an engineered embankment constructed of earthen materialsand lined with asphaltic pavement, as shown in Fig. 2. The north-ern side of the embankment, or dam, rose 47.2 m (155.0 ft) above aravine that would later become a channel of high velocity dam-break flood water. A spillway was located on the northeast cornerof the reservoir and was designed with a drain pipe that would, ifthe reservoir was inadvertently over-filled, direct water to a catchbasin just north of the reservoir. The reservoir was also engineeredwith an extensive drainage system designed to remove pore waterwhich penetrated the asphaltic lining of the reservoir, e.g., throughcracks resulting from differential settling. The drainage system di-rected water to the east side of the reservoir, where inlet and outletworks were also located (see Fig. 2) to support the water supplyfunction of the reservoir, and to the north side of the reservoir.Hence, the dam and spillway were located on the northern sideof the reservoir, while the water supply inlet and outlet workswere on the eastern side of the reservoir.

2.2. Failure sequence

December 14, 1963 began with approximately 975;200 m3

(790 acre-ft) in the reservoir and all systems operating normally.But at approximately 11:15 Pacific Standard Time (PST), the reser-voir caretaker observed an unusual amount of drainage water com-ing from the northeast corner of the reservoir. By 12:15, thedrainage had increased considerably and was observed to be mud-dy which indicated erosion of the dam. This water flowed east fromthe inlet/outlet works down a service road, then north along LaBrea avenue. By 13:00, water was observed leaking from the eastabutment of the dam, approximately 27 m (90 ft) below the spill-way crest. And at 13:30, water was also leaking from a crack thathad opened near the crest of the dam. These leaks would continueto grow over the next two hours before major breaching occurred.During this time, the region north of the dam was evacuated byemergency personnel, and LADWP personnel were taking all possi-ble steps to reduce the volume of water in the reservoir. The inletto the reservoir was closed, other reservoirs in the system were ta-ken off-line to focus system demand on Baldwin Reservoir, and anumber of ‘‘blow-off” valves in the water supply service area wereopened to maximize outflow. LADWP estimates that 12:8m3=s ð450 ft3

=sÞ of controlled flows were in place during this time.Efforts were also made to seal the crack in the dam (see 14:50photo in Fig. 2), but it continued to widen. Between 15:00 and15:15 the lower and upper leaks in the dam merged into one andformed an approximately 3 m (10 ft) wide breach. During this time,flows were contained in a catch basin just north of the dam. How-ever, at 15:20 the flow through the breach increased considerably,the crack continued to widen, and by 15:30 the catch basin wasovertopped. At 15:30, the final, major widening of the breach

Fig. 1. Baldwin Hills study area in Los Angeles, California including aerial imagery, observed flood extent, Ballona Creek gauging station location, and flood model boundary.

H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335 1325

occurred as shown in Fig. 2. Video coverage of the event shows thatthe final breach caused a rarefaction wave in the reservoir, a signa-ture feature of the so-called partial dam-break problem used forbenchmark testing of hydrodynamic models. At 15:38, the road-way over the breach collapsed (Fig. 2) and failure was complete.LADWP estimates that approximately 550;000 m3 were in the res-ervoir (half of its capacity of 897 acre-ft) upon the second and finalbreach [8].

The flood impacted the area north of the dam that is bordered,roughly, by Santa Barbara Avenue to the East (since renamed Mar-tin Luther King Blvd.), Jefferson Blvd. to the North, and BallonaCreek to the West as shown in Fig. 1. In addition, high velocitieswere reported on the ca. 7% slope below the dam, where homeswere torn from their foundation and considerable erosion oc-curred. On more level ground further North, the flood fanned outand smaller velocities were reported. Five people died, the reser-voir itself was lost, and flood damage was estimated at more than$15 million in 1964 dollars [36]. Structural damage included 41homes destroyed and 986 houses, 100 apartment buildings, and3000 automobiles damaged [40]. In addition, clean up and restora-tion efforts of streets, utilities, storm drains and repairs to the Bal-lona Creek Flood Control Channel were required. The cause offailure was investigated by California Department of Water Re-sources (CADWR) [36] who reported that earth movement underthe reservoir cracked the asphaltic lining and subsequent leakageunder pressure scoured the earthen fill within the embankment[36]. Today, the reservoir site has been transformed to a publicpark and one of the challenges addressed in this paper is the recon-struction of terrain as of 1963.

2.3. Data sources

Several sets of data were obtained to support modelparameterization and validation. Items (1)–(5) below are used formodel parameterization purposes, while (6) and (7) allow forvalidation:

(1) A 1.5 m (5 ft) resolution bare-earth Digital Terrain Model(DTM) from the 2006 LAR-IAC survey, as shown in Fig. 3.This was provided by the Los Angeles County Departmentof Public Works (LACDPW). The DTM exceeds National Stan-dard for Spatial Data Accuracy (NSSDA) and Federal Emer-gency Management Agency (FEMA) standards for verticalaccuracy, with a RMSE of 8.5 cm [23].

(2) A set of 10 cm (4 in.) resolution digital orthophotos from the2006 LAR-IAC survey, as shown in Fig. 1. These data, pro-vided by LACDPW were obtained for resistance parameterestimation and geo-referencing purposes. The orthophotosexceed NSSDA standards for horizontal accuracy with aradial RMSE of 26 cm [24].

(3) Parcel outline data were obtained from LACDPW to supportthe landcover classification and resistance parameterizationshown in Fig. 4.

(4) Contour maps depicting the reservoir and dam breach geom-etry, as shown in Fig. 3, were obtained from the CADWRreport [36]. The contour intervals were 6 m (20 ft) for thereservoir geometry and 3 m (10 ft) for the breach geometry.These data were scanned, geo-referenced, and digitizedusing polylines in ArcGIS 9.2 (ESRI, Redlands, CA).

Fig. 2. Progression of the dam failure. Photographs reproduced with permission from Los Angeles Times.

1326 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

(5) Catch-basin locations in the study area were obtained fromthe City of Los Angeles Bureau of Engineering and are shownin Fig. 4. Catch basins collect water from street gutters anddivert it to sub-surface pipes that transfer flow to BallonaCreek. A field survey by UC Irvine personnel was completedto verify the existence of these basins as of 1963 and to char-acterize the type and size. Catch basins were largely of thecurb-inlet type with a 20 cm (8 in.) height and a 2.1 m(7 ft) length. A small number of grate inlets were also foundand noted.

(6) Flood extent data, shown in Fig. 1, were obtained from aUSACE report [38]. This consisted of a map with hand-drawnmarkings of flooding. This was scanned, geo-referenced, anddigitized using polylines in ArcGIS 9.2 (ESRI, Redlands, CA).

(7) Ballona Creek stream flow data at the gauging station shownin Fig. 1 were obtained from a USACE report [38]. This islimited to the following information: drainage water firstarrived at 14:10 PDT, a peak flow of approximately170 m3=s ð6000 ft3

=sÞ occurred at 16:40, flow exceeded56:7 m3=s ð2000 ft3

=sÞ between 16:10 and 17:00 anddecreased to 5:7 m3=s ð200 ft3

=sÞ by 19:10.

2.4. Terrain modeling

ArcGIS 9.2 (ERSI, Redlands, CA) was used to merge the LiDARDTM and reservoir and breach contour data into a Triangular Irreg-

ular Network (TIN) reflective of 1963 conditions, as shown in Fig. 3.Contours were available only as printed drawings or plates, so eachimage was scanned and geo-referenced. Contours were then man-ually digitized as polylines and their nodes converted to x, y, zpoints. The LiDAR DTM was also converted from a raster formatto x, y, z points, and a combined set of x, y, z points was obtainedby filtering LiDAR points in areas of overlap. Finally, the merged setof points was converted to a TIN DTM as shown in Fig. 3.

Street flows are important in urban flood hydrology [17,33], andwe are assuming that 2006 terrain data provide a good descriptionof 1963 terrain heights in the vast majority of the flood zone. Thisappears justified based on a comparison of modern digital ortho-photos and historical aerial photos (not shown), which shows thatthe street layout has not changed. The photographic comparisonalso shows differences in the size and configuration of buildings,which is expected considering the damage of the flood. However,it should be stressed that the DTM is designed to capture bare-earth heights.

2.5. Flood inundation modeling

To predict dam-break flood inundation, the 2D shallow-waterequations were solved using BreZo, a Godunov-based finite volumecode that runs on an unstructured mesh of triangular cells similarto a TIN [5]. The TIN computational mesh is different from theTIN DTM shown in Fig. 3, as it is configured for model efficiency,

Fig. 3. (a) LiDAR DTM (Raster), (b) reservoir and breach geometry (contours), and (c) merged DTM (TIN).

H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335 1327

accuracy, and stability purposes. However, elevation data for theformer is extracted from the latter.

BreZo uses an approximate Riemann solver to estimate massand momentum fluxes. This accommodates mixed flow regimescommon to dam-break floods and handles wetting and dryingproblems without loss of stability, accuracy or conservation [3,5].BreZo has been previously validated in a rural dam-break study[4], and applied to simulate urban flooding caused by overtoppingof a culvert [33], but has not previously been applied to an urbandam-break application such as Baldwin Hills.

The TIN computational mesh used by BreZo defines groundheight at vertices and assumes that ground height varies linearlywithin each triangle; this achieves second-order accuracy relativeto terrain height truncation errors. To minimize numerical dissipa-tion, BreZo switches locally between two first-order accuratemethods of variable reconstruction [5]. In practical test cases, thecombination of a second-order accurate terrain model and a first-order accurate flow solver has been found to strike the best balancebetween numerical error and computational effort. In contrast toearlier versions of BreZo which used a global time step [5], herea three-level local time stepping (LTS) scheme is used to reducerun times [30] as in the study by Schubert et al. [33]. Cells are as-signed a time step of either Dt; 2Dt, or 4Dt; the largest that satis-fies the Courant, Friedrichs, Lewy (CFL) condition is used. Tomaintain conservation with LTS, flux calculations and solution up-

dates must be carefully sequenced but otherwise there is no loss ofaccuracy compared to global time stepping schemes.

Curb inlets in the study area, shown in Fig. 4, divert surfacewater through sub-surface pipes to Ballona Creek. To account forthis, the continuity equation solved by BreZo was modified witha set of point sink and source terms corresponding to curb inletsand sub-surface pipe outlets, respectively. Each time step, the vol-umetric flow rate into each curb inlet was computed with a mod-ified weir equation as follows,

QdðtÞ ¼ CDLh0ðtÞffiffiffiffiffiffiffiffiffiffiffighðtÞ

q; h0ðtÞ ¼min½hðtÞ;ho� ð1Þ

where g is the gravitational constant, h is the local depth of flow, ho

is the height of the curb, L is the length of the inlet measured alongthe curb, and CD is a dimensionless discharge coefficient set by trialand error to 0.5. This selection was motivated by a local experimen-tal study by the City of Los Angeles Bureau of Engineering [7], ofcatch-basin inflows, which indicates that CD falls between 0.1 and0.5. Values of ho and L were measured for several catch basins byUCI personnel as described in Section 2.3. Time integration of thesink/source terms was implemented with an explicit, fractional stepmethod. In the first step, the continuity equation was updated to ac-count for all fluxes of surface water. In the second step, the continu-ity equation was updated to account for each source/sink termusing the result of the first step to evaluate the right hand side of

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Fig. 4. Landcover classification and Manning n value, and location of catch basins and storm drain outlets.

1328 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

Eq. (1). Note that many of the curb inlets share the same outlet alongBallona Creek, as a result, a few cells are updated multiple timeseach time step. For stability purposes and to avoid negative depthpredictions, the volumetric flow rate from each storm drain waslimited so no more than 50% of the available volume could be with-drawn in a single time step.

The preceding approach is proposed as a simple alternative toaddress the problem of catch-basin diversions in 2D dam-breakFIM, compared to a fully coupled 1D/2D solver. There are clearlylimitations to the method, for example there is no restriction toflow through the network (only flow into the network), the modelcannot predict sewer surcharging which is often a driver of urbanflooding, and the model assumes that flow is instantaneously rou-ted from catch basins to the storm drain outlet. Further, this type ofapproach should not be used to design sub-surface storm drains.However, dam-break studies have rarely considered sub-surfacestorm drains on the grounds that sub-surface flow is a small frac-tion of overland flow. Hence, we utilize this relatively simple ap-proach as a first step to judge the importance of sub-surfaceflows in an urban flooding scenario. The overall complexity ofthe storm drain flows, including clogging by sediment and debris,provides further motivation for simplicity as a first step.

2.6. Mesh generation and model parameterization

A mesh of triangular cells was generated using Triangle, a flex-ible and powerful open source tool for 2D constrained Delaunaymesh generation [32]. The input to Triangle is an ASCII file that de-

fines the boundary of the domain with a list of vertices and linesegments, what graph theorists call a Planar Straight Line Graph(PSLG). Triangle enforces user supplied angle and cell area con-straints for mesh quality purposes. Area constraints control theresolution of the mesh, and variable resolution meshes can be eas-ily created. Further, meshes can be customized to study sites byaligning edges with building walls or street curbs, which improvesmodel accuracy with relatively coarse meshes [33]. However,nearly uniform meshes were utilized in this study for simplicityand we do not attempt to resolve buildings with the mesh. Thiswould require too fine a resolution for the available computationalresources. Instead, the mesh was designed to resolve street depres-sions in the land surface, which are thought to act as channels dur-ing urban flooding, and to resolve heterogeneity in landcover(roads, developed parcels, vegetated open space, etc.) which affectsflow resistance.

Once a few preliminary runs had been completed to identify theimpacted region, a PSLG was circumscribed around the area ofinterest to define the boundary (Fig. 1) and support mesh genera-tion. The boundary was set back sufficiently far from the flood zonethat boundary conditions became irrelevant, with one exception.Ballona Creek directs water south from the study area towardsthe Pacific Ocean. Here, a non-reflecting boundary condition wasused so water can freely exit [28]. The boundary was placed down-stream of the gauging station, where data are available, to facilitatecomparisons between predictions and observations of stream flow.

Meshes were generated using a 30� minimum angle constraintand a dual-zone maximum area constraint. An area constraint of

H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335 1329

9:3 m2 ð100 ft2Þ was used in a region surrounding the breach, dueto its narrow cross-section, and an area constraint of either 9.3,37.2, or 149:0 m2 ð100;400;1600 ft2Þ was used everywhere else.This created a set of three meshes, respectively: Mesh A with1,337,155 triangles or cells, Mesh B with 336,681 cells and MeshC with 86,835 cells. The resolution of these meshes, taken as thesquare root of the average cell area, corresponds to 2.5, 4.9, and9.6 m, respectively. Typical street widths in Los Angeles Countyare 18 m (60 ft). Hence, Mesh A, B, and C resolve streets with atleast 7, 3, and 1 cell, respectively. In addition, Ballona Creek is ca.60 m wide so it is spanned by ca. 24, 12, and 6 cells with MeshA, B, and C, respectively. Most predictions in the study utilize MeshB, because it is fine enough to resolve street depressions but coarseenough (336,681 cells) for execution on a desktop computer in afew hours. Mesh A allows us to report the convergence error ofMesh B, and Mesh C allows us to report the consequences of anoverly coarse mesh that does not accurately depict street depres-sions. Following mesh generation, ground elevation at mesh verti-ces was interpolated from the merged TIN DTM. Note that TINsutilize a linear reconstruction of terrain height which is the basisfor interpolating ground elevation at mesh vertices.

A Manning n was assigned to each cell in accordance with asimple landcover classification that was manually created fromparcel outlines and digital orthophotos supplied by LACDPW. Par-cel outlines were used as a mask to define the road network, anddigital orthophotos were used to manually outline apartmentbuilding footprints, asphalt parking lots and vegetated open spaceareas which, based on the review of a historical orthophoto [36],were confirmed to exist at the time of the flood. As shown inFig. 4, Manning n values of 0.014, 0.016, 0.013, 0.30, and0:050 m�1=3 s were assigned to roads, channels, reservoir, devel-oped parcels with buildings, and vegetated open space, respec-tively. A value of 0:014 m�1=3 s is typical of asphalt pavement,0:016 m�1=3 s is typical of concrete channels with gravel and sedi-ment along the channel bottom, 0:013 m�1=3 s is typical of smoothconcrete surfaces, and 0:050 m�1=3 s corresponds to pasture withhigh grass [9]. This was chosen because the vegetated areas in-cluded many shrubs and small trees. Further, a value of0:30 m�1=3 s has been recommended for developed parcels withbuildings [39], but this would likely depend on the flow obstruc-tion. Both historical and modern photos show that at least 50% ofparcel footprints are occupied by buildings.

2.7. Initial conditions

The failure sequence described in Section 2.2 and shown inFig. 2 indicates that the breaching process began gradually before15:00 and effectively ended at 15:30 with a major widening. Fur-ther, LADWP officials estimated that storage in the reservoir wasapproximately half its capacity at 15:30, ca. 550;000 m3 (ca.449 acre-ft). However, the volume at the beginning of the majorbreaching processes, around 15:20, is not clear. The volume at thistime is important as it represents what flooded north into thestudy area. Approximately 980;000 m3 (790 acre-ft) were storedat the beginning of the day, but LADWP took a number of stepsto lower the level prior to catastrophic dam failure.

Using design drawings of the reservoir which include the slopeand height of the dam face, and photogrammetric scaling tech-niques, the height of the reservoir at 15:20 and 15:30 was esti-mated from the photographs shown in Fig. 2. Results suggest thatthe reservoir elevation was between 140.9 and 141.5 m (462 and464 ft) at 15:20 and between 138.7 and 139.3 (455 and 457 ft) at15:30. Based on the geometry of the reservoir, this corresponds to720;000—770; 000 m3 at 15:20 and 580;000—620;000 m3 at15:30. Note that the volume at 15:30 is consistent with the LADWP[8] report that the reservoir was ‘‘half full” at 15:30. Further, this

analysis suggests that the combination of controlled and uncon-trolled flows sent approximately 230;000 m3 (186 acre-ft) fromthe reservoir before catastrophic failure.

After careful analysis of all available information, breaching ofthe dam was modeled as a two-stage process. In the first stage,the breach was assumed to instantaneously open at 15:20 to atrapezoidal shape approximately 21.3 m (70.0 ft) wide at the crestof the dam and 7.6 m (25.0 ft) at the base of the dam. This roughlyapproximates the breach geometry around 15:20. In the secondstage, which was assumed to instantaneously occur at 15:30, thebreach was assumed to take on the final geometry reported byCADWR and shown in Figs. 2 and 3. The reservoir elevation at15:20 was taken as 141.1 m (463.0 ft) based on the 15:20 reservoirphoto; this represents the initial condition.

BreZo was run for 10 min using the first breach geometry, andrestarted using the second breach geometry at 15:30. BreZo pre-dicted a reservoir volume of 620;000 m3 at 15:30; this is consis-tent with the 15:30 reservoir photo and the LADWP assessmentof a half full reservoir. BreZo was integrated for a total period of3 h to simulate the flood. The solution was saved at 4–8 min inter-vals for analysis purposes, the maximum depth and velocity wassaved in each computational cell, and the discharge in BallonaCreek and through the storm drain system was also saved.

3. Results

3.1. Validation of the flood prediction

The progression of dam-break flooding predicted by the model isshown in Fig. 5 from 15:20 onward. This shows the flood quicklyfunnelled north through the steep canyon below the dam, reachingthe relatively flat terrain north of Coliseum St. by 15:25. Over thenext 5 min, the flood pushed further north to Rodeo Rd. and spreadlaterally. By 15:30, the flood is shown to be fingering west along Ro-deo Rd. and flooding those streets perpendicular and parallel to it. By15:54, it appears that flood water reached Ballona Creek, which thendirected water south towards the Pacific Ocean. Fig. 5 shows waterin Ballona Creek prior to the arrival of surface flows along Rodeo Rd.which is due to routing through storm drains. USACE [38] reported asmall baseflow in Ballona Creek prior to the dam-break flood, andattributed this to storm drain routing of the initial dam leakage be-cause Ballona Creek is typically dry in the absence of rainfall.

Eastward flooding is also evident in Fig. 5, for example between15:38 and 15:54, the model shows that flood water subsequentlyspread north into the junction of Jefferson and Exposition Blvd.,and southeast along Santa Barbara Ave. Fig. 4 shows a number ofcatch basins along Jefferson and Exposition Blvd., and as watermoved relatively slowly into this area compared to the westwardflooding, these helped to prevent further flooding northward.

There is evidence of flood recession by 16:18 as terrain in theeastern portion of the flood zone is shown to be drying. Recessionof the flood becomes clearly evident by 17:02 and nearly 90 min la-ter at 18:30, the situation changes very little which reflects a rela-tively slow recession of the flood compared to the initial surge.

As described in Section 2.6, Mesh B was designed to validate themodel. To quantify the accuracy of the flood extent prediction, a fitmeasure FE ¼ 0:76 was computed, which compares favorably withother FIM studies [14]. The fit was computed as follows [14],

FE ¼EP \ EM

EP [ EMð2Þ

where E indicates flood extent (m2) and P and M correspond to pre-diction and measurement, respectively. The symbol \ indicates theintersection of two domains, and [ represents the union of twodomains.

Fig. 5. Progression of flooding predicted by model (Run 1). Red outline represents observed flood extent. (For interpretation of the references to colour in this figure legend,the reader is referred to the web version of this article.)

1330 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

Fig. 7a presents predicted (labeled ‘‘Run 1”) and observedstream flow in Ballona Creek. Error bars on the observed streamflow data correspond to a 10% level of uncertainty, which is a roughestimate typical of stage-discharge errors. A fit measure for thepeak stream flow FQ ¼ 1:08 was computed as follows,

FQ ¼Q P

Q Mð3Þ

where Q indicates peak stream flow (m3/s) at the gauging stationand P and M are the same as in Eq. (2). This is within the assumedlevel of uncertainty (ca. 10%). A fit measure for the prediction of tra-vel time FT ¼ 1:06 was also computed as follows,

FT ¼TP

TMð4Þ

where T represents the time elapsed from 15:20 until peak flow atthe gauging station. Note that for all three fit measures, F ¼ 1

H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335 1331

corresponds to perfect agreement. Furthermore, for FQ and FT , avalue greater than one indicates an over-prediction and a value lessthan one indicates an underprediction. Hence, Run 1 slightly over-predicts the peak stream flow and travel time. Further, the modelappears to more accurately predict the rising limb of the hydro-graph than the falling limb. The model over-predicts stream flowat 17:00, although between 18:00 and 19:00 the prediction is againconsistent with observations.

The flood extent predictions shown in Fig. 6 and the stream flowpredictions shown in Fig. 7a clearly validates the 2D model formu-

Fig. 6. Flood extent predictions for Runs 1–12. Wh

lation, configuration, and parameterization. Run 1 does benefitfrom calibration; CD values of 0.1, 0.3, and 0.5 were tested to arriveat 0.5. However, the notion of calibrating and validating modelparameters should not be confused with the validation of a model-ing approach.

Model predictions also highlight the complexity of urban dam-break flood flows: flow is highly unsteady and transported alongpreferential flow paths (streets) where terrain is depressed like ariver thalweg and resistance is minimal due to a relatively smoothsurface (concrete or asphalt) compared to natural surfaces.

ite outline represents observed flood extent.

14:00 15:00 16:00 17:00 18:00 19:00 20:000

50

100

150

200

250

m3 /s

MeasurementRun 1Run 7 (Uniform n)Run 8 (Smaller CD)Run 9 (Higher Res. Level)Run 12 (Trap. Breach Geom.)

14:00 15:00 16:00 17:00 18:00 19:00 20:000

50

100

150

200

250MeasurementRun 1 (1.5 m LiDAR)Run 4 (9.1 m LiDAR)Run 5 (10 m NED)

14:00 15:00 16:00 17:00 18:00 19:00 20:000

50

100

150

200

250m

3 /s

m3 /s

MeasurementRun 1Run 2 (Fine)Run 3 (Coarse)

14:00 15:00 16:00 17:00 18:00 19:00 20:000

50

100

150

200

250

m3 /s

MeasurementRun 10 (W/H=1)Run 11 (W/H=2)Run 12 (W/H=3)

(a) (b)

(c) (d)

Fig. 7. Ballona Creek hydrograph predictions for Runs 1–12 at gauging station shown in Fig. 1, compared to observations.

1332 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

Previous studies have also emphasized the importance of streetflows, and the need to accurately depict street geometry and resis-tance within the model framework [33].

These results suggest that a rich set of urban geospatial data isneeded to accurately depict urban flooding, including high-resolu-tion terrain data, spatially distributed resistance parameters, stormdrain network data, knowledge of the reservoir level at the time offailure, as well as the breach geometry. Advances in remote sensingand information technologies will undoubtedly make some ofthese data more readily accessible in the future, while other factorssuch as the breach geometry will rarely be known a priori for pre-dictive modeling purposes. Next in Section 3.2, several additionalmodel simulations are presented to examine the relative impor-tance of these data sources and modeling techniques. The sensitiv-ity of model predictions to these factors are measured, and the

Table 1Attributes of model runs and performance metrics: FE; FQ , and FT . Run 1 represents the b

Run Mesh Manning n Breach process Water level (m) DTM

1 B Distributed 2 stage 141.20 1.5 m LiDAR2 A Distributed 2 stage 141.20 1.5 m LiDAR3 C Distributed 2 stage 141.20 1.5 m LiDAR4 B Distributed 2 stage 141.20 9.1 m LiDAR5 B Distributed 2 stage 141.20 10 m NED6 B Distributed 2 stage 141.20 30 m SRTM7 B Uniform 2 stage 141.20 1.5 m LiDAR8 B Distributed 2 stage 141.20 1.5 m LiDAR9 B Distributed 2 stage 143.90 1.5 m LiDAR

10 B Distributed 1 stage 141.20 1.5 m LiDAR11 B Distributed 1 stage 141.20 1.5 m LiDAR12 B Distributed 1 stage 141.20 1.5 m LiDAR

most critical aspects are identified along with modeling guidelinesfor future studies.

3.2. Sensitivity analysis

A total of 12 model runs are presented, including the base case(Run 1) shown in Section 3.1. Table 1 presents the attributes of the12 runs, labeled Runs 1–12. Each run differs from Run 1 in only onerespect as follows:

� Runs 2 and 3 utilize a twice finer (Mesh A) and twice coarser(Mesh C) computational mesh versus the base case (Mesh B),respectively.

� Runs 4–6 utilize different sources and resolution of terrain data.Run 4 uses a DTM that was coarsened to 9.1 m (30 ft) by window

ase case presented in Section 3.1.

Catch basin CD Comment FE FQ FT

0.50 Base case 0.76 1.08 1.060.50 Finer mesh 0.79 1.15 0.940.50 Coarser mesh 0.63 0.72 1.330.50 Coarsened DTM 0.71 1.11 1.020.50 National DEM for USA 0.47 1.07 1.050.50 Global DEM 0.31 0.00 NA0.50 Uniform n 0.73 0.59 1.860.30 Less flow to catch basins 0.69 0.98 1.090.50 Higher reservoir level 0.68 1.37 0.950.50 Breach width = dam height 0.73 1.05 0.800.50 Breach width = 2 � dam height 0.68 1.14 0.840.50 Breach width = 3 � dam height 0.65 1.16 0.82

H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335 1333

averaging the 1.5 m (5 ft) LiDAR DTM, Run 5 uses 1/3 arc-s (10 mor 33 ft) National Elevation Data (NED), and Run 6 uses of 3 arc-s(30 m or 99 ft) Shuttle Radar Topography Mission (SRTM) data.

� Run 7 uses a spatially uniform Manning n ¼ 0:2 m�1=3 s. Thisvalue (coincidentally, perhaps) represents: (a) the spatial aver-age of the distributed Manning n shown in Fig. 4 and (b) theeffective value of Manning n resulting from the application ofHejl’s method [13], which considers the fraction of the flood-plain available for conveyance (i.e., not blocked by buildings).

� Run 8 uses a smaller catch-basin inflow coefficient, CD ¼ 0:3.� Run 9 uses a higher initial reservoir level, 143.9 m (472 ft),

which represents a typical operating level.� Runs 10–12 use a single-stage trapezoidal breach approximation

with a bottom width B ¼ H, 2H, and 3H, respectively, where H isthe height of the dam, and a 1:1 side slope.

Fig. 6 shows flood extent predictions corresponding to Runs 1–12, Fig. 7 shows hydrographs for Ballona Creek, and Table 1 showsFE; FQ , and FT . First consider the impact of mesh resolution. Fig. 6shows that an increase in mesh resolution (Run 2, FE ¼ 0:79) im-proves the flood extent prediction very slightly compared to Run1 ðFE ¼ 0:76Þ. For example, south of Coliseum street, just to the eastof the primary flood path below the dam, there is a case of streetflow that is more accurately depicted by Run 2 than Run 1. Also,Run 2 more accurately depicts flooding at the junction of Jeffersonand Exposition Blvds. At the gauging station, Fig. 7a and Table 1show that Run 2 leads to a 7% greater peak stream flow, and 12%shorter travel time compared to Run 1. These differences are smallcompared to the consequences of using a coarser mesh (Run 3).Run 3 shows a significant over-prediction of flood extent in thenortheast corner of the flood zone which leads to FE ¼ 0:63. Fur-ther, peak stream flow is significantly under-predicted FQ ¼ 0:72and the travel time is significantly over-predicted FT ¼ 1:33. Previ-ous dam-break modeling studies with BreZo have shown predic-tions are overly dissipative when the mesh is too coarse, causingan underprediction of peak stream flow and flood propagationspeed [4].

Consider now the source of terrain data. Fig. 6 and Table 1 showthat coarsened LiDAR (Run 4), NED (Run 5), and SRTM degrade theaccuracy of flood extent predictions to different extents:FE ¼ 0:71; 0:47, and 0.31 for Runs 4–6, respectively. Neither NEDnor SRTM resolve street-scale topographic variations, but NED re-solves the larger scale features that appear to bound the primaryflood path north from the dam and west toward Ballona Creek.Where NED performs poorly is in the northeast corner of the studysite, where NED does not resolve street scale variations in the ter-rain that appear to bound the flood zone. SRTM depicts relativelyflat terrain with a non-physical waviness that has been termed ‘‘ra-dar speckle” [11,18], and predictions of flooding at similar spatialscales have shown non-physical pools of water corresponding tolocal minima in the DTM [29]. This pooling effect is evident inRun 6 shown in Fig. 6, and the flood extent prediction is notablycrude. However, in the canyon North of the dam, flood extentbased on SRTM is little different from Run 1 based on LiDAR. Theseresults show that the DTM can have a significant effect on flood ex-tent accuracy, but interestingly, the impact on stream flow predic-tions at the gauging station are relatively small with the exceptionof SRTM (Run 6), which does not resolve the geometry of the floodcontrol channel and therefore cannot support modeling of flowthrough it. Fig. 7b shows predicted and measured hydrograph data,and Table 1 shows that FQ and FT values across Run 1, Run 4, andRun 5 differ by at most 4%.

Fig. 6 also shows that a spatially uniform Manning n has rela-tively little impact on flood extent (Run 7), particularly when com-pared to a smaller catch-basin discharge coefficient CD ¼ 0:3 (Run8) and a higher initial water level (Run 9) which both significantly

increase flood extent in the northeast corner of the study site.Stream flow at the gauging station is also sensitive to these factors.For example, Fig. 7d shows that a spatially uniform Manning nleads to a significant under-prediction of peak stream flowFQ ¼ 0:59 and over-prediction of travel time FT ¼ 1:86. Fig. 7dshows that an increase in the initial reservoir height leads to anover-prediction of stream flow FQ ¼ 1:37 and a slight under-pre-diction of travel time FT ¼ 0:95. Finally, Fig. 7d shows that a smal-ler CD has relatively little impact on the stream flow hydrograph,compared to the base case.

Runs 10–12 examine the effect of an increasing breach width.Fig. 6 shows that flood extent increases with breach width, andall three single-stage breach scenarios show a greater flood extentthan the two-stage breach scenario used in Run 1. However, Fig. 7cshows that breach width has relatively little impact on the streamflow at the gauging station even compared to the base case (Run 1).

4. Discussion

Every perturbation of the model set-up, with the exception ofRun 2 (finer mesh) resulted in a larger flood extent compared toRun 1. This was most notable in the northeast corner of the sitewhere flooding was incorrectly predicted north of Jefferson Blvd.Terrain is gently sloped to the northwest here, so gravitational ef-fects tend to stretch out the slightest over-prediction of flooding.

It appears that no aspect of the model set-up described here canbe simplified without sacrificing either flood extent or stream flowaccuracy. The source and resolution of terrain data, reservoir vol-ume, breach configuration, computational mesh resolution, andsub-surface storm drains all affected flood extent predictions bya similar amount. Resistance parameters and the reservoir volumeaffected stream flow more than other factors.

Previous studies of dam-break flood modeling have noted aninsensitivity of flood extent predictions to resistance parameters[4], but stream flow predictions here show that distributed resis-tance parameters are essential for accurately routing the floodacross the street network and along the flood control channel. Sim-ilar findings have resulted from modeling studies of rural flooding[16]. Further, distributed resistance parameters are needed for lo-cal predictions of velocity [2,14] which may be needed for damageassessments or predictions of sediment erosion and deposition.

Street widths appear to be a useful guide for selecting a meshresolution. In a county where street widths of 18 m are typical,Mesh B with a resolution of 4.9 m (3 cells across street) gave goodpredictions ðFE ¼ 0:76Þ but Mesh C with a resolution of 9.6 m (1 cellacross street) significantly degraded flood extent accuracyðFE ¼ 0:63Þ. Similarly, when LiDAR terrain resolution was coarsenedto 9.1 m (Run 4), a loss of accuracy was also observed ðFE ¼ 0:71Þcompared to the base case. These results show that flow alongstreet depressions in the land surface should be resolved to accu-rately depict flood extent in urban settings. The meshing require-ments may depend slightly on the mesh type (e.g., structuredversus unstructured) and whether streets are aligned with the grid,so the common practice of convergence testing is recommended toensure that the mesh is sufficiently resolved.

What do these results say about good modeling practice for ur-ban dam-break studies? Essentially, high-resolution terrain data,aerial imagery and catch-basin data can and should be obtained tosupport flood modeling because the potential exists for a high de-gree of accuracy ðFE � 0:8Þ. NED is attractive because it can be ob-tained without charge from the USGS. However, results here showthat flood extent is overpredicted using NED compared to LiDAR.Secondly, urban flooding is characterized by preferential flow alongstreets; thus heterogeneity in flow resistance parameters should beresolved to accurate depict overland flow. Third, flow through

1334 H.A. Gallegos et al. / Advances in Water Resources 32 (2009) 1323–1335

sub-surface storm drains can be important but it may be possible touse a relatively simplistic modeling approach that essentially trans-fers water from catch basins to the storm drain outlet. Otherwise,flood extent is likely to be over-predicted. Lastly, modelers shouldstrive to resolve streets with at least three computational cells.Otherwise, models are likely to over-predict flood extent, under-predict peak flows downstream, and over-predict travel time.

What about the predictability of dam-break flood inundation?What appears most challenging is the reservoir level at the timeof failure, and its volume. Water level sensors, either in situ or re-mote (e.g, satellite altimetry), stand to enable the real-time moni-toring that could support real-time dam-break emergencymanagement efforts with flood forecasts. In case of real-time mon-itoring through satellite sensors, spatial resolution and re-visittime are important factors and the Surface Water Ocean Topogra-phy (SWOT) mission planned by NASA for the coming decade mayprovide critical information [35]. The breaching process appearsless important than the reservoir volume, but more researchshould be done to evaluate the best strategies to couple modernbreaching models (e.g., [10,21]) with dam-break flood models.

5. Conclusions

Urban dam-break flood modeling demands a rich set of high-resolution geospatial data for accuracy purposes, based on the re-sults of this study. High-resolution terrain data such as LiDAR areneeded to depict street depressions in the land surface, and anunstructured mesh similar to the one used here should be refinedwith at least three cells across each street. Landcover heterogeneityshould be resolved to guide the spatial distribution of resistanceparameters, and the location of catch basins and storm drain out-lets should be considered. Efforts to simplify model formulationor coarsen the resolution generally cause an over-prediction offlood extent or inaccurate stream flow predictions. In addition,poor flood extent accuracy was achieved with NED and SRTM ter-rain data. Further, a spatially uniform resistance parameter lead topoor stream flow accuracy compared to a spatially distributedparameter with the same mean value.

A simple method of routing flow through storm drains wasintroduced here and successfully implemented. This involved pairsof sink and source terms in the continuity equation co-located withcatch basins and storm drain outlets, respectively. A modified weirequation was used to scale flow into each catch basin, based on itsheight and curb length, and the model was validated with a dimen-sionless discharge coefficient CD ¼ 0:5. This falls at the upper endof what is expected (0.1–0.5) based on a laboratory study ofcatch-basin inflows by the City of Los Angeles.

Water volume in the reservoir at the time of failure is a criticalfactor for accurate flood predictions, and over- or under-estimateof water levels will lead to an over- or under-prediction, respec-tively of flood extent and stream flow, all else being equal. A lesscritical but still important factor is the breach geometry. Use of atrapezoidal breach with a 1:1 side slope and a bottom width equalto the dam height reproduced flood extent better than breacheswith wider bottom widths. Given the sensitivity of flood dynamicsto the reservoir level, these results suggest that more detailedmodeling of the breach geometry can be justified if the reservoirlevel is known with a high degree of certainty. Finally, dam safetyprograms should monitor water levels in real-time to support sim-ulation based emergency management of dam-break flooding.

Acknowledgements

This work was supported by a grants from the UC Water Re-sources Center (WR-1016), the National Science Foundation

(CMMI-0825165), and the UC Irvine Urban Water Research Center(Contribution # 39) whose support is gratefully acknowledged. Theauthors also thank LADWP, LACDPW, LAR-IAC, City of Los AngelesBureau of Engineering, and USACE (Los Angeles District) for theircooperation. Lastly, the authors thank the reviewers for construc-tive comments that improved the paper.

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