Two-dimensional, high-resolution modeling ofurbandam-breakflooding:A case study of Baldwin Hills, California
Humberto A. Gallegosa, Jochen E. Schubertband Brett F. Sandersa,,,
aDepartment of Civil and Environmental Engineering, University of California, Irvine, CA 92697-2175, USA
bIESSG, The University of Nottingham, Nottingham NG7 2RD, UK
Received 9 March 2009;
revised 17 May 2009;
accepted 19 May 2009.
Available online 28 May 2009.
Modeling of dam-break flooding in an urban residential area in southern California is presented. Modeling is performed using BreZo, an unstructured grid, Godunov-type, finite volume model that solves the shallow-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 spatially distributed Manning coefficient based on a landcover classification derived from digital orthophotos and vector data (e.g., parcel outlines) is also used, and the interception of flow by storm drains is modeled with sink terms in the 2D continuity equation. The model is validated with flood extent and stream flow measurements, and a sensitivity analysis is completed to identify the necessary level of data and model complexity for accuracy purposes. Results show street depressions in the land surface should be resolved by the computational mesh for flood extent and stream flow accuracy. A ca. 5 m resolution mesh that spans streets by approximately 3 cells achieves a good balance between accuracy and computational effort. Results also show that heterogeneous resistance is important for stream flow accuracy, and the interception of overland flow by storm sewers is important for flood extent accuracy. The sensitivity of predictions 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.
Urban flooding is becoming more frequent as a consequence of several factors including continued watershed development with impervious surfaces, population growth which places increasing pressure on communities to develop in flood prone areas  and , climate change which has magnified the intensity of rainfall , sea level rise which threatens coastal developments, and decaying or poorly engineered flood control infrastructure such as the levee system of California’s Sacramento-San Joaquin river delta . Furthermore, the consequences of flooding are greater in urbanversus rural sites due to the relative economic value and population density  and . To manage the risk of flooding, damage assessments are needed and should consider not only economic but also social and environmental factors . This can be accomplished by first applying hydraulic models to predict the depth and velocity distribution of probable floods, and then overlaying these data upon assets of an economic, social and environmental nature to quantify probable damages.
Government at all levels is increasingly investing in Geographical Information Systems (GIS) to organize and efficiently utilize geospatial data for a diverse number of management and operational objectives. In Los Angeles County, for example, a consortium of public agencies known as the Los Angeles Area Imagery Acquisition Consortium (LAR-IAC) jointly funded the acquisition of several county-wide, high-resolution data sets including Light Detection and Ranging (LiDAR) terrain data, digital orthophotos, and oblique aerial photos. These data make it possible to resolve landscape geometry and surface features with a spatial resolution (ca. 1 m) and vertical accuracy (e.g., <10 cm RMSE) that is ideal for flood inundation modeling (FIM) ,  and . Damage estimates can subsequently be integrated in GIS.
High-resolution modeling of urban flooding from a dam failure is the focus of this study. A two-dimensional (2D) flood inundation model based on the shallow-water equations is applied and parameterized using LiDAR terrain data, digital orthophotos and other supporting data, and predictions of flood extent and stream flow are compared to observations for validation purposes.
A number of 2D urban FIM studies have recently appeared in the literature. Researchers have addressed questions such as the necessary grid resolution ,  and , resistance parameterization ,  and , role of sub-surface storm drains , tradeoffs between shallow-water and diffusive wave routing schemes , and models for the impact of buildings on flood dynamics , , ,  and  including use of porosity methods, , , ,  and . These studies have shown that urban flood flows manifest as a combination of sub- and super-critical flow along streets and between buildings, depending on street slopes and flood dynamics, and 2D models are poised to resolve these dynamics when important flow paths such as streets and gaps between buildings are resolved. This may require a grid resolution of 2 m or less  and  using structured grids or a variable resolution unstructured mesh that is constrained by building walls .
There remains a need for more urban FIM validation studies, to develop a sound understanding of good modeling practice (e.g., model formulation, data requirements, mesh resolution) and assess the overall predictability of urban flooding, particularly in the context of dam failures. Mignot et al. simulated two flood events in Nimes, France where water is channeled along city streets. The model was found to accurately depict flood extent, as the site was bounded by steep topography, but relatively large root-mean-square (rms) errors in flood depth, ca. 50 cm or 50%, were reported despite efforts to calibrate model parameters. Neal et al.  modeled fluvial flooding of Carlisle, England using a considerably coarser resolution (25 m) than other urban flood modeling studies have suggested is necessary for resolving street flows and depicting building effects ,  and . After extensive calibration, model predictions of flood depth yielded smaller rms errors (ca. 30 cm) than the Mignot et al. study . Valiani et al.  validated a 2D shallow-water model prediction of the Malpasset dam-break flood in France in 1959, but modeling was focused on the basin scale so smaller scale features germane to urban centers were not examined. Similarly, Begnudelli and Sanders  validated a 2D shallow-water model prediction of the St. Francis dam-break flood, but the flood zone was exclusively rural and the scale of predictions was relatively large compared to recent high-resolution studies of urban flooding (e.g., , , ,  and ). Notwithstanding these differences in scale, the Malpasset and St. Francis applications show that Godunov-type finite volume shallow-water models perform well in practical applications, readily accommodating the challenge of transcritical over natural terrain with wetting and drying. This has motivated use of similar models in other FIM studies ,  and .
Here, we present a high-resolution 2D FIM study of an urban dam-break flood that occurred in 1963 in the Baldwin Hills region of Los Angeles, California. Several key datasets have been obtained to support FIM including a LiDAR Digital Terrain Model (DTM), digital orthophotos of the study site, and post-disaster reports on the reservoir, its hydraulic infrastructure and the failure sequence  and . Two types of field data have been obtained for validation purposes: (1) a survey of flood extent completed by the US Army Corps of Engineers (USACE) , and (2) stream flow data for the main channel below the flood zone, Ballona Creek . To the knowledge of the authors, this represents the first attempt to validate a 2D urban dam-break floodingmodel that utilizes high-resolution data including LiDAR, aerial imagery and other miscellaneous vector data.
The remainder of the paper is organized as follows,
• Section 2 describes the hydrodynamic routing methodology including mesh generation, terrain and resistance parameterization, treatment of sub-surface storm drains, dam breach modeling, and model initialization.
• Validation of the model is presented in Section 3.1, followed by a sensitivity analysis in Section 3.2 to identify the most important factors relative to model accuracy.
• Section 4 provides a discussion of results, followed by conclusions in Section 5.
2. Materials and methods
2.1. Site description
Baldwin Hills Reservoir was placed into service in 1951 by the Los Angeles Department of Water and Power (LADWP) for water supply purposes. The reservoir was situated on the north slopes of Baldwin Hills, approximately 3.2 km (2 miles) south of Interstate 10 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 purposes, having sufficient elevation near the service area, though it was close to the Inglewood fault which at that time was one of the most active in California . The reservoir capacity was 1,110,000 m3 (897 acre-ft) and the surface area was estimated at 79,200 m2 (20 acre) at the spillway crest, elevation 145.5 m (477.5 ft). The reservoir was rectangular in shape and encircled by an engineered embankment constructed of earthen materials and lined with asphaltic pavement, as shown in Fig. 2. The northern side of the embankment, or dam, rose 47.2 m (155.0 ft) above a ravine that would later become a channel of high velocity dam-break flood water. A spillway was located on the northeast corner of the reservoir and was designed with a drain pipe that would, if the reservoir was inadvertently over-filled, direct water to a catch basin just north of the reservoir. The reservoir was also engineered with an extensive drainage system designed to remove pore water which penetrated the asphaltic lining of the reservoir, e.g., through cracks resulting from differential settling. The drainage system directed water to the east side of the reservoir, where inlet and outlet works were also located (see Fig. 2) to support the water supply function of the reservoir, and to the north side of the reservoir. Hence, the dam and spillway were located on the northern side of the reservoir, while the water supply inlet and outlet works were on the eastern side of the reservoir.
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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.
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Fig. 2. Progression of the dam failure. Photographs reproduced with permission from Los Angeles Times.
2.2. Failure sequence
December 14, 1963 began with approximately (790 acre-ft) in the reservoir and all systems operating normally. But at approximately 11:15 Pacific Standard Time (PST), the reservoir caretaker observed an unusual amount of drainage water coming from the northeast corner of the reservoir. By 12:15, the drainage had increased considerably and was observed to be muddy which indicated erosion of the dam. This water flowed east from the inlet/outlet works down a service road, then north along La Brea avenue. By 13:00, water was observed leaking from the east abutment of the dam, approximately 27 m (90 ft) below the spillway crest. And at 13:30, water was also leaking from a crack that had opened near the crest of the dam. These leaks would continue to grow over the next two hours before major breaching occurred. During this time, the region north of the dam was evacuated by emergency personnel, and LADWP personnel were taking all possible steps to reduce the volume of water in the reservoir. The inlet to the reservoir was closed, other reservoirs in the system were taken off-line to focus system demand on Baldwin Reservoir, and a number of “blow-off” valves in the water supply service area were opened to maximize outflow. LADWP estimates that of controlled flows were in place during this time. Efforts were also made to seal the crack in the dam (see 14:50 photo in Fig. 2), but it continued to widen. Between 15:00 and 15:15 the lower and upper leaks in the dam merged into one and formed an approximately 3 m (10 ft) wide breach. During this time, flows were contained in a catch basin just north of the dam. However, at 15:20 the flow through the breach increased considerably, the crack continued to widen, and by 15:30 the catch basin was overtopped. At 15:30, the final, major widening of the breach occurred as shown in Fig. 2. Video coverage of the event shows that the final breach caused a rarefaction wave in the reservoir, a signature feature of the so-called partial dam-break problem used for benchmark testing of hydrodynamic models. At 15:38, the roadway over the breach collapsed (Fig. 2) and failure was complete. LADWP estimates that approximately were in the reservoir (half of its capacity of 897 acre-ft) upon the second and final breach .
The flood impacted the area north of the dam that is bordered, roughly, by Santa Barbara Avenue to the East (since renamed Martin Luther King Blvd.), Jefferson Blvd. to the North, and Ballona Creek to the West as shown in Fig. 1. In addition, high velocities were reported on the ca. 7% slope below the dam, where homes were torn from their foundation and considerable erosion occurred. On more level ground further North, the flood fanned out and smaller velocities were reported. Five people died, the reservoir itself was lost, and flood damage was estimated at more than $15 million in 1964 dollars . Structural damage included 41 homes destroyed and 986 houses, 100 apartment buildings, and 3000 automobiles damaged . In addition, clean up and restoration efforts of streets, utilities, storm drains and repairs to the Ballona Creek Flood Control Channel were required. The cause of failure was investigated by California Department of Water Resources (CADWR)  who reported that earth movement under the reservoir cracked the asphaltic lining and subsequent leakage under pressure scoured the earthen fill within the embankment . Today, the reservoir site has been transformed to a public park and one of the challenges addressed in this paper is the reconstruction of terrain as of 1963.
2.3. Data sources
Several sets of data were obtained to support model parameterization and validation. Items (1)–(5) below are used for model parameterization purposes, while (6) and (7) allow for validation:
(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 Department of Public Works (LACDPW). The DTM exceeds National Standard for Spatial Data Accuracy (NSSDA) and Federal Emergency Management Agency (FEMA) standards for vertical accuracy, with a RMSE of 8.5 cm .
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Fig. 3. (a) LiDAR DTM (Raster), (b) reservoir and breach geometry (contours), and (c) merged DTM (TIN).
(2) A set of 10 cm (4 in.) resolution digital orthophotos from the 2006 LAR-IAC survey, as shown in Fig. 1. These data, provided by LACDPW were obtained for resistance parameter estimation and geo-referencing purposes. The orthophotos exceed NSSDA standards for horizontal accuracy with a radial RMSE of 26 cm .
(3) Parcel outline data were obtained from LACDPW to support the landcover classification and resistance parameterization shown in Fig. 4.
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Fig. 4. Landcover classification and Manning n value, and location of catch basins and storm drain outlets.
(4) Contour maps depicting the reservoir and dam breach geometry, as shown in Fig. 3, were obtained from the CADWR report . The contour intervals were 6 m (20 ft) for the reservoir geometry and 3 m (10 ft) for the breach geometry. These data were scanned, geo-referenced, and digitized using polylines in ArcGIS 9.2 (ESRI, Redlands, CA).
(5) Catch-basin locations in the study area were obtained from the City of Los Angeles Bureau of Engineering and are shown in Fig. 4. Catch basins collect water from street gutters and divert it to sub-surface pipes that transfer flow to Ballona Creek. A field survey by UC Irvine personnel was completed to verify the existence of these basins as of 1963 and to characterize the type and size. Catch basins were largely of the curb-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 found and noted.
(6) Flood extent data, shown in Fig. 1, were obtained from a USACE report . This consisted of a map with hand-drawn markings of flooding. This was scanned, geo-referenced, and digitized using polylines in ArcGIS 9.2 (ESRI, Redlands, CA).
(7) Ballona Creek stream flow data at the gauging station shown in Fig. 1 were obtained from a USACE report . This is limited to the following information: drainage water first arrived at 14:10 PDT, a peak flow of approximately occurred at 16:40, flow exceeded between 16:10 and 17:00 and decreased to by 19:10.
2.4. Terrain modeling
ArcGIS 9.2 (ERSI, Redlands, CA) was used to merge the LiDAR DTM and reservoir and breach contour data into a Triangular Irregular Network (TIN) reflective of 1963 conditions, as shown in Fig. 3. Contours were available only as printed drawings or plates, so each image was scanned and geo-referenced. Contours were then manually digitized as polylines and their nodes converted to x, y, z points. The LiDAR DTM was also converted from a raster format to x, y, z points, and a combined set of x, y, z points was obtained by filtering LiDAR points in areas of overlap. Finally, the merged set of points was converted to a TIN DTM as shown in Fig. 3.
Street flows are important in urban flood hydrology  and , and we are assuming that 2006 terrain data provide a good description of 1963 terrain heights in the vast majority of the flood zone. This appears justified based on a comparison of modern digital orthophotos and historical aerial photos (not shown), which shows that the street layout has not changed. The photographic comparison also 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-water equations were solved using BreZo, a Godunov-based finite volume code that runs on an unstructured mesh of triangular cells similar to a TIN . The TIN computational mesh is different from the TIN DTM shown in Fig. 3, as it is configured for model efficiency, accuracy, and stability purposes. However, elevation data for the former is extracted from the latter.
BreZo uses an approximate Riemann solver to estimate mass and momentum fluxes. This accommodates mixed flow regimes common to dam-break floods and handles wetting and drying problems without loss of stability, accuracy or conservation  and . BreZo has been previously validated in a rural dam-break study , and applied to simulate urban flooding caused by overtopping of a culvert , but has not previously been applied to an urbandam-break application such as Baldwin Hills.
The TIN computational mesh used by BreZo defines ground height at vertices and assumes that ground height varies linearly within each triangle; this achieves second-order accuracy relative to terrain height truncation errors. To minimize numerical dissipation, BreZo switches locally between two first-order accurate methods of variable reconstruction . In practical test cases, the combination of a second-order accurate terrain model and a first-order accurate flow solver has been found to strike the best balance between numerical error and computational effort. In contrast to earlier versions of BreZo which used a global time step , here a three-level local time stepping (LTS) scheme is used to reduce run times  as in the study by Schubert et al.. Cells are assigned a time step of either , or 4Δt; the largest that satisfies the Courant, Friedrichs, Lewy (CFL) condition is used. To maintain conservation with LTS, flux calculations and solution updates must be carefully sequenced but otherwise there is no loss of accuracy compared to global time stepping schemes.
Curb inlets in the study area, shown in Fig. 4, divert surface water through sub-surface pipes to Ballona Creek. To account for this, the continuity equation solved by BreZo was modified with a set of point sink and source terms corresponding to curb inlets and sub-surface pipe outlets, respectively. Each time step, the volumetric flow rate into each curb inlet was computed with a modified weir equation as follows,
(1) 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 along the curb, and CD is a dimensionless discharge coefficient set by trial and error to 0.5. This selection was motivated by a local experimental study by the City of Los Angeles Bureau of Engineering , of catch-basin inflows, which indicates that CD falls between 0.1 and 0.5. Values of ho and L were measured for several catch basins by UCI personnel as described in Section 2.3. Time integration of the sink/source terms was implemented with an explicit, fractional step method. In the first step, the continuity equation was updated to account for all fluxes of surface water. In the second step, the continuity equation was updated to account for each source/sink term using the result of the first step to evaluate the right hand side of Eq. (1). Note that many of the curb inlets share the same outlet along Ballona Creek, as a result, a few cells are updated multiple times each time step. For stability purposes and to avoid negative depth predictions, the volumetric flow rate from each storm drain was limited so no more than 50% of the available volume could be withdrawn in a single time step.
The preceding approach is proposed as a simple alternative to address the problem of catch-basin diversions in 2D dam-break FIM, compared to a fully coupled 1D/2D solver. There are clearly limitations to the method, for example there is no restriction to flow through the network (only flow into the network), the model cannot predict sewer surcharging which is often a driver of urban flooding, and the model assumes that flow is instantaneously routed from catch basins to the storm drain outlet. Further, this type of approach should not be used to design sub-surface storm drains. However, dam-break studies have rarely considered sub-surface storm drains on the grounds that sub-surface flow is a small fraction of overland flow. Hence, we utilize this relatively simple approach as a first step to judge the importance of sub-surface flows in an urban flooding scenario. The overall complexity of the 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 flexible and powerful open source tool for 2D constrained Delaunay mesh generation . The input to Triangle is an ASCII file that defines the boundary of the domain with a list of vertices and line segments, what graph theorists call a Planar Straight Line Graph (PSLG). Triangle enforces user supplied angle and cell area constraints for mesh quality purposes. Area constraints control the resolution of the mesh, and variable resolution meshes can be easily created. Further, meshes can be customized to study sites by aligning edges with building walls or street curbs, which improves model accuracy with relatively coarse meshes . However, nearly uniform meshes were utilized in this study for simplicity and we do not attempt to resolve buildings with the mesh. This would require too fine a resolution for the available computational resources. Instead, the mesh was designed to resolve street depressions in the land surface, which are thought to act as channels during urban flooding, and to resolve heterogeneity in landcover (roads, developed parcels, vegetated open space, etc.) which affects flow resistance.
Once a few preliminary runs had been completed to identify the impacted region, a PSLG was circumscribed around the area of interest to define the boundary (Fig. 1) and support mesh generation. The boundary was set back sufficiently far from the flood zone that boundary conditions became irrelevant, with one exception. Ballona Creek directs water south from the study area towards the Pacific Ocean. Here, a non-reflecting boundary condition was used so water can freely exit . The boundary was placed downstream of the gauging station, where data are available, to facilitate comparisons between predictions and observations of stream flow.
Meshes were generated using a 30° minimum angle constraint and a dual-zone maximum area constraint. An area constraint of was used in a region surrounding the breach, due to its narrow cross-section, and an area constraint of either 9.3, 37.2, or was used everywhere else. This created a set of three meshes, respectively: Mesh A with 1,337,155 triangles or cells, Mesh B with 336,681 cells and Mesh C with 86,835 cells. The resolution of these meshes, taken as the square root of the average cell area, corresponds to 2.5, 4.9, and 9.6 m, respectively. Typical street widths in Los Angeles County are 18 m (60 ft). Hence, Mesh A, B, and C resolve streets with at least 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 Mesh A, B, and C, respectively. Most predictions in the study utilize Mesh B, because it is fine enough to resolve street depressions but coarse enough (336,681 cells) for execution on a desktop computer in a few hours. Mesh A allows us to report the convergence error of Mesh B, and Mesh C allows us to report the consequences of an overly coarse mesh that does not accurately depict street depressions. Following mesh generation, ground elevation at mesh vertices was interpolated from the merged TIN DTM. Note that TINs utilize a linear reconstruction of terrain height which is the basis for interpolating ground elevation at mesh vertices.
A Manning n was assigned to each cell in accordance with a simple landcover classification that was manually created from parcel outlines and digital orthophotos supplied by LACDPW. Parcel outlines were used as a mask to define the road network, and digital orthophotos were used to manually outline apartment building footprints, asphalt parking lots and vegetated open space areas which, based on the review of a historical orthophoto , were confirmed to exist at the time of the flood. As shown in Fig. 4, Manning n values of 0.014, 0.016, 0.013, 0.30, and were assigned to roads, channels, reservoir, developed parcels with buildings, and vegetated open space, respectively. A value of is typical of asphalt pavement, is typical of concrete channels with gravel and sediment along the channel bottom, is typical of smooth concrete surfaces, and corresponds to pasture with high grass . This was chosen because the vegetated areas included many shrubs and small trees. Further, a value of has been recommended for developed parcels with buildings , but this would likely depend on the flow obstruction. Both historical and modern photos show that at least 50% of parcel footprints are occupied by buildings.
2.7. Initial conditions
The failure sequence described in Section 2.2 and shown in Fig. 2 indicates that the breaching process began gradually before 15:00 and effectively ended at 15:30 with a major widening. Further, LADWP officials estimated that storage in the reservoir was approximately half its capacity at 15:30, ca. (ca. 449 acre-ft). However, the volume at the beginning of the major breaching processes, around 15:20, is not clear. The volume at this time is important as it represents what flooded north into the study area. Approximately (790 acre-ft) were stored at the beginning of the day, but LADWP took a number of steps to lower the level prior to catastrophic dam failure.
Using design drawings of the reservoir which include the slope and height of the dam face, and photogrammetric scaling techniques, the height of the reservoir at 15:20 and 15:30 was estimated from the photographs shown in Fig. 2. Results suggest that the reservoir elevation was between 140.9 and 141.5 m (462 and 464 ft) at 15:20 and between 138.7 and 139.3 (455 and 457 ft) at 15:30. Based on the geometry of the reservoir, this corresponds to at 15:20 and at 15:30. Note that the volume at 15:30 is consistent with the LADWP  report that the reservoir was “half full” at 15:30. Further, this analysis suggests that the combination of controlled and uncontrolled flows sent approximately (186 acre-ft) from the reservoir before catastrophic failure.
After careful analysis of all available information, breaching of the dam was modeled as a two-stage process. In the first stage, the breach was assumed to instantaneously open at 15:20 to a trapezoidal shape approximately 21.3 m (70.0 ft) wide at the crest of the dam and 7.6 m (25.0 ft) at the base of the dam. This roughly approximates the breach geometry around 15:20. In the second stage, which was assumed to instantaneously occur at 15:30, the breach was assumed to take on the final geometry reported by CADWR and shown in Fig. 2 and Fig. 3. The reservoir elevation at 15:20 was taken as 141.1 m (463.0 ft) based on the 15:20 reservoir photo; this represents the initial condition.
BreZo was run for 10 min using the first breach geometry, and restarted using the second breach geometry at 15:30. BreZo predicted a reservoir volume of at 15:30; this is consistent with the 15:30 reservoir photo and the LADWP assessment of a half full reservoir. BreZo was integrated for a total period of 3 h to simulate the flood. The solution was saved at 4–8 min intervals for analysis purposes, the maximum depth and velocity was saved in each computational cell, and the discharge in Ballona Creek and through the storm drain system was also saved.
3.1. Validation of the flood prediction
The progression of dam-break flooding predicted by the model is shown in Fig. 5 from 15:20 onward. This shows the flood quickly funnelled north through the steep canyon below the dam, reaching the relatively flat terrain north of Coliseum St. by 15:25. Over the next 5 min, the flood pushed further north to Rodeo Rd. and spread laterally. By 15:30, the flood is shown to be fingering west along Rodeo Rd. and flooding those streets perpendicular and parallel to it. By 15:54, it appears that flood water reached Ballona Creek, which then directed water south towards the Pacific Ocean. Fig. 5 shows water in Ballona Creek prior to the arrival of surface flows along Rodeo Rd. which is due to routing through storm drains. USACE  reported a small baseflow in Ballona Creek prior to the dam-break flood, and attributed this to storm drain routing of the initial dam leakage because Ballona Creek is typically dry in the absence of rainfall.
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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.)
Eastward flooding is also evident in Fig. 5, for example between 15:38 and 15:54, the model shows that flood water subsequently spread north into the junction of Jefferson and Exposition Blvd., and southeast along Santa Barbara Ave. Fig. 4 shows a number of catch basins along Jefferson and Exposition Blvd., and as water moved relatively slowly into this area compared to the westward flooding, these helped to prevent further flooding northward.
There is evidence of flood recession by 16:18 as terrain in the eastern portion of the flood zone is shown to be drying. Recession of the flood becomes clearly evident by 17:02 and nearly 90 min later at 18:30, the situation changes very little which reflects a relatively slow recession of the flood compared to the initial surge.
As described in Section 2.6, Mesh B was designed to validate the model. To quantify the accuracy of the flood extent prediction, a fit measure FE=0.76 was computed, which compares favorably with other FIM studies . The fit was computed as follows ,
(2) where E indicates flood extent (m2) and P and M correspond to prediction and measurement, respectively. The symbol ∩ indicates the intersection of two domains, and represents the union of two domains.
Fig. 7a presents predicted (labeled “Run 1”) and observed stream flow in Ballona Creek. Error bars on the observed stream flow data correspond to a 10% level of uncertainty, which is a rough estimate typical of stage-discharge errors. A fit measure for the peak stream flow FQ=1.08 was computed as follows,
(3) where Q indicates peak stream flow (m3/s) at the gauging station and P and M are the same as in Eq. (2). This is within the assumed level of uncertainty (ca. 10%). A fit measure for the prediction of travel time FT=1.06 was also computed as follows,
(4) where T represents the time elapsed from 15:20 until peak flow at the gauging station. Note that for all three fit measures, F=1 corresponds to perfect agreement. Furthermore, for FQ and FT, a value greater than one indicates an over-prediction and a value less than one indicates an underprediction. Hence, Run 1 slightly overpredicts the peak stream flow and travel time. Further, the model appears to more accurately predict the rising limb of the hydrograph than the falling limb. The model over-predicts stream flow at 17:00, although between 18:00 and 19:00 the prediction is again consistent with observations.
The flood extent predictions shown in Fig. 6 and the stream flow predictions shown in Fig. 7a clearly validates the 2D model formulation, configuration, and parameterization. Run 1 does benefit from calibration; CD values of 0.1, 0.3, and 0.5 were tested to arrive at 0.5. However, the notion of calibrating and validating model parameters should not be confused with the validation of a modeling approach.
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Fig. 6. Flood extent predictions for Runs 1–12. White outline represents observed flood extent.