Advances in Water Resources
Volume 32, Issue 8, August 2009, Pages 1323-1335
doi:10.1016/j.advwatres.2009.05.008 | How to Cite or Link Using
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Two-dimensional, high-resolution modeling of urban
dam-break flooding: A case study of Baldwin Hills,
California
Humberto A. Gallegosa, Jochen E. Schubertb and Brett F. Sandersa,
,
,
a
Department of Civil and Environmental Engineering, University of California, Irvine, CA 92697-2175,
USA
b
IESSG, 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.
Abstract
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.
Keywords: Urban hydrology; Flood inundation modeling; Shallow-water equations; Dam-break;
Finite volume method; DTM; High resolution; LiDAR; National Elevation Data; Shuttle Radar
Topography Mission
Article Outline
1. Introduction
2. Materials and methods
2.1. Site description
2.2. Failure sequence
2.3. Data sources
2.4. Terrain modeling
2.5. Flood inundation modeling
2.6. Mesh generation and model parameterization
2.7. Initial conditions
3. Results
3.1. Validation of the flood prediction
3.2. Sensitivity analysis
4. Discussion
5. Conclusions
Acknowledgements
References
1. Introduction
Urban flooding is becoming more frequent as a consequence of several factors including
continued watershed development with impervious surfaces[15], population growth which places
increasing pressure on communities to develop in flood prone areas [6] and [22], climate change which
has magnified the intensity of rainfall [19], 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 [37]. Furthermore, the consequences of flooding are greater
in urban versus rural sites due to the relative economic value and population density [22] and [33].
To manage the risk of flooding, damage assessments are needed and should consider not only
economic but also social and environmental factors [41]. 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) [1], [2] and [29]. 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 twodimensional (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 [44], [6] and [33], resistance
parameterization [26], [6] and [22], role of sub-surface storm drains [15], tradeoffs between shallowwater and diffusive wave routing schemes [17], and models for the impact of buildings on flood
dynamics [44], [6], [20], [33] and [27] including use of porosity
methods[44], [45], [12], [25], [34] and [31]. 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 [6] and [17] using structured grids or a variable resolution unstructured
mesh that is constrained by building walls [33].
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. [26]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. [27] 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 [6], [17] and [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] 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 [4] 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., [26], [6], [20], [17] and [33]). 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 [43], [33] and [30].
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 [36] and [38].
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) [38], and (2) stream flow data for the main
channel below the flood zone, Ballona Creek [38]. To the knowledge of the authors, this represents the
first attempt to validate a 2D urban dam-break flooding model 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 [36]. 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.
Full-size image (173K)
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.
Full-size image (161K)
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 [8].
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 [36].
Structural damage included 41 homes destroyed and 986 houses, 100 apartment buildings, and 3000
automobiles damaged [40]. 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) [36] who reported that earth
movement under the reservoir cracked the asphaltic lining and subsequent leakage under pressure
scoured the earthen fill within the embankment [36]. 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 [23].
Full-size image (158K)
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 georeferencing purposes. The orthophotos exceed NSSDA standards for horizontal accuracy with a radial
RMSE of 26 cm [24].
(3) Parcel outline data were obtained from LACDPW to support the landcover classification and
resistance parameterization shown in Fig. 4.
Full-size image (106K)
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 [36]. 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 subsurface 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 [38]. 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 [38]. This is limited to the following information: drainage water first arrived at 14:10
PDT, a peak flow of approximately
exceeded
to
occurred at 16:40, flow
between 16:10 and 17:00 and decreased
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 georeferenced. 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 [17] and [33], 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 [5]. 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 [3] and [5]. BreZo has been previously
validated in a rural dam-break study [4], and applied to simulate urban flooding caused by
overtopping of a culvert [33], but has not previously been applied to an urban dam-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 [5]. 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 [5], here a three-level local time stepping (LTS) scheme is used to
reduce run times [30] as in the study by Schubert et al.[33]. 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 [7], 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 [32]. 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 [33].
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 [28]. 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 [36], 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 [9]. 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 [39], 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 [8] 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. Results
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 [38] reported a small baseflow in Ballona Creek prior to the dambreak flood, and attributed this to storm drain routing of the initial dam leakage because Ballona Creek
is typically dry in the absence of rainfall.
Full-size image (172K)
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 [14]. The fit was computed as follows [14],
(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.
Full-size image (190K)
Fig. 6. Flood extent predictions for Runs 1–12. White outline represents observed flood extent.
Full-size image (71K)
Fig. 7. Ballona Creek hydrograph predictions for Runs 1–12 at gauging station shown in Fig. 1,
compared to observations.
Model predictions also highlight the complexity of urban dam-break flood flows: flow is highly
unsteady and transported along preferential flow paths (streets) where terrain is depressed like a river
thalweg and resistance is minimal due to a relatively smooth surface (concrete or asphalt) compared to
natural surfaces. Previous studies have also emphasized the importance of street flows, and the need
to accurately depict street geometry and resistance within the model framework [33].
These results suggest that a rich set of urban geospatial data is needed to accurately depict
urban flooding, including high-resolution terrain data, spatially distributed resistance parameters,
storm drain network data, knowledge of the reservoir level at the time of failure, as well as the breach
geometry. Advances in remote sensing and information technologies will undoubtedly make some of
these data more readily accessible in the future, while other factors such as the breach geometry will
rarely be known a priori for predictive modeling purposes. Next in Section 3.2, several additional model
simulations are presented to examine the relative importance of these data sources and modeling
techniques. The sensitivity of model predictions to these factors are measured, and the most critical
aspects are identified along with modeling guidelines for 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 the 12 runs, labeled Runs 1–12. Each run differs from Run 1 in only one
respect 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 averaging the 1.5 m (5 ft) LiDAR DTM, Run 5 uses 1/3 arc-s
(10 m or 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
. This value (coincidentally, perhaps)
represents: (a) the spatial average of the distributed Manning n shown in Fig. 4 and (b) the effective
value of Manning n resulting from the application of Hejl’s method [13], which considers the fraction of
the floodplain available for conveyance (i.e., not blocked by buildings).
• Run 8 uses a smaller catch-basin inflow coefficient, CD=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=H, 2H,
and 3H, respectively, where H is the height of the dam, and a 1:1 side slope.
Table 1.
Attributes of model runs and performance metrics:
presented in Section 3.1.
, and FT. Run 1 represents the base case
Wat
er
lev DTM
el
(m)
Catc
h
basi
n CD
Comment
FE
FQ FT
Me
sh
Manni
ng n
Brea
ch
proc
ess
1
B
Distrib
uted
2
stag
e
141
.20
1.5 m
LiDAR
0.50
Base case
0.
76
1.
08
1.
06
2
A
Distrib
uted
2
stag
e
141
.20
1.5 m
LiDAR
0.50
Finer mesh
0.
79
1.
15
0.
94
3
C
Distrib
uted
2
stag
e
141
.20
1.5 m
LiDAR
0.50
Coarser mesh
0.
63
0.
72
1.
33
4
B
Distrib
uted
2
stag
e
141
.20
9.1 m
LiDAR
0.50
Coarsened DTM
0.
71
1.
11
1.
02
5
B
Distrib
uted
2
stag
e
141
.20
10 m
NED
0.50
National DEM for
USA
0.
47
1.
07
1.
05
6
B
Distrib
uted
2
stag
e
141
.20
30 m
SRTM
0.50
Global DEM
0.
31
0.
00
N
A
7
B
Unifor
m
2
stag
e
141
.20
1.5 m
LiDAR
0.50
Uniform n
0.
73
0.
59
1.
86
8
B
Distrib
uted
2
stag
e
141
.20
1.5 m
LiDAR
0.30
Less flow to catch
basins
0.
69
0.
98
1.
09
9
B
Distrib
uted
2
stag
e
143
.90
1.5 m
LiDAR
0.50
Higher reservoir
level
0.
68
1.
37
0.
95
10
B
Distrib
uted
1
stag
e
141
.20
1.5 m
LiDAR
0.50
Breach
0.
width = dam height 73
1.
05
0.
80
11
B
Distrib
1
141
1.5 m
0.50
Breach
1.
0.
R
u
n
0.
R
u
n
Me
sh
Manni
ng n
uted
12
B
Distrib
uted
Brea
ch
proc
ess
stag
e
1
stag
e
Wat
er
lev DTM
el
(m)
.20
LiDAR
141
.20
1.5 m
LiDAR
Catc
h
basi
n CD
0.50
Comment
FE
FQ FT
width = 2 × dam
height
68
14
84
0.
65
1.
16
0.
82
Breach
width = 3 × dam
height
Fig. 6 shows flood extent predictions corresponding to Runs 1–12, Fig. 7 shows hydrographs for
Ballona Creek, and Table 1 shows
, and FT. First consider the impact of mesh resolution. Fig.
6 shows that an increase in mesh resolution (Run 2, FE=0.79) improves the flood extent prediction very
slightly compared to Run 1 (FE=0.76). For example, south of Coliseum street, just to the east of the
primary flood path below the dam, there is a case of street flow that is more accurately depicted by
Run 2 than Run 1. Also, Run 2 more accurately depicts flooding at the junction of Jefferson and
Exposition Blvds. At the gauging station, Fig. 7a and Table 1 show that Run 2 leads to a 7% greater
peak stream flow, and 12% shorter travel time compared to Run 1. These differences are small
compared to the consequences of using a coarser mesh (Run 3). Run 3 shows a significant overprediction of flood extent in the northeast corner of the flood zone which leads to FE=0.63. Further,
peak stream flow is significantly under-predicted FQ=0.72 and the travel time is significantly overpredicted FT=1.33. Previous dam-break modeling studies with BreZo have shown predictions are
overly dissipative when the mesh is too coarse, causing an underprediction of peak stream flow and
flood propagation speed [4].
Consider now the source of terrain data. Fig. 6 and Table 1 show that coarsened LiDAR (Run 4), NED
(Run 5), and SRTM degrade the accuracy of flood extent predictions to different
extents:
, and 0.31 for Runs 4–6, respectively. Neither NED nor SRTM resolve
street-scale topographic variations, but NED resolves the larger scale features that appear to bound
the primary flood path north from the dam and west toward Ballona Creek. Where NED performs
poorly is in the northeast corner of the study site, where NED does not resolve street scale variations
in the terrain that appear to bound the flood zone. SRTM depicts relatively flat terrain with a nonphysical waviness that has been termed “radar speckle” [11] and [18], and predictions of flooding at
similar spatial scales have shown non-physical pools of water corresponding to local minima in the
DTM [29]. This pooling effect is evident in Run 6 shown in Fig. 6, and the flood extent prediction is
notably crude. However, in the canyon North of the dam, flood extent based on SRTM is little different
from Run 1 based on LiDAR. These results show that the DTM can have a significant effect on flood
extent accuracy, but interestingly, the impact on stream flow predictions at the gauging station are
relatively small with the exception of SRTM (Run 6), which does not resolve the geometry of the flood
control channel and therefore cannot support modeling of flow through it. Fig. 7b shows predicted and
measured hydrograph data, and Table 1 shows thatFQ and FT values across Run 1, Run 4, and Run 5
differ by at most 4%.
Fig. 6 also shows that a spatially uniform Manning n has relatively little impact on flood extent (Run 7),
particularly when compared to a smaller catch-basin discharge coefficient CD=0.3 (Run 8) 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 n leads to a significant under-prediction of peak stream
flow FQ=0.59 and over-prediction of travel time FT=1.86. Fig. 7d shows that an increase in the initial
reservoir height leads to an over-prediction of stream flow FQ=1.37 and a slight under-prediction of
travel time FT=0.95. Finally, Fig. 7d shows that a smaller 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, and all three single-stage breach scenarios show a greater flood extent than the
two-stage breach scenario used in Run 1. However, Fig. 7c shows that breach width has relatively little
impact on the stream flow at the gauging station even compared to the base case (Run 1).
4. Discussion
Every perturbation of the model set-up, with the exception of Run 2 (finer mesh) resulted in a larger
flood extent compared to Run 1. This was most notable in the northeast corner of the site where
flooding was incorrectly predicted north of Jefferson Blvd. Terrain is gently sloped to the northwest
here, so gravitational effects tend to stretch out the slightest over-prediction of flooding.
It appears that no aspect of the model set-up described here can be simplified without sacrificing either
flood extent or stream flow accuracy. The source and resolution of terrain data, reservoir volume,
breach configuration, computational mesh resolution, and sub-surface storm drains all affected flood
extent predictions by a similar amount. Resistance parameters and the reservoir volume affected
stream flow more than other factors.
Previous studies of dam-break flood modeling have noted an insensitivity of flood extent predictions to
resistance parameters [4], but stream flow predictions here show that distributed resistance
parameters are essential for accurately routing the flood across the street network and along the flood
control channel. Similar findings have resulted from modeling studies of rural flooding [16]. Further,
distributed resistance parameters are needed for local predictions of velocity [2] and [14] which may be
needed for damage assessments or predictions of sediment erosion and deposition.
Street widths appear to be a useful guide for selecting a mesh resolution. 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 good
predictions (FE=0.76) but Mesh C with a resolution of 9.6 m (1 cell across street) significantly degraded
flood extent accuracy (FE=0.63). Similarly, when LiDAR terrain resolution was coarsened to 9.1 m (Run
4), a loss of accuracy was also observed (FE=0.71) compared to the base case. These results show
that flow along street depressions in the land surface should be resolved to accurately depict flood
extent in urban settings. The meshing requirements may depend slightly on the mesh type (e.g.,
structured versus unstructured) and whether streets are aligned with the grid, so the common practice
of convergence testing is recommended to ensure that the mesh is sufficiently resolved.
What do these results say about good modeling practice for urban dam-break studies? Essentially,
high-resolution terrain data, aerial imagery and catch-basin data can and should be obtained to
support flood modeling because the potential exists for a high degree of accuracy (FE
0.8). NED
is attractive because it can be obtained without charge from the USGS. However, results here show
that flood extent is overpredicted using NED compared to LiDAR. Secondly, urban flooding is
characterized by preferential flow along streets; thus heterogeneity in flow resistance parameters
should be resolved to accurate depict overland flow. Third, flow through sub-surface storm drains can
be important but it may be possible to use a relatively simplistic modeling approach that essentially
transfers water from catch basins to the storm drain outlet. Otherwise, flood extent is likely to be overpredicted. Lastly, modelers should strive 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 time of failure, and its volume. Water level sensors, either in situ or remote (e.g,
satellite altimetry), stand to enable the real-time monitoring that could support real-time dam-break
emergency management efforts with flood forecasts. In case of real-time monitoring through satellite
sensors, spatial resolution and re-visit time are important factors and the Surface Water Ocean
Topography (SWOT) mission planned by NASA for the coming decade may provide critical
information [35]. The breaching process appears less important than the reservoir volume, but more
research should be done to evaluate the best strategies to couple modern breaching models
(e.g., [10] and [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 results of this study. High-resolution terrain data such as LiDAR are needed to
depict street depressions in the land surface, and an unstructured mesh similar to the one used here
should be refined with at least three cells across each street. Landcover heterogeneity should be
resolved to guide the spatial distribution of resistance parameters, and the location of catch basins and
storm drain outlets should be considered. Efforts to simplify model formulation or coarsen the
resolution generally cause an over-prediction of flood extent or inaccurate stream flow predictions. In
addition, poor flood extent accuracy was achieved with NED and SRTM terrain data. Further, a
spatially uniform resistance parameter lead to poor stream flow accuracy compared to a spatially
distributed parameter with the same mean value.
A simple method of routing flow through storm drains was introduced here and successfully
implemented. This involved pairs of sink and source terms in the continuity equation co-located with
catch basins and storm drain outlets, respectively. A modified weir equation was used to scale flow
into each catch basin, based on its height and curb length, and the model was validated with a
dimensionless discharge coefficient CD=0.5. This falls at the upper end of what is expected (0.1–0.5)
based on a laboratory study of catch-basin inflows by the City of Los Angeles.
Water volume in the reservoir at the time of failure is a critical factor for accurate flood predictions, and
over- or under-estimate of water levels will lead to an over- or under-prediction, respectively of flood
extent and stream flow, all else being equal. A less critical but still important factor is the breach
geometry. Use of a trapezoidal breach with a 1:1 side slope and a bottom width equal to the dam
height reproduced flood extent better than breaches with wider bottom widths. Given the sensitivity of
flood dynamics to the reservoir level, these results suggest that more detailed modeling of the breach
geometry can be justified if the reservoir level is known with a high degree of certainty. Finally, dam
safety programs should monitor water levels in real-time to support simulation based emergency
management of dam-break flooding.
Acknowledgements
This work was supported by a grants from the UC Water Resources Center (WR-1016), the National
Science Foundation (CMMI-0825165), and the UC Irvine Urban Water Research Center
(Contribution # 39) whose support is gratefully acknowledged. The authors also thank LADWP,
LACDPW, LAR-IAC, City of Los Angeles Bureau of Engineering, and USACE (Los Angeles District) for
their cooperation. Lastly, the authors thank the reviewers for constructive comments that improved the
paper.
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Corresponding author. Tel.: +1 949 824 4327; fax: +1 949 824 3672.