Advances in Water Resources



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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 3.1Table 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: , and FT. Run 1 represents the base case presented in Section 3.1.



Run

Mesh

Manning n

Breach process

Water level (m)

DTM

Catch basin CD

Comment

FE

FQ

FT

1

B

Distributed

2 stage

141.20

1.5 m LiDAR

0.50

Base case

0.76

1.08

1.06

2

A

Distributed

2 stage

141.20

1.5 m LiDAR

0.50

Finer mesh

0.79

1.15

0.94

3

C

Distributed

2 stage

141.20

1.5 m LiDAR

0.50

Coarser mesh

0.63

0.72

1.33

4

B

Distributed

2 stage

141.20

9.1 m LiDAR

0.50

Coarsened DTM

0.71

1.11

1.02

5

B

Distributed

2 stage

141.20

10 m NED

0.50

National DEM for USA

0.47

1.07

1.05

6

B

Distributed

2 stage

141.20

30 m SRTM

0.50

Global DEM

0.31

0.00

NA

7

B

Uniform

2 stage

141.20

1.5 m LiDAR

0.50

Uniform n

0.73

0.59

1.86

8

B

Distributed

2 stage

141.20

1.5 m LiDAR

0.30

Less flow to catch basins

0.69

0.98

1.09

9

B

Distributed

2 stage

143.90

1.5 m LiDAR

0.50

Higher reservoir level

0.68

1.37

0.95

10

B

Distributed

1 stage

141.20

1.5 m LiDAR

0.50

Breach width = dam height

0.73

1.05

0.80

11

B

Distributed

1 stage

141.20

1.5 m LiDAR

0.50

Breach width = 2 × dam height

0.68

1.14

0.84

12

B

Distributed

1 stage

141.20

1.5 m LiDAR

0.50

Breach width = 3 × dam height

0.65

1.16

0.82


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 over-prediction 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 over-predicted 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 non-physical 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=1.86Fig. 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 urbansettings. 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 (FE0.8). 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 over-predicted. 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.
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