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IMPACT OF SPATIAL RESOLUTION ON DOWNSTREAM FLOOD HAZARD
DUE TO DAM BREAK EVENTS USING PROBABILISTIC FLOOD MODELING
Ebrahim Ahmadisharaf1, Md Nowfel Mahmud Bhuyian2, Alfred Kalyanapu3
Abstract
With up to 14,000 high-hazard potential dams in the US, a dam break is a serious safety
hazard for downstream locations and an operational concern for dam managers. Dam break
simulation using computer-based flood models require topography, generally represented
using digital elevation models (DEM) as a significant input which may affect the model
accuracy. Until recently, most flood model simulations were conducted deterministically without
incorporating uncertainties from model parameters. A clear understanding on the spatial
resolution in a probabilistic context by incorporating uncertainties in model parameters such as
dam break hydrographs, is needed for comprehensive dam break modeling analysis. The
objective of this study is to address the impact of spatial resolution on the relative accuracy
of downstream flood hazard after a dam break event. It is hypothesized that higher spatial
resolution will significantly increase the model predictive ability and the accuracy of flood
hazard maps. The current study employs a two-dimensional (2D) flood model, Flood2D-GPU
in a probabilistic framework to investigate these spatial resolution impacts by applying dam
break simulations on Burnett Dam near Asheville, NC. The dam break hydrograph is chosen
as the uncertain parameter as it adds greater source of uncertainties in most situations. Using
GoldSim®, Monte Carlo modeling software, 99 stochastic dam break hydrographs representing
various possible scenarios are generated. These hydrographs are input into Flood2D-GPU to
produce probability weighted flood hazard maps. The probabilistic simulations are carried out
for 9m, 31m, 46m, 62m and 93m spatial resolutions. The results indicate that increasing the
resolution from 93m to 9m causes a slight 0.8% increase in overall flood hazard extent.
Although, resolution improvement from 93m to 31m leads to increase in high-danger zone by
8.4% agreeing with the hypothesis. Analysis of relative hazard underestimation reveals that
31m grid resolution minimizes this parameter and thus is recommended for the study area.
However, the results cannot be replicated to other areas and further analyses are required to
confirm the findings of current study. The outcomes of this study will assist dam break
modelers to enhance their Emergency Action Plans by providing recommendations for suitable
spatial resolution and to avoid increased modeling time.
Key Words: Spatial resolution, Flood2D-GPU, Monte Carlo Simulation, GoldSim®,
Probabilistic flood modeling, Flood hazard.
Introduction
Dam break event is a serious concern for floodplain managers all over the world. According to
-
1 PhD Student, Civil and Environmental Engineering Department, Tennessee Technological University,
eahmadish42@students.tntech.edu
2 MS Student, Civil and Environmental Engineering Department, Tennessee Technological University,
nowfel_mahmud@yahoo.com
3 Assistant Professor, Civil and Environmental Engineering Department, Tennessee Technological University,
akalyanapu@tntech.edu
2
hazard-potential dams in the US (USACE, 2013). The failure of these dams may result in a
high amount of social, environmental and economic damages. According to the Association of
State Dam Safety Officials (ASDSO), repair costs are estimated to be $50
billion and $16 billion investment is needed to repair high hazard potential dams (American
Society of Civil Engineers (ASCE), 2009). With the ASCE rating the current conditions in the
dam hazards
such as dam breaks.
Flood models are important tools in simulating a dam failure event. Available flood
models can be generally categorized into one-dimensional (1D), two-dimensional (2D) and
coupled 1D-2D models. Dam break modeling using these computer-based flood models
require terrain data which are generally represented using digital elevation models (DEM). 1D
models cannot provide sufficiently accurate inundation mapping results due to inaccuracies in
cross-section discretization and thus disabilities in flow representation in the floodplain such as
lateral flow diffusion (Kalyanapu et al., 2011; Qi and Altinakar, 2012). 2D models have
addressed this drawback by a higher order of topographic representation, desirable flood
pathways in the simulations as well as existing and planned structures (Kalyanapu et al.,
2011). Multiple sources of uncertainty are involved in dam break flood hazard mapping
problem. Previous studies generally indicate that the spatial resolution affects the model
accuracy. There have been some efforts on exploring the scaling impacts on flood modeling
results. Hardy et al. (1999) showed that spatial resolution causes a wide variation in model
performance and inundation extent predicted by 2D TELEMAC-2D model (Hervoeut and Van
Haren, 1996; Bates et al., 1995). Horritt and Bates (2001) investigated the effects of scaling
properties on a 1D LISFLOOD-FP model (Bates and De Roo, 2000) performance in inundation
mapping. Resolutions of 1000m to 10m were analyzed and the results showed that the
maximum model performance is at 100m spatial resolution and 500m resolution proved to be
sufficient for water level prediction. Cook and Merwade (2009) indicated that higher spatial
resolution and vertical accuracy of terrain model reduces the predicted inundation area using
1D HEC-RAS model (USACE, 2006) and 2D FESWMS model (Federal Highway
Administration (FHWA), 2002). Nevertheless, most of the flood simulations were conducted
based on single parameter set for a single flood simulation or limited number of simulations
without incorporating uncertainties from model inputs. Hence, a clear understanding on the
spatial resolution in a probabilistic context by incorporating the model parameter uncertainties
such as dam break hydrographs is needed for comprehensive dam break analysis. This is
because, as spatial resolution changes, it will affect the inundation extent and bulk flow
characteristics which accordingly influence the floods hazard extent. In this study the flood
hazard is defined as the potential adverse impact on human life and any downstream
developments if a dam fails (ACER, 1988). For any location, flood hazard is characterized as
low hazard, judgment and high hazard zones, depending the velocities and flood depths
simulated at that location.
The objective of this study is to address the impact of spatial resolution on the relative
accuracy of downstream flood hazard after a dam break event. It is hypothesized that higher
spatial resolution will significantly increase the model predictive ability and the accuracy of
flood hazard maps. Supported with a probabilistic dam break hydrograph simulator, numerous
dam failure scenarios are generated to incorporate various uncertainties such as time to
failure, breach width, breach side slope and final elevation of breach. The hydrographs are
employed as inputs to the 2D flood model to simulate dam break events. The general
procedure of the study by Kalyanapu et al. (2012) is followed here for probabilistic flood hazard
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estimation and extended to dam break simulation. Downstream of the dam is classified into
different hazard zones for each spatial resolution based on the flood modeling results. This
investigation is performed on the Burnett Dam located in Swannanoa River watershed near
Asheville, North Carolina. The presented framework is flexible and can also be performed for
similar studies at different locations.
Methodology
A probabilistic dam break modeling framework is used in this study which contains the
following three modules: 1) Monte Carlo Simulation (MCS); 2) Geospatial flood modeling; and
3) Flood hazard analysis. The framework is used to model dam break for five different DEM
spatial resolutions and relative accuracy of various categories of flood hazard extent at these
spatial resolutions is analyzed. Figure 1 visualizes the schematic of framework used in this
study.
Figure 1. Probabilistic flood hazard framework schematic
In the MCS module, a dynamic simulation software GoldSim® is used to produce
stochastic dam break hydrographs based on dam break features in which each parameter is
characterized by a stochastic variable. Normal Probability Density Function (PDF) is applied
for time to total failure, breach width and final elevation of breach, and Discrete PDF is used for
breach side slope. The PDFs are visualized in Figure 2 (a) to (d). The methodology presented
by Fread (1988) is adopted herein to generate flow hydrographs which are presented in the
equations 1 to 3:
(1)
(2)
4
(3)
In which Qb is breach outflow, Cv is approach velocity correction factor, Ks is weir submergence
correction factor, bt is instantaneous bottom width of the breach, hw is water surface elevation,
hbt is instantaneous elevation of the breach bottom, bf is final bottom width of the breach, hd is
elevation of the top of the dam, t is time from beginning of the breach, is total failure time and
is a constant between 1 and 4. It is to be noted that the units should be in US Customary
System. The resulting hydrographs are used as randomly varying inputs to a 2D flood model
since they generally add most uncertainties into dam break modeling.
(a)
(b)
(c)
(d)
Figure 2. Probability distribution curves of: a) time to total failure; b) final bottom width of the
breach; c) final elevation of breach bottom; and d) side slope of breach width
In the geospatial flood modeling module, a 2D unsteady numerical flood model,
Flood2D-GPU (Kalyanapu et al., 2011) is employed. The model was coded in NVIDIA's CUDA
programming environment and solves the non-linear shallow water equations using a first-
order accurate upwind difference scheme to generate flood depths and velocities. Primary
datasets needed are topography, surface roughness and flow hydrograph.
A flood model realization is generated for each randomly sampled hydrograph. The
flood inundation boundary is delineated by calculating the water depth at each grid cell and
identifying inundated cells (i.e. non-zero floodwater depth) using a GIS-based post-processing
framework. Inundation probability is determined as the number of times a grid cell is flooded
divided by the total number of flood simulations (Kalyanapu et al., 2012). The outputs of this
module are GIS raster flood probability map as well as flood depth and velocity for each
stochastic hydrograph.
In the flood hazard analysis module, probabilistic spatial flood hazard maps are
generated. The maximum flood depth and velocity are estimated from flood modeling module
and are multiplied with the flood probability to create probability weighted flood hazard maps
(Kalyanapu et al., 2012). Depth-velocity curves (Figure 3), derived from Assistant
5
Commissioner Engineering and Research (ACER) (1988) are used to determine the hazard
intensity. The flood hazard level is classified into three different groups of low-danger,
judgment and high-danger zones. In the low-danger zone, the possible lives-in-jeopardy is
assumed to be zero. In the high-danger zone, it is assumed that all lives are in threat. The
judgment zone represents a zone where the lives-in-jeopardy is considered to be uncertain
and may vary between zero to total lives in threat.
Figure 3. Floodwater depth velocity hazard classification. Source: ACER (1988)
Case Study
The impact of spatial resolution on dam break is investigated on Burnett Dam in Swannanoa
River Watershed located in Buncombe County, NC. Burnett dam is a part of Asheville
municipal water supply, has reservoir area of 7 mi2, and a drainage area of 22 mi2. The total
capacity at crest of spillway is 11,600 ft3/s-day and the sea-level altitude is 2601 ft. It is
selected in this study because of its proximity to urban areas including cities of Swannanoa,
Black Mountain, and Asheville along the Swannanoa River.
There was no prior information on PMF studies on Burnett Dam to compare the
performance of Flood2D-GPU to previous studies. To address this issue, Taum Sauk Dam
break event of 2005 was used to calibrate the Flood2D-GPU. Taum Sauk dam is a
hydroelectric plant located in Reynolds County, MO. It failed on December 14th 2005 due to
prolonged minor leaks. This failure event was simulated by Flood2D-GPU using 9m DEM
accuracy and potential applicability to other case studies. Thus it is applied for the Burnett
Dam break probabilistic simulations in this study.
DEM of 9.43m spatial resolution for the area was generated from the National Map
website (http://nationalmap.gov/). Furthermore, 31.03m, 46.56m, 62.07m and 93.11m DEMs
were synthesized based on 9.43m spatial resolutions using nearest-neighbor resampling
method. Hence, total of five DEMs were produced for the analysis. These resolutions will be
henceforth referred to as 9m, 31m, 46m, 62m and 93m in the remaining of the paper.
Topographic slopes of each DEM were generated using GIS Slope Function. Range of slope
variation is represented in Figure 5. The minimum slope is zero in each resolution and the
maximum changes from 88.1% at 93m resolution to 342.5% at 9m spacing with an increasing
6
trend. 1 is used to represent the vegetation and short
grass in the study region (McCuen, 1998).
Figure 4. Location of Burnett Dam in Swannanoa River
Figure 5. Maximum ground slope variation in different spatial resolutions
Results and Discussion
As discussed in the methodology section, using 99 randomly produced hydrographs by
GoldSim model as inputs to Flood2D-
GPU, probabilistic dam break simulations were performed. Raw outputs from the model were
processed within GIS environment for 9m, 31m, 46m, 62m and 93m spatial resolutions. Figure
0
50
100
150
200
250
300
350
400
93
62
46
31
9
Slope (%)
Spatial Resolution (m)
7
6 shows change in the run time with respect to number of computational cells. Higher number
of computational cells obviously represents finer spatial resolution. Total run time remarkably
increases by resolution refinement as expected (Kalyanapu et al., 2011). The increase in the
run time can be well represented by a linear equation where correlation coefficient (R2) is
99.96%. Regression analysis reveals that average of 0.4 second computational time is
required for each cell. In addition, computational times show a significant improvement
compared to a regular CPU-based 2D flood model. Same simulation would require
approximately up to 979, 147, 70, 53 and 43 days for 9m, 31m, 46m, 62m and 93m spatial
resolutions, respectively when implemented in the CPU-based version of the flood model
(rough CPU estimates based on Kalyanapu et al., 2011).
Figure 6. Maximum ground slope variation in different spatial resolutions
Preliminary outputs of Flood2D-GPU including inundation depth and velocity are
discussed here. Maximum inundation depth ranges between of 18.4 m to 31.5 m by varying
grid resolution. Flood depth of higher than 21.5 m is only observed at 9m resolution,
immediately downstream of the Burnett Dam where steep slopes are existed. This hilly area
has average slope of 9.9% and the higher the slope, the greater depth will occur. The lowest
maximum flood depth is 18.4 m and occurs at 31m resolution. Higher inundation depths than
this value often occur at steep slopes at all of the other resolutions. An interesting point that
can be concluded is that with steeper slopes, the difference between estimated flood
parameters (depth and velocity) by different DEM resolutions intensifies. Therefore,
significance of selecting a suitable DEM is highlighted in the regions with steep slopes.
Figure 7 presents the inundation area within the simulation domain. The predicted
inundation area decreases from 18.4% to 7.8% with grid resolution refinement from 93m to
9m. This is in agreement with the results of Cook and Merwade (2009) for the deterministic
simulations by both 1D HEC-RAS and 2D FESWMS models. The main reason of reduction in
inundation area is due to better terrain representation by higher resolution and loss of
topography in lower grid spacing. To give a better insight about relative change in the
inundation maps at different spatial resolutions, F statistic (Bates and De Roo, 2000) is used
as measure of fit. The parameter F can be computed by Equation 4:
(4)
0
50
100
150
200
250
300
350
0 1000000 2000000 3000000
Computational Time (hr)
Number of Computational Cells
8
Where Ai and Aj are inundated area at spatial resolutions of i and j, Ai Aj is the inundation
area predicted by both resolutions i and j, and Fi/j is the relative accuracy of resolution i in
respect with resolution j. The parameter was generally employed to determine the inundation
prediction discrepancy from observed data. However, it can be applied to determine the
discrepancy between the base map and other inundation maps attained from different
simulation scenarios in the absence of observed data (Cook and Merwade, 2009). Here it is
used to compare the inundation areas estimated by two different DEM resolutions. Finer
resolution is considered as the base map and the discrepancy of the coarser resolution from
this is quantified. Table 1 presents this parameter along with the percentage of inundation area
for different grid resolutions. Based on the table, the F statistic varies in the range of 65.5%
84.6% from 93m to 31m DEMs. The parameter is 100% for 9m apparently since it is compared
with itself.
Figure 7. Spatial variation of maximum inundation area for different spatial resolutions
Table 1. Comparison relative accuracy of inundation area predicted at different spatial
resolutions
Spatial Resolution (m) Inundation Area (%) F Statistic (%)
93 12.6 65.5
62 8.6 77.1
46 6.9 78.8
31 5.8 84.6
9 5.3 100.0
9
The resulting probability weighted flood hazard maps are presented in Figure 8.
Histogram plot of each flood hazard class at different spatial resolutions are shown in Figure 9.
Increasing the resolution from 93m to 9m leads to a minor 0.4% increase in overall flood
hazard and also a slight 0.7% increase in class extent. With improving the
resolution from 93m to 31m, high danger zone by overall hazard has been
increased by 6.8% agreeing with the hypothesis. It can be concluded that as the spatial
resolution increases, more locations are classified to a higher danger level. This could be
because, with improved spatial resolution, the grid cells that were classified as judgment
and/or low hazard are converted to high hazard zone. However, after refining the resolution
from 31m to 9m, 0.7% reduction occurs in percentage of danger class by overall hazard.
To give a better understanding of hazard variation with DEM resolution, trend of each
danger class and overall hazard with spatial resolution was also analyzed. Figure 10 presents
the variation of different danger classes and overall hazard with grid scale. An increasing trend
high and overall hazard can be seen by increasing the resolution which is in
accordance with the expectations. zones show a
decreasing trend by increase in resolution from 93m and reaches a minimum and then
judgment classes. It is to be noted that these results can be because of definition of danger
classes by the reference curves applied here and other hazard classifications may change the
results. This indicates the significant role of hazard definition in the final results.
(a)
(b)
10
(c)
(d)
(e)
Figure 8. Flood hazard maps for spatial resolutions of: a) 9m; b) 31m; c) 46m; d) 62m; and e)
93m
Figure 9. Area of different hazard classes for 9m, 31m, 46m, 62m and 93m grid resolutions
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
Low
Judgement
High
93m
62m
46m
31m
9m
11
Figure 10. Trend of different hazard classes with spatial resolutions
Another analysis was to investigate the hazard intensity change with respect to spatial
resolution. Spatial distribution of relative bias (underestimation/overestimation) was obtained
between each two different grid resolutions. Relative bias is considered as the change from a
lower to higher danger class. For doing so, hazard rasters were resampled to the higher
resolution cell size using nearest-neighbor approach. Relative underpredicted area for different
resolutions is presented in Figure 11. From this figure, relative underestimation does not show
any specific trend is not minimum anywhere. Therefore, an optimal grid resolution cannot be
suggested for the study area.
Figure 11. Relative underestimated area for different spatial resolutions
To investigate the effects of topography on the underestimated locations, ground slope
was generated for each resolution based on the DEMs. Relative underestimation layers were
overlaid with the topographic slope to explore the characteristics of the underpredicted cells.
Figure 12 shows the percentage of relative underestimated area for different slope ranges. The
0.0%
1.0%
2.0%
3.0%
4.0%
5.0%
6.0%
7.0%
8.0%
0 20 40 60 80 100
Percent of Total Area
Cell Size (m)
Overall hazard
Low
Judgement
High
0
500000
1000000
1500000
2000000
2500000
3000000
3500000
93m to 62m
62m to 46m
46m to 31m
31m to 9m
Underestimated Area (m2)
Spatial Resolution Change
12
results indicate that 81.9% to 91.9% of the underestimated cells are located in the slopes of
greater than 2.5% in which 56.7% to 78.5% of them are in the slopes of greater than 5%
varying with spatial resolution. This means that more than a half of underestimations occur in
the areas with slopes greater than 5%. This highlights key role of topographic resolution in the
hilly areas. Moreover, it implies that the selection of an appropriate spatial resolution depends
on the topographic characteristics of the case study. In other words, a general advice about
the sufficient spatial resolution cannot be given based on the results of this study. Further
studies should be performed in other areas with different topographic characteristics to verify
the results of this study and to determine an adequate topographic scale for dam break
simulations. This will be useful to reach the highest model performance and also to avoid the
redundant computational time simultaneously.
Figure 12. Percent of relative underestimated cells for different slope ranges
Finally, it is to be noted that the hazard was estimated based on flood depth and
velocity here. Other parameters such as warning time which have been suggested in the
previous studies (e.g. Graham, 1999) are not taken into account which incorporates another
uncertainty to the results. This can affect the number of cells in each hazard class and
accordingly the conclusions about the trend of hazard variation with spatial resolution. Thus, it
is suggested that the same procedure being repeated in the future by using other hazard
estimation methods to verify findings of this study.
Summary and Conclusion
A probabilistic dam break simulation was carried out in order to investigate the spatial
resolution effects on downstream flood hazard. Five different spatial resolutions including 93m,
62m, 46m, 31m and 9m were used to generate spatial flood hazard maps. A 2D flood model,
Flood2D-GPU is employed in a probabilistic framework to investigate these spatial resolution
impacts by applying dam break simulations on Burnett Dam located in Buncombe County, NC.
The dam break hydrograph is chosen as the uncertain parameter as it adds greater source of
uncertainties in most situations. 99 stochastic dam break hydrographs representing various
possible dam failure scenarios are generated by GoldSim® MCS software. These hydrographs
are input into Flood2D-GPU to produce probabilistic flood hazard maps. The probabilistic
0
10
20
30
40
50
60
70
80
90
100
>2.5%
>5%
>7.5%
Percent of Relative
Underestimated Cells
Spatial Resolution Change
31m to 9m
46m to 31m
62m to 46m
93m to 62m
13
simulations were carried out for 9m, 31m, 46m, 62m and 93m spatial resolutions. The most
important findings for this study can be summarized as:
The inundation area extent predicted through Flood2d-GPU decreases with finer
spatial resolution. This is mainly due to difference in terrain description by different
resolutions of DEM.
Increasing the resolution from 93m to 9m will lead to a slight change in overall flood
hazard and high d extent.
High danger area generally increased with improving the DEM spatial resolution. It
can be concluded that as the spatial resolution increases, more locations are
classified to a higher danger level. This could be because, with improved spatial
resolution, the grid cells that were classified as judgment and/or low hazard are
converted to high hazard zone.
More than a half of relative underestimated cells are located in the areas with slopes
greater than 5%. This emphasizes the significance of topographic resolution in the
hilly environments. Therefore, a coarse terrain model is not suggested for the areas
mostly covered by steep slopes.
To provide general recommendations to dam safety officers and floodplain managers,
studies similar to the current studies need to be performed. This will be useful to reach the
highest model performance and also to avoid the redundant computational time
simultaneously.
Acknowledgment
The authors are grateful to the Center of Management Utilization and Protection of Water
Resources, Department of Civil and Environmental Engineering and the College of
Engineering at Tennessee Technological University for their support.
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