Modeling and Risk Analysis for Floods due to Failure of Water Control Infrastructures
ABSTRACT There are currently about 79,000 dams in the USA. Of these, about 14% are high-hazard dams and 16% are classified as significant hazard dams. Their failure may cause loss-of-life as well as damage to property and infrastructures. According to the National Inventory of Dams (NID), 92% of high-hazard and 67% of significant-hazard dams are required to have an Emergency Action Plan (EAP). Unfortunately, at the moment 48% of high hazard dams and 71% of significant hazard dams do not yet have an EAP. There is an urgent need for the development of efficient, robust, and accurate numerical tools that can be reliably used to perform risk and vulnerability studies for dams by making use of the recent developments in GIS and remote sensing technologies. Most of the dam safety studies to investigate the consequences of catastrophic floods due to failure of water control infrastructures are currently carried out using one-dimensional steady and/or unsteady hydraulic models. A standard approach based on two-dimensional (2D) flood modeling has not yet been adopted. This paper presents an integrated GIS-based Decision Support System (DSS), which uses the results of 2D flood simulation due to dam/levee break/breach simulations to estimate loss-of-life, urban and agricultural property damage by taking into account various types of uncertainties that are involved. Developed at the National Center for Computational Hydroscience and Engineering of the University of Mississippi, this DSS also has additional modules to rank flood management alternatives by using spatial compromise programming, and to track cascading infrastructure failures.
- SourceAvailable from: Mustafa S. Altinakar[Show abstract] [Hide abstract]
ABSTRACT: Dams and levees are one of the eighteen Critical Infrastructure and Key Resource sectors identified by the National Infrastructure Protection Plan. Failure of dams could lead to highly dynamic, catastrophic floods that could potentially cause loss of life, urban and agricultural property damage, environmental degradation, and cascading failures in other critical sectors. Predicting and assessing these potential impacts are therefore important, and there is a clear need for cost-effective methods, tools and technologies for studying the impacts of dam failures based on new technologies.01/2009;
MODELING AND RISK ANALYSIS FOR FLOODS
DUE TO FAILURE OF WATER CONTROL INFRASTRUCTURES
Mustafa S. Altinakar1, Marcus Z. McGrath2, Yavuz Ozeren3 and Hamzeh Omari4
1 Associate Director and Research Professor, NCCHE, The University of Mississippi
Carrier Hall, Room 102, P.O. Box 1848, University, MS 38677, USA, email: firstname.lastname@example.org
2 Graduate Student, NCCHE, The University of Mississippi
Carrier Hall, Room 102, P.O. Box 1848, University, MS 38677, USA, email: email@example.com
3 Graduate Student,, NCCHE, The University of Mississippi
Carrier Hall, Room 102, P.O. Box 1848, University, MS 38677, USA, email: firstname.lastname@example.org
4 Graduate Student,, NCCHE, The University of Mississippi
Carrier Hall, Room 102, P.O. Box 1848, University, MS 38677, USA, email: email@example.com
There are currently about 79,000 dams in the USA. Of these, about 14% are high-hazard dams
and 16% are classified as significant hazard dams. Their failure may cause loss-of-life as well as
damage to property and infrastructures. According to the National Inventory of Dams (NID),
92% of high-hazard and 67% of significant-hazard dams are required to have an Emergency
Action Plan (EAP). Unfortunately, at the moment 48% of high hazard dams and 71% of
significant hazard dams do not yet have an EAP. There is an urgent need for the development of
efficient, robust, and accurate numerical tools that can be reliably used to perform risk and
vulnerability studies for dams by making use of the recent developments in GIS and remote
Most of the dam safety studies to investigate the consequences of catastrophic floods due to
failure of water control infrastructures are currently carried out using one-dimensional steady
and/or unsteady hydraulic models. A standard approach based on two-dimensional (2D) flood
modeling has not yet been adopted. This paper presents an integrated GIS-based Decision
Support System (DSS), which uses the results of 2D flood simulation due to dam/levee
break/breach simulations to estimate loss-of-life, urban and agricultural property damage by
taking into account various types of uncertainties that are involved. Developed at the National
Center for Computational Hydroscience and Engineering of the University of Mississippi, this
DSS also has additional modules to rank flood management alternatives by using spatial
compromise programming, and to track cascading infrastructure failures.
In the USA, Homeland Security Presidential Directive 7 of 5/7/2007 classified dams and levees
among the 17 critical infrastructure and key resource sectors “that require protective actions to
prepare for, or mitigate against, a terrorist attack or other hazards identified.” Failure of dams
and levees may lead to highly dynamic catastrophic floods that can cause significant loss-of-life,
and bring considerable socio-economic hardship by damaging property and infrastructures.
Pollution caused by cascading failure of hazardous chemical production and/or storage centers
may also lead to environmental disasters and affect the ecosystem.
Fig. 1 Cumulative number of fatalities
due to dam failures during the period
1850-2005 (adapted from NPDP, 2008b).
The database of the National Dam Performance Program (NPDP, 2008a) lists a total of 1019
dam failures of varying importance since 1850. A total of about 4,000 lives were lost during
these incidents (Fig. 1). The majority of these failed dams are earthfill embankments. As shown
in Fig. 2 (NPDP, 2008b), the principal cause of dam failures is the overtopping due to extreme
hydrologic events. The second important cause is the piping.
US National Inventory of Dams (NID, 2008) currently lists about 79,000 dams in the USA,
including those in Guam and Puerto Rico. Only about 5% of these dams are owned by the federal
government. The majority of the remaining dams are privately owned and they are under the
responsibility of the states. Although federal guidelines exist (FEMA, 2004a), hazard potential
classification for dams is ultimately under the responsibility of states. Therefore, small variations
should be expected from one state to the other. In general, however, the dams are classified into
three hazard levels based on the vulnerabilities downstream and the expected impact of a failure,
rather than the quality of their structure and/or the probability of their failure:
• A High Hazard (or Category I or Class C) dam is a dam whose failure may cause loss-of-life,
serious damage to homes, industrial or commercial buildings, important public utilities, main
highways, or railroads.
Fig. 2 Causes of all dam failures that occurred
during the period 1975-2001 (adapted from NPDP,
• A Significant Hazard (Category II, or Class B) dam is a dam whose failure poses no threat to
life, but may cause significant damage to main roads, minor roads, or cause interruption of
public utilities’ services.
• A Low Hazard (Category III, or Class A) dam is a dam whose failure would at most result in
damage to agricultural land, farm buildings (excluding residences), or minor roads.
Fig. 3 Classification of “High Hazard” dams in the USA by height versus EAP Status (left) and
by age versus EAP status (right), based on the entries in the National Inventory of Dams
(9/28/2008). Legend for EAP status: Y= Yes EAP exists, NR= EAP not required, and N= No
EAP does not exist.
Fig. 4 Classification of “Significant Hazard” dams in the USA by height versus EAP Status (left)
and by age versus EAP status (right), based on the entries in the National Inventory of Dams
(9/28/2008). Legend for EAP status: Y= Yes EAP exists, NR= EAP not required, and N= No
EAP does not exist.
Out of the 79,000 existing dams, 11,243 are classified as high hazard and 12,656 as significant
hazard dams. In principle, all high hazard dams are required to have an Emergency Action Plan.
Federal guidelines for dam safety published by FEMA (2004b) define EAP as “a formal
document that identifies potential emergency conditions at a dam and specifies preplanned
actions to be followed to minimize property damage and loss of life.” The EAP also contains
inundation maps and the procedures and information to assist the dam owner/operator in issuing
early warning and notification messages to responsible downstream emergency management
authorities. In Figs 3 and 4, the EAP status of high hazard and significant hazard dams is plotted
based on height and age of the dam. As it can be seen, 5,035 high hazard dams and 6,013
significant hazard dams do not yet have an EAP. It is important to note that 1,858 high-hazard
dams and 2,533 significant hazard dams were built before 1940, thus having reached the end of
their useful life.
The situation is in fact probably more serious than it appears from these statistics. The first issue
concerns the validity of the existing EAPs. The public version of the NID, unfortunately, does
not list the date of establishment for the existing EAPs. Some of the existing EAPs may be very
old and not reflect the true vulnerabilities downstream. The new developments at the
downstream of the dam may even necessitate a reclassification of some of the dams. The second
issue is the quality of the EAP. Not all the EAPs follow the standard guidelines set forth by
FEMA or by the states. In some extreme cases, the EAP can be just a sheet containing a list of
telephone numbers to call in case of emergency.
To remedy this situation, there is an urgent need to develop efficient, robust, and accurate
numerical tools that can be reliably used for performing risk and vulnerability studies for dams
by making use of the recent developments in GIS and remote sensing technologies.
CURRENT PRACTICE OF FLOOD MODELING AND RISK ANALYSIS
The estimation of the consequences of floods and the risk analysis are generally performed using
either the HEC-FDA (USACE, 2000) program, developed by the Hydrologic Engineering Center
of the US Army Corps of Engineers, or Flood Component of HAZUS-MH software developed
by FEMA (2007). HEC-FDA uses a risk-based analysis method to integrate hydrologic,
hydraulic, and economic relationships. The two primary outputs from HEC-FDA include
expected annual damage estimates and project performance statistics. This program has a very
primitive user interface and does not offer any GIS capability. The flood component of HAZUS-
MH includes methods for assessing both riverine and coastal flooding and damage assessment
for all classes of structures and infrastructures based on damage data bases of FEMA and the
U.S. Army Corps of Engineers. It also includes modules to estimate damage to utility lifelines,
agricultural areas and facilities, debris generation and shelter requirements. It takes into account
flood warnings and flood velocity effects. HAZUS-MH is a GIS-based tool and is now the
standard software used in the USA for flood loss analyses.
With the current practice of flood simulation, both of these models are generally driven by flood
maps that are obtained from one-dimensional steady or unsteady numerical flood simulations
carried out by H&H (Hydrology and Hydraulics) specialists, who are often engineers with a
background in hydrology and hydraulics. One-dimensional simulation results are converted into
two-dimensional maps by rather crude interpolations between 1D model cross sections, based on
digital elevation maps (see Fig. 5). The use of one-dimensional models has several drawbacks: 1)
The procedure for the development of two-dimensional flood plans from one-dimensional
simulation results is quite involved, takes a relatively long time and involves engineering
judgment calls; 2) The interpolation inaccuracies in case of highly dynamic floods resulting from
failure of dams and levees may be quite important. Moreover, the mass conservation is violated;
and 3) One-dimensional models can only be used for cases where a channelized flow exists. In
case of dam and levee break floods over a flat terrain, the one-dimensional approach can no
longer be used reliably.
Fig. 5 Steps for converting one-dimensional simulation results into two-dimensional flood
delineation maps (adapted from FEMA, 2003). Flood elevations between adjacent sets of cross-
sections are calculated by interpolation based on the topography. Flood elevations for tributaries
are calculated by carrying out backwater calculations.
At the moment, despite their obvious advantages, two-dimensional models are rarely used and
there are no commonly accepted procedures for the use of two-dimensional modeling in flood
simulation and/or consequence analysis.
INTEGRATED DAM BREAK MODELING AND RISK ANALYSIS
The National Center for Computational Hydroscience and Engineering (NCCHE) at the
University of Mississippi has been working on the development of a GIS-based integrated
decision support environment for water infrastructural security that allows a detailed evaluation
of the consequences of a catastrophic flood based on two-dimensional realistic, reliable
numerical simulations. The organizational structure of this decision support environment, called
DSS-WISE (Decision Support System for Water Infrastructural Security), for is depicted in Fig.
Fig. 6 Organizational structure of DSS-WISE software developed by NCCHE.
A state-of-the-art 2D numerical model, CCHE2D-FLOOD, and a collection of GIS-based
decision support tools constitute the core of the system. The numerical flow model solves 2D
shallow-water equations using a very robust, shock-capturing finite-volume scheme. The
numerical model provides the information about the extent of the flooded area, spatial
distributions of flood depth and flood velocities in two horizontal directions, arrival time of the
flood and its duration at each point of the computational domain. To carry out the simulation, the
model receives information from various sources. The topography is supplied directly as Digital
Elevation Maps (DEMs). The user also provides the information on the structure to be analyzed,
protection measures that need to be taken into account, and defines the hazard scenario to be
The collection of GIS-based decision support tools relies on the two-dimensional flow simulation
results computed by CCHE2D-FLOOD, which are converted into raster layers, to carry out
analyses of loss of life, urban damage, rural and agricultural damage, and risk and vulnerability.
It also allows evaluation of the efficiency of emergency response plans, structural and non-
structural flood protection and mitigation measures, etc. Engineering alternatives for flood
control and management, emergency response, etc., can be comparatively evaluated and ranked
using the Spatial Compromise Programming (SCP), which takes into account spatial variations
of the relative efficiency of the alternatives. To carry out these tasks, the GIS decision support
toolbox needs complementary information regarding the nonstructural measures, various
geospatial information, such as land use, census data, infrastructure data, urban data, agricultural
data, economic data, etc. The damage relationships for different structure types and crop types,
rules and regulations to be considered in evaluating the efficiency or adequacy of engineering
solutions are taken from a knowledge base that needs to be established. The stochastic module
supplies probability distributions for hazard scenarios, uncertainties for various parameters, event
trees, etc., in order to take into account the uncertainties during the analyses and decision making
Fig. 7 Cartesian coordinate system used in writing shallow water equations in two dimensions.
NUMERICAL MODEL: CCHE2D-FLOOD
The numerical model CCHE2D-FLOOD solves the conservative form of the two-dimensional
shallow water equations (Saint-Venant Equations) in conservative form over a complex
topography defined by a regular mesh. Referring to the coordinate system depicted in Fig. 7, the
shallow water equations, or Saint-Venant equations, that describe the unsteady two-dimensional
flow can be written as follows:
direction, and sources, respectively. They are defined as:
, , and are the vectors of conserved variables, fluxes in the x and y
in which Z represents the water surface elevation and C the Chezy friction coefficient. Cell-centered
finite-volume discretization of Eq. 1 over a rectangular control volume leads to the following explicit
x and y directions, and t Δ is the time step. The intercell
fluxes are computed using a first order upwinding (Ying et al., 2004):
2/ 1,2/ 1 ,, 2 / 1, 2 / 1
where and are the cell dimensions in
To avoid dry bed condition a very small water depth is maintained over the entire computational mesh.
CCHE2D-FLOOD was tested and validated using analytical solutions as well as data from laboratory
experiments, model tests, and past dam break events (see Ying et al., 2003a and b; Ying and Wang, 2004,
and Ying et al., 2004). These tests show that the model is stable, oscillation-free, robust, and conserves
mass rigorously. Figure 8 shows the application of CCHE2D-FLOOD to simulate a hypothetical complete
break of the Sardis Dam on the Tallahatchie River, MS, which has been in operation since 1940. The dam
has a crest length of 15,300 ft and an average height of 97 feet. Maximum storage capacity is 1,512,000
acre-feet, and the dam has a drainage area of 1,545 square miles. A DEM with a resolution of 100m was
used for this 72-hour simulation.
Fig. 8 Simulation of the hypothetical sudden break of the Sardis Dam, Mississippi using
CCHE2D-FLOOD. A DEM with a resolution of 30m was used for this simulation
Immediately downstream of the dam the flow is channelized and follows the little Tallahatchie
valley among the bluff hills. In this section, the use of a one-dimensional model may also be
acceptable. At the 8th hour, the flood flows reach flat terrain of the Mississippi Delta. The spread
of the flood in this extremely flat area without a defined channel would be impossible using a
CUT-CELL MODELING TO REPRESENT LINEAR TERRAIN FEATURES
Although the direct use of a DEM as computational mesh considerably simplifies data
preparation, it also has some drawbacks. As shown in Fig. 8, Highway I-55 crosses Little
Tallahatchie valley on an embankment which is 3 to 4 meters higher than the valley floor. It can
therefore constitute an obstacle and retard the propagation of the flood front by storing
considerable amount of water at the upstream side. At the cell size of 100m used in this study
linear terrain features, such as roads, railroads, dikes, cannot be adequately captured. This may
lead to important errors.
CCHE2D-FLOOD provides a cut-cell boundary capability to represent linear terrain features
even when using relatively coarse mesh sizes. This capability requires the knowledge of the
linear terrain feature as a three-dimensional polyline defined as a series of vertices in a shape
layer. When this polyline is projected onto the regular mesh, it cuts through regular mesh
elements and divides them into two irregular-shaped elements as shown in Fig. 9. The projection
has to obey three rules: 1) A cell is only allowed to be cut by a single straight line; 2) The line
joining the centers of two adjacent cells sharing a common edge can only be cut by a single
straight cut-line; and 3) When two adjacent cells sharing a common edge are both cut by a line,
the cut lines should meet at the same point on the common edge. It may therefore be necessary to
somewhat simplify the polyline in some cases.
Fig. 9 Representation of a cut-cell
boundary and different types of cells.
Ghost cells are marked for the case the
water is on the upper side of the barrier.
(Taken from Altinakar et al., 2008)
Fig. 9 shows a regular mesh with a projected cut-line representing a linear terrain feature. The
computational stencil is described by eq. 3. To compute the value of unknowns in a given cell
center at time t+Δt, the values at the centers of the four neighboring cells that share a common
edge with the computed cell are required at time t. For cells neighboring a cut-line, some of these
Fig. 10 Schematic representation of two-sided
ghost fluid method. Computed cell is marked by
a solid circle at the center. The cell on the other
side of the cut is treated as a ghost cell. (Taken
from Altinakar et al., 2008)
neighboring cells may be located on the other side of the cut-line. CCHE2D-FLOOD uses the so-
called Ghost-Fluid method, which is a special version of the Immersed Boundary Method (Mittal
and Iaccarino, 2005; and Ghias et al., 2007), to solve for these special cells with incomplete
stencil. Since overtopping of the water from one side of the cut-line to the other is allowed and
the water can exist on both sides, a generalized two-sided ghost fluid method is implemented.
Without going into the details, which can be found in Miglio et al. (2008), the main idea of the
method can be described with reference to Fig. 10. In the figure on the left, in order to compute
the cell at the center, one also needs the value of the cell GP located below, which is on the other
side of the cut-line. On the cut-line, the following boundary conditions can be imposed:
Fig. 11 Simulation of a controlled release from the Sardis Dam using CCHE2D-FLOOD with
cut-cell boundary capability. The I-55 crossing the Little Tallahatchie Valley downstream of the
dam is modeled using a cut-cell line.
In order to be able to use the standard stencil, it is needed to assign values at the center of the cell
GP such that the boundary conditions given in eq. 5 are satisfied along the cut-line. This is done
by orthogonally projecting the point GP to RP, which is on the same side of the cut-line as the
computed cell. The values of the variables at point RP are interpolated using the values at the cell
centers 1 to 4. The value interpolated at RP is then linearly extrapolated back to point GP. This
value is then used in the normal stencil to compute the variables in the center cell. When
calculating the center bottom cell, the center cell becomes GP and the calculation proceeds in a
manner similar to the one described above. As it can be seen in the figure, special situations may
arise when all the cells required for the interpolation are not on the same side of the cut-cell. The
missing cell values are simply replaced by the boundary condition. The overtopping discharge is
calculated using a weir equation, which takes into account the water depths and velocities on
both sides of the cut-line. Fig. 11 shows the application of CCHE2D-FLOOD with cut-cell
capability to simulate the controlled release of a flood discharge from Sardis Dam, MS. In this
test case, Highway I-55 is modeled using a cut-line. The resolution of the mesh is 100m. The
flood front reaches the I-55 at t=7 hours. The water back up behind the embankment of the road
finally overtops at t=20hours, and the flood propagates downstream.
Figure 12 A special version of cut-cell boundary is used to couple a one-dimensional shock
capturing unsteady model with CCHE2D-FLOOD. The cut-line projected onto the two-
dimensional grid represents a river with user-defined cross sections. (Taken from Altinakar et al.,
2008). Exchanges between 1D and 2D models can take place on both sides of the line.
It is interesting to note that the cut-line can also be used to represent a one-dimensional river
flow in a two-dimensional mesh. In this case, the planview of the river is projected onto the
DEM (Fig. 12). The river is represented by user-defined cross sections. A one-dimensional
version of the shock capturing finite-volume scheme is employed to calculate the flow in the
river by taking into account incoming and outgoing lateral discharges. Coupled 1D-2D
simulation capability can be used to model levee overtopping scenarios during a single run. Two
examples of the use of 1D-2D model coupling are shown in Figs 13 and 14. These figures show
the water surface elevation of the flow in both 2D and 1D models at different times. In both test
cases, the 1D river represented as a cut-line starts and ends outside of the DEM. In Fig. 13,
initially a uniform discharge is flowing in the river. At a certain time, discharge starts to increase
linearly up to a maximum value and then decreases linearly back to its original value. When the
water depth rises in the channel, the water starts to flow into the 2D model first from the low
point on the left bank at x=210m, then from the low point on the right bank at x = 320-360m, and
finally again from the left bank at x = 350m. Discharges flowing out of the 1D model propagate
in the 2D model based on the topography.
Fig. 13 Test case of overtopping 1D river flow to demonstrate the use of cut-cell method in
coupled 1D-2D computations. In this example the unsteady flow overtopping the banks of the
1D river, represented as a cut-line boundary, propagates in the 2D model.
In Fig. 14, the same planview of the river is used but the elevations of left and right banks are
slightly different. Initially, a very small water depth exists in the river. In the 2D model, a 4m
high dam that extends over the entire width of the computational domain breaks suddenly. When
the flood water hits the left bank of the river, a shock wave forms. Eventually water overtops the
low point on the left boundary at x = 310m and enters the river. Water flowing in the river
overtops the right boundary and starts spreading.
Other test cases for the application of cut-cell boundary for representing linear terrain features
and 1D river flow can be found in Altinakar et al. (2008) and Miglio et al. (2008).
Fig. 14 Test case to demonstrate the use of cut-cell method in coupled 1D-2D computations. In
this example a dam break flood is interacting with a 1D river flow represented as a cut-line
EVALUATION OF THE FLOOD IMPACT AND RISK ANALYSIS
Simulations with CCHE2D-FLOOD provide the following information: 1) flow depths over the
entire mesh at prescribed times; 2) velocity components in x and y directions over the entire
mesh at prescribed times; 3) One file of maximum depth values for the entire mesh; 4) One file
of maximum velocity vectors for the entire mesh; 5) Flood arrival time for all cells; and 6) Flood
duration times for all cells. These files are available as raster files and can be readily imported
into the GIS platform.
The decision support system DSS-WISE is written as an extension to the ArcMap 9.2 software
developed by ESRI. It implements a series of tools that allow importing numerical simulation
results into the ArcGIS platform and interfaces them with geospatial socio-economic data such
as census block data, urban building stock, agricultural land and farm data, infrastructure data,
etc., (Altinakar and Qi, 2006). Fig. 15 shows the screen shot of the ArcGIS screen with all the
toolbars developed for flood impact and consequence analysis. Some of the developed tools are
briefly described in the following subsections.
Fig. 15 ArcGIS screen shot showing the floating menu bars of some of the programmed decision
Loss of life
Risk assessment and emergency management studies and the establishment of EAPs require the
estimation of the potential loss-of-life that would result from the failure of a dam or a levee. The
DSS-WISE follows the USBR (United States Bureau of Reclamation) procedure developed by
Graham (1999) based on data all historical dam failures that resulted in more than 50 fatalities
and the loss-of-life data for all dam failures that occurred after 1960.
According to Graham (1999), loss of life resulting from flooding is highly influenced by 3
factors: 1) The number of people occupying the floodplain, which is also called people at risk
(PAR); 2) The amount of warning that is provided to the people exposed to dangerous flooding;
and 3) The severity level of the flooding.
Risk and uncertainty analyses are also needed for estimating the fatality rate for different areas of
the floodplain. In the past, the flood routing is typically modeled in a one-dimensional computer
simulation model (Dise, 2002), so evaluation of the loss of life is also based on one-dimensional
results. Usually, the floodplain is divided into several reaches, and the unique values of PAR,
warning time and severity are assigned for each reach throughout the analysis. In DSS-WISE,
spatial variability of the above factors is taken into account for each cell within the area of
interest; i.e. a fully two-dimensional approach is adopted.
In order to determine the PAR value, the census block data, which is usually a vector polygon
layer (for example, in TIGER format), are used in the GIS environment. Census blocks are areas
bounded on all sides by visible features, such as streets, roads, streams, and railroad tracks, and
by invisible boundaries, such as city, town and county limits, property lines, and short, imaginary
extensions of streets and roads. Generally, these polygons are small in area showing population
variation. After importing this layer into ArcGIS, the population density is first calculated by
using the total population of each census block and its area. Then this feature polygon layer is
converted to a raster layer which has the same cell size as the flood computation results. The cell
value, which represents the PAR living and working inside each cell, is reclassified according to
the product of population density and the cell area. This operation would obtain a raster layer
showing the PAR distribution.
The typical definition of warning time of a flood is the length of time from when the first public
warning is issued until the flood wave reaches the first person in the PAR (Aboelata et. Al.,
2002). In a 2D raster layer format, this definition can be written as in Eq (3.1):
In the above equation, for each cell location of the floodplain,
is the warning time,
the flood wave arrival time; and
is the initial time of public warning. Since the
time that the flood event occurs is defined as time “0”,
the warning is given after the flood event happens, or negative, which means the warning is
given before the flood event happens. Graham (1999) provides a table of suggested values (see
Table 1) for estimating the warning time for failure of earthfill dams. The warning time depends
on the type of failure, drainage area at the dam, date and time of failure, and presence of
observers at dam. The earliest warning time in the table is ¼ hours before the failure, and the
latest is 1 hour after the flood wave reaches a populated area.
The flood severity definition is usually associated with the flood depth. Low, medium and high
severity can be categorized according to Graham (1999). Using the flood severity based method
for estimating loss-of-life, the intersection of modified census block information with inundation
depth and warning time results in raster layers produces a map showing the spatial distribution of
potential loss-of-life estimation. Raster calculation for the loss-of-life is triggered by using a
can be either positive, which means