All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
However, the document contains useful guidance to support implementation of the new standards.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
D.4.5 Wave Setup, Runup, and Overtopping
This section provides methodology for establishing the static and fluctuating waterlevel
characteristics in the nearshore including wave setup, runup, and overtopping of sandy beaches
and natural or constructed barriers. Additionally, procedures for calculating attenuation of waves
propagating over flooded areas, including dissipative bottoms and through vegetation, are
presented.
D.4.5.1 Wave Setup and Runup
D.4.5.1.1 Introduction
The wave, meteorological, and bathymetric characteristics for the Pacific Coast are quite
different from those on the Atlantic and Gulf coasts for which methodology to quantify the 1%
chance water levels has been developed previously. The wave differences are due to the longer
period waves and generally distant generation locations for the Pacific Coast whereas the
meteorological differences are fewer hurricanes and thus lower winds. The major bathymetric
differences are due to the relatively narrow Pacific Coast continental shelf widths. There are two
major consequences of these differences for the 1% annual chance Pacific Coast hazards: (1) the
wind surge component is relatively small due to the lower wind velocities coupled with the
narrow shelf widths, and (2) the narrow spectra result in a substantial oscillating component of
the wave setup with periods of tens to hundreds of seconds. Thus, the oscillating wave setup is a
significant component of the total wave runup and a major contributor to coastal hazards on the
Pacific Coast.
Wave setup and runup recommendations presented are based on a literature review, new
developments, and comparison of available methods for quantifying these processes. Where
possible, the most physicsbased approaches have been identified and recommended.
D.4.5.1.2 Background, Definitions, and Approaches
Wave setup and runup contribute significantly to the damage potential of severe waves along the
Pacific Coast. The total runup, R , includes three components: (1) static wave setup, .
, (2)
dynamic wave setup, .$, and (3) incident wave runup, Rinc, i.e., conceptually:
=+
$
inc (D.4.51)
R ..+R
in which . and .$ are the magnitudes of the mean and oscillating wave setup components and
Rinc the runup component due to the incident waves. In application, the two oscillating
components ( .$and Rinc) are combined statistically to determine exceedance levels. Unless stated
differently in this document, R refers to 2% runup conditions. The oscillating component of wave
setup is a type of infragravity wave and is referred to here as dynamic wave setup. Each of the
three components of total runup is defined and discussed below.
D.4.51 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Wave setup is the additional elevation of the water level due to the effects of transferring wave
related momentum to the surf zone. Momentum is transferred from winds to waves in the wave
generating area (usually in deep water for the Pacific Coast) and then is conveyed to shore by the
waves similar to the manner that waves transport energy from the generating area to shore; see
Figure D.4.51. A main difference between energy and momentum is that energy is dissipated in
the surf zone whereas momentum is transferred to the water column. This transfer is equivalent
to a shorewarddirected “push” on the water column that causes a tilt of the water surface; see
Figure D.4.52. The wave setup is small and negative seaward of the surf zone (setdown) and
begins to rise in the surf zone due to the transfer of momentum; see Figure D.4.53. If only one
wave of a constant height and period were present, the wave setup would be steady.
Figure D.4.51. Schematic of Energy and Momentum Transfer from Winds to Waves
within the Wavegenerating Area, and to the Surf Zone and Related Processes
D.4.52 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Wind Direction
Figure D.4.52. Wave Setup Due to Transfer of Momentum
Wind Direction
Figure D.4.53. Static Wave Setup Definitions at Still Water Level, .o ,
and Maximum Setup, .max
For a single wave component, the static setup, .
(h), at any water depth, h, can be expressed as:
h =
.
(3/ 8) .
(3/ 8) .
2
.() ( +
)H 
h (D.4.52)
2 b 2
16 1+
(3/8) .
1+(3/ 8) .
where .
is the ratio (assumed a constant) of the breaking wave height to water depth within the
surf zone and h is the still water depth, i.e., the depth in the absence of waves or wave effects.
The wave setup at the still water line, .
, and the maximum wave setup, .
, can be expressed
o max
from Equation D.4.52 in terms of the breaking wave height, Hb :
D.4.53 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
.
(3/ 8) .
.
( +
)
=
H (D.4.53)
o 2 b
16 1+(3/ 8) .
The equivalent expression for the maximum wave setup, .max , is:
..
(3/ 8) ..
(+
)
.
2 .
.
16 1+
(3/ 8) ..
.=.
.
H (D.4.54)
max 2 b
(3/ 8) .
.
(1
2) .
.
1(3/8) .
..
.+
For the usual value of . = 0.78, the following relations result:
.() =
0.189Hb
h 0.186h
(D.4.55)
.=0.189
o Hb (D.4.56)
.=0.232H (D.4.57)
max b
More realistic wavebreaking models that account for the actual profile will usually reduce the
wave setup for the relatively mild profile slopes of the Pacific Coast. For a wave system
consisting of more than one wave component (i.e., a wave spectrum), the breaking wave height
in the above expressions is replaced by the root mean square breaking wave height, (Hb ). Of
rms
significance on the Pacific Coast is that for wave systems consisting of more than one wave
component, the setup is oscillating consisting of a steady and a socalled dynamic component;
see Figure D.4.54. The dynamic wave setup component is larger for narrower wave spectra and
is substantial on the Pacific Coast during extreme storms and thus will require quantification for
Figure D.4.54. Definitions of Static and Dynamic Wave Setup
and Incident Wave Runup
D.4.54 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
flood mapping purposes. In addition to contributing to the total wave runup and thus the
shoreward reach of the waves, dynamic wave setup can carry floating debris such as logs at high
velocities and thus increase the hazards and damage potential in coastal areas. Figure D.4.54
illustrates the three components that define the upper limit of wave effects.
Incident wave runup on natural beaches or barriers is usually expressed in a form originally due
to Hunt (1959) in terms of the socalled Iribarren number, .
, as follows:
.=
HLm
(D.4.58)
in which m is a representative profile slope and is defined, depending on the application, as the
beach slope or the slope of a barrier that could be either a dune or constructed element such as a
breakwater or revetment. H and L are wave height and length, respectively. The wave
characteristics in the Iribarren number can be expressed in terms of breaking or deep water
characteristics. For purposes here, two wave characteristics in the Iribarren number are used
including that based on the significant deep water wave height, Ho , and peak or other wave
period, T, of the deep water spectrum, and that based on the significant wave height at the toe of
a barrier. The first definition for a sandy beach is as follows:
m
.o =
HL
oo
(D.4.59)
where Lo is the deep water wave length:
g
Lo =T 2
2p
(D.4.510)
and g is the gravitational constant. The beach profile slope is the average slope out to the
breaking depth associated with the significant wave height. Other definitions of the Iribarren
number are defined later in this section as needed.
The 2% incident wave runup on natural beaches, Rinc, is expressed in terms of the Iribarren
number as:
m
Rinc =0.6 Ho (D.4.511)
HL
oo
Several definitions are relevant to the determination of runup and overtopping considered later in
this section. The term still water level (SWL) has an accepted definition in coastal engineering as
the water level in the absence of wind waves and their effects and thus would include the
astronomical tide, El Niño, and surge due to wind effects, but would not include either of the
wave setup components. However, the wave setup components are included in the base water
level for calculating wave runup and overtopping. Thus, the term static water level (STWL) is
D.4.55 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
defined here as the sum of the SWL and the static wave setup, .
. Terminology is also useful to
describe the sum of the static water level and a X% dynamic wave setup component. For
purposes here, this will be defined as the dynamic water level X% (DWLX%). For example, the
elevation corresponding to a 2% Dynamic Water Level would be the sum of the SWL (including
astronomical tide, El Niño, and wind surge if present), the static wave setup, and the 2% dynamic
wave setup. The term reference water level (RWL) is used as general terminology to refer to the
water level that is appropriate for the particular application being discussed. As defined in
Section D.4.2, the total water level (TWL) is the sum of the SWL, the wave setup, and wave
runup.
D.4.5.1.3 General Input Requirements
The wave transformation element of the Guidelines and Specifications (Section D.4.4) produces
a nearshore shallow water wave spectrum outside the breaking zone and an equivalent deep
water wave spectrum. The approaches detailed in the following subsections base the total wave
runup on the equivalent deep water wave spectrum for the case of natural beaches or for the case
of runup on a barrier, the significant wave height at the toe of the barrier. To apply some of these
methods, a parameterized (Joint North Sea Wave Project [JONSWAP]) spectrum is developed.
The following wave characteristics are quantified: (1) equivalent deep water significant wave
height, (2) peak wave period, and (3) spectral width (here spelled out as Gamma to avoid
confusion with the Greek letter . used to denote other parameters in this subsection). Large
values of Gamma are associated with narrow spectra. Additionally, in some of the methods, an
approximate uniform nearshore slope of the profile, m, must be established.
The deep water significant wave height and the peak period can be determined using the
information provided from the wave transformation output. The recommended basis for
determination of the spectral peakedness parameter (Gamma) is described below.
A parameter defined by LonguetHiggins to quantify the spectrum narrowness (or peakedness) is
based on the moments of the frequency spectrum, mi, defined previously as Equation D.4.421 in
Section D.4.4 and refined below as Equation D.4.512:
N
i
mi =SfS f () (D.4.512)
nn
n=1
where S(fn) is the wave energy at the discrete frequency, fn . The LonguetHiggins definition of
the spectral narrowness, .
, is expressed in terms of the spectral moments:
1/ 2
.mm .
.=
o2 1
..
m
.
12 .
(D.4.513)
such that for an infinitely narrow spectrum, . = 0. For purposes here, the two spectral
peakedness parameters, . and Gamma, have been plotted for JONSWAP spectra and the results
are presented in Figure D.4.55. The spectral moments, m0, m1, and m2, for the actual equivalent
deep water spectrum are provided from the wave transformation analysis effort (Section D.4.4),
D.4.56 Section D.4.5
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Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
and . is determined from Equation D.4.513 and then Gamma determined from Figure D.4.55
as input into the total wave runup methodology for the case of natural beaches.
Figure D.4.55. Spectral Width Parameter Versus Gamma for JONSWAP Spectra
D.4.5.1.4 Setup and Runup on Beaches: Descriptions and Recommendations
A basic difficulty exists in applying the usual total runup equations to Pacific Coast conditions.
The total runup shall include wave setup; however, when these equations are applied to
approximate 1% annual chance Pacific Coast wave conditions, the total wave runup can be less
than predicted for static and dynamic wave setup alone. This apparent paradox stems from the
fact that most laboratory experiments on which these equations are based were conducted under
conditions much different than those of concern on the Pacific Coast and the equations governing
wave setup and incident wave runup have different dependencies on the variables (beach slope
and wave characteristics) and thus the methods based on available experimental data cannot be
extended outside the range of variables for which the experiments were conducted. Thus, it is
necessary to account for this limitation of the usual equations for total wave runup in developing
recommendations for the Pacific Coast.
The Direct Integration Method (DIM) was developed for calculating static and dynamic
(infragravity) components of wave setup accounting for as much of the physics as possible. This
onedimensional method accounts for the spectral shape, the detailed bathymetry, and is based
on integration of the governing equations from deep to shallow water. DIM can be applied by a
simple set of empirical equations and by full implementation of the numerical model.
Three general approaches to address the wave setup components of the total wave runup on
natural beaches are available: (1) empirical methods, (2) DIM developed in conjunction with this
effort, and (3) advanced wave models, primarily the Boussinesq type. Because the dynamic wave
D.4.57 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
setup is considered to be very significant on Pacific Coast shorelines and depends on the spectral
width and DIM is the only method (other than the Boussinesq models) that can account for
variable spectral width, DIM is the preferred method for application.
D.4.5.1.4.1 Direct Integration Method
Because the DIM approach does not include the effects of incident wave runup, it is
recommended that the 2% incident runup be incorporated and added statistically as discussed in
more detail later. The recommended formulation is:
R =FH
.
(D.4.514)
inc Roo
The coefficient FR in the above equation will differ for sandy beaches and barriers as discussed
in the following subsections. The DIM approach allows the wave and bathymetric characteristics
to be taken into consideration. Specifically, the spectral shape and actual bathymetry can be
represented. A detailed discussion of the DIM program is presented in a User’s Manual in the
supporting documentation to these Guidelines and Specifications. Two applications of DIM are
available to the Mapping Partner: the computer program and a set of equations. The equations
available are based on parameterized spectra (the JONSWAP spectrum that allows various
spectral widths to be considered) and uniform profile slopes. The program DIM calculates the
total wave setup and provides as output the static (average) wave setup, .
, and the root mean
square (rms), .rms , of the fluctuating wave setup around the average. Static and dynamic wave
setup increase with wave period and the rms of the fluctuating setup component has been found
to increase with the narrower spectra. The static setup component, .
, and rms of the dynamic
setup component, .rms , can be determined using the DIM program or the following equations:
.=4.0FFF F
H T Gamma Slope
(D.4.515)
and
.=2.7GGG G
rms H T Gamma Slope
(D.4.516)
where the units of . and .rms are in feet and the factors are for wave height (FH and GH), wave
period , (FT and GT), JONSWAP spectrum narrowness factor (FGamma and GGamma), and nearshore
slope (FSlope and GSlope). These factors are defined in Table D.4.51. With the exception of the
spectral narrowness factors, the F and G factors are the same. The nearshore slope is the average
slope between the runup limit and twice the break point of the significant wave height with the
depth, hb, at this point defined as hb = Hb / .
. For purposes here, .
can be taken as 0.78.
Because the wave setup components vary with the 0.2 power of this effective slope, these values
are not overly sensitive to the value of effective slope.
D.4.58 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Table D.4.51. Summary of Factors to Be Applied with DIM
Variable Wave Height
FactorWave Period
for
Spectral
Narrowness
Nearshore Profile
Slope
.
(
)0.826.2oH (
)0.4T 20.0 1.0 (
)0.2 m 0.01
rms .
(
)0.826.2oH (
)0.4T 20.0 (
)0.16 Gamma (
)0.2 m 0.01
In applying the DIM method (whether from the program DIM or from the equations and Table
D.4.51), it is necessary to develop the statistics of the oscillating wave setup and incident wave
runup. This combination is based on the rms values (or standard deviations, s
) of each
component. The standard deviation of setup fluctuations, s
(=.
) , is determined from the
1 rms
program or from the guidance provided in Table D.4.51. The recommended standard deviation
for the incident wave oscillations, s2 , on natural beaches is given by:
s=0.3.
H (D.4.517)
2 oo
and the standard deviation associated with the relatively steep barriers is addressed later. With
the two standard deviations (s1 and s2 ) available, the total oscillating contribution to the 2%
total wave runup, .$
T , is determined as the combination of the two standard deviations of the
fluctuating components, s1 and s2:
.$
T =
2.0 s12 +s22 (D.4.518)
The results of the computations using DIM suggest that the fluctuating component of the wave
setup is normally distributed and that the maxima of the fluctuating component of wave setup are
Rayleighdistributed, similar to the general behavior found by Hedges and Mase (2004) in
laboratory experiments of wave setup and wave runup.
D.4.5.1.4.2 Advanced Wave Models
Wave models are becoming more sophisticated and able to account for the complexities of water
waves. A rapidly developing class of these is the socalled Boussinesq models, which are both
commercially and publicly available with the commercial models generally being the more user
friendly. In addition to wave setup, Boussinesq models can calculate wave runup. In conjunction
with the development of these Guidelines and Specifications, onedimensional Boussinesq
models have been applied to calculate total wave runup and the average and oscillating
components were calculated separately. The comments below are based on an assessment of
these Boussinesq results.
Based on comparison with other methods, Boussinesq models yield generally realistic results.
The main concern with Boussinesq modeling is the “learning curve” required to carry out these
types of computations with confidence. Additionally, it was difficult to carry out calculations for
D.4.59 Section D.4.5
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Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
deep water waves with a small directional dependency. The reason for this difficulty lies in the
associated substantial longshore wave lengths and the need for them to be represented by a two
dimensional model. One possible Federal Emergency Management Agency (FEMA) application
that would avoid the repeated learning curve requirement would be to carry out computations on
a regional basis using Boussinesq models. The rate of improvement/development of Boussinesq
models is moderate at present; however, it is likely that this type of model will be much more
capable in 10 to 20 years than at present. Thus, at this stage, a Mapping Partner may elect to
apply Boussinesq models; however, for application on a regional basis, it is preferable to wait for
further developments and improvements. If a Boussinesq model is applied, the Mapping Partner
shall obtain FEMA approval and it is suggested that calculations also be carried out using the
DIM methodology for comparison of results.
D.4.5.1.5 Runup on Barriers
D.4.5.1.5.1 Special Considerations Due to Dynamic Wave Setup
Previous discussions have emphasized that a large wave runup event on the Pacific Coast is
anticipated to have a more substantial dynamic wave setup than is present in the database on
which available runup methods are based. Thus, special consideration is required in the
calculation of wave runup and wave overtopping, which is the subject of a later subsection. The
issues are to include the dynamic wave setup appropriately without double inclusion of the static
and dynamic wave setup components that are inherent in the empirical database from which the
runup and overtopping methodology were based. Table D.4.52 describes the recommended
methodology for both open coast and sheltered water settings. This methodology is illustrated
through example calculations and separate supporting documentation.
Table D.4.52. Recommended Procedure to Avoid
Double Inclusion of Wave Setup Components
Case Procedure
Open Coast, Sandy Beach Apply DIM for wave setup with statistically combined incident
runup, Equations D.4.517 and D.4.518
Open Coast, Coastal Barrier Present Apply DIM for wave setup and reduce dynamic wave setup by
amount considered to be most likely present in laboratory tests
on which runup equations are based
Sheltered Waters, Sandy Beach Same as open coast, sandy beach
Sheltered Waters, Coastal Barrier
Present
Same as open coast, coastal barrier present
D.4.5.1.5.2 Methodology for Calculating Wave Runup on Barriers
In this subsection, barriers include steep dune features and coastal armoring structures such as
revetments. Runup elevations on barriers depend not only on the height and steepness of the
incident wave (and its interaction with the preceding wave), but also on the geometry (and
construction) of the structure. Runup on structures can also be affected by antecedent conditions
resulting from the previous waves and structure composition. Due to these complexities, runup
on structures is best calculated using equations developed with tests on similar structures with
D.4.510 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
similar wave characteristics. Runup equations generally take the form of Equation D.4.514, with
coefficients developed from laboratory or field experiments. Following Equation D.4.51, the
incident wave runup (Rinc) for structures is added to the wave setup values (.
and .$) statistically
based on application of DIM. Also, DIM is applied to estimate the setup water surface at the toe
of the structure, as appropriate, in most cases where the structure toe will be within the surf zone.
The recommended approach to calculating wave runup on structures is based on the Iribarren
number (.) and reduction factors developed by Battjes (1974), van der Meer (1988), de Waal &
van der Meer (1992), and described in the Coastal Engineering Manual (CEM) (USACE, 2003).
The approach is referred to as the TAW (Technical Advisory Committee for Water Retaining
Structures) method and is clearly articulated in van der Meer (2002) and includes reduction
factors for surface roughness, the influence of a berm, structure porosity, and oblique wave
incidence. The TAW method is useful as it covers a wide range of wave conditions for
calculating wave runup on both smooth and rough slopes. In addition to being well documented,
the TAW method agrees well with both small and largescale experiments.
It is important to note that other runup methods and equations for structures of similar form may
provide more accurate results for a particular structure. The Mapping Partner shall carefully
evaluate the applicability of any runup method to verify its appropriateness. Figure D.4.56
shows a general crosssection of a coastal structure, a conceptual diagram of wave runup on a
structure, and definitions of parameters.
SWL + $..+
= DWL2% Total Runup
Still Water Level (SWL)
Total Water Level
Armor Layer
Figure D.4.56. Runup on Coastal Structures, Definition Sketch
Most of the wave runup research and literature shows a clear relationship between the vertical
runup elevation and the Iribarren number. Figure D.4.57 shows the relative runup (R/Hmo)
plotted against the Iribarren number for two different methods: (1) van der Meer (2002), and (2)
Hedges & Mase (2004). In Figure D.4.57, both runup equations are derived from laboratory
experimental data and are plotted within their respective domains of applicability for the
Iribarren number. Each equation shows a consistent linear relationship between the relative
D.4.511 Section D.4.5
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Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
runup and .om for values of .om below approximately 2. For values of .om above approximately 2,
only the van der Meer method is applicable. Moreover, due to its long period of availability and
wide international acceptance, the van der Meer relationship (also referred to as the TAW runup
methodology) is recommended here. The Mapping Partner shall characterize the wave conditions
in terms of .om and be aware of the runup predictions provided by the various methods available
in the general literature.
0
1
2
3
NonDimensional Total Runup, R/Hmo
HedgesandMase(2004)
TAW(vanderMeer,2002)
01234
Iribarren Number, .
om
Figure D.4.57. Nondimensional Total Runup vs. Iribarren Number
The general form of the wave runup equation recommended for use is (modified from van der
Meer, 2002):
.1.77...
.
.
0.5 =..
<
1.8.
rb ß
Pom bom
.
..
.
..
=.
RHmo ..
1.6 .
(D.4.519)
....
.
4.3 
.
1.8 =..
.
rb ß
P
b om .
.
.
.
..
om .
..
.
where:
R is the 2% runup = 2s2
H= spectral significant wave height at the structure toe
mo
.r = reduction factor for influence of surface roughness
.b = reduction factor for influence of berm
.ß = reduction factor for influence of angled wave attack
.P = reduction factor for influence of structure permeability
D.4.512 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Equations for quantifying the .
parameters are presented in Table D.4.53. The reference water
level at the toe of the barrier for runup calculations is DWL2%. Additionally, because some
wave setup influence is present in the laboratory tests that led to Equation D.4.519, the
following adjustments are made to the calculation procedure for cases of runup on barriers.
Table D.4.53. Summary of . Runup Reduction Factors
Runup Reduction
Factor Characteristic/Condition Value of . for Runup
Roughness
Reduction Factor,
r.
Smooth Concrete, Asphalt
and Smooth Block
Revetment
r. = 1.0
(D.4.520)
1 Layer of Rock With
Diameter, D.
/sHD = 1 to 3.
r. = 0.55 to 0.60
2 or More Layers of Rock.
/sHD = 1.5 to 6.
r. = 0.5 to 0.55
Quadratic Blocks r. = 0.70 to 0.95. See Table V53
in CEM for greater detail
Berm Section in
Breakwater,
b.
, B = Berm
Width,
hd
x
.
p
.
.
.
.
.
in radians
Berm Present in Structure
Crosssection. See Figure
D.4.58 for Definitions of
B, Lberm, and Other
Parameters
1 1 cos , 0.6 1.0
2
h
b B
berm
dB
L x
p.
..
..
.=
+
<
<.
..
..
..
.
0
2 0 2
h
mo mo
h
mo
mo
dRRif
H H
x
dHif
H
.
=
=..
=
.
.
=
=
..
(D.4.521)
Minimum and maximum values of
b. = 0.6 and 1.0, respectively
Wave Direction
Factor, .
ß
,
ß
is in degrees and
= 0o for normally
incident waves
LongCrested Waves .
ß
1.0, 0 10
cos( 10 ),10 63
0.63, 63
o
o o o
o
ß
ß
ß
ß
.
<
<
.
..
=

<
<.
.
>..
(D.4.522)
ShortCrested Waves
1 0.0022 , 80
1 0.0022 80 , 80
o
o
ßß
ß

=

=
(D.4.523)
Porosity Factor, P.
Permeable Structure Core
P. = 1.0, om.
< 3.3; P. = 0.46
2.0
1.17( )om.
, om.
> 3.3
and porosity = 0.5. for smaller porosities,
proportion P. according to porosity .
See Figure D.4.59 for definition of porosity
(D.4.524)
D.4.513 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
dh
Lberm
Hmo
Hmo B
Figure D.4.58. Berm Parameters for Wave Runup Calculations
Figure D.4.59. Structure Porosity Definition
The steps below are based on the consideration of laboratory tests conducted with a JONSWAP
Gamma equal to 3.3, which is the average of the spectra entering into the development of the
JONSWAP spectrum. Also, see Table D.4.52.
1.
Calculate, using DIM methodology, .$
(= s
) for: (1) Gamma equal to 3.3, and (2) the
rms 1
Gamma value of interest for the 1% percent chance conditions.
2.
Reduce the dynamic wave setup at the toe of the structure by the difference between the
2% dynamic wave setup values associated with the Gamma of interest and Gamma = 3.3,
i.e., s
(Gamma > 3.3) = s
(Gamma of interest)  s
(Gamma = 3.3). For cases in which
11
1
the Gamma of interest is less than 3.3, set the value of s1 = 0 (Equations D.4.517 and
D.4.518).
D.4.514
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
For a smooth impermeable structure of uniform slope with normally incident waves, each of the
. runup reduction factors is 1.0.
In calculating the Iribarren number to apply in Equation D.4.519, the Mapping Partner shall use
Equation D.4.59 and replace Ho with Hmo and replace T with Tm1.0 (the spectral wave period) in
Equation D.4.510. Hmo and Tm1.0 are calculated as:
H mo =
4.0mo (D.4.525)
Tp
T =
(D.4.526)
m1.0
1.1
where Hmo is the spectral significant wave height at the toe of the structure and Tp is the peak
wave period. In deep water, Hmo is approximately the same as Hs, but in shallow water, Hmo is
1015% smaller than the Hs obtained by zero up crossings (van der Meer, 2002). In many cases,
waves are depthlimited at the toe of the structure and Hb can be substituted for Hmo, with Hb
calculated using a breaker index of 0.78 unless the Mapping Partner can justify a different value.
The breaker index can be calculated based on the bottom slope and wave steepness by several
methods, as discussed in the CEM (USACE, 2003). As noted, the water depth at the toe of the
structure shall include the static wave setup and the 2% dynamic wave setup, calculated with
DIM. In terms of the Iribarren number, the TAW method is valid in the range of 0.5 < .om < 810,
and in terms of structure slope, the TAW method is valid between values of 1:8 to 1:1. The
Iribarren number as described above is denoted .om as indicated in Equation D.4.519.
Runup on structures is very dependent on the characteristics of the nearshore and structure
geometries. Hence, better runup estimates may be possible with other runup equations for
particular conditions. The Mapping Partner may use other runup methods based on an
assessment that the selected equations are derived from data that better represent the actual
profile geometry or wave conditions. See CEM (USACE, 2003) for a list of presently available
methods and their ranges of applicability.
D.4.5.1.5.3 Special Cases—Runup from Smaller Waves
In some special cases, neither of the previously described methods (Subsection D.4.5.1.4, Setup
and Runup Beaches: Description and Recommendations, or Subsection D.4.5.1.5 Runup on
Barriers) is applicable. These special cases include steep slopes in the nearshore with large
Iribarren numbers or conditions otherwise outside the range of data used to develop the total
runup for natural beach methods. Also, use of the TAW method is questionable where the toe of
a structure, or naturally steep profile such as a rocky bluff, is high relative to the water levels,
limiting the local wave height and calculated runups to small values. In these cases, it is
necessary to calculate runup with equations of the form of Equation D.4.5.119 and to avoid
double inclusion of the setup as discussed in Subsections D.4.5.1.5.1 and D.4.5.1.5.2 and Table
D.4.52 and to carry out the calculations at several locations across the surf zone using the
average slope in the Iribarren number. With this approach, it is possible that calculations with the
largest waves in a given sea condition may not produce the highest runup, but that the highest
runup will be the result of waves breaking at an intermediate location within the breaking zone.
D.4.515 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
The recommended procedure is to consider a range of (smaller) wave heights inside the surf zone
in runup calculations. For this approach, for all depths considered, the dynamic setup is reduced
if the Gamma of interest exceeds 3.3 as described in Subsections D.4.5.1.5.1 and D.4.5.1.5.2 and
Table D.4.52. For each depth considered, the static setup is calculated with Equation D.4.55
with the water level including the 2% dynamic wave setup replacing the depth, h, in that
equation. With the 2% dynamic water level available, methods of calculating wave runup on
barriers is applied and are described in greater detail below.
The concept of a range of calculated runup values is depicted schematically in Figure D.4.510
where an example transect and setup water surface profile are shown. Figure D.4.510 also
shows the corresponding range of depthlimited breaking wave heights calculated based on a
breaker index and plotted by breaker location on the shore transect. The Iribarren number was
also calculated and plotted by breaker location in Figure D.4.510. The calculation of . at each
location uses the deshoaled deepwater wave height corresponding to the breaker height, the
deepwater wave length and the average slope calculated from the breaker point to the
approximate runup limit. Note that this average slope (also called composite slope, as defined in
the CEM [USACE, 2003] and SPM [USACE, 1984] increases with smaller waves because the
breaker location approaches the steeper part of the transect near the shoreline. This increases the
numerator in the . equation. Also, the wave height decreases with shallower depths, reducing the
wave steepness in the denominator of the . equation. Hence, as plotted in Figure D.4.510, .
increases as smaller waves closer to shore are examined, increasing the relative runup (R/H).
However, because the wave height decreases, the runup value, R, reaches a maximum and then
decreases.
The following specific steps are used to determine the highest wave runup caused by a range of
wave heights in the surf zone:
1.
Calculate, using DIM, the reduced 2% dynamic wave setup based on the Gamma of
interest and Subsections D.4.5.1.5.1 and D.4.5.1.5.2 and Table D.4.52. Calculate the
static wave setup based on Equation D.4.55 for the crossshore location considered.
Replace h in that equation with the sum of the still water depth at the location and the 2%
dynamic wave setup.
2.
Calculate the runup using the methods described earlier for runup on a barrier. This
requires iteration for this location to determine the average slope based on the differences
between the runup elevation and the profile elevation at the location and the associated
crossshore locations. Iterate until the runup converges for this location.
3.
Repeat the runup calculations at different crossshore locations until a maximum runup is
determined.
D.4.516
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Crossshore Distance, y
Wave Runup at Shoreline Resulting From
Breaking at Crossshore Location, y
Depth Limited Wave HeightVariables as a Functionof Breaker LocationIribarren Number
y
Breaker Location Causing
Maximum Runup
2% Setup Level
Total Maximum
Potential Runup
Figure D.4.510. Example Plot Showing the Variation of Surf Zone Parameters
D.4.517 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
D.4.5.1.6 Example Computations of Total Runup
Four examples corresponding to the four settings in Table D.4.52 are examined and total runup
values presented. The conditions for the four examples are presented in Table D.4.54. These
examples have been selected to illustrate application of the methodology for several settings. The
supporting documents provide a detailed stepbystep presentation of the calculations associated
with these four examples and seven additional examples..
Table D.4.54. Example Characteristics
Example Water Level and
Wave Conditions
Profile
Conditions Barrier Characteristics
1. Open Coast,
Sandy Beach
Astronomical tide = 3 feet
above NAVD* and wind
surge = 2 feet. moH = 26.2
feet; T = 20 sec; Gamma =
30 in JONSWAP spectrum
Slope = 1:60 No barrier
2. Open Coast With
Structure Present
Same as Example 1 Slope = 1:60 Slope = 1:1.5, 1 layer rock of
3 feet diameter, toe depth = 2
feet below NAVD. porosity
considered to be 0.2
3. Sheltered Water,
Sandy Beach
Astronomical tide = 3 feet,
above NAVD and wind
surge = 1 foot. moH = 6.0
feet; T = 5 sec; Gamma = 1
in JONSWAP spectrum
Slope = 1:60 No barrier
4. Sheltered Water With
Structure Present
Same as Example 3 Slope = 1:60 Same as Example 2
* NAVD = North American Vertical Datum
Example 1: Open Coast, Sandy Beach
The actual bathymetry for this example is presented in Figure D.4.511 and is approximated here
as a uniformly sloping profile with slope of 1:60 out to twice the approximate significant wave
height breaking point. The deep water Iribarren number, .o , for this case is calculated to be
0.147.
Table D.4.55 presents the 2% exceedance results based on the DIM program and coefficients in
Table D.4.51 with a nearshore slope of 1:60 as well as the results from the Boussinesq model
calculations. To illustrate the role of the spectral width, the results for a Gamma of unity based
on the equations have been presented as a footnote to Table D.4.55.
D.4.518 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Figure D.4.511. Offshore Profile for Example Problem
Table D.4.55. Comparison of Results from Various Methods of
Calculating 2% Total Runup for Examples
Example Method
2% Total Runup (ft)
Static
Setup
(ft)
Combined Dynamic Setup
and Incident Wave Runup
(ft)
Total
Runup
(ft)
1 Boussinesq Equations 5.33 8.71 14.04
1 DIM Program 4.89 10.11 15.53*
1
Equations (Table D.4.51)
Based on DIM 4.43 10.58 15.01
2
Equations (Table D.4.51) Based
on DIM and Equation D.4.519 4.43 23.44 27.87
3
Equations (Table D.4.51)
(Based on DIM) 0.78 1.10 1.88
4
Equations (Table D.4.51) Based
on DIM and Equation D.4.519 0.78
9.20 (Incident Wave Runup)
(Dynamic Setup = 0.0) 9.98
* Note: For a Gamma (JONSWAP spectral peakedness) value of 1.0, the 2% total runup by the DIM method is 10.85 feet. The
total runup for all examples is above SWL.
D.4.519 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Example 2: Open Coast with Structure Present
The runup reduction factors determined for this example from Table D.4.53 are: .r = 0.6, .b =
1.0, .ß = 1.0, and .P = 0.86. Values of the runup were based on the DIM methodology and
Equation D.4.519 with adjustment for the dynamic setup considered to occur in the model tests
that led to Equation D.4.519. The total 2% dynamic water depth at the toe of the structure was
found to be 14.49 feet, which yielded an approximate significant wave height at the structure toe
of 11.30 feet for use in Equation D4.519. The value of .om is 8.16. The total runup above SWL
was determined to be 27.87 feet.
Example 3: Sheltered Waters, Natural Beach
The deep water Iribarren number based on the conditions in this example is: .o = 0.077. The
total 2% runup above SWL was determined to be 1.88 feet.
Example 4: Sheltered Waters with Structure Present
The runup reduction factors determined for this example were obtained from Table D.4.53 and
are the same as for Example 2: .r = 0.6, .b = 1.0, .ß = 1.0, and .P = 0.86. The total runup
value was based on the DIM methodology and Equation D.4.519 with adjustment for the
dynamic setup considered to occur in the model tests that led to Equation D.4.519. This resulted
in a dynamic setup, .rms = 0. The total 2% dynamic water depth at the toe of the structure was
found to be 6.78 feet resulting in Hmo =5.29 feet. The relevant Iribarren number at the breakwater
toe is: .om = 2.95. The total runup elevation above SWL was determined to be 9.98 feet.
D.4.5.1.7 Documentation
The Mapping Partner shall document the procedures and values of parameters employed to
establish the 1% chance total wave runup on the various transects on natural beaches and barriers
that could include steep dunes and structures. In particular, the basis for establishing the runup
reduction factors and their values shall be documented. The documentation shall be especially
detailed in case the methodology deviates from that described herein and/or in the
recommendations in the supporting documentation. Any measurements and/or observations shall
be recorded as well as documented or anecdotal information regarding previous major storm
induced runup. Any notable difficulties encountered and the approaches to addressing them shall
be described clearly.
D.4.5.2 Overtopping
D.4.5.2.1 Overview
Wave overtopping occurs when the barrier crest height is lower than the potential runup level;
waves running up the face of a barrier reach and pass over the barrier crest. If the total runup
elevation (calculated in Subsection D.4.5.1) exceeds the crest elevation, zc, then the overtopping
of the structure is potentially significant and requires evaluation to define hazard zones.
D.4.520 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
There are three physical forms of overtopping:
1.
Green water overtopping occurs when waves break onto or over the barrier and the
overtopping volume is relatively continuous.
2.
Splash overtopping occurs when waves break seaward of the face of the structure, or
where the barrier is high in relation to the wave height, and overtopping is a stream of
droplets. Splash overtopping can be carried over the barrier under its own momentum or
may be driven by onshore wind.
3.
Spray overtopping is generated by the action of wind on the wave crests immediately
offshore of the barrier. Without the influence of a strong onshore wind, this spray does
not contribute to significant overtopping volume.
Mapping hazard zones due to green water and splash overtopping requires an estimate of the
velocity or discharge of the water that is propelled over the crest, and the envelope of the water
surface, defined by the water depth, landward of the crest. Ideally:
.
Base Flood Elevations (BFEs) are determined based on the water surface envelope
landward of the barrier crest.
.
Hazard zones are determined based on the inland extent of greenwater and splash
overtopping, and on the depth and force of flow in any sheet flow areas.
The calculation methods for the hazard zones landward of the barrier crest differ for green water
overtopping and splash overtopping and depend on the ratio R '/ zc ' as illustrated in Figure
/ z < 2, splash overtopping dominates and for 'D.4.512. For 1 < R '' R '/ z > 2, bore
c
c
propagation dominates. Each of these types results in the occurrence of a hazard zone, although
the calculations quantifying the hazard zones differ as described later in this subsection. Note
that R' and zc ' are relative to the DWL2%.
Figure D.4.513 shows the parameters that may be available for use in mapping BFEs and flood
hazard zones and are listed in Table D.4.56 (availability depends on the runup and overtopping
methods employed). Again, the reference water level for overtopping calculations is the
DWL2%. The remainder of this subsection is organized as follows. First the methodology for
calculating overtopping rates is reviewed. Secondly, methods are presented for calculating the
hazard zones landward of the crest of the barrier for the two types of overtopping discussed
above and illustrated in Figure D.4.512.
D.4.521
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Splash Over
DWL2%
'R' cz
1 < '/ ' cR z < 2
Potential Runup
Splash Over Occurs
a) Conditions for Splash Overtopping
' cz
Bore
DWL2%
'R
'/ ' cR z > 2
Propagating Bore Occurs
Potential Runup
b) Conditions for Bore Propagation Overtopping
Figure D.4.512. Definition Sketch for Two Types of Overtopping
D.4.522 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
y
z
R.
Figure D.4.513. Parameters Available for Mapping BFEs and Flood Hazard Zones
Table D.4.56. Overtopping Parameters Used in Hazard Zone Mapping
Parameter Variable Units
Total potential runup elevation R ft
Mean overtopping rate q cfs/ft
Landward extent of green water and splash overtopping yG,Outer ft
Depth of overtopping water at a distance y landward of crest h(y) ft
Due to the complexity of overtopping processes and the wide variety of structures over which
overtopping can occur, wave overtopping is highly empirical and generally based on laboratory
experimental results and on relatively few field investigations.
D.4.5.2.2 Background
Overtopping calculations are subject to more uncertainty than runup calculations. While runup
models may replicate observed runup values with errors of about 20%, predicted overtopping
rates are often in error by a factor of 2 or more (Kobayashi, 1999). Some overtopping predictions
may be even less accurate, given the fact that subtle changes in wave conditions, water level,
structure geometry and characteristics can have a very large effect on overtopping rates.
D.4.5.2.2.1 Empirical Equations
Wave overtopping may be predicted by a number of different methods, but chiefly by semi
empirical equations that have been fitted to hydraulic model tests using irregular waves for
specific structure geometries. These empirical equations have the general form:
(bF )
'
Qae
'
=() b
=QaF
or (D.4.527)
D.4.523 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
where Q is a dimensionless average discharge per unit length of structure and F’ is a
dimensionless freeboard. It is noted that these two dimensionless quantities are defined
differently depending on the researcher and the structure characteristics. Overtopping rates
predicted by these formulae generally include green water and splash overtopping because both
parameters are recorded during the model tests.
Section VI52b of the CEM (USACE, 2003) describes several different methods that have been
developed for particular geometries. The choice of method depends upon the form of wave
behavior at or on the structure, and the nature of the structure.
D.4.5.2.2.2 Types of Wave Behavior
Any discussion on wavestructure interaction requires that the key wave processes be
categorized, so these different processes may be separated. Four key terms, nonbreaking or
breaking on normally sloped structures and reflecting or impacting on steeper structures, are
defined below to describe breaking and overtopping processes.
For beaches and normally sloping structures, the simplest division is to separate breaking
conditions where waves break on the structure from nonbreaking waves. These conditions can
be identified using the surf similarity parameter (or Iribarren number) defined in terms of beach
or structure slope (tan a), and wave steepness (Hmo/Lo):
tan a
tan a
.=
= (D.4.528)
op
mo op
o
H S
L
where Sop is wave steepness as defined above.Breaking on normally sloped (1:1.5 to 1:20)
surfaces generally occurs where .op = 1.8, and nonbreaking conditions when .op > 1.8.
On very steep slopes or vertical walls, reflecting overtopping occurs when waves are relatively
small in relation to the local water depth and of lower wave steepness. The structure toe or
approach slope does not critically influence these waves. Waves run up and down the wall,
giving rise to relatively smoothly varying loads. In contrast, impacting breaking on steep slopes
occurs when waves are larger in relation to local water depths, perhaps shoaling up over the
approach bathymetry or structure toe itself.
For simple vertical walls, the division between reflecting and impacting conditions is made using
the parameter h .
*
h .
2p
h .
h* =.
2 .
(D.4.529)
Hmo .
gTm .
Reflecting conditions can generally be said to occur where h = 0.3, and impacting conditions
*
when h* < 0.3.
D.4.524 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
D.4.5.2.2.3 Nature of the Structure
The relative freeboard, Fc/Hs, is a very important parameter for predicting overtopping.
Increasing wave height or period increases overtopping discharges as does reducing the crest
freeboard, either by lowering the crest or raising the water level.
For structures with small relative freeboards, various prediction methods of overtopping
discharge converge, indicating that the slope of the structure no longer has much influence in
controlling overtopping. Over the normal range of freeboards, the characteristics for slope of 1:1
to 1:2 are similar, but overtopping reduces significantly for slopes flatter than 1:2. Empirical
methods for sloping structures are applicable over specific slope ranges – structures tested
usually lie between 1:1 and 1:8 with occasional tests at 1:15 or lower. Vertical and very steep
walls (1:1 or steeper) have different prediction tools due to their distinct physical overtopping
regimes as noted in the preceding section.
Most empirical methods were developed initially for smooth slopes and have been subsequently
extended and modified for rough slopes. This is often accomplished by the inclusion of a
reduction factor for surface roughness, .r, and other features as discussed previously in
Subsection D.4.5.1.5.2 and summarized in Table D.4.53.
Increasing permeability of the structure decreases runup and overtopping as a larger proportion
of the flow takes place inside the structure. Increasing porosity also reduces runup and
overtopping because a larger volume of water can be stored in the voids. These differences in
response characteristics make it convenient to distinguish between impermeable and permeable
structures through a porosity reduction factor, .
P .
Berms can also have a considerable impact on the runup and overtopping. van der Meer (2002)
defines a reduction factor for berms, .b, that takes into account both the depth of water over the
berm and its width. Berms are most effective in reducing runup and overtopping if the horizontal
surface is close to SWL. Their effectiveness decreases with depth and can be neglected when the
depth of water over the berm is greater than 2Hmo.
D.4.5.2.2.4 Selection of Empirical Methods
The Mapping Partner is responsible for selecting and applying a suitable method to predict
overtopping. Because the methods available for predicting overtopping are empirically based, the
choice of method is substantially influenced by the characteristics of the transect that is being
analyzed. Section VI52b of the CEM (USACE, 2003) shall be reviewed to determine if a
similar structure geometry has been tested. Care shall be taken to determine whether the transect
being analyzed falls within the range of conditions for the model tests. Table D.4.57 presents
overtopping relationships for various types of structures and conditions. The conditions
associated with these different situations are discussed below.
If the structure to be analyzed has not been tested, generalized methods for predicting wave
overtopping on sloping and vertical structures are available and can be applied.
D.4.525 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
•
Normally sloping structures (slopes milder than 1:1.5 vertical to horizontal): For the
majority of structures with impermeable smooth or rough slopes and with straight or
bermed slopes, the formulation developed progressively by de Waal and van der Meer
(1992), van der Meer and Janssen (1995), and van der Meer et al. (1998) is suitable. This
is shown in Table VI511 of the CEM (USACE, 2003) and the method is fully
articulated in van der Meer (2002).
•
Steep and vertical walls: For this case, the formulation developed by Besley et al. (1998),
Besley (1999), Besley and Allsop (2000), as extended by Allsop et al. (2004) is suitable.
These general methods are described in more detail in the following subsections and the
recommended equations are summarized in Table D.4.57.
Table D.4.57. Equations for Wave Overtopping
Quantity and General
Conditions
Characteristic/
Condition Relationships
NonDimensional (Q)
and Dimensional (q)
Mean Overtopping Rates
Normally Sloping
Structures
1:15 tan 1:1.5 a<
<
Breaking Waves
1.8op.
=
'
3
4.7tan , 0.06 Fmo
op
gHqQ Q eS
a
=
=
' 1
tan
opc
mo r B P
SFF
H ßa
..
.
.
=
(D.4.530)
Note: If the overtopping rate (q) from this
equation exceeds that for nonbreaking waves
below, use the result for nonbreaking waves
below
NonBreaking Waves
1.8op.
>
' 3 2.3 , 0.2 F
moqQ gH Q e=
=
' 1c
mo r
FF
H ß.
.
=
(D.4.531)
NonDimensional (Q)
and Dimensional (q)
Mean Overtopping Rates
Steeply Sloping or
Vertical Structures (at or
steeper than 1:1.5).
Some Approaching
Waves Not Broken
NonBreaking Waves
(Reflecting)
* 0.3h =
3
moqQ gH =
2.78 /0.05 c mo FHQ e= (D.4.532)
*
mo om
h hh
H L
.
.
=
.
.
.
.
Breaking Waves
(Impacting)
* 0.3h <
3 2
*
4 3.24 1.37 10 ( ')
qQ gh h
Q x F

=
=
'
*
c
mo
FF h
H
= (D.4.533)
D.4.526
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Table D.4.57. Equations for Wave Overtopping
(cont.)
Quantity and General
Conditions
Characteristic/
Condition Relationships
NonDimensional (Q)
and Dimensional (q)
Mean Overtopping Rates
Steeply Sloping or
Vertical Structures (at or
steeper than 1:1.5). All
Approaching Waves
Broken
Structure Toe Below
DWL2% Water Level
*
32
*
3.24( / )0.27 10 4 c mo FH h
qQ gh h
Q x e
=
=
valid for *(/ ) 0.03 c mo FH h =
(D.4.534)
Structure Toe Above
DWL2% Water Level
0.17
32
*
4.70.06 coPFS
qQ gh h
Q e 
=
=
(D.4.535)
Shallow Foreshore
Slopes
Foreshore Slope < 1:2.5
7oP.
>
'
32
*
30.21 F
mo
qQ gh h
Q gH e
=
=
'
(0.33 0.022 )
c
r mo oP
FF
ß
H.
.
.
=
+
(D.4.536)
Note: H is the spectral significant wave height at the toe of the structure.
mo
D.4.5.2.3 Data Requirements
Overtopping is a function of both hydraulic and structure parameters:
q =(
Tp s )
f Hmo ,, ß, Fc , h , geometry (D.4.537)
where Hmo is the significant wave height at the toe of the structure, Tp is the peak period, ß is the
angle of wave attack, Fc is the freeboard as shown in Figure D.4.513, and hs is the 2% depth of
water at the toe of the structure. The Mapping Partner shall take care to follow the specification
for the hydraulic parameters as described in the chosen method. In most methods, the wave
conditions is specified at the toe of the structure.
In addition to a description of the waves and water levels, a description of the structure geometry
is required. Depending on the method used, the geometry of the structure, especially complex
geometries such as berms, may be specified in particular ways. The Mapping Partner shall ensure
that the specification for the structure geometry are followed as described in the chosen method.
D.4.5.2.4 Mean Overtopping Rate at the Crest
D.4.5.2.4.1 Sloping Structures (van der Meer, 2002)
The prediction method for simple smooth and armored slopes, as described in van der Meer
(2002), distinguishes between breaking and nonbreaking waves on the basis of .op and use
different definitions of dimensionless discharge and dimensionless freeboard. Influence factors,
.b, .p, .f, .ß, have been described previously in Subsection D.4.5.1.5.2. There is one difference in
D.4.527 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
the definitions of the runup reduction factors (.
parameters), which is for the direction of wave
approach ß
. For this case,
o
.1.0 
0.0033
ß
, (0 =
ß
=
80 )
.
.
(D.4.538)
ß
=.
o
1.0 
0.0033
80
,(
ß
=
80 )
.
.
For breaking waves .op = 1.8, the overtopping rate, is calculated as defined in Table D.4.57,
Equation D.4.530 in which Q is a dimensionless overtopping discharge for plunging breaking
waves and F’ is the dimensionless freeboard for breaking waves (see Figure D.4.513).
Similar relationships are available for nonbreaking waves when .op > 1.8, using different
dimensionless parameters as defined in Table D.4.57, Equation D.4.531.
D.4.5.2.4.2 Steep and Vertical Walls (Besley and Allsop, 2000)
The calculation procedure for steep and vertical walls described by Besley and Allsop (2000)
distinguishes between plunging and surging waves on the basis of h* (see Equations D.4.532
and D.4.533) and use different definitions of dimensionless discharge and dimensionless
freeboard.
For h = 0.3, reflecting waves predominate and a dimensionless discharge can be calculated
*
with Equation D.4.532 in Table D.4.57.
For impacting conditions, h < 0.3, mean overtopping is given by Equation D.4.533 in Table
*
D.4.57.
For conditions under which waves reaching the wall are all broken, two formulae are suggested
depending upon whether the toe of the structure is above or below the DWL2% level.
For structures with the toe below the DWL2% level, refer to Equation D.4.534 in Table D.4.57.
For structures with the toe above the DWL2%, refer to Equation D.4.535 in Table D.4.57.
D.4.5.2.4.3 Shallow Foreshore Slope
For a shallow foreshore slope (m<1:2.5), apply Equation D.4.536 in Table D.4.57.
D.4.5.2.5 Limits of Overtopping and Hazard Zones Landward of the Barrier Crest
As discussed previously and illustrated in Figure D.4.512, hazard zones landward of the barrier
crest can be a result of splash overtopping, which occurs for 1< R '/ zc ' < 2, or for bore
overtopping, which occurs for R '/ zc ' > 2. The methodologies to calculate the limits of the
hazard zones for each of these cases is described below. These methodologies are approximate
and both consider the Froude number to be 1.8 as found by Ramsden and Raichlen (1990).
D.4.528 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
D.4.5.2.5.1 Overtopping by Splash
Figure D.4.514 presents a detailed view of the associated variables for this type of overtopping.
,GzNegative as Shown
cV
ch
,GOuter
,G Inner ycay
z
R.Potential Wave Runup
Figure D.4.514. Definition Sketch for Wave Overtopping by Splash
First, the calculation steps are presented and then the associated calculations discussed in greater
detail. The following steps define the approach to establishing the splashdown distance for the
1% annual event and the landward limit of the hazard zone defined as: hV 2 =200 ft3/sec2.
1. Calculate the excess potential runup, .R =
R 
z , V cos a and h . V =1.1 g.R and
c
ccc
hc=
0.38.R . In the case of a vertical seawall, apply Equations D.4.59 and D.4.519
replacing the numerator: tana by 1.0 for calculation of the excess runup, .R .
2. Estimate, based on data, the associated onshore wind component, Wy . Use Wy = 44 ft/sec
as a minimum.
3.
Calculate an enhanced onshore water velocity component (denoted by prime):
(V cos a)' =
V cosa+
0.3( W V cos a) . In the case of a vertical seawall, this simplifies
cc yc
to(cos a
)' =
0.3 W
Vc y .
4. Determine an effective angle, a , where tan a=
V sin a
(Vc cos a)’.
eff eff c
5. Apply Figure D.4.515 for the particular geometry to quantify the outer limit of the splash
region, yGOuter , where V =
[(Vc cosa
)] '2 +[V sina]2 .
, c
c
D.4.529
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
6. Calculate the total energy, E, of the splashdown: E =.R zG , where both variables are
relative to the barrier crest elevation.
7. Calculate the initial splashdown Vo and ho according to: Vo=1.1 gE and ho=
0.19E
8.
Calculate the landward limit of hV 2 = 200 ft3/sec2, where h is the water depth given by
the CoxMachemehl method (discussed below) and V is considered to be uniform, i.e.,
VVo.
=
Splashdown Limits
The landward splashdown limit is based on consideration of the trajectory of the splash as shown
schematically in Figure D.4.514. This landward splashdown limit is determined by use of Figure
D.4.515 where the horizontal axis is (z 
zV 2 sin 2 a
/2 ] , where V includes the wind
) /[ g
Gcc eff
c
effect (Steps 3 and 4 above) and the vertical axis is the nondimensional distance, , . Note
yGOuter
that in most cases, the horizontal axis is negative.
Figure D.4.515. Solution of Trajectory Equations for Splashdown Distances
D.4.530
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
The CoxMachemehl Method
The CoxMachemehl (CM) method is applied to both the splash case and the bore propagation
case of wave overtopping. The form recommended here is modified slightly from that developed
by CM. Given the initial depth, ho, the depth decays with distance as:
.
2
.
5( yyo ) .

() =
ho 
hy
.
.
AgT 2 .
.
.
(D.4.539)
where ho is determined from Step 6 and for an initial approximation, the nondimensional
parameter A may be taken as unity. For nonzero slopes landward of the barrier, mLW , the A
value in the denominator of the above equation shall be modified by Am =
A(1 
2.0mLW ) , where
Am includes the effect of the landward slope and the value in the parentheses is limited to the
range 0.5 to 2.0. Note that mLW is positive sloping upwards in the landward direction. If the
maximum distance of bore propagation does not appear reasonable or match observations, the
Mapping Partner shall carefully examine the results to determine if a factor A different than
described above is warranted to increase or decrease inland wave transmission distance as
appropriate.
D.4.5.2.5.2 Bore Propagation
For this case, the Mapping Partner shall apply the CM method considering a Froude number =
1.8 as for the case shown in Figure D.4.512 and refined below as Figure D.4.516.
' cz
ho V
Bore
DWL2%
'R
'/ ' cR z > 2
Potential Runup
Figure D.4.516. Overtopping Resulting in Bore Propagation
D.4.531
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
The steps required to calculate the distance to hV 2 =200 ft3/sec2are described below.
1. Calculate the initial velocity, Vo, and initial depth, ho, as: Vo=
1.1 g.R and
ho=
0.38.R .
2.
Calculate the landward limit of hV 2 = 200 ft3/sec2, where h is the water depth given by
the CM method, including the effect of landward slope, mLW , as appropriate and V is
considered to be uniform, i.e., VVo.
=
D.4.5.2.6 Documentation
The methods and results obtained in quantifying the 1% annual chance overtopping values shall
be described in detail. The following shall be provided for the overtopped transects: (1) profiles,
(2) assumptions and considerations including runup reduction factors, (3) overtopping values
associated with the 1% chance event, and (4) basis for establishing the 1% splash zones landward
of the barrier including any assumptions made. Any measurements and/or observations and
documented or anecdotal information from previous major storminduced overtopping and
damage shall be recorded. Any notable difficulties encountered and the approaches to addressing
them shall be described clearly.
D.4.5.3 Wave Dissipation and Overland Wave Propagation
This subsection provides guidance for estimating wave dissipation over broad, shallow areas, and
quantifying wave height decrease during overland propagation. Due to the relatively steep
nearshore on most of the Pacific Coast, coastal flooding is typically governed by total runup and
overtopping. Therefore, consideration of wave dissipation and overland propagation is usually
not required. In the paragraphs below, enhanced wave dissipation refers to dissipation by the
mechanisms discussed in this subsection.
Wave energy is dissipated when propagating over relatively broad, shallow areas due to
increased bottom friction, percolation in sandy seabeds, movement of cohesive seabeds, and drag
induced by vegetation; see Figure D.4.517 for a conceptual definition sketch. Dissipation
mechanisms can result in smaller wave heights than predicted by typical shoaling and depth
induced breaking relationships. Available analysis methods rely on parameters that have a wide
range of values that can be difficult to quantify reliably. Therefore, the overall approach required
to quantify dissipation may entail use of empirical data, possibly collected by the Mapping
Partner at the study site or available from a similar site. In most situations, the amount of
dissipation is small when compared to the effort required to analyze the dissipation processes. In
addition, the risk of overestimating wave dissipation with available tools, resulting in an
underestimation of flood risk, can be significant.
On the Pacific Coast, enhanced wave dissipation in excess of depthinduced breaking is most
likely to occur when high tidal waters cause overland wave propagation in lowlying coastal
areas. The Wave Height Analysis for Flood Insurance Studies (WHAFIS) computer program has
D.4.532
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Figure D.4.517. Schematic of Wave Attenuation Processes
been developed to address overland wave propagation and is recommended for use on the Pacific
Coast. Because WHAFIS was developed for the Atlantic and Gulf coasts, minor modifications
are required for use on the Pacific Coast, hence the Mapping Partner shall obtain approval from
FEMA.
D.4.5.3.1 Assessment of Enhanced Wave Dissipation
Damping of waves occurs due to the effects of bottom friction, percolation in sandy seabeds,
viscous damping by cohesive bed movements, and drag imparted on the wave motions by
vegetation. These processes are influenced by water depth, the distance waves travel over a
sandflat, mudflat or through vegetation. Other important factors include vegetation type and
whether wave regeneration occurs due to winds.
The Mapping Partner shall consider the attenuation of wave height and energy. Initial
considerations shall be based on whether the wave attenuation is of sufficient magnitude to
warrant including in a Flood Insurance Study (FIS). In general, enhanced wave dissipation shall
not be considered unless calculations indicate wave heights are attenuated by more than 20%
and/or the reduction in wave heights has a significant effect on total runup or the wave input to
the overland propagation analysis.
If waves are propagating in the presence of an onshore wind field, enhanced dissipation shall be
considered only within a scheme that allows additional windwave generation. This can be
accomplished with windwave generation and transformation models (see Section D.4.4) and
WHAFIS (Subsection D.4.5.3.3). However, if the site is sheltered and wave height regeneration
is unlikely, wave attenuation by sandflats, mudflats, or vegetation can be considered in an
independent calculation. Initial considerations for the Mapping Partner are:
•
What are the physical site characteristics?
•
Is the area within the prevailing wind field?
•
Are there sheltered areas where wind regeneration does not occur?
•
Will the effect of the sandflat, mudflat, or vegetation be significant?
D.4.533 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
At this time, available information on the Pacific Coast is insufficient to provide sitespecific
data and results for the Mapping Partner. Therefore, calculations involving a range of relevant
parameters are required. If the attenuation is deemed to be potentially significant, sitespecific
data, calibration, and verification may be necessary for FIS applications.
D.4.5.3.2 Wave Attenuation by Bottom and Vegetation Interactions
If attenuation is significant, the following methodology can be employed to perform an initial
assessment to determine if more detailed calculations are necessary. Bottom dissipation
mechanisms can be mathematically expressed as a negative forcing term in the conservation of
wave energy equation for steadystate, longshore uniform conditions as follows:
dECG
=
e
dy
(D.4.540)
where E is the wave energy density, CG is the wave group velocity, e is the energy dissipation
rate per unit bottom area, and y is the direction of wave propagation. Dissipation can occur at the
surface, the bottom of the water column, and within the water column due to wave breaking. One
may consider e as the sum of energy dissipations due to wave breaking and bottom and internal
effects. Dissipation due to bottom and internal effects dominates in areas of nonbreaking waves
whereas dissipation due to breaking dominates within the breaking zone. Equations discussed in
Subsections D.4.5.3.2.1 and D.4.5.3.2.2 and summarized in Table D.4.58 can be used to develop
an initial assessment of the magnitude of enhanced wave dissipation due to bottom effects and
vegetation. If this dissipation is considered significant, the Mapping Partner may elect to use
equations within these subsections to calibrate a method. Calibration could be based on pairs of
measured wave heights and distances over approximately uniform depth conditions, and
collected at a location similar to the study site, i.e., similar site geometry and similar wave
conditions. Data used to calibrate the method shall be collected along the direction of wave
propagation showing changes in wave height and period across the site. The following
subsections present methodology for calculating wave dissipation resulting from various
mechanisms. Table D.4.58 summarizes the equations governing wave attenuation by various
processes and recommends ranges of required parameters to calculate attenuation.
D.4.5.3.2.1 Wave Attenuation by Bottom Interactions
Wave Attenuation Due to Bottom Friction
For a rough bottom, Dean and Dalrymple (1991) express energy dissipation due to bottom
friction as shown in Table D.4.58, Equation D.4.541. In addition to the equation for e
, this
table presents the approximate range of the unknown friction factor, f, the equation governing
attenuation, and the expression for the unknown friction factor if the wave heights at two
locations are known. The variables appearing in the expressions are defined as a table footnote.
Wave Attenuation Due to Percolation
For a porous bottom, Dean and Dalrymple (1991) express energy dissipation due to bottom
percolation as shown in Table D.4.58, Equation D.4.542.
D.4.534 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners[January 2005]
Table D.4.58. Summary of Equations for Overland Propagation (Over Uniform Depth)
WaveDampingBy
e
Unknowns and
Approximate Ranges
Solution for Wave Heights, H1
and H2 , for Waves Propagating
Over Distance
y2 – y1
Value of Unknown
For Measured Wave Heights, H1 and H2
Over Distance
y 2 – y1
BottomFriction
3 3
3 48 sinhfH
kh
.
s
p
0.04 0.16<
f
<
2
3
1 2 11
3
1
( ) 1
12 sinhG
H
f Hy yH
C kh
s
p
=

+
3
1 2
3
2 1 2 1
12 sinh( )
( )
GCg khH H f
HH y yp

=

(D.4.541)
Percolation 2 2
8cosh2gKkHkh
..
10%3.3 30%K D=
±
,
10%D = Diameter forWhich 10% is Smaller in cm
2 2 1 ( )
2 1
2 2
,
2 cosh
Ay y
G
H H e
gKk A
C kh.

=
=
2
1
2 1 2
cosh
( )
GC kh H K n
y y gk H
.
=

(D.4.542)
MuddyBottom
2
2 2 2 2 2
2 ( )
16
kh H
e gk
.
s.
s
s

3
2 3 4.5 slugs / ft<
.
<
2
2 0.1 1 ft / sec<
.
<
3 2 1 ( )
2 1
2 2 2 2 2
3 2
,
( )
4
Ay y
kh
G
H H e
gKk
A e gk
Cg.s.
s
.s


=
=

3/ 2
1
2 2 2 2 2
2 1 2
2
( ) ( )
G
kh
C g H n
y y e gk H
s...
=

l(D.4.543)
Vegetation 3/ 2 3
2 1/ 2 12
D pgC C DHSh
.
p
2< D p CC <6 2
1 2 1 1
2
1
( )
1
3
D p
H
CC DH y y H
pSh
=

+
2
1 2
2 1 2 1
3( )
( ) p D
H H S h CC
HH D y y
p
=
(D.4.544)
Definitions: f = Bottom friction coefficient; s and k = Wave angular frequency and wave number, respectively; . and 2.
= Water and mud kinematic viscosity, respectively; . and
2.
= Water and mud mass density, respectively; D C and P C = Stem and plant drag coefficients, respectively; S is plant stem spacing.
D.4.535 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Wave Attenuation Due to a Viscous Bottom
Mudflats are common Pacific Coast features within lagoons and bays. Waves are damped when
traveling across mudflats, due to the movement of sedimentrich water column and bed. The
viscous, plastic nature of mudrich sediments allows the soft bottom to deform in response to
wave forces, resulting in the absorption of some of the wave energy. There are several methods
for developing a preliminary estimate of wave dissipation due to viscous damping.
Dean and Dalrymple (1991) and Lee (1995) express energy dissipation due to a viscous bottom
as shown in Table D.4.58, Equation D.4.543. If the Mapping Partner determines that wave
attenuation over mudflats is important, additional methods are provided in Massel (1996);
however, any method to determine wave attenuation by mudflats shall be used with care. Ranges
of values of .2 are 3 to 4.5 slugs/ft3 and .2 ranges from 0.1 to 1.0 ft2/s.
D.4.5.3.2.2 Wave Attenuation by Vegetation
Investigators have shown that vegetation damps wave energy, e.g., Dean (1978, 1979), Knutson
(1982, 1988), Moeller et al. (1996, 1999, 2002), and Hansen (2002). Vegetation reduces
incoming wave heights by imparting resistance (drag) on incoming waves, thereby causing a
reduction in wave height and steepness, which results in a decrease in wave height and energy.
Mapping Partners working in areas where extensive marsh vegetation exists shall determine if
the reduction in wave height by vegetation is significant. Applying Equation D.4.544 in Table
D.4.58 by Knutson (1988) provides a method to determine whether further quantification of
wave attenuation by vegetation is required.
Methods for calculating wave damping by vegetation that are included within the Guidelines and
Specifications Appendix D (2003) may be employed in the Pacific Coast region. Important
variables include drag coefficient, plant drag coefficient, stem diameter, spacing, water depth,
stand width, and bottom slope.
It shall be noted that marsh vegetation differs from region to region and with salinity levels.
Cordgrass (shown in Figures D.4.518 and D.4.519), although present on both coasts, varies in
stature, with Pacific cordgrass (Spartina foliosa) being less substantial than Atlantic cordgrass
(Spartina alterniflora).
However, the effects of these differing vegetation types on attenuating incoming wave energy for
sitespecific cases requires verification.
To account for wave attenuation by vegetation, the following is required:
•
Determine the initial wave height seaward of vegetation;
•
Determine the distance waves will travel through marsh vegetation;
•
Quantify plant characteristics, i.e., stem diameter and spacing;
D.4.536 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Figure D.4.518. Native Pacific Cordgrass Meadow at Blackie’s Pasture, Marin County
Figure D.4.519. Tall Stand of Atlantic Smooth Cordgrass Hybrids Invading a Native Patch
of Pacific Cordgrass Meadow near Tiburon, California
•
Apply plant drag coefficients (CD = original drag coefficient approximately 1.0, CP =
plant drag coefficient approximately 5.0); and
•
Calculate wave attenuation for the site in question (Equation D.4.544).
The Mapping Partner may choose to perform a field study to determine the amount of wave
attenuation by vegetation. Relatively simple survey and data acquisition techniques can be
performed to measure wave attenuation by vegetation. Using pressure sensors and/or current
meters, wave characteristics in the study area can be determined. Surveying instruments can be
D.4.537
Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
used to characterize the site. The procedures include: installing instrumentation to measure wave
heights offshore of the area with vegetation, using survey techniques to measure the distance that
the waves will travel through the vegetation and site characteristics (i.e., water depth, bed slope,
etc.), and measurement of plant characteristics (i.e., stem diameter, height, spacing, density).
Application of field results obtained to Equation D.4.544 will provide guidance on the
significance of wave dissipation for a particular site.
If calculations predict greater than 20% reduction, the Mapping Partner shall include the effects
in the FIS. If results are not significant, the Mapping Partner may ignore attenuation by
vegetation.
D.4.5.3.3 Overland Wave Propagation (WHAFIS)
The Guidelines and Specifications, Appendix D (2003) consider water wave transformations by
marsh vegetation (pages D67 to D87). The fundamental analysis of wave effects for a flood
map project is conducted with the WHAFIS computer program, which estimates the changes in
wave height due to interactions with vegetation. WHAFIS simulates the vegetation effects on
wave height and energy dissipation by both rigid and flexible vegetation. Consistent with other
coastal analyses, the WHAFIS model considers the study area by representative transects. For
WHAFIS, transects are selected with consideration given to major topographic, vegetative, and
cultural features. The ground profile is defined by elevations referenced to an appropriate vertical
datum (typically National Geodetic Vertical Datum [NGVD] or NAVD). The profile usually
begins at elevation 0.0 and proceeds landward until either the wave crest elevation remains less
than 0.5 feet above the mean water elevation for the 1% annual chance flood or another flooding
source is encountered. Currently, WHAFIS in its entirety is only approved for use on the Atlantic
and Gulf coasts.
Use of the model is explained in detail in the Guidelines and Specifications Appendix D.
Mapping Partners wishing to use the WHAFIS model to estimate wave attenuation by Pacific
Coast marshes must use care with preparation and input of required site data.
Several factors must be addressed before application of the WHAFIS model to the Pacific Coast.
First, local marsh vegetation must be characterized. Default values within the model are coded
for Atlantic and Gulf coast vegetations only. To use the model with Pacific Coast vegetation,
vegetation parameters must be input manually into the model. Second, wind velocity parameters
within the currently approved model are based on Atlantic and Gulf coast storms associated with
hurricane conditions. These wind speeds are too high for most Pacific Coast conditions.
D.4.5.3.3.1 Characterization of Pacific Coast Vegetation
Application of WHAFIS to Pacific Coast vegetation has been partially confirmed. Certain types
of vegetation are common to the Atlantic Coast, Gulf Coast, and Pacific Coast regions and
described in more detail in Table D.4.59. WHAFIS can be used for limited Pacific Coast
vegetation types that are the same or similar to those already represented in WHAFIS, but test
cases are needed to verify the validity of the model for use with most Pacific Coast vegetation
types.
D.4.538 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.
Guidelines and Specifications for Flood Hazard Mapping Partners [January 2005]
Table D.4.59. Common Vegetation Types on Atlantic, Gulf, and Pacific Coasts
Species Common Name
New
England Southeast
Gulf
Coast
Southern
California
Northern
California
Pacific
Northwest
Batis maritime Saltwort x x
Distichlis spicata Salt Grass x x x x
Scirpus americanus Olney's Bulrush x x
Scirpus olneyi Olney Three square x x
Scirpus robustus Salt Marsh Bulrush x x x
Scirpus validus Soft Stemmed Bulrush x x x
Spartina alterniflora Smooth Cord Grass x x x x
D.4.5.3.3.2 Use of WHAFIS for Dissipation Only
Although WHAFIS is not approved for use in Pacific Coast regions, certain features are
appropriate. The program can be used to determine whether a vegetation type in a specific area
will attenuate wave heights regardless of wind speed. This is taken into account in the model by
using the Vegetation Elevation card (using equivalent rigid vertical cylinders) only. For this case,
there is only damping; no energy input from wind is included even though the wind might be
strong and the vegetation might be sparse. The Mapping Partner shall choose vegetation values
for stem diameter, height, spacing, and a drag coefficient. The wind speed, implicitly, will be
zero.
D.4.5.3.3.3 Use of WHAFIS for Dissipation and Wind Wave Generation
The Marsh Grass card provides more flexibility with the vegetation parameters. This is the only
WHAFIS card type that considers both energy input and energy dissipation. This card accounts
for energy input by wind over the free surface, which is especially important if the vegetation is
fully submerged and damping by the vegetation occurs; however, this card will impose a wind
speed of 60 mph. Care must be taken with use of the Marsh Grass card because wind speeds are
based on Atlantic and Gulf Coast (hurricane) conditions.
A modified version, PWHAFIS, has been written that allows for variation of wind speed and
therefore can be used in a generation wind field. This recently modified version has been tested
but has not been approved by FEMA for unrestricted use. If the Mapping Partner chooses to use
PWHAFIS, prior approval from FEMA is required.
D.4.5.3.4 Documentation
Areas where wave attenuation was examined and the results obtained shall be described. The
characteristics of these areas that led to the consideration of wave attenuation and the values of
the attenuation parameters used in the analysis shall be quantified. Results of interest include the
potential effect of wave attenuation on the hazard zones and the decisions reached as to whether
to further include wave attenuation in the analysis leading to hazard zone delineation. Any field
measurements and/or observations shall be recorded as well as documented or anecdotal
information regarding previous overland damping during major storms, perhaps by runup events
less than expected in the lee of attenuation features as discussed in this subsection. Any notable
difficulties encountered and the approaches to addressing them shall be clearly described.
D.4.539 Section D.4.5
All policy and standards in this document have been superseded by the FEMA Policy for Flood Risk Analysis and Mapping.