D.4.12	Notation
Symbol
Description

Typical Units


Units
English
SI
A
Equilibrium beach profile coefficient
L?
ft?
m?
B
Berm height 
L
ft
m
C
Wave phase velocity or celerity
L/T
ft/s
m/s
CG
Wave group velocity
L/T
ft/s
m/s
Ck
Sample kurtosis
--
--
--
Cp
Plant drag coefficient
--
--
--
Cs
Sample skewness
--
--
--
C0
Deepwater wave celerity, gT / 2?
L/T
ft/s
m/s
D
Quarrystone diameter
Dune height
L
L
ft
ft
m
m
D50
Size of 50th percentile of sediment
L
mm
mm
dh
Depth over berm
L
ft
m
E
Wave energy
Crest elevation of structure
LF/L
L
ft-lb/ft
ft
N-m/m
m
EHotSpot
Extra profile lowering at a hot spot
L
ft
m
Ej
Beach-dune juncture elevation
L
ft
m
EjMLWP
Beach-dune juncture elevation for the 
MLWP
L
ft
m
EjStorm
Beach dune juncture elevation during 
a storm
L
ft
m
ET
Total still water elevation
L
ft
m
e
Base of natural logarithms (=2.718)
--
--
--
F
Cumulative probability function
--
--
--
Fc
Freeboard
L
ft
m
F'
Dimensionless freeboard
--
--
--
FH, FT, Fgamma,
Fslope
Static setup coefficients in DIM 
model
--
--
--
Fn
Discrete spectral frequency
1/T
hz
hz
FR
Wind wave runup coefficient
--
--
--
f
Wave frequency
Darcy-Weisbach resistance 
coefficient
Probability density function
1/T
--

--
hz
--

--
hz
--

--
fe
Coriolis coefficient
1/T
1/S
1/S
fp
Spectral peak frequency, 1/Tp
1/T
hz
hz
GH,GT, Ggamma, 
Gslope
Dynamic setup coefficients in DIM 
model
--
--
--
G0
Normalizing function for directional 
spectrum spreading function
--
--
--
G(?)
Directional spectrum spreading 
function
--
--
--
G(f,?)
Directional spreading function
--
--
--
g
Gravitational acceleration
L/T2
ft/s2
m/s2
H
Wave height
L
ft
m
 
Unrefracted deep water wave height 
L
ft
m
Hb
Breaking wave height
L
ft
m
Hm0
Spectral significant wave height
L
ft
m
Ho
Deep water wave height
L
ft
m
Hs
Significant wave height
L
Ft
m
Hx
Wave height at x location in surf 
zone
L
ft
m
h*
Wave structure parameter
--
--
--
h
Water depth
L
ft
m
hb
Breaker depth
L
ft
m
hc
Depth over crest
L
ft
m
hm
Height of the land barrier
L
ft
m
ho
Depth over crest
L
ft
m
Ks
Shoaling coefficient
--
--
--
Ks(fn)
Spectral shoaling coefficient
--
--
--
Kr(fn, ?o,n,m)
Spectral refraction coefficient
--
--
--
k
Wave number, 2p / L
Bluff erosion parameter
rad/T
--
rad/ft
--
rad/m
--
L
Likelihood
--
--
--
LL
Log-likelihood
--
--
--
Lberm
Berm width
L
ft
m
Lom
Spectral deep water wave length
L
ft
m
L0
Deep water wave length, gT2 / 2?
L
ft
m
M(n)
Number of direction components in 
spectrum at fn
--
--
--
m
Beach slope (rise/run)
L/L
--
--
mn
nth moment of spectral density, 
 
L2/Tn
ft2/sn
m2/sn
?
Degrees of freedom of a chi-squared 
distribution
Number of waves
--

--
--

--
--

--
P
Average porosity of rubble structure 
cover layer
Precipitation rate
Probability

--
L/T
--

--
in./hr
--

--
mm/hr
--
Q
Dimensionless overtopping
--
--
--
q
Mean overtopping rate per unit 
length
L2/T
ft2/s
m2/s
R
Total wave runup
Spearman statistic
L
--
ft
--
m
--
Riuc
Incident wind wave runup
L
ft
m
Rm
Reduced recession due to storm 
duration
L
ft
m
RTotal
Total runup (static setup plus 
dynamic setup plus incident wave 
runup.)
--
--
--
R2%
Runup exceeded by 2% of the runup 
crest 
L
ft
m
R8
Maximum potential profile recession
L
ft
m
R8HotSpot
Potential recession at a hot spot
L
ft
m
R8storm
Potential recession for storm
L
ft
m
r
Linear correlation coefficient



S
Water level change
L
ft
m
Sc
Compressive strength of bluff 
material
F/L2
lb/ft2
N/m2
S(f)
Spectral density
L2-T2
ft2/hz
m2/hz
S(f,?)
Directional spectral density
L2T/deg
(ft2/hz)/deg
(m2/hz)/deg
S0 (fn, ?o,n,m)
Discrete directional spectrum in deep 
water
L2-T2
ft2/hz
m2/hz
Sns (fn, ?o,n,m)
Discrete directional spectrum in 
nearshore
L2-T2
ft2/hz
m2/hz
s
Sample standard deviation
--
--
--
S(f)
Continuous spectrum
L2T
ft2/hz
m2/hz
T
Wave period
T
s
s
TD
Storm duration
T
hr
hr
Tp
Spectral peak period, 1/fp
T
s
s
Ts
Significant wave period
Time scale for beach profile response
T
--
S
--
S
--
t
Time
T
s
s
Vc
Velocity at crest
L/T
ft/s
m/s
Vf
Fall velocity
L/T
ft/s
m/s
Vmax
Maximum overtopping volume per 
wave per unit length
L2/wave
ft2/wave
m2/wave
v
Horizontal (y) component of local 
fluid velocity (water particle 
velocity)
L/T

L/T
ft/s

ft/s
m/s

m/s
W
Wind speed
L/T
mi/hr
m/s
Wb
Surf zone width to breaker line
L
ft
m
Wc
Wind stress coefficient term
L/T
mph
kph
Wx
x component of wind speed
L/T
mi/hr
m/s
Wy
y component of wind speed
L/T
mi/hr
m/s
X
Accumulated bluff to erosion
L
ft
m
 
Sample mean
--
--
--
x,y,z
Right-handed Cartesian coordinates
L
ft
m
yG,inner
Seaward extent of overtopping
L
ft
m
yG,outer
Landward extent of overtopping
L
ft
m
y0
Cross-shore location of structure 
crest
L
ft
m
zc
Structure crest elevation
L
ft
m
zG
Elevation behind crest
L
ft
m
( )b
Term evaluated at the breaker line
--
--
--
( )o
Term evaluated in deep water
--
--
--
tan a
Structure slope
--
--
--
a
Storm duration recession reduction 
factor
JONSWAP Spectrum term
--

L2T
--

ft2/hz
--

m2/hz
ac
Structure crest slope
--
--
--

Storm profile response coefficient
Wave angle at structure
--
deg
--
deg
--
deg
?
Specific gravity of a fluid
F/L3
lb/ft3
N/m3

Peak enhancement factor used in the 
JONSWAP spectrum 
--
--
--
?b
Breaker depth index
Runup berm coefficient
--
--
--
--
--
--
?r ?p ?b ?f, ?
Runup reduction coefficients
--
--
--
?f
Frequency increment
1/T
hz
hz
?R
Potential excess runup
L
ft
m
e
Energy dissipation rate
F/LT
lb/s-ft
n/m-s
 
Dynamic or oscillating setup
L
ft
m
 
Mean or static wave setup
L
ft
m
 b
Static setdown at the breaker point
L
ft
m
 max
Maximum static wave setup
L
ft
m
 min
Minimum static wave setup
L
ft
m
 o
Static setup at the shoreline
L
ft
m
?(x,t)
Displacement of water surface 
relative to SWL
L
ft
m
 
Mean square of water surface 
fluctuations
L2
ft2
m2
?3
Coefficient of skewness
--
--
--
?4
Coefficient of kurtosis
--
--
--
?i
Water surface displacement by 
incident wave
L
ft
m
?rms
rms value of free surface elevation
L
ft
m
 
Overall mean wave direction 
deg
deg
deg
?
Direction of wave propagation
deg
deg
deg
?main
Main wave direction in a directional 
spectrum
deg
deg
deg
?m
Discrete wave direction
deg
deg
deg
?m(f)
Mean wave direction as a function of 
frequency.
deg
deg
deg
?
Breaker index
Wind stress factor
--
--
--
--
--
--

Population Mean 
--
--
--
?
Spectral narrowness parameter
--
--
--
?

Surf similarity parameter or Iribarren 
number
--
--
--
?om
Spectral deep water ?
--
--
--
?0
Deep water ?
--
--
--
p
Constant = 3.14159
--
--
--
?
Mass density of water
M/L3
slug/ft3
kg/m3
?a
Mass density of air
M/L3
slug/ft3
kg/m3
?fw
Mass density of fresh water 
M/L3
slug/ft3
kg/m3
?s
Mass density of sediment
M/L3
slug/ft3
kg/m3
O
Rotational speed of the earth
rad/T
rad/S
rad/S
f
Latitude
deg
deg
deg
tx,ty
Wind stress
F/L2
lb/ft2
N/m2
s
Population standard deviation
L
ft
m

 
 
 
 
Guidelines and Specifications for Flood Hazard Mapping Partners [November 2004]
	D.4.12-1	Section D.4.12
Notation	1	17 August 2004