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 -- -- -- ß 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, ?ß 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 -- -- -- -- -- -- µ 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