Runup height estimates are based on beach slope in the foreshore region (landward of the break point) and deepwater parameters height Ho and wavelength Lo. Deepwater wavelength depends only on wave period as Lo = gT2/(2π) where g is gravitational acceleration (9.81 m/s). Runup height is a combination of setup <η> (elevation of the sea surface by shoaling) and variance of the swash associated with incident waves Sinc and low-frequency infragravity waves SIG (sometimes called surf beat). Total runup R2 (based on the highest 2%) is calculated as R2 = 1.1 (<η>+S/2) where S = sqrt(Sinc2 + SIG2; Stockdon et al., 2006, eqns. 9 and 7). Sinc and SIG are calculated from Stockdon et al. (2006), eqns. 11 and 12. For very dissipative conditions (low-angle beaches with Iribarren number ξ = βf sqrt(Lo/Ho)< 0.3), R2 = 0.043 sqrt(Ho Lo) (Stockdon et al., 2006, eqn. 18).
Runup distance x = R2/sin(arctanβf) is the distance that swash extends across the sloping shoreface from the mean waterline.
There are three different ways to use these calculations, depending on where the waves are measured. The radio-button selection allows you to specify this:
Reverse shoaling involves estimating deepwater conditions from measurements at shallow or intermediate depths, using linear wave theory as follows. The wavenumber k at measurement depth h (or hb) is calculated from the dispersion relationship, shoaling coefficient Ks is calculated according to Neilsen (2009, eqn. 1.7.5), and deepwater wave height Ho is determined as Ho = Hb/Ks. Because wave period T remains constant as waves shoal, deepwater wavelength can be calculated as above.
Komar, P. D. (1976) Beach Processes and Sedimentation. Prentice-Hall, Inc., 429 pp.
Nielsen, P. (2009) Coastal and Estuarine Processes. Vol. 29, Advanced Series on Ocean Engineering, World Scientific, 343 pp.
Plant, N. G., R. A. Holman, M. H. Freilich, and W. A. Birkemeier (1999) A simple model for interannual sandbar behavior. Journal of Geophysical Research, 104(C7): 15,755-15,776.
Stockdon, H. F., R. A. Holman, P. A. Howd, and A. H. Sallenger Jr. (2006) Empirical parameterization of setup, swash, and runup. Coastal Engineering, 53: 573-588.
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Last revised: 28 April 2015