The following section details the procedure above for the first group of waves (Long elevated waves). The same procedure applies to every other group, therefore only the final runup equations are presented in this paper. Detailed information on the regression analysis for individual wave groups can be found in Charvet (2012). The first subset of data to be used in the regression

is long elevated waves (group ET/Tb<1ET/Tb<1). Only those combinations of k  , K  , L  , h  , and a   that result in a high value of R2R2, a zero mean error, and which satisfy all the linearity assumptions, are kept. Table 5 presents the regression coefficients, characteristic lengths variables and uncertainties associated with the combinations BIBF-1120 displaying a significant degree of

linearity between x   and y   (R2⩾0.80R2⩾0.80). In the present analysis, outliers are defined as data for which associated residuals are located more than 2.5 standard deviations away from their mean e¯ and they are removed. The methodology applied to verify the statistical assumptions presented in Table 5 is described in Appendix C. The results of Table 5 indicate that for long elevated waves, there is a unique combination of the parameters a  , h  , L   and EPEP that gives a strong linear relationship (R2=0.94R2=0.94) with unbiased estimates logK=2.32logK=2.32 and k=0.89k=0.89. These regression selleck screening library coefficients are close to 2 and 1 and are tested against the two null hypotheses: H01:logK=2H01:logK=2 Pregnenolone and H02:k=1H02:k=1 (t-test). The t-test used for this purpose is described in Appendix D,

and the results show that the runup relationship can be expressed as: equation(18) logRh=2+loga3ρgEP. This suggests that a linear relationship describes well the evolution of runup as a function of parameters of the wave form. The residual and normality plot associated with the regression are displayed in Fig. 10, and the 95% confidence intervals associated with the regression curve are also constructed (methodology described in Appendix E), and plotted together with the regression results in Fig. 11. The same procedure is applied to all the other groups of waves. Laws of the form of Eq. (16) are summarized in Table 6, with confidence intervals for k and K, for each group of waves. The results from this table are discussed in the next section. The literature review has shown that a number of previous studies on runup of solitary/elevated waves have determined that the runup approximately scales as the amplitude of the incoming wave. Posing Ep≈ρgLa2Ep≈ρgLa2, Eq. (19) indicates that: Rh∝aL. Moreover, 0.18