Statistics of significant storm events using one- and two-dimensional analyses of the natural and protected coasts of the Dziwnów Spit

In this paper, one- and two-dimensional statistical analyses of significant storm parameters were conducted along natural and protected coasts of the Dziwnów Spit, based on quantiles and concentration ellipses. In the one-dimensional analysis, the quantiles of 0.9, 0.99 and 0.999 erosion magnitude D, sea level F, significant wave height H and storm duration T were determined, and these quantiles correspond to significant storm occurrence once every 10, 100 and 1000 years, respectively. To account for the influence of other variables on the erosion magnitude, log-linear models describing the linear dependence of log(D) on F and log(D) on F and H were built. Based on these models, the corresponding quantiles for the erosion magnitude D were also determined. In the multivariate case, using the 2-dimensional normal distribution, (log(D), F), (log(D), H), and (log(D), T) concentration ellipses were determined for the above pairs of parameters for probabilities of 0.9, 0.99 and 0.999, respectively. The application of one-dimensional distribution results in the lowest values of eroded material of dune, while the use of concentration ellipses estimates the highest values of dune erosion. Moreover, the developed log-linear models better predict the values of eroded material of dune along natural coast than on protected one.