#Ocean waves storm series

Further, we present some statistical properties of the largest waves in storms. We then derive new analytical expressions for both R( H s > h) and R( H max > H) as function of p A and perform a sensitivity analysis with respect to λ to assess the deviations from the ETS predictions. For the “generalized” model, the associated storm peak density p A stems from the analytical solution of a Volterra integral equation of the first kind. Boccotti’s ETS model is recovered for λ = 1. In particular, we describe an actual storm in time t in the form of a generic power law | t − t 0| λ, where λ is a shape parameter and t 0 is the time of the storm peak. In this paper, we extend and generalize Boccotti’s triangular storm model to include other possible and plausibly more realistic descriptions of the temporal history of the significant wave heights observed at a fixed point during a sea storm. These analytical results have been compared against buoy measurements, demonstrating their relevance to the design of coastal and offshore structures ( Arena and Pavone 2006, 2009).

Further, Arena and Pavone (2009) derived the solution of the return periods R N( R ≥ N) of a storm during which exactly N waves (at least N waves) exceed a given threshold. Recently, Arena (2004) and Arena and Pavone (2006) exploited the ETS model to define the return period R( C max > C) of a storm during which the largest nonlinear crest height C max exceeds a fixed threshold C. Boccotti (1986, 2000) also derived the return period R( H max > H) of a storm where the maximum individual wave height H max exceeds a fixed threshold H. Arena (2004) extended this result to account for seasonal effects and wave directionality.

In particular, Boccotti (2000) derived an analytical solution for the return period R( H s > h) of a storm during which the maximum H s exceeds h as that of a triangle storm whose a is above h. Then, the estimates of wave extremes and their associated statistics simply follow from the density p A with no need for data fitting. This type of equivalence defines the probabilistic structure of the ETS model, which depends on wave data only via the observed significant wave height exceedance P( h) = Pr( H s > h) and the conditional average duration b( a) = B| A = a, both estimated via regression. So, the significant wave height history or the actual storm sequence is stochastically equivalent to a succession of random triangle storms. Then, the storm peak probability density function (pdf) p A( a) = Pr is not fitted directly to the observed storm peak data via ad hoc regressions, but it follows analytically by requiring that the average times spent by the equivalent and actual storm sequences above any threshold h be identical. It is then assumed that a and b are realizations of two random variables, say, A and B, respectively. The statistical equivalence is achieved by requiring that a equal the actual maximum H s in the storm, and b is chosen so that the maximum expected wave height during the storm is the same as that of the triangular storm ( Borgman 1970, 1973). In this model, a storm is described in time as a triangle of height a indicative of storm intensity and base b as a measure of duration. Given a succession of storm events in time, Boccotti (1986, 2000) proposed the equivalent triangular storm (ETS) model to predict the return period of extreme wave events. With T l, we then have a succession of storms where each storm, according to Boccotti (2000), is identified as a nonstationary sequence of sea states in which H s exceeds 1.5 times the mean annual significant wave height, say, H sm at a given site, and it does not fall below that level during an interval of time longer than 12 h (see also Arena 2004).

#Ocean waves storm series

As a result, wave parameters such as H s, mean periods, and mean wavelengths can be easily estimated from either the time series of surface elevations or the associated spectrum. In doing so, it is reasonable to assume that with T s, the sea state is a homogenous and stationary stochastic field whose properties are fully characterized by the directional spectrum of the sea surface and associated moments. In these methods, the effects of the sea state on the short-term scales of T s ∼ 1–3 h are accumulated to predict the wave conditions on the long-term time scales of T l ∼ yr. The reviews of several methods used for this can be found in the work of Isaacson and Mackenzie (1981), Guedes Soares (1989), and Goda (1999).

Stochastic modeling of time series of the significant wave height H s recorded at a given ocean site is the principal focus of statistical methods employed in the long-term prediction of extreme wave events during sea storms ( Krogstad 1985 Prevosto et al.