Return Periods of Summer-Time Sea Storms in the Central Mediterranean Sea

Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 Return periods of summer-time sea storms in the central Mediterranean Sea P. Filianoti Department of Mechanics and Materials, Reggio Calabria University, Italy Abstract From an analysis of wave data from the Italian buoy network we obtain the probability of exceedance of the significant wave height in the summer-time. Then the return period of the summer storms in which the significant wave height exceeds some fixed threshold is obtained by means of Boccotti's equation. Summer waves prove to be much smaller off the Italian south-eastem coast then off the Italian western coast. The return periods obtained in the paper are useful for the design of facilities such as barriers against pollution and mucilage and removable moorings for yachts and sailboats which are used only in summer. 1 Introduction The significant wave height (H, ) represents a random process of time, gradually variable and strongly not stationary because of a seasonal component (Cunha and Guedes Soares [3]). The analytic form of the exceedance probability P(H, > h) in many locations is well represented by a Weibull in two parameters (Guedes Soares [4]). Where the wave buoy data are available, the return period of a sea storm in which H, exceeds a fixed threshold is usually obtained by where At,,, is the sampling interval (Massel [5]). Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 300 Coastal Engineering V: Computer Modelling of Seas and Coastal Regions The return period R(H, > h) can be obtained through the closed form solution based on the rule of equivalent triangular storms (Boccotti [l]): where p(H, = h) is the probability density function relative to the probability of exceedance P(H, > h) : and where b(h) is the regression durations-heights of equivalent triangular storms (e.t.s.). To our knowledge there are no studies in literature on the probability P(H, > h) > and return periods R(H, h) in regards of the season. The present paper proposes a study of such nature analysing P(H, > h) and R(H, > h) relative to the summer-time in the Italian seas. P(H, > h) will be estimate from the data of the Italian Sea Wave Measurement Network (SWaN). R(H, > h) will be obtained through eqn (2) which is of general validity. The regression durations- heights which is present in this equation will be obtained for the various locations by examining the hlstory of the storms. To this aim, for each actual storm we will obtain the relative e.t.s. The utility of our study is that many facilities pertaining bathing activities, are put into the sea only in the summer-time. Typically these structures are piers, moorings, and barriers against pollution and mucilage. Designing these structures with the maximum expected wave height relative to all seasons in the lifetime, leads to dimensions really too heavy. The design, as we will see in an example, must be made with the maximum expected wave height during the summer-time in the lifetime and dimensions result much smaller. 2 The probability of H, in the summer-time Let us define At(h, summer) P*(H, > h) = total summer time ' At(h, summer) P(H, >h) = total time ' Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 Coastal Engineering V: Computer Modelling of Seas and Coastal Regions 301 where At(h,surnmer) is the time in whch H, is greater than h in the summer time (June, July, August and September). Clearly fiom the definitions we have P*(H, >h) is shown in fig. 1. The figure shows also the probability of H, relative to the waves of all seasons of the year. We have resorted to the ancillary variables X and Y which are defined by 1 X = lOOln(2Sh) with h inmetres, Y r 100lnln-. (7) P With this choice if the data points exhbit a linear trend on the plane X - Y then the probability P(H, > h) can be fitted by that is a Weibull distribution whose parameters u and W depend on the considered location. As we can see the data point shown in fig. 1 exhibit a linear trend starting fiom Y = 50 (P = 0.19) and the U, W values of table 1 represent this linear trend. The data of H, used for this table and for fig. 1 are those of the Italian SWaN, for the period 1989-1998. These data are taken at a rate of 113 per hour by means of eight directional pitch-roll buoys. The network's efficiency (number of three- hourly observations / number of expected data in whole summer periods) was greater than 94% for all the stations with the exception of Mazara del Vallo (88%). 3 Storm durations We have singled out all the sea storms recorded in the summer-time by the eight buoys of the Italian SWaN. By "sea storm" we mean an episode in which H, exceeds the threshold of 1.5< H, > , where < H, > is the mean value of H, in the summer-time. This mean value ranges between 0.45 m for the Jonian Sea and the Adnatic Sea to 0.9 m for the sea off the western coast of Sardinia. The overall number of analysed storms is 1800. Figure 2 shows the history of a storm recorded at Mazara del Vallo and its e.t.s. The duration of e.t.s. is obtained after a few attempts so that the maximum expected wave height of the e.t.s. is equal to the maximum expected wave height of the actual storm. The maximum expected wave height is obtained by Borgman's solution [2].In all the 1800 episodes we have found confirmation of the rule of e.t.s., that is to say: P(H,, >H) of the Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 302 Coastal Engineering V: Computer Modelling of Seas and Coastal Regions T Y La Spezia Alghero 250 f 200 1 summer-tme wave 150 - 100 100 II Eeasons waves 50 50 - X X Ponza 250 Y Mazara del Vallo 100 50 0 0 100 200 300 Y Catania I seasons waves X Y Monopoli 250 250+ Pescara 150 150 100 100 - VIseasons waves 50 50 - X t X Figure 1. Italian seas: P*(H, > h) for the summer-time, and P(H, > h) for all seasons of the year. [The ancillary variables X and Y have been defined by eqn (V1 Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 Coastal Engineering V: Computer Modelling of Seas and Coastal Regions 303 e.t.s. practically coincident with the P(H,, >H) of the actual storm, P(H,, > H) being the probability that the maximum wave height in the storm exceeds any fixed H (see fig. 2). Our aim is to obtain the regression b(h) relating durations to amplitudes of e.t.s. (that is base b to height a of triangles like that of fig. 2). Thls regression was obtained by Boccotti [l] for all storms, that is for storms of all seasons of the year. He proposed the form &(a) = K,b,, exp K, - , l,) ( where a,, is the average a of the set of N (= number of years x 10) strongest storms in the time span under examination, and b,, is the average b of this set. Parameters a,, ,b,, depend on the special location. Parameters K, and K, depend on the geographic area (Boccotti gives K, and K, for the central Mediterranean Sea, the North Western Atlantic, and the North Eastern Pacific). Regressions are decreasing, that is K, proves to be negative. Values of K, and K, for the central Mediterranean Sea are We repeated the examinations of b(a) considering only the summer storms, and we found confirmation of the decreasing monotonic trend. The regression is shown in fig. 3. Each point refers to a single storm: the abscissa represents the quotient ala,, and the ordinate represents the quotient b/blo . Values of a,, and b,, for each location are given in table 2. Data points of fig. 3 include the 100 heavier storms recorded in each of the 8 locations of the Italian SWaN in ten years. The line represents the function (9) that best-fits the regression. The values of parameters K, and K, are Equation (9) with values (1 1) of K, and K, and table 2 pennit to calculate the regression b(a) for each location. 4 Return periods Using P*(H, > h) of 4 2, b(a) of 3 and eqn (2) we obtain the return periods R(H, > h). Fig. 4 shows the R(H, > h) for the Italian seas. For comparison we Transactions on the Built Environment vol 58 © 2001 WIT Press, www.witpress.com, ISSN 1743-3509 304 Coastal Engineering V: Compu:er Modelling of Seas and Coastal Regions have represented also the R(H, > h) relative to all seasons of the year. Table 1. Parameters of P*(H, > h) for the Italian seas. LOCATION I w [m] I u I La Spezia 0.580 0.975 Alghero 0.930 1.069 Ponza 0.537 0.948 1 1 1 Mazara del Vallo 1 0.666 1 1.213 1 Catania 1 0.339 1 1.113 1 Crotone 1 0.427 ( 1.195 ( Monopoli 1 0.520 / 1.226 ( Pescara / 0.377 1 0.980 ] The difference between waves of summer periods and waves of all seasons is much bigger in the south-eastem Italian seas than in the western Italian seas, as fig 4 shows clearly.

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