Comprehensive Wind and Wave Statistics and Extreme Values for Design and Analysis of Marine Structures in the Adriatic Sea

Journal of Marine Science and Engineering

Article Comprehensive Wind and Wave Statistics and Extreme Values for Design and Analysis of Marine Structures in the Adriatic Sea

Marko Katalini´c 1 and Joško Parunov 2,*

1 Faculty of Maritime Studies, University of Split, 21000 Split, Croatia; [email protected] 2 Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, 10000 Zagreb, Croatia * Correspondence: [email protected]; Tel.: +385-(0)1-6168-226

Abstract: Wind and waves present the main causes of environmental loading on seagoing ships and offshore structures. Thus, its detailed understanding can improve the design and maintenance of these structures. Wind and wave statistical models are developed based on the WorldWaves database for the Adriatic Sea: for the entire Adriatic Sea as a whole, divided into three regions and for 39 uniformly spaced locations across the offshore Adriatic. Model parameters are fitted and presented for each case, following the conditional modelling approach, i.e., the marginal distribution of significant wave height and conditional distribution of peak period and wind speed. Extreme significant wave heights were evaluated for 20-, 50- and 100-year return periods. The presented data provide a consistent and comprehensive description of metocean (wind and wave) climate in the Adriatic Sea that can serve as input for almost all kind of analyses of ships and offshore structures.

Keywords: offshore Adriatic Sea; significant wave height; peak period; wind speed; extreme value; conditional modelling; joint distributions Citation: Katalinić,M.; Parunov, J. Comprehensive Wind and Wave Statistics and Extreme Values for Design and Analysis of Marine 1. Introduction Structures in the Adriatic Sea. J. Mar. Wave (re-analysis) databases, comprising numerical wave model hindcasts and assimi- Sci. Eng. 2021, 9, 522. https:// lated altimetry satellite data, present a comprehensive state-of-the-art source for analysis of doi.org/10.3390/jmse9050522 metocean data that serve as input for the design and assessment of oceangoing vessels and offshore structures [1]. The WorldWaves database was used in this study to derive wind Academic Editor: Wei-Bo Chen and wave statistics for the Adriatic Sea, which is a semi-enclosed sea basin with specific wind–wave climate. The basin is analyzed as a whole, divided into three regions and at Received: 19 April 2021 39 evenly spaced locations. Procedures and concepts applied in the study resulted with en- Accepted: 7 May 2021 Published: 12 May 2021 vironmental wind and wave models that provide a detailed and structured insight into the wind–wave climate of this basin. Joint probability distributions of significant wave height

Publisher’s Note: MDPI stays neutral and peak periods and distribution of wind speed to significant wave height are developed with regard to jurisdictional claims in together with extreme wave height estimation for 20, 50 and 100 year return periods. published maps and institutional affil- The obtained results are useful for the design, operation planning, maintenance iations. and life-time extension of marine-related engineering objects in the Adriatic. Specific calculations such as: extreme sea states analysis for the design of marine structures [2], coupled aero- and hydro-dynamic analysis of floating offshore wind turbines [3], long-term fatigue calculations [4], structural reliability [5] and mooring analyses [6], can benefit from the input of the developed data. Wave statistics in the Adriatic is also used for exploring Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. wave energy potential [7,8] and for planning and evaluating the performance of high- This article is an open access article requirement service vessels such as the coastal patrol boat developed for the Adriatic [9]. distributed under the terms and Safety analysis of a fishing vessel due to roll in a seaway [10] and organization of special conditions of the Creative Commons marine operations [11] are other examples where accurate wave statistics for the Adriatic Attribution (CC BY) license (https:// is indispensable. creativecommons.org/licenses/by/ In the second half of 20th century, wave statistics in the Adriatic was based on visual 4.0/). observations collected from merchant and meteorological vessels and published in the

J. Mar. Sci. Eng. 2021, 9, 522. https://doi.org/10.3390/jmse9050522 https://www.mdpi.com/journal/jmse J. Mar. Sci. Eng. 2021, 9, 522 2 of 25

wave climatology atlas [12]. Wave statistics was rather roughly graphically presented in the form of wave roses that were later digitalized and studied in terms of extreme values [13]. These data, however, suffer from known inaccuracies of visual wave observations and lack of extreme events due to heavy weather avoidance by ships [14]. Later, measurements have been performed from four floating buoys installed along the west coast of the Adriatic [15]. However, these data were recorded and are available only for limited time of 5 years, with some interruptions due to failure and maintenance. One of the most comprehensive wave- data sources in general are the measurements from the Aqua Alta oceanographic tower, located near Venice in the north part of the Adriatic [16]. Although 38 years of continues uninterrupted measurements are available, they refer only to one specific location and cannot be used for the whole Adriatic Sea. The present study represents the first complete wave and wind statistics for the whole Adriatic Sea, representing progress compared to previous studies [17]. The way the data are presented enables its application to almost all purposes related to marine structural design and analysis, as reviewed in the preceding paragraphs. Site specific design (e.g., for offshore structures) might require spatial interpolation of presented data; however, it can be directly applicable for the analysis of ships, as they are not confined to a specific location. Particular attention is paid to the accuracy of calculated extreme values, to avoid too conservative results that could lead to non-economical and over-dimensioned structures [18]. The paper is organized as follows. Initially, the WorldWaves database, used as the underlying material for the study, is described in Section2 along with preliminary data structuring such as the development of sea-state and wind contingency tables, wave roses visualizations and example validations against existing buoy data. In Section3 the theoretical background of applied methods is presented for the development of the joint probability distribution models. In Section4, all model parameters and extreme values are presented graphically, both regionally and per individual location analyzed. Section5 gives a discussion on the results and Section6 presents the conclusion. At the end of the paper, AppendixA provides basic data, such as location coordinates and regional subdivision and AppendixB gives detailed tabulated results that are graphically presented in Section4.

2. Data The underlying data used for the analysis of wave and wind climate analysis in the Adriatic Sea were extracted from the WorldWaves (WW) database. The database represents numerical wave model hindcasts with assimilated available satellite altimetry measurements [19,20]. It includes 39 locations, evenly distributed across the Adriatic Sea with 0.5◦ × 0.5◦ (lat.-long.) spacing, in the period from September 1992 to January 2016. The underlying numerical wave model WAM (Wave Modelling) is run at the ECMWF (European Centre for Medium-Range Weather Forecasts) which acts as a European meteorological institute providing numerical atmospheric and ocean forecasts, archiving data and improving forecasting models. WAM is extensively validated in the literature [21,22]. Satellite altimetry measurements are, in general, validated by in-situ measurements made with wave buoys and are considered an empirical source of data for larger domains but lack in continuity as they are conﬁned by individual satellite tracks and overﬂight times. WW includes satellite altimetry data from satellite missions taking measurements over the Mediterranean (i.e., the Adriatic): European Remote Sensing Satellites (ERS-1 and ERS-2), Ocean Topography Experiment (TOPEX), Geosat Follow-On, Jason and Environmental Satellite (Envisat).

WW Data Subdivision, Preparation and Preliminary Considerations A total of 39 locations were available within the WW database for the Adriatic Sea. The locations were analyzed: individually, grouped into regions (southern, central and northern Adriatic, according to DHMZ–Croatian Meteorological and Hydrological Service ofﬁcial subdivision) and joint together for the basin as a whole. Location, their numbering J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 3 of 24

2.1. WW Data Subdivision, Preparation and Preliminary Considerations J. Mar. Sci. Eng. 2021, 9, 522 A total of 39 locations were available within the WW database for the Adriatic3 of Sea. 25 The locations were analyzed: individually, grouped into regions (southern, central and northern Adriatic, according to DHMZ–Croatian Meteorological and Hydrological Ser- vice official subdivision) and joint together for the basin as a whole. Location, their and regional subdivision are presented in Figure1, and exact geographic coordinates are numbering and regional subdivision are presented in Figure 1, and exact geographic co- given in AppendixA Table A1 . ordinates are given in Appendix A Table A1.

FigureFigure 1. 1.Studied Studied locations locations in in the the Adriatic Adriatic Sea Sea as as available available from from the the WW WW database. database.

AtAt each each location, location, 12 12 physical physical wave wave and and wind wind parameters parameters are are available available at 6-h at intervals6-h inter- (fourvals per(four day) per as day) presented as presented in Appendix in AppendixA Table AA2 Table and forA2 eachand locationfor each therelocation are there total ofare 34,460total of lines 34,460 of records. lines of records. MaximumMaximum recorded recorded significant significant wave wave heights, heights, along along with with accompanying accompanying parameters, parameters, werewere extracted extracted and and are are presented presented in in Appendix AppendixA A Table Table A3 A3.. The The single single highest highest significant significant wavewave height height in in the the database database is is recorded recorded at at location location 9 9 (E14.5 (E14.5°–N44.◦–N44.0◦0°)) 16.11.2002, 16.11.2002, reading reading HHs s= = 6.726.72m mduring during southeast southeast wind wind (local (local names namesjugo/scirocco jugo/scirocco).). For For comparison, comparison, the the single single highesthighest wave wave measuredmeasured untiluntil nownow alongalong thethe easteast coastcoast reads Hmax == 10.87 10.87 m m off off the the city city of ofDubrovnik Dubrovnik on on 12.11.2019, 12.11.2019, associated associated with with the the significant significant wave wave height height of H ofs H= s4.75= 4.75 m. The m. Thehighest highest significant significant wave wave height height so sofar far is is measured measured from from the the gas platformplatform inin thethe north north AdriaticAdriatic and and reads reads 7.5 7.5 m m [ 23[23].]. VisualizationVisualization of ofH Hs stime time series series for for a a one-year one-year period, period, presented presented in in Figure Figure2, 2, confirms confirms expectedexpected higher higher variability variability during during winter winter months. months. An example validation of WW data against available in-situ wave buoy measurement data from the Italian RON project [15] is shown for Hs and Tp on locations nearby for one winter month period, in Figures3 and4. The WW and RON locations compared in Figures3 and4 are about 26 km apart. The time series shows a good match, especially for significant wave heights. General Hs trends match well and peaks coincide. Variations between extremes in Figure3 can be accounted to distance between the compared locations (with influence of the coastline and surrounding orography), to physical and numerical limitations and settings of the numerical model and measurement buoy properties. Deviations between wave period Tp records are slightly larger than for Hs. Buoy data for wave periods show local “jumps” which could suggest that the buoy data possibly need additional filtering.

J. J.Mar. Mar. Sci. Sci. Eng. Eng. 2021 2021, 9, ,9 x, xFOR FOR PEER PEER REVIEW REVIEW 4 4of of 24 24

J. Mar. Sci. Eng. 2021HsHs, [m] 9 [m], x FOR PEER REVIEW 4 of 24 J. Mar. Sci. Eng. 2021, 9, 522 4 of 25 6 6

Loc_5Loc_5 (North) (North) 5 5 Hs [m] LocLoc 17 17 (Central) (Central) 4 4 6 LocLoc 27 27 (South) (South) 3 Loc_5 (North) 3 5 Loc 17 (Central) 2 2 4 Loc 27 (South) 1 1 3

0 0 2

Figure 2. Hs time series during 2015 at three locations, in North, Central and South Adriatic. Figure0 2. Hs time series during 2015 at three locations, in North, Central and South Adriatic.

AnAn example example validation validation of of WW WW data data against against available available in-situ in-situ wave wave buoy buoy measure- measure- s p mentment data data from from the the Italian Italian RON RON project project [15] [15] is is shown shown for for H Hs andand T Tp on on locations locations nearby nearby for for one winter month period, in Figures 3 and 4. FigureFigure 2. H2.s oneHtimes time winter series series duringmonth during 2015 period, 2015 at at three inthree Figures locations, locations, 3 inand in North, North,4. Central Central and and South South Adriatic. Adriatic.

4 4 An example validation of WW data against available in-situ wave buoy measure- Hs,Hs, RON RON ment data from the Italian RON project [15] is shown for Hs and Tp on locations nearby for 3 3 one winter month period, in Figures 3 and 4. Hs,Hs, WorldWaves WorldWaves HsHs [m] [m]2 2 4 1 1 Hs, RON 3 0 0 Hs, WorldWaves 01.01. - 31.- 31. January January 2013. 2013. Hs [m] 2 s FigureFigure 3. 3. H Hs timetime series series from from WW WW database database (locat (locationion 4) 4) and and RON RON buoy buoy “Ancona” “Ancona” (13°43 (13°43◦ ′100′10″ ″E–43°49 E–43°49◦ ′260′26″ ″N) N). . Figure 3. Hs time1 series from WW database (location 4) and RON buoy “Ancona” (13 43 10” E–43 49 26” N).

0 1515 Tp, RON 01. - 31. January 2013. Tp, RON Tp,Tp, WorldWaves WorldWaves Figure 3. H10s10 time series from WW database (location 4) and RON buoy “Ancona” (13°43′10″ E–43°49′26″ N). TpTp [sek] [sek] 5 5 15 Tp, RON Tp, WorldWaves 0 010 01.01. - 31.- 31. January January 2013. 2013. Tp [sek] ◦ 0 ◦ 0 FigureFigureFigure 4. 4. 4. TpTp Tp timetime time series series5 series from from from WW WW WW database database database (loc (location (locationation 4) 4) 4) and and and RON RON RON buoy buoy buoy “Ancona” “Ancona” “Ancona” (13°43 (13 (13°4343′1010”′10″ ″E–43°49 E–43E–43°4949′26′26”26″ ″N) N). . To prepare the data for analysis, the following frequency of occurrence tables were 0 TheThe WW WW and and RON RON locations locations compared compared in in Figures Figures 3 3and and 4 4are are about about 26 26 km km apart. apart. The The 01. - 31. January 2013. extracted from the WW database: s timetime series series shows shows a agood good ma match,tch, especially especially for for significant significant wave wave heights. heights. General General H Hs Figure 4. Tp time trendsseries1.trends fromSea match match stateWW well database tableswell and and (H (locpeakss –Tppeaksation), coincide. for coincide.4) theand following:RON Variations Variations buoy “Ancona” between between (13°43 extremes extremes′10″ E–43°49 in in Figure Figure′26″ N) 3. 3can can be be accountedaccounted• Theto to distance distance Adriatic between Seabetween with the allthe locationcompared compared merged locations locations as presented (with (with influence influence in Table of 1of; the the coastline coastline andand surrounding surrounding• TheAdriatic WW and orography), orography), regions RON aslocations presentedto to physical physical compared in Appendixan andd numericalin numerical FiguresA (North, 3limitations andlimitations Table 4 are A4 aboutand ;and Central, settings 26settings kmTable apart. of of the A5the The ; numericalnumericaltime series modeland model shows South, and and measurement Table ameasurement good A6 );match, buoy buoy especially prop properties.erties. for Deviations significantDeviations between wavebetween heights. wave wave period periodGeneral Tp Tp H s s recordsrecordstrends• are are matchEach slightly slightly ofwell the larger largerand 39 locations peaksthan than for forcoincide. individually. H Hs. .Buoy Buoy Variations data data for for wavebetween wave periods periods extremes show show in local Figurelocal “jumps” “jumps” 3 can be whichwhichaccounted could could suggest tosuggest distance that that thebetween the buoy buoy datathe data comparedpossibly possibly need needlocations additional additional (with filtering. influencefiltering. of the coastline 2. Wind speed to signiﬁcant wave height (uw–Hs), for the following: andToTo surroundingprepare prepare the the data orography),data for for analysis, analysis, to physical the the follow follow anding ingnumerical frequency frequency limitations of of occurrence occurrence and tablessettings tables were were of the • The Adriatic Sea with all location merged as presented in Table2; extractedextractednumerical from from model the the WW WWand database: measurementdatabase: buoy properties. Deviations between wave period Tp • Adriatic regions (North, Central and South) as presented in AppendixA (North, records1. are Sea slightly state tables larger (H thans–Tp), for for H thes. Buoy following: data for wave periods show local “jumps” 1. SeaTable state A7 ;tables Central, (Hs Table–Tp), forA8 ;the and following: South, Table A9); which could suggest that the buoy data possibly need additional filtering. • Each of the 39 locations individually. To prepare the data for analysis, the following frequency of occurrence tables were extracted from the WW database:

1. Sea state tables (Hs–Tp), for the following:

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Table 1. Sea state table–entire Adriatic Sea basin, period September 1992–January 2016.

Tp/Hs 0.0–0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0–4.5 4.5–5.0 5.0–5.5 5.5–6.0 6.0–6.5 Sum 0–1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1–2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2–3 221,186 65,034 754 7 0 0 0 0 0 0 0 0 0 286,981 3–4 149,331 225,790 32,459 1233 39 1 1 0 0 0 0 0 0 408,854 4–5 36,859 130,876 80,830 19,669 1732 109 7 1 0 0 0 0 0 270,083 5–6 17,747 52,597 54,473 38,089 15,605 3194 469 54 3 0 0 0 0 182,231 6–7 10,379 24,193 20,917 17,297 14,389 8836 3255 731 183 32 5 2 1 100,220 7–8 3704 8591 8993 6373 4838 3810 3141 1879 701 215 54 18 10 42,327 8–9 1863 3459 3515 2727 1930 1361 956 677 470 197 78 13 8 17,254 9–10 1174 1055 1115 819 654 495 336 231 156 92 48 26 3 6204 10–11 376 434 420 294 217 120 98 64 40 22 6 2 1 2094 11–12 363 105 107 81 91 31 26 16 10 9 5 2 1 847 12–13 434 39 23 10 8 10 7 7 2 2 1 1 0 544 13–14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sum 443,416 512,173 203,606 86,599 39,503 17,967 8296 3660 1565 569 197 64 24 1,317,639 Note. Total of 73% of sea states are less than 1 m.

Table 2. Wind speed—signiﬁcant wave height occurrence—entire Adriatic, Sept 1992–Jan 2016.

uw/Hs 0–0.25 0.25–0.5 0.5–0.75 0.75–1 1–1.25 1.25–1.5 1.5–1.75 1.75–2 2–2.25 2.25–2.5 2.5–2.75 2.75–3 3–3.25 3.25–3.5 Sum 0–1 20,070 33,291 10,955 3152 1198 462 187 81 29 26 4 3 1 0 69,459 1–2 32,250 68,242 25,570 7861 2803 1134 453 200 83 23 9 7 2 2 138,639 2–3 27,155 84,153 38,583 12,391 4471 1707 703 313 131 61 23 17 5 3 169,716 3–4 14,064 81,193 52,240 18,013 6548 2608 1067 437 209 86 47 24 7 9 176,552 4–5 5139 54,153 66,294 24,730 9238 3666 1504 614 306 104 70 23 26 8 165,875 5–6 1666 16,761 68,671 35,231 12,912 5099 2161 990 425 209 90 48 16 6 144,285 6–7 393 3321 37,421 45,709 18,845 7541 3211 1419 628 295 132 63 38 17 119,033 7–8 103 964 8754 37,098 26,470 11,372 4919 2082 954 452 232 97 39 26 93,562 8–9 33 310 1519 13,596 25,426 16,301 7712 3415 1534 731 317 160 57 30 71,141 9–10 11 77 416 2830 12,104 16,639 10,722 5572 2490 1196 502 235 96 75 52,965 10–11 6 23 129 625 3206 8879 10,611 7563 3966 1962 815 426 175 112 38,498 11–12 4 16 44 168 770 2781 5704 6793 5306 3051 1556 700 328 155 27,376 12–13 0 10 33 51 161 779 1995 3477 4147 3606 2245 1206 585 249 18,544 13–14 0 6 9 31 66 207 585 1191 2063 2588 2283 1684 975 545 12,233 14–15 0 2 8 15 28 88 192 397 709 1194 1425 1365 1087 698 7208 15–16 0 0 4 9 11 32 69 141 243 398 604 724 823 709 3767 Sum 100,894 342,522 310,650 201,510 124,257 79,295 51,795 34,685 23,223 15,982 10,354 6782 4260 2644 13,088 J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 6 of 24

12–13 0 10 33 51 161 779 1995 3477 4147 3606 2245 1206 585 249 18544

13–14 0 6 9 31 66 207 585 1191 2063 2588 2283 1684 975 545 12233

14–15 0 2 8 15 28 88 192 397 709 1194 1425 1365 1087 698 7208

15–16 0 0 4 9 11 32 69 141 243 398 604 724 823 709 3767

Sum 100894 342522 310650 201510 124257 79295 51795 34685 23223 15982 10354 6782 4260 2644 13088 J. Mar. Sci. Eng. 2021, 9, 522 6 of 25

Additionally, the well-known directionality of higher wave height associated with S-SE windsAdditionally, (jugo/scirocco the well-known) and NE winds directionality (bura/bora of), higher as the wave Adriatic height basin associated specificities with due S-SE winds (jugo/scirocco) and NE winds (bura/bora), as the Adriatic basin speciﬁcities due to the surrounding orography, is confirmed by wave roses. Wave roses for the Adriatic as to the surrounding orography, is conﬁrmed by wave roses. Wave roses for the Adriatic as a a wholewhole are are presented presented inin Figure Figure5. 5.

NORTH NORTH 20% 20%

15% 15% 10% 10% 5% 5% WEST EAST WEST EAST

5- 6 5- 6 4- 5 4- 5 3- 4 3- 4 2- 3 2- 3 1- 2 1- 2 0- 1 0- 1 SOUTH SOUTH (a) (b)

FigureFigure 5. Wave 5. Wave roses roses for forthe the entire entire Adriatic Adriatic basin: basin: ( (a) all seasea statesstates and and (b ()b sea) sea states states with withHs > Hs 2.5 > m. 2.5 m.

ThereThere is isa noticeable a noticeable amount amount of smallersmaller N–NW N–NW waves waves accounted accounted to theto the same same direc- direc- tion (maestral/maestrale) wind—a typical daily coastal circulation, caused by temperature tion (maestral/maestrale) wind—a typical daily coastal circulation, caused by temperature oscillation between land and sea during summer months, which is important to the leisure oscillationnautical sectorbetween due land to its and predictability sea during and summer mild character. months, Regional which wave is important roses are avail-to the lei- sureable nautical in Appendix sectorA due Figures to its A1 predictability and A2 and suggest and mild higher character. dominance Regional of S–SE wave waves roses in are availableSouth andin CentralAppendix Adriatic A Figures and NE A1 high and wave A2 dominance and suggest in the higher North Adriaticdominance region. of S–SE waves in South and Central Adriatic and NE high wave dominance in the North Adriatic region.3. Methods The WW data were analyzed in accordance with Det Norske Veritas (DNV) classi- 3. Methodsfication society recommendations for determining environmental conditions and loads on marine structures [2]. A joint distribution is applied, consisting of a marginal three- parameterThe WW Weibull data were distribution analyzed of significantin accordance wave with heights Det and Norske a conditional Veritas log-normal (DNV) classi- ficationdistribution society for recommendations peak periods. For for wind determ speeds,ining a conditional environmental distribution conditions is given and as loads on functionmarine ofstructures significant wave[2]. A height joint and distribution described by is a two-parameterapplied, consisting Weibull distribution.of a marginal three-parameter Weibull distribution of significant wave heights and a conditional log-normal3.1. Joint Distributiondistribution of Significantfor peak periods. Wave Height For and wind Peak speeds, Periods a conditional distribution is given asBased function on sea of state significant tables, both wave regional height and and per described individual location,by a two-parameter a joint probability Weibull distribution.distribution model was derived with the aim to optimize the parameters that will later be used to determine extreme sea states for return periods longer than the database span and to provide a consistent approach for determination of loads for fatigue and strength 3.1. Joint Distribution of Significant Wave Height and Peak Periods analyses of ships and offshore structures. BasedCMA on approach sea state (Conditional tables, both Modelling regional Approach) and per isindividual applied for location, modelling a thejoint joint proba- bilitydistribution distribution of significant model was wave derived height andwith peak the (spectral) aim to optimize period. In the general, parameters this method that will laterdefines be used the to probability determine density extreme function sea states (PDF) for by return a marginal periods distribution longer than and the a set database of spanconditional and to provide probability a consistent densities, eachapproach of which for isdetermination modelled by aof parametric loads for function fatigue and strengthwhose analyses parameters of areships optimized and offshore by mathematical structures. fitting techniques to represent data from the WW database in the best possible way. The CMA approach of fitting joint distribution CMA approach (Conditional Modelling Approach) is applied for modelling the joint to the wave data was first proposed by Bitner-Gregersen and Haver [24] and discussed distributionin detail in of Reference significant [25 wave]. It is height currently and an peak integral (spectral) part of period. standardized In general, engineering this method definesprocedures the probability (e.g., Reference density [2]) andfunction scientific (PDF) practice by (e.g.,a marginal Reference distribution [26]). and a set of

J. Mar. Sci. Eng. 2021, 9, 522 7 of 25

3.1.1. Marginal Distribution of Significant Wave Height The proposed CMA model uses the three-parameter Weibull distribution to describe a PDF of significant wave height Hs as first proposed in Reference [27].   !βH −1 !βH β Hˆ − γ s  Hˆ − γ s  ˆ Hs s Hs s Hs fHS Hs = exp − (1) αHs αHs  αHs 

where αHs is the scaling parameter, βHs is the shape parameter and γHs is the location parameter. The parameters are optimized on linearized scale with the least square method (LSM). The cumulative 3-parameter Weibull probability density function (CDF) then follows:

" #βH Hˆ − γ s ˆ s Hs ˆ F(HS) = P Hs < HS = 1 − exp − , HS, Hs ≥ γHs (2) αHs where P Hˆ s < HS represents the probability that a certain random signiﬁcant wave height Hˆ s will take on a value less than HS. Probability of exceedance is than given as Q Hˆ s = 1 − P Hˆ s (3)

When a large number of observations are available, as in the WW database, a common approach is to sort the data into Hs,i bins, as presented in the sea-state tables, e.g., Table1 . The empirical probability of exceeding of each bin is then determined by the usual expression [13]: i ∑j=1 fj Q(H ) = (4) s,i N + 1 i where ∑ fj represents the cumulative frequency of all values equal to or greater than Hs,i, j=1 while N is the total number of observations (the sum of all observations as shown in the sea state tables). The theoretical probability P Hˆ s,i that Hs,i will not be exceeded can be determined according to Equation (2). To ﬁt the theoretical distribution to the empirical points, calculated from the database, the distribution parameters αHs and βHs were optimized using the least squares method on a linearized double-log scale.

ˆ ˆ ln(−ln F (Hs = βHs ∗ ln (Hs − γHs − αHs ∗ ln(βHs ) (5)

Shape and scale parameters are determined from the linearized model coefﬁcients (y1–slope and y0–ordinate intersection) according to the following:

αHs = y1 (6)

− y0 y1 βHs = e (7)

The choice of the third parameter—the proper threshold parameter γHs—whilst per- mitting some data points to lay below is an anomaly that is sometimes dealt with by discarding (censoring) smallest empirical CDF data points prior to ﬁtting the theoretical CDF. For example, suggestions given in Reference [5], in order to formalize such an approach, recommended discarding the data points corresponding to the probability level F = 0.2 and below, but simultaneously argued that such criterion does not work equally well on all datasets. The threshold parameter γHs in this paper is chosen without discarding any data and in accordance with the procedure given in Reference [28]. The procedure concept is to test different values of γHs which then obviously affects the quality of the ﬁt. Since J. Mar. Sci. Eng. 2021, 9, 522 8 of 25

the expected relationship in Equation (5) is expected to be linear the assumption is that the optimal threshold parameter γHs will provide the best possible approximation to a linear model. This argument is formalized by applying an optimization algorithm to maximize the coefficient of determination R2, as a statistical measure of accuracy, of a linear ˆ ˆ regression on the transformed variables ln (Hs − γHs and ln(−ln F (Hs across all possible threshold values. It was also noticed that the choice of the bin size used to calculate the empirical probability of exceedance in Equation (4) has a significant influence on the theoretical model because it determines the resolution of the empirical CDF data points on which the theoretical model is fitted. A too-coarse resolution loses precision and increases error, while too fine resolution results in sporadic empty bins in the upper Hs range thus creating false points of the empirical cumulative density function that would influence the results and respective evaluated extremes. After initial testing of model behavior on the analyzed dataset, the bin size was determined by defining 30 equally spaced bins between the minimum and the maximum recorded value on each location separately.

3.1.2. Conditional Distribution of Peak Periods Depending on Signiﬁcant Wave Height

The conditional distribution of peak period Tp based on Hs is modelled by the log- normal PDF, as ﬁrst proposed by Bitner-Gregersen and Haver in Reference [24] (see also Reference [29]):

( 2 ) 1 lnTˆp − µ f Tˆ Hˆ = √ exp − (8) TP|HS p s 2 σ Tˆp 2 π 2σ where the distribution parameters µ is the mean logarithmic value of the variable µ = E lnTp , and σ is the standard deviation of the variable logarithmic value σ = std lnTp [16]. Both parameters are, easy to calculate statistical quantities, dependent on Hs. Since Hs is divided into bins, according to Table1, the change of σ and µ calculated for each bin is modelled as follows: µ = a0lnHs + a1 (9)

σ = a2 ∗ lnHs + a3 (10)

Coefﬁcients a0, a1, a2 and a3 are calculated for each location individually, regionally and for the entire Adriatic Sea.

3.2. Joint Distribution of Significant Wave Height and Wind Speed Like joint distribution of significant wave height and peak period, a statistical model for joint distribution of significant wave height and wind speed is developed. The wind speed uw is defined as a variable dependent on the significant wave height, Hs. Although physically inversing the cause and consequence, such description, together with results from Section 3.1, presents a complete metocean description dependent on a single variable, i.e., Hs. Wind speed and direction data are an integral part of the underlying WW database and refer to the data used by ECMWF to force WAM model. Wind speeds are given at 10 m above sea level with an assumed duration of 6 h (as for the corresponding sea state). The conditional distribution of the wind speed as a function of the significant wave height can be described by the two-parameter Weibull distribution as proposed by Bitner- Gregersen and Haver [24] and included in DNV RP C-205 [2]: " # u k−1 u k f (u |H ) = k w exp − w (11) U|HS w s k Uc Uc J. Mar. Sci. Eng. 2021, 9, x FOR PEER REVIEW 9 of 24

( | | = − (11)

where the scale parameter Uc and the shape parameter k are estimated from the available J. Mar. Sci. Eng. 2021, 9, 522 data, using the following model: 9 of 25

= + = + (12)

where the scale parameter Uc and the shape parameter k are estimated from the available 3.3.data, Extremes using the Values following of Significant model: Wave Height for Long Return Periods

Extreme Hs values, for return periods (RP) longer than the scope of the WW data- k = c + c Hc3 U = c + c Hc6 (12) base, can been evaluated based1 on2 usings c the4 three-parameter5 s Weibull distribution fit described3.3. Extremes in ValuesSection of Significant3.1.1. The Wave fitted Height distribution for Long Return upper Periods tail is extrapolated to theoretical sRP s probabilityExtreme of H sexceedancevalues, for return Q(H periods) of a certain (RP) longer H value than the and scope return of the period WW database, RP. Probability ofcan exceedance been evaluated Q(H basedsRP) is on generally using the determined three-parameter as follows: Weibull distribution fit described in Section 3.1.1. The fitted distribution upper tail is extrapolated to theoretical probability of RP 1 exceedance Q(Hs ) of a certain Hs value( and return = period∗ RP. Probability of exceedance (13) RP Q(Hs ) is generally determined as follows: where TREG is the duration of uninterrupted observations within the database (23.5 year), T 1 and N is the total number of dataQ H records.RP = REG Once∗ the 3-parameter Weibull CDF(13) (as given s N RP in Equation (2)) is fitted to data, the significant wave height that will be exceeded once forwhere certainTREG returnis the duration period can of uninterrupted be determined observations as its inverse: within the database (23.5 year), and N is the total number of data records. Once the 3-parameter Weibull CDF (as given in / Equation (2)) is fitted to data, the significant= ∗ (−ln wave(( height that will+ be exceeded once for (14) certain return period can be determined as its inverse:

1/β 4. Results RP RP Hs H = αHs ∗ −ln Q H + γHs (14) Within this section,s models parameters,s as described in Section 3, fitted to data are presented4. Results graphically for brevity and the same tabulated data are presented in Appen- dix B. Within this section, models parameters, as described in Section3, fitted to data are presented graphically for brevity and the same tabulated data are presented in AppendixB . 4.1. Parameters of the Joint Distribution of Significant Wave Height and Peak Wave Periods 4.1. ParametersThe three-parameter of the Joint Distribution Weibull ofdistribution Significant Wave parameters Height and were Peak fitted WavePeriods for each of the 39 location,The three-parameterfor data merged Weibull according distribution to the parameters regional weresubdivision fitted for and each for of thethe 39 all lo- location merged,cation, for i.e., data the merged entire according Adriatic toSea. the An regional example subdivision fitting andon a for linearized the all location scale, as per merged, i.e., the entire Adriatic Sea. An example fitting on a linearized scale, as per Equation (5), is presented in Figure 6 for location 9, where the maximum Hs was record- Equation (5), is presented in Figure6 for location 9, where the maximum Hs was recorded edwithin within the database.the database.

2.5

2 WW data 1.5 model

0.5

-0.5 ln(-ln(1- F(Hs))) -1

-1.5

-2 -3 -2 -1 0 1 2 ln(Hs - γ), [m] FigureFigure 6.6. ParameterParameter Weibull Weibull parameter parameter ﬁt for fit marginalfor marginal distribution distribution of Hs. (Eof 14.5–NHs. (E 44.0).14.5–N 44.0).

The fitfit presented presented in Figurein Figure6 shows 6 shows an example an ex validationample validation of the model. of the All model. 39 location All 39 loca- 2 fits were visually inspected, and the calculated coefficient of determination, R , ranging be- 2 tion fits2 were visually inspected,2 and the calculated coefficient of determination, R , tween R min = 0.9971 and R max = 0.9996, confirms that the model is appropriate. Likewise, ranging between R2min = 0.9971 and R2max = 0.9996, confirms that the model is appropriate. an example fit is presented in Figure7 of the log-normal distribution fit for a conditional distribution of peak periods dependent on significant wave height.

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J. Mar. Sci. Eng. 2021, 9, 522 10 of 25 Likewise, an example fit is presented in Figure 7 of the log-normal distribution fit for a Likewise, an example fit is presented in Figure 7 of the log-normal distribution fit for a conditional distribution of peak periods dependent on significant wave height. conditional distribution of peak periods dependent on significant wave height.

Figure 7. Log-normal conditional distribution fit of Tp on Hs, e.g., Hs = 0.5–1.0 m; E 14.5–N 44.0. FigureFigure 7. Log-normal 7. Log-normal conditional conditional distribution distribution ﬁt of Tp on fitHs ,of e.g., TpH ons = 0.5–1.0Hs, e.g., m; H Es 14.5–N = 0.5–1.0 44.0. m; E 14.5–N 44.0.

The sea state, Hs and Tp description are completed by determining the mean and the The sea state, Hs and Tp description are completed by determining the mean and the standardstandardThe deviation deviation sea state, values values Hs that and that deﬁne T pdefine description the log-normalthe log- arenormal distribution completed distribution for by the determining for entire the bin entire range thebin rangemean and the ofofstandardH Hs,s, asas presented presented deviation in in Figure Figure values8. 8. that define the log-normal distribution for the entire bin range of Hs, as presented in Figure 8. 8 8 6

Tp WW data - Mean

σ 6 4 Theoretical - Mean ,

Tp WW data - Mean

Tp WW data - Stand.Dev σ

μ 4 Theoretical - Mean , 2 Theoretical - Stand.Dev

Tp WW data - Stand.Dev

μ 0 2 Theoretical - Stand.Dev -1.5 -1 -0.5 0 0.5 1 1.5 2 ln(Hs) 0 -1.5 -1 -0.5 0 0.5 1 1.5 2 FigureFigure 8.8. Mean and standardstandard deviationdeviation for for calculation calculation of ofTp Tpdistribution distribution across acrossHs Hsbin bin range; range; E ln(Hs) E14.5–N 14.5–N 44.0. 44.0. Figure 8. Mean and standard deviation for calculation of Tp distribution across Hs bin range; E TheThe model model parameters parameters for thefor joint the distributionjoint distributi of significanton of significant wave height wave and height peak pe- and peak 14.5–N 44.0. riodperiod are finallyare finally presented presented in Table 3in for Table regions, 3 for and regions, Figures9 andand 10 Figures for individual 9 and locations. 10 for individual locations. Table 3. TheModel model parameters parameters for joint distribution for the ofjointHs and distributiTp. Adriaticon regional of significant subdivision. wave height and peak

TableperiodRegion 3. Model are finally parametersαHs presented for jointβHs distributionin TableγHs 3 of for Hs regions,anda0 Tp. Adriatic aand1 Figures regionala2 subdivision.9 anda3 10 for individual locations.Adriatic Sea 0.553 0.987 0.071 1.7862 5.1201 −0.2003 1.0634 North AdriaticRegion 0.527αHs 0.955βHs 0.076γHs 1.6161a0 4.8126 a1− 0.2876 a1.05082 a3 CentralTableAdriatic 3. Adriatic Model Sea parameters 0.6590.553 for 1.091 joint0.987 distribution 0.0680.071 1.8676 of1.7862 Hs and 5.0563 Tp5.1201. Adriatic−0.1995 − regional0.20030.9285 subdivision.1.0634 SouthNorth Adriatic Adriatic 0.7620.527 1.166 0.955 0.0910.076 1.93531.6161 5.2776 4.8126−0.1492 −0.28761.0775 1.0508 CentralRegion Adriatic 0.659α Hs 1.091 βHs 0.068 γHs1.8676 a05.0563 a−10.1995 a0.92852 a3 SouthAdriatic Adriatic Sea 0.7620.553 1.166 0.987 0.091 0.071 1.9353 1.7862 5.2776 5.1201−0.1492 −0.20031.0775 1.0634 North Adriatic 0.527 0.955 0.076 1.6161 4.8126 −0.2876 1.0508 Central Adriatic 0.659 1.091 0.068 1.8676 5.0563 −0.1995 0.9285 South Adriatic 0.762 1.166 0.091 1.9353 5.2776 −0.1492 1.0775

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1.4

1.2 1.4

Hs γ 1 1.2 ,

Hs Hs γ β 0.8 1 , , Hs Hs β

α 0.8

0.6 , α Hs Hs

α 0.6 β α 0.4 Hs Hs γ β 0.4 Hs Hs Coefficient 0.2 γ Hs Coefficient 0.2 0 5 10 15 20 25 30 35 0 5 Location10 number15 20 25 30 35 Location number Figure 9. Model parameters for marginal distribution of significant wave height per location. FigureFigure 9. 9. ModelModel parameters parameters for for marginal marginal distribution distribution of of significant signiﬁcant wave wave height height per per location. location.

6 6

3 5 3 5 a0 a0 , a , , a , 2 4 2 4 a1 a1 , a , a 1 1 a2 a2 3 3 , a , a a3 a3 0 0 2 2

1 1

Coefficient a Coefficient 0

Coefficient a Coefficient 0 -1 -1 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Location number Location number Figure 10. Model parameters for mean and standard deviation across Hs bin range to model FigureFigure 10. Model10. Model parameters parameterslog-normal for mean for distribution andmean standard an ofd peakstandard deviation period deviationacross Tp-perHs location. binacross range Hs to bin model range log-normal to model distribution of peaklog-normal period Tp-per distribution location. of peak period Tp-per location. For precision, and to enable repeatability and practical usage, numerical parameters For precision,for and individual Forto enable precision, locations repeatability and are to enablegiven and in repeatability practicalAppendix usage, B and Table practical numerical A10. usage, parameters numerical parameters for individual locations are given in AppendixB Table A10. for individual locations are given in Appendix B Table A10. 4.2. Parameters of the Joint Distribution of Wind Speed and Significant Wave Height 4.2. Parameters of the Joint Distribution of Wind Speed and Signiﬁcant Wave Height For Hs bins, the theoretical distribution of wind speeds proposed by the model in 4.2. Parameters of the JointFor DistributionH bins, the of theoretical Wind Speed distribution and Significant of wind Wave speeds Height proposed by the model in Equation (11)s is derived. The model parameters k and Uc are optimized using the non- For Hs bins, thelinearEquation theoretical least (11) squares is distribution derived. method. The An modelof example wind parameters speeds fit of the kproposedand two-parameterUc are by optimized the Weibull model using distribution in the nonlinear of least squares method. An example ﬁt of thec two-parameter Weibull distribution of wind Equation (11) is derived.wind speed The for model bin H sparameters = 2.25–2.5 m kfor and the Uentire are Adriaticoptimized is shown using in the Figure non- 11. linear least squares speedmethod. for binAnH examples = 2.25–2.5 fit mof forthe the two-parameter entire Adriatic Weibull is shown distribution in Figure 11. of wind speed for bin Hs = 2.25–2.5 m for the entire Adriatic is shown in Figure 11.

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Figure 11. Fitting the model to WW data; entire Adriatic; Hs,i = 2.25–2.5 m.

Figure 11. Fitting the model to WW data; entire Adriatic; Hs,i = 2.25–2.5 m. By repeating the same procedure for each Hs,i bin, a model of fit parameters k and Uc is obtained. Their resultsBy for repeating the entire the sameAdriatic procedure are presented for each Hs,i inbin, Figure a model 12 of as ﬁt a parameters function kofand Uc is obtained. Their results for the entire Adriatic are presented in Figure 12 as a function Hs. of Hs.

Figure 12. Distribution ofFigure k and 12. UcDistribution for Adriatic of k asand a Ucwhole.for Adriatic as a whole.

A data scattering of WW data points for the shape parameter k can be seen for higher A data scattering of WW data points for the shape parameter k can be seen for higher Hs values. This feature is even more pronounced having a more detailed look for certain Hs values. This featurelocations is even and more is due pronounced to small amount having of data a at more high Hs detailed. Poor agreement look for of certain the statistical locations and is duemodel to small at higher amount values of alsodata has at a high negative Hs.effect Poor on agreement poorer agreement of the ofstatistical the model with model at higher valuesdata also at lower has values. a negative It was ef foundfect thaton poorer more than agreement 99.5% of the of recorded the model data with are usually data at lower values.below It was signiﬁcant found that wave more height than of 3.25–3.75 99.5% of m. the In orderrecorded to achieve data aare better usually agreement data corresponding to the highest 0.5% Hs were discarded, both for individual locations below significant waveanalysis height and groupedof 3.25–3.75 data, havingm. In order in mind to that achieve such ﬁltering a better makes agreement the model data acceptable corresponding to thefor fatiguehighest or 0.5% seakeeping Hs were considerations discarded, of offshore both for structures individual but not locations for the extreme analysis and groupedvalue data, analysis. having in mind that such filtering makes the model acceptable for fatigue or seakeepingThe model considerations parameters for of the offshore joint distribution structures of wind but speed not and for significant the extreme wave height are finally presented in Table4 for regions, and Figures 13 and 14 for individual locations. value analysis. The model parametersTable 4. Model for parametersthe joint fordistribu joint distributiontion of wind of Hs and speedu_w. Adriaticand significant regional subdivision. wave height are finally presented in Table 4 for regions, and Figures 13 and 14 for individual Region c c c c c c locations. 1 2 3 4 5 6 Adriatic Sea 1.6533 2.2548 1.1557 −0.3633 7.7434 0.5817 North Adriatic 1.6910 1.8402 1.2730 −0.0925 7.4936 0.6245 Table 4. Model parametersCentral for Adriaticjoint distribution 1.4848 of Hs 2.5383 and u_w. 1.0783Adriatic regional−0.2775 subdivision. 7.7063 0.5978 South Adriatic 1.5796 2.5238 1.0601 −0.2048 7.5145 0.5886 Region c1 c2 c3 c4 c5 c6 Adriatic Sea 1.6533 2.2548 1.1557 −0.3633 7.7434 0.5817 North Adriatic 1.6910 1.8402 1.2730 −0.0925 7.4936 0.6245 Central Adriatic 1.4848 2.5383 1.0783 −0.2775 7.7063 0.5978 South Adriatic 1.5796 2.5238 1.0601 −0.2048 7.5145 0.5886

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6 c1 5 6 c2 3 c1 c3 , c

2 4 5 c2 3

, c c3 1 , c 3 2 4 , c 1 3 2 2 Coefficient c Coefficient 1

Coefficient c Coefficient 1 0 0 5 10 15 20 25 30 35 40 0 0 5 10 15Location20 number25 30 35 40

Location number

Figure 13. Model parameters c1–c3 for description of the joint distribution of uw and Hs per location. FigureFigure 13.13.Model Model parametersparametersc c11––cc33 for for description description of of the the joint joint distribution distribution of ofu uwwand andHs Hsper perlocation. location.

10 10 6

8 6 8 , a , a 5 6 5 6 , a , , a , 4 4 c4 c4 4 4 c5 c5 2 2 c6 c6 0 Coefficient a 0Coefficient Coefficient a Coefficient -2 -2

0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Location number Location number Figure 14. Model parameters c4–c6 for description of the joint distribution of uw and Hs per location. FigureFigure 14. Model 14. Model parameters parameters c4c–4c6–c6 forfor description description of of the the joint joint distribution distribution of u ofw anduw andHs per Hs location.per location. For precision, and to enable repeatability and practical use, parameters for individ- ualFor locationsFor precision, precision, are given and and totoin enableAppendixenable repeatability repeatability B-Table A11. and and practical practical use, parametersuse, parameters for individual for individ- locations are given in AppendixB-Table A11. ual locations are given in Appendix B-Table A11. 4.3. Extreme Wave Heights for Different Return Periods 4.3. Extreme Wave Heights for Different Return Periods Once the three-parameter Weibull distribution parameters were evaluated (Table 3), 4.3. ExtremeOnce theWave three-parameter Heights for Different Weibull Return distribution Periods parameters were evaluated (Table3), determining a theoretical significant wave height probability of occurrence, an extreme determiningOnce the three-parameter a theoretical significant Weibull wave distribution height probability parameters of occurrence, were evaluated an extreme (Table 3), Hs value prediction was possible for return periods longer than the initial database by determiningHs value prediction a theoretical was possiblesignificant for returnwave periodsheight probability longer than theof occurrence, initial database an extreme by extrapolatingextrapolating thethe distributiondistribution “upper“upper tail”tail” toto anan appropriateappropriate probabilityprobability ofof occurrenceoccurrence Hs (Equationsvalue prediction (13) and was(14)). possible Most probable for return extreme peri significantods longer wave than heights the initialfor 20-, database50- and by extrapolating(Equations (13) the and distribution (14)). Most probable“upper tail” extreme to an significant appropriate wave heightsprobability for 20-, of 50- occurrence and 100-year100-year returnreturn periods,periods, accordingaccording to to regional regional subdivision, subdivision, are are presented presented in in Table Table5. 5. (Equations (13) and (14)). Most probable extreme significant wave heights for 20-, 50- and Table 5. Most probable extreme significant wave height for 20-, 50- and 100-year return periods. 100-yearTable 5. returnMost probable periods, extreme according significant to waveregional height subdivision, for 20-, 50- and are 100-year presented return in periods. Table 5. Region RP = 20 year RP = 50 year RP = 100 year Table 5. MostRegion probable extreme RP significant = 20 Year wave height RP =for 50 20-, Year 50- and 100-year RP = 100 return Year periods. Adriatic Sea 5.94 6.47 6.87 Adriatic Sea 5.94 6.47 6.87 North Adriatic 6.12 6.69 7.12 NorthRegion Adriatic RP 6.12 = 20 year RP 6.69 = 50 year RP 7.12 = 100 year CentralAdriaticCentral Adriatic Adriatic Sea 5.645.645.94 6.106.106.47 6.446.44 6.87 NorthSouthSouth AdriaticAdriatic Adriatic 5.725.726.12 6.146.146.69 6.466.46 7.12 Central Adriatic 5.64 6.10 6.44 South Adriatic 5.72 6.14 6.46

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The difference between Hs,max_recorded, the recorded maximum within the WW The difference between Hs,max_recorded, the recorded maximum within the WW database and Hs,max_calculated, the most probable theoretical extreme for the exact same database and Hs,max_calculated, the most probable theoretical extreme for the exact same return period as the database, per location, is presented in Figure 15. return period as the database, per location, is presented in Figure 15.

7 H recorded s,max H calculated s,max 6.5

6 HsRP [m]

5.5

5 5 10 15 20 25 30 35 Location number

Figure 15. HsFigure comparison, 15. Hs comparison, per location, per of location,most probable of most theoretical probable theoretical extreme and extreme recorded and recordedmaximum maximum within WW database (duration 23.5 year). within WW database (duration 23.5 year).

The average differenceThe average between differenceHs,max_recorded between Hs,max_recordedand Hs,max_calculated and Hs,max_calculatedis 4.1% in is 4.1% in average acrossaverage all locations across withall locations a standard with deviation a standard of 4.7%,deviation i.e., Hs,max_calculatedof 4.7%, i.e., Hs,max_calculated overestimatesoverestimatesHs,max_recorded Hs,max_recordedby 0.23 m in average by 0.23 withm in aaverage standard with deviation a standard of 0.27 deviation m. of 0.27 m. For precision,For and precision, to enable repeatabilityand to enable and repeatability practical use, and parameters practical use, for individualparameters for individ- locations are givenual locations in Appendix are givenB-Table in Appendix A12. B-Table A12.

5. Discussion5. Discussion The results presentedThe results in Sectionpresented4 provide in Section parameters 4 provide for parameters a systematic for theoretical a systematic theoretical model of windmodel and waveof wind statistics and wave for the statistics Adriatic for Sea. the TheAdriatic distributions Sea. The aredistributions fitted to the are fitted to the data from thedata WorldWaves from the databaseWorldWaves for thedatabase period for 1992–2016. the period As 1992–2016. such, the resultsAs such, are the results are limited with precisionlimited with and accuracyprecision of and the underlyingaccuracy of database. the underlying Each data-acquisition database. Each tech- data-acquisition nique or modellingtechnique approach or modelling has limitations approach but has the limitati used datasetons but currentlythe used dataset represent currently the represent state-of-the-artthe by state-of-the-art combining a third-generation by combining a numericalthird-generation model hindcast,numerical that model provides hindcast, that pro- the systematicvides character the systematic in space and character time, with in space the available and time, satellite with altimetrythe available measure- satellite altimetry ments. If a specificmeasurements. random location If a specific would random be of interestlocation between would be the of analyzed interest between location, the analyzed four-point interpolationlocation, four-point can be used. interpolation As for the near-shorecan be used. region, As for winds the near-shore and consequent region, winds and waves in the Adriaticconsequent are waves highly in locally the Adriatic influenced are byhighly surrounding locally influenced land topography, by surrounding i.e., land to- mountains andpography, islands; thus,i.e., mountains results should and beislands; extrapolated thus, results in those should regions be withextrapolated care or in those re- used only as boundarygions with conditions care or used for only site specificas boundary studies. conditions for site specific studies. The applied three-parameterThe applied three-parameter Weibull and log-normal Weibull distributions,and log-normal used distributions, for the CMA used for the approach for jointCMA distribution approach for of significant joint distribution wave height of signif andicant peak wave period, height showed and excellent peak period, showed agreement withexcellent the data agreement (e.g., Figures with the6 and data7). (e.g., The Figures upper tail6 and of 7). the The fit, upper essential tail forof the fit, essential extremes evaluation, is always sensitive to fewer data records of high sea states. It thus for extremes evaluation, is always sensitive to fewer data records of high sea states. It caries a greater uncertainty also subject to distribution model choice/data preparation thus caries a greater uncertainty also subject to distribution model choice/data prepara- and parameter-fitting technique [17,30]. The applied method however remains a common tion and parameter-fitting technique [17,30]. The applied method however remains a choice and recommendation by classification societies guidelines [2]. The shape and scale common choice and recommendation by classification societies guidelines [2]. The shape parameters in Figure9 of the three-parameter Weibull distribution show a slight increasing and scale parameters in Figure 9 of the three-parameter Weibull distribution show a linear trend going towards higher location numbers, i.e., towards the south of the Adriatic. slight increasing linear trend going towards higher location numbers, i.e., towards the The coefficients for Tp distribution modelling across the Hs range, shown in Figure 10, show south of the Adriatic. The coefficients for Tp distribution modelling across the Hs range, almost constant values and could be used as such. On the other hand, the adequacy of shown in Figure 10, show almost constant values and could be used as such. On the other the chosen linear model for the mean value parameters across the Hs range, as given in hand, the adequacy of the chosen linear model for the mean value parameters across the Equations (9) and (10) and presented in Figure8, exhibits a slight non-linear trend and considering aH highers range, order as given model in could Equations be beneficial. (9) and (10) and presented in Figure 8, exhibits a slight non-linear trend and considering a higher order model could be beneficial.

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As for the wind speed to significant wave height fit it should be noted that the J. Mar. Sci. Eng. 2021, 9, 522 highest 0.5% of data were filtered out due to high scatter (Figure 12) to improve15 of 25 fit quality but this makes the model less appropriate for possible upper tail extremes extrapolation. The shape scale parameter Uc shows greater fit confidence than the shape parameter k across theAs forHs therange wind (Figure speed to 12). significant wave height fit it should be noted that the highest In0.5% general, of data were the filtered best outaccuracy due to high is scatteralways (Figure expected 12) to improve by applyi fit qualityng butlocation this or re- makes the model less appropriate for possible upper tail extremes extrapolation. The shape gion-specific parameters without generalization as their fit parameters were optimized scale parameter Uc shows greater fit confidence than the shape parameter k across the Hs simultaneously.range (Figure 12). ExtremesIn general, evaluation the best accuracy as presented is always in expected Figure by 16, applying noting location the location or region-specific regional subdivision (North,parameters 1–9; without Central, generalization 10–22; South, as their fit23– parameters39), show were that optimized highest simultaneously. extremes can be ex- Extremes evaluation as presented in Figure 16, noting the location regional subdivision pected(North, in North 1–9; Central, and South 10–22; Adriatic South, 23–39), and showsmaller that highestin the extremesCentral canAdriatic be expected with in several lo- cationsNorth (20, and 21, South 22) Adriaticin its southeast and smaller that in the are Central closest Adriatic to South with several Adriatic locations and (20,exposed 21, to SE wind22) (jugo/scirocco in its southeast) show that are high closest extremes to South Adriaticas well. and The exposed highest to SE recorded wind (jugo/scirocco significant) wave heightshow within high the extremes WW asdatabase well. The reads highest 6.72 recorded m (location significant 9) wave and heightthe comparable, within the WW theoretical, most databaseprobable reads 20-year 6.72 m calculated (location 9) and on themerged comparable, data theoretical,for the entire most probableAdriatic 20-year reads 5.94 m, calculated on merged data for the entire Adriatic reads 5.94 m, thus being un-conservative thus beingand highlighting un-conservative issues of generalization.and highlighting issues of generalization.

7.5

6.5 HsRP [m] 6

5.5 HsRP = 20y 5 0 5 10 15 20 25 30 35 40 HsRP = 50y Location number HsRP = 100y

Figure 16. Most probable extreme significant wave height for RP = 20, 50 and 100 y per location. Figure 16. Most probable extreme significant wave height for RP = 20, 50 and 100 y per location. 6. Conclusions 6. ConclusionsThe paper analyzed the wind and wave WorldWaves database (1992–2016), which Theis an paper assimilation analyzed of numerical the wind hindcast and andwave satellite WorldWaves altimetry wave database measurements (1992–2016), for a which is specific wind–wave climate region in the Adriatic Sea. The Adriatic Sea is seeing increasing an assimilationcommercial activityof numerical and is a fragilehindcast ecological and systemsatellite due altimetry to its relatively wave small measurements area and for a specificbeing wind–wave a semi-enclosed climate basin deservingregion in thus the an Adri in-detailatic look. Sea. Based The onAdriatic the WW databaseSea is seeing in- creasingthe modelscommercial were developed: activity jointand distributionis a fragile of ecological significant wave system height due and to peak its relatively period; small area andextreme being significant a semi-enclosed wave height basin for long deserving return periods; thus jointan in-detail distribution look. of wind Based speed on the WW and wave height. The model parameters and the extremes are presented for each of the database39 uniformly the models spaced were locations developed: (0.5◦ × 0.5 ◦jointlat./long.) distribution across the of offshore signific Adriatic,ant wave divided height and peak inperiod; three regions extreme (North, significant Central andwave South height Adriatic) for long and forreturn the entire periods; Adriatic joint Sea distribution as a of windwhole speed (all and location wave data height. merged The together). model The parameters model parameters, and the as extremes well as the extremes,are presented for each ofcan the be found39 uniformly presented spaced in paper locations main body, (0.5° for the × 0.5° three lat./long.) regions and across the Adriatic the offshore as a Adri- atic, dividedwhole, either in asthree tabulated regions numerical (North, values Cent or graphically.ral and South Locations Adriatic) specific and results for are, the entire for brevity, only graphically presented in paper main body and the numerical tabulated Adriaticdata Sea are providedas a whole in the (all Appendix. location data merged together). The model parameters, as well as theThe extremes, presented models can be (Section found3) andpresented optimized in model paper parameters main (Sectionbody, 4for/Appendix) the three regions and theprovide Adriatic a complete as a descriptionwhole, either of main as windtabu andlated wave numerical value statistics. values Such or data graphically. can be Loca- tions usefulspecific for results the design, are, risk-based for brevity, operation only planning, graphically lifetime presented extension in and paper maintenance main body and of new and existing seagoing vessels and offshore installations in the Adriatic Sea. the numerical tabulated data are provided in the Appendix. The presented models (Section 3) and optimized model parameters (Section 4/Appendix) provide a complete description of main wind and wave value statistics. Such data can be useful for the design, risk-based operation planning, lifetime extension and maintenance of new and existing seagoing vessels and offshore installations in the Adriatic Sea.

J. Mar. Sci. Eng. 2021, 9, 522 16 of 25

Author Contributions: J.P. provided conceptualization, methodology and supervision; and M.K. executed the formal analysis, investigation and writing. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Croatian Science Foundation, under the project MODUS lP-2019-04-2085, and the Faculty of Maritime Studies–University of Split, under the project VIF- 2674./2017. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data presented in this study are available within the article, mainly in AppendixA & AppendixB. Restrictions apply to the availability of the underlying WorldWaves database that is the property of Fugro OCEANOR [www.fugro.com; www.oceanor.info, accessed on 5 May 2021]. Acknowledgments: The WorldWaves database is provided by Fugro OCEANOR. The presented work was derived from MK’s doctoral thesis, “Modelling of wind-generated waves in the Adriatic Sea for applications in naval architecture and maritime transportation” (in Croatian), under the mentorship of JP. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Appendix A

Table A1. Location numbering and coordinates with regional subdivision.

North Adriatic Central Adriatic South Adriatic Nb. Latitude Longitude Nb. Latitude Longitude Nb. Latitude Longitude 1 44.5◦ N 12.5◦ E 10 43.5◦ N 14.0◦ E 23 41.5◦ N 16.5◦ E 2 44.5◦ N 13.0◦ E 11 43.0◦ N 14.5◦ E 24 42.0◦ N 16.5◦ E 3 45.0◦ N 13.0◦ E 12 43.5◦ N 14.5◦ E 25 41.5◦ N 17.0◦ E 4 44.0◦ N 13.5◦ E 13 42.5◦ N 15.0◦ E 26 42.0◦ N 17.0◦ E 5 44.5◦ N 13.5◦ E 14 43.0◦ N 15.0◦ E 27 41.5◦ N 17.5◦ E 6 45.0◦ N 13.5◦ E 15 43.5◦ N 15.0◦ E 28 42.0◦ N 17.5◦ E 7 44.0◦ N 14.0◦ E 16 42.5◦ N 15.5◦ E 29 41.0◦ N 18.0◦ E 8 44.5◦ N 14.0◦ E 17 43.0◦ N 15.5◦ E 30 41.5◦ N 18.0◦ E 9 44.0◦ N 14.5◦ E 18 43.5◦ N 15.5◦ E 31 42.0◦ N 18.0◦ E - - - 19 42.5◦ N 16.0◦ E 32 40.5◦ N 18.5◦ E - - - 20 42.5◦ N 16.5◦ E 33 41.0◦ N 18.5◦ E - - - 21 42.5◦ N 17.0◦ E 34 41.5◦ N 18.5◦ E - - - 22 42.5◦ N 17.5◦ E 35 40.0◦ N 19.0◦ E ------36 40.5◦ N 19.0◦ E ------37 41.0◦ N 19.0◦ E ------38 41.5◦ N 19.0◦ E ------39 40.0◦ N 19.5◦ E

Table A2. Wind and wave parameters available for each location in in the WW database.

Symbol Name Unit

Hs Significant wave height m ◦ θmean Mean wave direction Tp Peak period of the 1D spectrum s 1 Tm Mean wave period s Hs,ww Significant wind–wave height m ◦ θww Mean wind direction. waves Tm,ww Mean period wind–waves s Hs,sw Significant wave height of swell m ◦ θsw Mean wave direction of sea Tm,sw Mean period of swell s uw Wind speed at 10 m m/s ◦ θw Wind direction at 10 m 1 Tm represents the energy period defined by spectral moments, Tm = m1/m0. J. Mar. Sci. Eng. 2021, 9, 522 17 of 25

Table A3. Maximum recoded wave heights, Hs, per location with accompanying parameters. Maximum marked in red.

◦ ◦ Latitude/Longitude Year mm dd hh Hs (m) θmean ( ) Tp (s) Tm (s) Uw (m/s) θw ( ) E12.5_N44.5 2015 2 6 6 5.59 75 9.22 8.35 24.07 55 E13.0_N44.5 1993 1 2 18 6.45 58 8.48 7.40 19.96 55 E13.0_N45.0 1993 1 2 18 5.60 59 7.71 6.64 20.26 54 E13.5_N44.0 1992 12 28 12 6.14 48 7.71 6.85 24.80 53 E13.5_N44.5 1993 1 2 18 6.34 56 7.71 6.97 22.77 55 E13.5_N45.0 1993 1 2 18 5.26 58 7.01 5.97 23.66 54 E14.0_N43.5 2002 11 16 12 5.09 132 8.39 7.07 14.21 141 E14.0_N44.0 2002 11 16 12 6.17 138 8.39 7.16 20.15 144 E14.0_N44.5 2002 11 16 12 6.19 145 7.63 7.00 20.69 148 E14.5_N43.0 2015 3 5 12 6.03 30 8.86 7.92 19.56 34 E14.5_N43.5 2004 11 14 12 5.52 39 8.39 7.98 19.73 40 E14.5_N44.0 2002 11 16 12 6.72 142 8.39 7.15 22.22 146 E15.0_N42.5 2003 12 23 12 5.71 22 8.12 7.40 20.94 22 E15.0_N43.0 2004 11 14 12 5.71 39 9.13 8.19 20.34 50 E15.0_N43.5 2008 12 11 18 5.59 138 9.23 8.35 18.85 150 E15.5_N42.5 2015 3 5 18 5.22 68 8.57 7.65 18.36 68 E15.5_N43.0 2008 12 11 18 5.17 138 9.20 8.12 20.15 148 E15.5_N43.5 2008 12 11 18 5.89 142 9.27 8.17 23.42 138 E16.0_N42.5 1992 12 8 18 5.08 131 8.48 7.55 17.87 149 E16.5_N41.5 1994 1 29 18 5.42 0 8.48 7.56 19.18 3 E16.5_N42.0 2008 12 11 12 5.05 130 9.02 8.00 17.82 143 E16.5_N42.5 1992 12 8 18 6.05 136 8.48 7.67 21.89 145 E17.0_N41.5 1994 1 29 18 5.19 355 8.48 7.66 18.24 6 E17.0_N42.0 1992 12 8 18 5.72 139 7.71 7.39 20.69 149 E17.0_N42.5 1992 12 8 18 6.33 142 8.48 7.65 22.75 143 E17.5_N41.5 1992 10 4 6 5.39 144 7.71 7.27 20.44 148 E17.5_N42.0 1992 12 8 18 6.07 147 7.71 7.39 22.38 146 E17.5_N42.5 1992 12 8 18 6.22 149 8.48 7.49 22.90 143 E18.0_N41.0 2012 1 6 18 5.37 344 8.45 7.58 19.21 354 E18.0_N41.5 2009 3 5 6 6.02 149 9.08 8.05 20.03 152 E18.0_N42.0 1992 10 4 6 5.76 150 7.71 7.41 23.16 138 E18.5_N40.5 2004 3 8 6 5.30 157 9.23 8.03 15.06 154 E18.5_N41.0 2008 12 17 18 5.79 159 9.23 8.19 20.47 158 E18.5_N41.5 2008 11 29 0 6.03 162 9.15 8.04 22.97 153 E19.0_N40.0 2009 1 14 6 6.16 162 11.92 10.15 17.71 138 E19.0_N40.5 2008 12 4 12 6.20 171 10.07 8.79 19.97 167 E19.0_N41.0 2015 1 30 18 5.47 193 9.04 7.73 20.15 196 E19.0_N41.5 2000 12 27 18 5.79 184 9.09 7.90 22.14 179 E19.5_N40.0 2015 1 30 18 5.76 217 9.29 7.93 19.58 201

Sea state tables: J. Mar. Sci. Eng. 2021, 9, 522 18 of 25

Table A4. Sea table for North Adriatic region (locations 1–9).

Tp/Hs 0.0–0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0–4.5 4.5–5.0 5.0–5.5 5.5–6.0 6.0–6.5 Sum 0–1 0 0 0 0 0 0 0 0 0 0 0 0 0 1–2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2–3 75,917 20,382 471 7 0 0 0 0 0 0 0 0 0 96,777 3–4 32,032 47,456 9372 776 32 1 1 0 0 0 0 0 0 89,670 4–5 9729 21,114 13,783 4780 992 88 7 1 0 0 0 0 0 50,494 5–6 6070 9268 7909 5909 3208 1203 353 46 3 0 0 0 0 33,969 6–7 3669 5239 3408 2151 1763 1265 716 304 124 22 4 2 1 18,668 7–8 1329 1363 1374 945 576 389 296 234 160 68 31 12 9 6786 8–9 744 523 313 199 127 106 79 43 31 17 8 6 2 2198 9–10 658 117 72 32 18 20 11 4 3 3 0 1 1 940 10–11 81 29 6 2 2 0 0 0 0 0 0 0 0 120 11–12 72 11 6 1 0 0 0 0 0 0 0 0 0 90 12–13 37 7 1 1 0 0 0 0 0 0 0 0 0 46 13–14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sum 130,338 105,509 36,715 14,803 6718 3072 1463 632 321 110 43 21 13 299,758 ◦ ◦ Note: 79% of waves are less than 1 m; Hmax = 6.72 m on 16.11.2002, location 14.5 E–44.0 N, wind SE.

Table A5. Sea table for Central Adriatic region (locations 10–22).

Tp/Hs 0.0–0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0–4.5 4.5–5.0 5.0–5.5 5.5–6.0 6.0–6.5 Sum 0–1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1–2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2–3 79,272 19,536 133 0 0 0 0 0 0 0 0 0 0 98,941 3–4 55,629 79,120 9121 218 4 0 0 0 0 0 0 0 0 144,092 4 -5 10,939 45,343 27,579 6231 307 12 0 0 0 0 0 0 0 90,411 5–6 4666 16,530 18,555 13,290 5146 897 54 3 0 0 0 0 0 59,141 6–7 2417 6113 6372 5555 4628 2937 1014 170 21 6 1 0 0 29,234 7–8 1015 1705 2128 1767 1442 1228 1024 655 236 71 11 2 0 11,284 8–9 590 690 673 554 492 313 245 173 124 49 21 4 6 3934 9–10 305 219 187 120 105 81 52 40 27 24 10 9 0 1179 10–11 147 92 66 26 13 6 2 1 0 0 0 0 0 353 11–12 197 35 17 12 1 0 1 0 0 0 0 0 0 263 12–13 350 15 7 2 1 0 0 0 0 0 0 0 0 375 13–14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 Sum 155,527 169,398 64,838 27,775 12,139 5474 2392 1042 408 150 43 15 6 439,207 ◦ ◦ Note: 74% of waves are less than 1 m; Hmax = 6.33 m on 08.12.1992, location 17.0 E–42.5 N, wind SE. J. Mar.J. Mar. Sci. Sci. Eng. Eng. 2021 2021, 9,, 9x, FORx FOR PEER PEER REVIEW REVIEW 1919 of of24 24

TableTable A6. A6. Sea Sea table table for for South South Adriatic Adriatic region region (locations (locations 22–39). 22–39).

Tp/HsTp/Hs 0.0–0.50.0–0.5 0.5–1.00.5–1.0 1.0–1.51.0–1.5 1.5–2.01.5–2.0 2.0–2.52.0–2.5 2.5–3.02.5–3.0 3.0–3.53.0–3.5 3.5–4.03.5–4.0 4.0–4.54.0–4.5 4.5–5.04.5–5.0 5.0–5.55.0–5.5 5.5–6.05.5–6.0 6.0–6.56.0–6.5 SumSum

0–10–1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1–21–2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

J.2–3 Mar.2–3 Sci.65997 Eng.65997 2021 25116, 925116, 522 150150 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9126391263 19 of 25

3–43–4 6167061670 9921499214 1396613966 239239 3 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 175092175092

4 -54 -5 1619116191 6441964419 3946839468 86588658 433433 9 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 129178129178

5–65–6 70117011 2679926799 2800928009 1889018890 72517251 10941094 62 62 5 5 0 0 0 0 0 0 0 0 0 0 8912189121 Table A6. Sea table for South Adriatic region (locations 22–39). 6–76–7 42934293 1284112841 1113711137 95919591 79987998 46344634 15251525 257257 38 38 4 4 0 0 0 0 0 0 5231852318 Tp/Hs 0.0–0.5 0.5–1.0 1.0–1.5 1.5–2.0 2.0–2.5 2.5–3.0 3.0–3.5 3.5–4.0 4.0–4.5 4.5–5.0 5.0–5.5 5.5–6.0 6.0–6.5 Sum 7–87–8 13601360 55235523 54915491 36613661 28202820 21932193 18211821 990990 305305 76 76 12 12 4 4 1 1 2425724257 0–1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1–2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 8–98–9 529529 22462246 25292529 19741974 13111311 942942 632632 461461 315315 131131 49 49 3 3 0 0 1112211122 2–3 65,997 25,116 150 0 0 0 0 0 0 0 0 0 0 91,263 9–103–4 61,670211 99,214719 13,966856 667 239 531 3394 0273 0187 0126 065 038 016 02 04085 175,092 9–104 -5 21116,191 71964,419 85639,468 6678658 531 433394 9273 0187 0126 065 038 016 02 04085 129,178 10–115–6 7011148 26,799313 28,009348 18,890266 2027251 1141094 96 6263 540 022 06 02 01 01621 89,121 10–116–7 1484293 31312,841 34811,137 2669591 202 7998 114 4634 96 152563 25740 3822 46 02 01 01621 52,318 7–8 1360 5523 5491 3661 2820 2193 1821 990 305 76 12 4 1 24,257 11–12 94 59 84 68 90 31 25 16 10 9 5 2 1 494 11–128–9 94 529 592246 842529 681974 90 1311 31 94225 63216 46110 3159 1315 492 31 0494 11,122 9–10 211 719 856 667 531 394 273 187 126 65 38 16 2 4085 12–13 47 17 15 7 7 10 7 7 2 2 1 1 0 123 12–1310–11 47 14817 31315 3487 2667 20210 1147 967 632 402 221 61 20 1123 1621 11–12 94 59 84 68 90 31 25 16 10 9 5 2 1 494 13–14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 13–1412–13 0 470 170 150 70 70 100 70 70 20 20 10 10 00 123 13–14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 SumSumSum 157551 157,551 157551 237266 237,266237266 102053102053 102,053 4402144021 44,021 2064620646 20,646 94219421 9421 4441 4441 4441 1986 1986 1986 836 836 836 309 309 309 111 111 111 28 28 28 5 5 578674 5578674 578,674

max ◦ ◦ Note:Note: 68%Note: 68% of 68%of waves waves of waves are are less areless than less than than 1 m;1 1m; H m; maxHH max= 6.20== 6.20 6.20 m m mon on 04.12.2008, 04.12.2008, location location location 19.019.0° 19.0°E–40.5 E–40.5° E–40.5°N, N, wind N, wind wind SE. SE. SE.

Wave roses: WaveWave roses: roses: NORTH NORTH NORTH NORTH NORTH 20%20% 20% NORTH 20% 20%20% 15%15% 15% 15% 15%15% 10%10% 10% 10% 10%10% 5%5% 5% 5% 5%5% WEST EAST WEST EAST WEST EAST WEST EAST WESTWEST EAST EAST

5- 5-6 6 4- 4-5 5 3- 3-4 4 2- 2-3 3 1- 1-2 2 0- 0-1 1 SOUTH SOUTH SOUTH SOUTH SOUTH SOUTH (a()a ) (b()b ) (c()c )

FigureFigureFigure A1. A1. A1. Wave WaveWave roses roses roses for for for all all all sea sea sea states: states: states: (a () (a aSouth)) South South Adriatic, Adriatic, Adriatic, (b () (b bCentral)) Central Central Adriatic Adriatic Adriatic and and and (c )( ( ccNorth)) North North Adriatic. Adriatic. Adriatic.

NORTH NORTH NORTH NORTH 20% 20% 20% 20% NORTH NORTH 20%20% 15%15% 15%15% 15%15% 10%10% 10%10% 10%10% 5%5% 5%5% 5%5% WEST WEST EAST EAST WEST WEST EAS EAST T WEST WEST EAST EAST

5- 5- 6 6 4- 4- 5 5 3- 3- 4 4 2- 2- 3 3 1- 2 SOUTH 1- 2 SOUTH SOUTH SOUTH 0- 0- 1 1 SOUTH SOUTH

(a()a ) (b()b ) (c()c ) FigureFigure A2. A2. Wave Wave roses roses with with Hs Hs > >2.5 2.5 m: m: (a ()a South) South Adriatic, Adriatic, (b ()b Central) Central Adriatic Adriatic and and (c ()c North) North Adriatic Adriatic Figure A2. Wave roses with Hs > 2.5 m: (a) South Adriatic, (b) Central Adriatic and (c) North Adriatic

Wind speed to signiﬁcant wave height simultaneous occurrence tables:

J. Mar. Sci. Eng. 2021, 9, 522 20 of 25

Table A7. Wind speed with signiﬁcant wave height for North Adriatic region (locations 1–9).

uw/Hs 0–0.25 0.25–0.5 0.5–0.75 0.75–1 1–1.25 1.25–1.5 1.5–1.75 1.75–2 2–2.25 2.25–2.5 2.5–2.75 2.75–3 3–3.25 Sum 0–1 8078 10,626 2985 805 250 105 46 19 9 5 1 1 0 22,930 1–2 11,964 19,039 5997 1675 575 209 88 44 14 5 0 1 1 39,612 2–3 10,067 22,010 8436 2556 873 342 129 60 35 13 7 5 3 44,536 3–4 5436 20,689 10,830 3536 1267 502 181 73 43 12 9 7 0 42,585 4 -5 2118 13,747 13,453 4941 1789 688 305 109 54 17 11 5 3 37,240 5–6 719 4251 14,188 6562 2358 910 339 183 72 31 20 11 4 29,648 6–7 169 894 7866 8210 3348 1377 520 227 97 49 26 14 9 22,806 7–8 51 281 2091 6700 4318 1943 791 333 150 75 28 14 3 16,778 8–9 21 106 399 2981 4323 2574 1223 510 237 126 38 29 10 12,577 9–10 6 27 102 805 2410 2649 1613 889 358 194 75 34 14 9176 10–11 3 13 48 221 806 1723 1656 1188 552 310 125 63 21 6729 11–12 4 9 9 56 247 695 1100 1150 795 438 262 117 50 4932 12–13 0 5 5 18 52 215 472 715 653 581 325 172 85 3298 13–14 0 3 3 10 20 65 166 370 480 456 349 258 158 2338 14–15 0 2 3 5 9 36 66 115 224 306 293 207 162 1428 15–16 0 0 2 3 2 18 28 42 80 134 158 150 177 794 Sum 38,636 91,702 66,417 39,084 22,647 14,051 8723 6027 3853 2752 1727 1088 700 297,407

Table A8. Wind speed with signiﬁcant wave height for Central Adriatic region (locations 10–22).

uw/Hs 0–0.25 0.25–0.5 0.5–0.75 0.75–1 1–1.25 1.25–1.5 1.5–1.75 1.75–2 2–2.25 2.25–2.5 2.5–2.75 2.75–3 3–3.25 Sum 0–1 7543 11,777 3808 1203 482 168 76 34 12 13 3 2 1 25,122 1–2 12,153 23,747 8439 2653 969 387 170 82 30 6 6 3 1 48,646 2–3 10,042 29,030 12,412 3968 1478 561 256 115 30 20 7 7 1 57,927 3–4 4932 27,955 16,813 5537 2050 843 366 155 67 26 12 10 3 58,769 4–5 1778 18,793 22,073 7547 2766 1113 476 170 93 30 28 2 10 54,879 5–6 551 5680 23,811 10,869 3830 1592 670 268 138 65 19 10 7 47,510 6–7 131 968 13,407 14,649 5586 2281 997 428 197 97 39 22 12 38,814 7–8 30 284 3085 12,290 8009 3387 1463 603 267 127 60 28 12 29,645 8–9 8 88 534 4712 8283 5092 2262 1022 427 200 108 41 15 22,792 9–10 3 17 141 1053 4216 5523 3403 1588 683 323 140 59 25 17,174 10–11 1 4 40 216 1263 3054 3619 2328 1157 588 229 118 54 12,671 11–12 0 5 13 53 313 1013 1929 2267 1696 842 443 190 77 8841 12–13 0 4 16 18 56 322 716 1211 1426 1084 679 322 143 5997 13–14 0 3 4 12 28 90 283 411 668 869 742 473 266 3849 14–15 0 0 4 6 14 30 86 180 223 397 484 444 321 2189 15–16 0 0 2 5 4 9 23 70 97 125 224 218 253 1030 Sum 37,172 118,355 104,602 64,791 39,347 25,465 16,795 10,932 7211 4812 3223 1949 1201 435,855 J. Mar. Sci. Eng. 2021, 9, 522 21 of 25

Table A9. Wind speed with signiﬁcant wave height for South Adriatic region (locations 22–39).

uw/Hs 0–0.25 0.25–0.5 0.5–0.75 0.75–1 1–1.25 1.25–1.5 1.5–1.75 1.75–2 2–2.25 2.25–2.5 2.5–2.75 2.75–3 3–3.25 3.25–3.5 Sum 0–1 4449 10,888 4162 1144 466 189 65 28 8 8 0 0 0 0 21,407 1–2 8133 25,456 11,134 3533 1259 538 195 74 39 12 3 3 0 1 50,380 2–3 7046 33,113 17,735 5867 2120 804 318 138 66 28 9 5 1 2 67,252 3–4 3696 32,549 24,597 8940 3231 1263 520 209 99 48 26 7 4 1 75,190 4–5 1243 21,613 30,768 12,242 4683 1865 723 335 159 57 31 16 13 4 73,752 5–6 396 6830 30,672 17,800 6724 2597 1152 539 215 113 51 27 5 2 67,123 6–7 93 1459 16,148 22,850 9911 3883 1694 764 334 149 67 27 17 8 57,404 7–8 22 399 3578 18,108 14,143 6042 2665 1146 537 250 144 55 24 13 47,126 8–9 4 116 586 5903 12,820 8635 4227 1883 870 405 171 90 32 17 35,759 9–10 2 33 173 972 5478 8467 5706 3095 1449 679 287 142 57 44 26,584 10–11 2 6 41 188 1137 4102 5336 4047 2257 1064 461 245 100 69 19,055 11–12 0 2 22 59 210 1073 2675 3376 2815 1771 851 393 201 89 13,537 12–13 0 1 12 15 53 242 807 1551 2068 1941 1241 712 357 151 9151 13–14 0 0 2 9 18 52 136 410 915 1263 1192 953 551 341 5842 14–15 0 0 1 4 5 22 40 102 262 491 648 714 604 413 3306 15–16 0 0 0 1 5 5 18 29 66 139 222 356 393 363 1597 Sum 25,086 132,465 139,631 97,635 62,263 39,779 26,277 17,726 12,159 8418 5404 3745 2359 1518 574,465 J. Mar. Sci. Eng. 2021, 9, 522 22 of 25

Appendix B

Table A10. Model parameters for joint distribution of Hs and Tp per location.

Location Latitude Longitude αHs βHs γHs a0 a1 a2 a3 1 44.5◦ N 12.5◦ E 0.4946 0.9278 0.0960 1.6508 4.9038 −0.1349 0.9996 2 44.5◦ N 13.0◦ E 0.5270 0.9174 0.0840 1.5989 4.8663 −0.2394 1.0083 3 45.0◦ N 13.0◦ E 0.4669 0.9277 0.0889 1.4343 4.7483 −0.3082 1.0595 4 44.0◦ N 13.5◦ E 0.5676 0.9551 0.0905 1.5737 4.9547 −0.3390 1.0692 5 44.5◦ N 13.5◦ E 0.5918 0.9709 0.0797 1.5241 4.7550 −0.2468 1.0163 6 45.0◦ N 13.5◦ E 0.4027 0.8991 0.1022 1.4205 4.7214 −0.3020 1.0980 7 44.0◦ N 14.0◦ E 0.5559 0.9996 0.1110 1.5487 4.8686 −0.3226 1.0741 8 44.5◦ N 14.0◦ E 0.6014 1.0001 0.0797 1.5590 4.7616 −0.2930 1.0929 9 44.0◦ N 14.5◦ E 0.5527 0.9864 0.0713 1.6962 4.7527 −0.3482 1.0131 10 43.5◦ N 14.0◦ E 0.6256 1.0219 0.0653 1.6257 5.0742 −0.1880 0.9436 11 43.0◦ N 14.5◦ E 0.6058 1.0498 0.0686 1.7686 5.0812 −0.2032 0.9557 12 43.5◦ N 14.5◦ E 0.5626 0.9730 0.0757 1.7560 5.0967 −0.3474 0.9452 13 42.5◦ N 15.0◦ E 0.6516 1.0504 0.0705 1.7682 5.1241 −0.2000 0.9650 14 43.0◦ N 15.0◦ E 0.6895 1.1006 0.0624 1.8519 5.0259 −0.2664 0.8547 15 43.5◦ N 15.0◦ E 0.6208 1.0658 0.0663 1.8665 5.0121 −0.3965 1.0147 16 42.5◦ N 15.5◦ E 0.6809 1.1377 0.0687 1.7760 5.1141 −0.1846 0.8368 17 43.0◦ N 15.5◦ E 0.7078 1.1593 0.0579 1.7639 4.9854 −0.1436 0.8805 18 43.5◦ N 15.5◦ E 0.6042 1.0587 0.0639 1.9243 4.9109 −0.3730 0.9135 19 42.5◦ N 16.0◦ E 0.7021 1.1666 0.0775 1.8357 5.1016 −0.1805 0.8747 20 42.5◦ N 16.5◦ E 0.5821 1.0806 0.1259 1.9280 5.0423 −0.2165 0.9552 21 42.5◦ N 17.0◦ E 0.7308 1.1965 0.0889 1.9765 5.0861 −0.2935 1.0112 22 42.5◦ N 17.5◦ E 0.7160 1.1083 0.0899 1.8923 5.1747 −0.3226 1.1380 23 41.5◦ N 16.5◦ E 0.7160 1.1924 0.0951 1.7637 5.0261 −0.1872 0.8867 24 42.0◦ N 16.5◦ E 0.7952 1.2018 0.0916 1.9159 5.0582 −0.1821 0.8742 25 41.5◦ N 17.0◦ E 0.7053 1.0845 0.0840 1.7589 5.0221 −0.1577 0.8663 26 42.0◦ N 17.0◦ E 0.7651 1.2108 0.0839 1.8765 5.0093 −0.1148 0.9245 27 41.5◦ N 17.5◦ E 0.7587 1.1403 0.0737 1.7333 5.0756 −0.2276 0.9040 28 42.0◦ N 17.5◦ E 0.6711 1.0414 0.0805 1.8172 5.0981 −0.2826 0.9866 29 41.0◦ N 18.0◦ E 0.8070 1.1981 0.0774 7/1992 5.0700 −0.2865 0.9567 30 41.5◦ N 18.0◦ E 0.8241 1.1597 0.0805 1.8929 5.0848 −0.2553 0.9996 31 42.0◦ N 18.0◦ E 0.7105 1.0937 0.0847 1.8282 5.2537 −0.1942 1.0828 32 40.5◦ N 18.5◦ E 0.7463 1.1540 0.0706 1.9343 5.4101 −0.1318 1.1505 33 41.0◦ N 18.5◦ E 0.8391 1.1704 0.0746 1.9085 5.2676 −0.2317 1.1422 34 41.5◦ N 18.5◦ E 0.7881 1.1276 0.0909 1.9653 5.2621 −0.2896 1.1458 35 40.0◦ N 19.0◦ E 0.7842 1.1158 0.1470 2.3429 5.6666 −0.1459 1.1775 36 40.5◦ N 19.0◦ E 0.7773 1.1160 0.1459 2.0690 5.6052 −0.1609 1.2272 37 41.0◦ N 19.0◦ E 0.7857 1.1541 0.1177 1.8779 5.5497 −0.1404 1.2359 38 41.5◦ N 19.0◦ E 0.6826 1.0750 0.1445 1.8826 5.5057 −0.3257 1.2906 39 40.0◦ N 19.5◦ E 0.7110 1.1167 0.1523 1.9860 5.8377 −0.1993 1.2479

Table A11. Model parameters for joint distribution of uw and Hs per location.

Location Latitude Longitude c1 c2 c3 c4 c5 c6 1 44.5◦ N 12.5◦ E 1.8287 0.8839 1.8706 0.4008 6.5230 0.6874 2 44.5◦ N 13.0◦ E 2.6996 0.4646 2.7946 −0.5785 7.6803 0.5720 3 45.0◦ N 13.0◦ E 2.3739 0.9366 2.3135 −0.3538 7.6986 0.6120 4 44.0◦ N 13.5◦ E 2.8672 0.1021 3.5395 0.3758 6.5210 0.6351 5 44.5◦ N 13.5◦ E 1.3584 2.7997 1.1344 −0.2716 7.7026 0.6375 6 45.0◦ N 13.5◦ E 0.9027 3.3056 0.8464 −0.1105 8.3417 0.6495 7 44.0◦ N 14.0◦ E 3.1583 0.2676 3.0993 0.2633 6.9271 0.6503 8 44.5◦ N 14.0◦ E 1.0656 3.5599 0.9325 −0.4680 8.4683 0.6078 J. Mar. Sci. Eng. 2021, 9, 522 23 of 25

Table A11. Cont.

Location Latitude Longitude c1 c2 c3 c4 c5 c6 9 44.0◦ N 14.5◦ E 3.4349 0.6648 2.4882 0.0210 7.4633 0.6163 10 43.5◦ N 14.0◦ E 2.2139 0.5802 1.8626 0.7982 5.6484 0.6907 11 43.0◦ N 14.5◦ E 1.7806 1.4912 1.4212 0.1227 6.8980 0.6447 12 43.5◦ N 14.5◦ E 1.6694 2.4990 1.2746 −0.2594 7.3387 0.6164 13 42.5◦ N 15.0◦ E 2.6457 0.4845 2.6885 −0.9321 8.3174 0.5338 14 43.0◦ N 15.0◦ E 1.5558 2.6546 1.3560 −0.4822 7.9338 0.5880 15 43.5◦ N 15.0◦ E 0.0975 5.3749 0.7278 −0.8914 8.5053 0.5586 16 42.5◦ N 15.5◦ E 2.4763 1.0616 2.0036 −0.1806 7.3984 0.6108 17 43.0◦ N 15.5◦ E 1.3398 3.2645 1.2099 −0.1325 7.6290 0.6445 18 43.5◦ N 15.5◦ E 0.6012 4.7120 0.7377 −0.8361 9.6300 0.5546 19 42.5◦ N 16.0◦ E 2.3045 1.6842 1.6936 −0.0628 7.4353 0.6090 20 42.5◦ N 16.5◦ E 1.5565 2.9451 1.1911 −0.4995 7.9883 0.5610 21 42.5◦ N 17.0◦ E 0.4484 4.3941 0.6586 −0.8094 8.3739 0.5384 22 42.5◦ N 17.5◦ E 2.7019 1.4317 1.6042 −2.2645 10.0111 0.4218 23 41.5◦ N 16.5◦ E 1.9212 2.1902 1.3027 −0.4685 8.0142 0.5814 24 42.0◦ N 16.5◦ E 2.5028 1.9846 1.5132 −0.4024 7.7330 0.5345 25 41.5◦ N 17.0◦ E 1.4263 3.3137 0.9603 0.1137 7.2428 0.6201 26 42.0◦ N 17.0◦ E 1.3069 3.4433 1.0381 −0.3364 7.3625 0.5786 27 41.5◦ N 17.5◦ E 1.6107 2.7539 1.1409 −0.3586 7.5308 0.5811 28 42.0◦ N 17.5◦ E 1.1066 3.3096 1.0187 −0.9027 8.2040 0.5321 29 41.0◦ N 18.0◦ E 2.1302 2.0997 1.4768 −0.3466 7.5308 0.5733 30 41.5◦ N 18.0◦ E 2.3992 1.4794 1.8260 −0.2249 7.2957 0.5767 31 42.0◦ N 18.0◦ E 3.2241 0.2731 3.1053 −0.9730 8.2339 0.5187 32 40.5◦ N 18.5◦ E 3.7825 0.1902 3.4631 −0.5351 7.8737 0.5565 33 41.0◦ N 18.5◦ E 1.9557 2.2628 1.3792 −0.2943 7.2896 0.5987 34 41.5◦ N 18.5◦ E 1.8915 2.0273 1.3252 −0.2834 7.3117 0.6024 35 40.0◦ N 19.0◦ E 1.5075 3.0655 0.8516 −1.6956 9.6439 0.4664 36 40.5◦ N 19.0◦ E 3.4256 0.4636 2.4093 −0.4509 8.2005 0.5608 37 41.0◦ N 19.0◦ E 1.9585 1.7032 1.4485 −1.0247 8.4629 0.5470 38 41.5◦ N 19.0◦ E 2.2952 1.0621 1.7132 −1.1432 8.9021 0.5206 39 40.0◦ N 19.5◦ E 2.6826 0.8658 1.5144 0.6763 7.0036 0.6234

Table A12. Most probable extreme signiﬁcant wave heights, HsRP (m), for various return periods.

Location Lat. Long. ~23 y Recorded 5 y 10 y 20 y 50 y 100 y 1 44.5◦ N 12.5◦ E 5.59 5.31 5.75 6.19 6.78 7.23 2 44.5◦ N 13.0◦ E 6.45 5.79 6.28 6.77 7.42 7.92 3 45.0◦ N 13.0◦ E 5.60 5.01 5.43 5.85 6.40 6.82 4 44.0◦ N 13.5◦ E 6.14 5.69 6.14 6.60 7.21 7.67 5 44.5◦ N 13.5◦ E 6.34 5.70 6.15 6.61 7.21 7.66 6 45.0◦ N 13.5◦ E 5.26 4.68 5.08 5.48 6.02 6.42 7 44.0◦ N 14.0◦ E 5.09 5.06 5.45 5.83 6.34 6.73 8 44.5◦ N 14.0◦ E 6.17 5.43 5.85 6.26 6.81 7.23 9 44.0◦ N 14.5◦ E 6.19 5.14 5.54 5.94 6.47 6.87 10 43.5◦ N 14.0◦ E 6.03 5.38 5.78 6.18 6.72 7.12 11 43.0◦ N 14.5◦ E 5.52 4.93 5.29 5.65 6.12 6.47 12 43.5◦ N 14.5◦ E 6.72 5.39 5.82 6.25 6.81 7.24 13 42.5◦ N 15.0◦ E 5.71 5.29 5.68 6.06 6.57 6.95 14 43.0◦ N 15.0◦ E 5.71 5.09 5.44 5.79 6.25 6.60 15 43.5◦ N 15.0◦ E 5.59 4.89 5.24 5.59 6.06 6.40 16 42.5◦ N 15.5◦ E 5.22 4.72 5.04 5.35 5.76 6.07 J. Mar. Sci. Eng. 2021, 9, 522 24 of 25

Table A12. Cont.

Location Lat. Long. ~23 y Recorded 5 y 10 y 20 y 50 y 100 y 17 43.0◦ N 15.5◦ E 5.17 4.72 5.03 5.34 5.75 6.05 18 43.5◦ N 15.5◦ E 5.89 4.83 5.18 5.52 5.98 6.33 19 42.5◦ N 16.0◦ E 5.08 4.65 4.95 5.25 5.65 5.94 20 42.5◦ N 16.5◦ E 5.42 4.53 4.84 5.16 5.57 5.88 21 42.5◦ N 17.0◦ E 5.05 4.63 4.92 5.21 5.59 5.88 22 42.5◦ N 17.5◦ E 6.05 5.23 5.59 5.95 6.42 6.77 23 41.5◦ N 16.5◦ E 5.19 4.57 4.86 5.15 5.53 5.81 24 42.0◦ N 16.5◦ E 5.72 4.99 5.31 5.62 6.03 6.33 25 41.5◦ N 17.0◦ E 6.33 5.38 5.75 6.13 6.63 7.00 26 42.0◦ N 17.0◦ E 5.39 4.74 5.03 5.33 5.71 6.00 27 41.5◦ N 17.5◦ E 6.07 5.23 5.58 5.93 6.38 6.73 28 42.0◦ N 17.5◦ E 6.22 5.55 5.96 6.37 6.91 7.31 29 41.0◦ N 18.0◦ E 5.37 5.08 5.40 5.72 6.14 6.45 30 41.5◦ N 18.0◦ E 6.02 5.51 5.87 6.23 6.70 7.05 31 42.0◦ N 18.0◦ E 5.76 5.33 5.70 6.07 6.55 6.92 32 40.5◦ N 18.5◦ E 5.30 5.03 5.36 5.69 6.12 6.45 33 41.0◦ N 18.5◦ E 5.79 5.50 5.86 6.22 6.68 7.03 34 41.5◦ N 18.5◦ E 6.03 5.57 5.94 6.32 6.81 7.17 35 40.0◦ N 19.0◦ E 6.16 5.71 6.09 6.48 6.98 7.36 36 40.5◦ N 19.0◦ E 6.20 5.66 6.04 6.42 6.92 7.29 37 41.0◦ N 19.0◦ E 5.47 5.34 5.69 6.04 6.49 6.83 38 41.5◦ N 19.0◦ E 5.79 5.36 5.74 6.11 6.60 6.97 39 40.0◦ N 19.5◦ E 5.76 5.19 5.54 5.88 6.34 6.68

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