New generation of wind and wave climate handbooks guide to naval architect and for offshore activity

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1 Marine Technology and Engineering Guedes Soares et al. (Eds) 2011 Taylor & Francis Group, London, ISBN New generation of wind and climate handbooks guide to naval architect and for offshore activity A.V. Boukhanovsky, E.S. Chernyshyova, S.V. Ivanov & L.I. Lopatoukhin The St.-Petersburg State University of an Information Technology of Mechanics and Optics, Russia The St.-Petersburg State University, Russia ABSTRACT: Modern handbooks of wind and climate are based on hindcasting (hydrodynamic spectral models WAM, Wave Watch, SWAN, etc. used) with following stochastic simulations (statistical data treatment). Input to spectral models is reanalysis data (NCEP/NCAR, ERA, some local). In reanalysis assimilation of additional data is needed as some storm situations may be lost. The choices of procedures depend from specific of the regime in a Sea and include either the regressions or Kalman filtering approach. Modern approach allowed calculating some statistics impossible in the case of traditional investigation. Russian Maritime Register of Shipping published three handbooks based on this approach. In 2003 the handbook for Barents, Okhotsk and Caspian Seas; in 2006 the handbook for Baltic, North, Black, Azov, and Mediterranean, and in 2009 for Kara and Sea of Japan. In each new edition collection of statistics is extended. e.g., in 2003 spatial storm statistics is firstly presented. In 2006 edition statistics for climatic frequency spectra and freak s are presented. In 2009 extreme (with n-year return periods) climatic two-dimensional spectra regarded in connection with the probability of different classes (wind s, swell, s and swell with different combinations). There also drawn maps of joint return periods for and wind. 1 INTRODUCTION For a long time (up to 70th of XX century) the basic source of the information about wind s, especially for open sea, were the visual observations from the ships of opportunity. Data of these handbooks played prominent role in understanding of a climate and not lost the importance just now. One of last handbook which is based on the visual data is Global Wave Statistics (Global, 1986), published in Great Britain also in the form of computer information system. Later Russian-Netherlands atlas based on visual observations, have as the basic purpose the analysis of global variability of a climate of the World Ocean (between 84 N and 84 S) and is not intended for the description of the extreme phenomena, especially on local water areas (Gulev et al., 1998). From the middle of 70-s of XX century appeared measurements from automatic buoys and offshore installations. However, this data concerns, basically, to coastal areas and therefore does not reflect climate of open seas. Measurements are mainly used for verification of calculations by numerical models and for the decision of specific research problems of a climate in a specific point of a sea. Progress in navigation and shipbuilding, development of World Ocean resources increased requirements to the climate information. Moreover there was a necessity for detailed information for local areas, in particular for a specific gas and oil fields. All this has demanded essentially other approaches to calculation of climate. The international scientific community, including the Russian researchers, had developed the concept of obtain of the information necessary for development of resources of oceans and the seas. Successful realization of this concept became possible thanks to the following basic circumstances which radically have changed the approach to calculation of climate. Elaboration of the numerical models for calculation the main parameters. Advent of data bases as the input to numerical models (due to performance of the international reanalysis projects). Progress in high speed computing has allowed creating giant fields of years duration and with any discreetness. These specified circumstances essentially have changed approaches to calculation of a climate and have allowed creating climate handbooks of a new generation. The basic scheme of 35

2 Table 1. Basic statistics of wind and climate, published in the Handbooks of Russian Maritime Register of Shipping. Handbook. Data base Barents, Okhotsk and Caspian Seas. 30 years of reanalysis Baltic, North, Black, Azov, Mediterranean. 40 years of reanalysis 2009 Sea of Japan and Kara. 45 years of reanalysis White and Bering Seas 40 years of reanalysis. Statistics Extreme statistics for regions: speed (with different averaging) for return periods 1, 5, 10, 25, 50, 100 years. Both directional and unidirectional. Wave heights, periods, length and crest heights, for return periods 1, 5, 10, 25, 50, 100 years. Operational statistics for regions and months: Probability: Directional wind speed; Directional heights. Persistence statistics: For wind speed; For heights. Joint probability (in total year and for Sea regions) of heights and periods and regression information. Extreme statistics for regions: speed (with different averaging) for return periods 1, 5, 10, 25, 50, 100 years. Both directional and unidirectional. Wave heights, periods, length and crest heights, for return periods 1, 5, 10, 25, 50, 100 years. Operational statistics for regions and months. Probability: Directional wind speed; Directional heights. Persistence statistics: For wind speed; For heights. Joint probability (in total year and for Sea regions) of heights and periods and regression information. Probability of classes of climatic spectra in total for a year. Extreme statistics for regions (tables for regions, directional and unidirectional statistics). speed (with different averaging) for return periods 1, 5, 10, 25, 50, 100 years. Both directional and unidirectional. Wave heights, periods, length and crest heights, for return periods 1, 5, 10, 25, 50, 100 years. Conditional mean periods, lengths, crest heights, associated with the height of different probability, for return periods 1, 5, 10, 25, 50 and 100 years; Conditional wind speeds associated with the for return periods 1, 5, 10, 25, 50 and 100 years; Charts of extreme statistics: Directional speed for return periods 1, 5, 10, 25, 50 and 100 years; Directional heights for return periods 1, 5, 10, 25, 50 and 100 years; Conditional periods, associated with heights for return periods 1, 5, 10, 25, 50 and 100 years; Conditional wind speed associated heights for return periods 1, 5, 10, 25, 50 and 100 years; Return periods (years) of joint probability: Wave heights with return periods 1, 10 and 25 years and wind speed with return periods 1, 10 and 25 years. (Continued) 36

3 Table 1. (Continued). Operational statistics (tables for regions) Probability, moments, and parameters of marginal and conditional distributions by month for: speed; Wave heights. Storm and weather windows statistics: speed by moth; Wave heights by month; Number of days with the s and winds below and above of some values. Joint probability (for regions of the Sea) of heights and periods, moments and parameters of distributions. Joint probability (for regions of the Sea) of heights and wind speed, moments and parameters of distributions. Tables for climatic spectra: Probability of classes of two-dimensional spectra and transient probability Statistics (moments of distributions and their parameters) of joint probability heights and periods for wind s and swell; Statistics (moments of distributions and their parameters) of joint probability heights (or swell) and peakdness parameters or angular distribution function; Parameters of angular climatic spectra with return periods 1, 10 and 100 years; Plots of climatic spectra. Charts of operational statistics: Probability (%) of wind speed more than 5, m/s with directions. Probability (%) of heights more than 2, 4 and 6 m for return periods 1, 5, 10, 25, 50 and 100 years; with directions. calculation of a climate includes following basic stages: 1. Preparation of the input information (bottom, ice cover, wind fields etc.) for numerical models. 2. Creation of data base by mean of numerical Snsimulation (spectral models are used). 3. Statistical generalizations of simulated data (probability models are used). Each stage can be subdivided into various numbers of steps. Step 3 in this scheme lead to a set of wind and statistics (operational and extreme by modern classification). The variety of statistics depends from the purpose of investigations, but mainly limited by traditional collection of longterm distributions and their parameters (see e.g., ( and 2004)). In our investigations in addition to traditional statistics some unique statistics are elaborated, calculated, and published. Since 2000 in Russia investigations for preparation wind and climate handbooks are renewed. In 2003 the Handbook of a wind and climate for Barents, Okhotsk and Caspian seas has been published ( and 2003). In 2006 the handbook for Baltic, North, Black, Azov and Mediterranean seas ( and 2006) was published. In 2009 the handbook for Sea of Japan and Kara was published ( and 2009). Handbooks of 2003, 2006 and 2009 are the publications of new generation including the last achievements in research of wind s, numerical simulations and computer technologies. In Table 1 the set of the main statistics, published by the Russian Maritime Register of Shipping is presented. It is obvious that each subsequent edition expands a set of statistics. For example, only in 2003 edition information about climatic spectra was presented; in the 2009 publication for the first time in world practice charts of probability of a wind and s joint extremes and detailed information about two-dimensional climatic spectra are presented. Below is description of some principally new statistics for climate. 2 CLIMATIC WAVE SPECTRA One of the important statistics needed for seaworthy qualities of ships is climatic spectra. This is the regime characteristic of spectral 37

4 structure, i.e. an estimation of a spectrum with it probability. The set of spectra (as primary result of hydrodynamic simulation) is a database for statistical generalizations in terms of frequency S f), and directional two-dimensional spectra S f, θ) ). For any grid point the number of spectra depends on duration of calculated time. For example, (30 years) (365 days) (8 terms per day) = spectra. Generalization of spectra is one of problems of the multidimensional probability analysis. For a lot of applied problems it is necessary to take into consideration not only the probability of spectra for some values of heights and periods (as in Buckley, 1993)), but specific of spectral structure, i.e., it is necessary to consider formation conditions. Genetically similar spectra or functionally similar classes of situations (for wind s, swell, the mixed s etc.) belong to corresponding steady conditions (some analogy to drawing set in terminology of attractors). In the Handbook of the Register ( and 2003) data on frequency climatic spectra is presented in the form of one table for each sea. In the table probabilities for each class of spectra and probability of transition from one class of spectra to another are given. The further development of this approach has been developed in the handbook of In this publication classification of two dimensional directional spectra is made and their approximation is given. Automatic classification of directional spectra S (ω, θ) or S (f, θ) demands working out of special procedures since for each grid point the data file consists approximately from 100 thousand spectra. The task in view decision includes two basic stages: Classifications of the directional spectra taking into account formation conditions; Approximation of spectra of each class by a set of parameters. The technique of automatic classification of spectra and some results for the North Sea are published in the paper (Boukhanovsky et al., 2007) and here are not duplicated. It is important that practically for any sea it is possible to select the following 5 basic classes of spectra. One-peak spectra (classes I and II) One system of s which can be either wind s (class I,), or swell (class II). Two-peak spectra (classes III, IV) There are simultaneously two systems. For two-peak spectra two subclasses depending on age of a swell are selected. s and fresh swell (class III) With close frequencies and various directions. In practice it is a spectrum of wind s with one-peak frequency spectrum f ) and two-peak directional spectrum S f, θ). s and matured swell (class IV) Includes all other situations with a two-peak spectrum with any ratio between frequencies f 0 and f 1. There are two obvious maxima ( f0, f 0) and ( f 1,,θ 1 ), divided both on frequency, and in a direction. Multipeaked spectra (class V) Complicated fields with two or more systems of swell. If necessary it is possible to calculate also an average spectrum, a variance of spectra and its some quintiles: Thus, spatial fields of spectra S f, θ, rt, ) are reduced to a final set of classes. The considered classes of spectra with different probability are valid for any water area. In Table 2 some generalized data for climatic spectra of some seas is cited. Classes of the directional (two-dimensional) spectra for the Sea of Japan are presented at Figure 1. Figures like 1 are known as «a star of climatic spectra». Here probabilities of transition from one class to another are shown in the form of the arrows corresponding to various probabilities of transition. For example, the probability of transition (during 3 hours) from wind s (class 1) to wind s and a fresh swell (class 3) is 2%, and on the contrary (from class 3 to class 1) 4%. The probability of preservation of spectra of the same class on Figure 1 is shown by an arch. For wind s it is 81%. For each class of spectra the following sets of statistics are calculated: Probability of classes (I-V) of two-dimensional spectra for different heights. Τtransitive probabilities for classes of spectra. Table 2. Probability (%) of occurrence of spectra classes. Sea Classes of spectra I II III IV V Baltic (SE part) North (Central part) Black (South part) Azov Mediterranean (South part) Japan Kara

5 for the first time in the world practice are given the unique maps of the joint return periods of heights and wind speeds, each of which is possible 1 time in 10 or 25 years. These maps (Fig. 3) clearly show that return period of such combinations can Figure 1. Star of climatic spectra for Sea of Japan. Directional probability and statistics of distribution of wind s. Directional probability and statistics of distribution of s of swell. Joint Probability and statistics of distribution of wind heights h and the periods of peak Tp of a spectrum. Joint Probability and statistics of distribution of swell heights and periods of peak of a spectrum; Joint Probability and statistics of distribution of wind heights and peakdness γ of spectrum. Joint Probability and statistics of distribution of swell heights and peakdness γ of spectrum; Joint Probability and statistics of distribution of heights of wind s and parameter s of angular distribution. Joint Probability and statistics of distribution of heights of swell and parameter s of angular distribution. Figure 2. Joint probability of heights and wind speed. 1 distribution of ordinary s, 2 distribution of freak s (multiplied on 100), 3 common distribution of freaks and ordinary s. 3 JOINT EXTREMES In connection with offshore activity knowledge of joint extremes are of a great importance. In particularly it is declared Department 1990): «designer of an offshore installation should ensure that the installation can withstand any foreseeable combination of forces arising from the environmental factors. Joint distribution of heights and wind speed is shown on the Figure 2. There also drawn the regressions m Vh and m h 3% V 3% h, and curve of 100 year return period. Number 100 on the figure are the marginal values of V and h of this return period. It seen, that the estimates with the same return periods may have a lot of values. It is also seen, that the highest s are not during the severest winds, and v.v. This means, that the estimate of return periods for a couple of variables is of the high importance and interest. In the handbook ( and 2009) Figure 3. Return periods for joint occurrence of heights and wind speed. Return periods 10 years (left) and 25 years (right). Sea of Japan. 39

6 Table 3. Parameters of extreme angular two-dimensional spectra. Sea of Japan. 1 year 10 year 100 year Parameters I (45%) IV (55%) I (48%) IV (52%) I (50%) IV (50%) Swell swell Swell h 3%, m 11,3 9,6 6,0 14,2 12,1 7,5 17,9 15,2 9,4 Tp, s 11,6 10,9 12,7 12,6 11,8 13,9 13,7 12,9 15,3 γ 2,0 2,0 1,3 2,1 2,1 1,3 2,2 2,2 1,2 s 2,1 2,1 5,1 2,1 2,1 5,1 2,2 2,2 5,2 Direction 0 θ p Note: h 3% height of 3% probability (h 3% = 1.33h sign ), Tp period of spectral peak, γ peakdness parameter, s power of cos in angular distribution. change in the dependence on the area of sea and it is always less than the initial probability. For example, the 10 years return period of both marginal heights and wind speed always exceed 10 years can reach 50 and more years. Similar maps for 25 years return periods may exceed 300 years. 3.1 Extreme spectra as joint extremes It became obvious, that extreme spectra are only a subset of all ensembles of climatic spectra. Results of hindcasting, based numerical models (WaveWatch and SWAN in our investigations) allows to estimate extreme spectra for prescribed return period. Parameters for extreme angular climatic spectra are at the Table 3. 4 FREAK WAVES The big (extreme) s in World Ocean as a rule do not represent basic danger to navigation because of a small steepness. However among extreme s there are s which parameters do not correspond to the standard representations about wind s. About such s it is known on failures of ships and offshore constructions, from the information given by navigators, and last years and on field measurements. These are so-called unusual, abnormal, freak or rogue s or even s killers (in popular publications). In years about such s enough frequently mentioned in the literature, tried to explain the reasons of their formation and to designate areas of their most often occurrence. Among water areas where occurrence of such s the most likely is the southeast coast of Africa. There were number of damages and losses of ship,s and unusual s have received the local name cape rollers. Some time the publications about unusual s have almost stopped. Now the problem of unusual s has received new development as the set of automatic recorders has appeared. In 2000, 2004 and 2008 in Brest (France) the international conferences completely devoted to questions of studying of unusual s have been carried out, and results are published (Rogue 2000, ). As a result of accumulation of the data on unusual s it became clear, that the unusual can arise in any water area of World Ocean. The reasons of formation of unusual s can be divided on internal and external ( and Wave 2006, Lopatoukhin & Boukhanovsky 2004; Lopatoukhin et al., 2005). The external reasons are metocean, bottom topography, the opposing -current interaction, refraction around shoals or from inclined seabed, caustics from diffraction at coastlines, crossing systems, etc. The internal reasons are due to specific of propagation in media and are mainly the frequency and (or) amplitude modulation in a random sea, cooperative effect of four and five interactions, the high-order nonlinearities and nonlinear focusing. Really, hypotheses of freak generation allow their arising in any place of the Ocean, and not only in the well-known dangerous regions, such as South shore of Africa etc. Any metocean event described by a system of nonlinear thermo hydrodynamic equations, possesses their own freaks. As a rule, unusual means suddenly arising which in 2 times and more exceed significant height hs and has the unusual form. The most known example of freak was so-called «a New Year s», measured on oil platform Ekofisk (56,5 N, 3,2 E) in North Sea on January, 1, Its height has reached 25,6 m, crest 18,5 m, a trough 7,1 m. The international resonance had the fact of registration of unusual s on Black sea in area near Gelendzhik (Divinsky et al. 2004, Lopatoukhin & Boukhanovsky 2004). From almost 4 million measured s three s were unusual (on December, 16 of 2000, on November, 40

7 22 and 24, of 2001). It is expedient to note, that this buoy in February 2003 measured 12,34 m height (with period 10,3 s), i.e., is higher, than in three cases with freaks in the Black sea. However the form of this not unusual. Freak s are unusual not only by their height, but also by their form. This uncommonness specified by means of a set of parameters: height h > 2,4 h s, crest c > 0,65 h, unusual steepness δ of it front or back slope, deep trough, etc. Not all of these parameters are realized simultaneously, but as a rule at least three can be achieved. Freak can be considered as some random pulse of rare probability in sequence of usual wind s. Parameters of such pulse Ξ are random variables. Some definitions of freak s as set of parameters Ξ={,,,, c,... }, characterizing the shape of the and the steps of it selection from a record are presented in the Figure 4. The example of recent freak event is the loss of ship Aurelia (Class of Russian Register of shipping) in February 2005 in the North Pacific. Aurelia sunk during passing of atmospheric front with veering wind, changing wind s and presence of swell. Fig. 5 shows possible parameter of freak during this case. 4.1 Probabilistic scenarios for freak s generation There are two ways to formulate the conditions of freak generation. The first way considers the arising of the different external conditions, leading to possibility of freak generation, and computation the joint probability of these conditions (e.g., combinations the severe s, opposite currents etc.). But the real input of this approach is not obvious, because it is hard to take into account all the driving factors. Another way considers the Figure 5. Possible freak during loss of ship «Aurelia». 2005, February 2, N. Pacific. ensemble of all s (their heights h, periods τ, crests c etc.) and estimate occurrence of its crucial combinations, leads to freak arising. This approach seems more reliable in practice, because it is based on the consideration of freak s as the elements of the same ensemble, as all the s. But, it requires the sophisticated statistical techniques for rare events analysis, because the extreme combinations of the parameters belong to the tails of its joint probability function. The problem of freak occurrence, and associated scenarios, include the procedures of statistical analysis and synthesis of huge data samples, because freak is very rare event. Moreover, due to multiscale and spatio-temporal variability of sea s, the numerical simulation here is very resource-consuming procedure. It requires the development of special approach for stochastic simulation, that allows investigating the freak s occurrence. One of the main objectives of investigation is a probabilistic treatment of a field ζ (, t) as contaminated distribution. Such type of distributions had been introduced by Tukey (1977): Φ (, r, ) (1 ) (x) r ˆ ( x r ). (1) ς ) Ξ ( Ξ Here F ( x ) joint distribution of parameters (e.g., height, crest, steepness), F ˆ( ) asymptotic distribution of this parameters, ε(, t) probability of freak arising in specific place at a moment t. Ξ multivariate system of random values (h, c, δ, ). The first term in (1) describes background distribution of Ξ in short-term domain. It is represented as, F Ξ( X ) = Fh ( x1) F ch (xx 2 x 1) Fδ h (xx3 x 1). (2) Figure 4. General scheme of freak generation scenarios. The second term in (1) incorporates contamination (litters) of a background distribution by freak. Analysis if records (with freak 41

8 s also) shows, that two Rayleigh distributions with different parameters may be used in (1). Namely, the first term is Rayleigh distribution with ( / h ) = 1, 0, and second term with h equal to mean value of freak s. Some explanations are in the Fig. 6. Joint distributions Fh x ) F c h (x x 2 x 1 ) and Fh x ) F h (x x 3 x1 ) are presented at Fig. 7. This fig. is generalization of about 5000 records, but Figure 6. Contaminated distribution of heights. 1 distribution of ordinary s, 2 distribution of freak s (multiplied on 100), 3 common distribution of freaks and ordinary s. Figure 7. Joint distribution of parameters, c / } (a) and {, δ} } (b). 1 Lines of equal probability; 2 Regression. without freaks. The equal probability (p%) curves for values {h,c/h} {h,δ}, are drawn. It is seen, that value { h/ h,, c / h, } for any δ, or { h/ h,,, } for any c/h have the probability Probability defined from three-dimensional distribution P{ h h c h } = 0, 12. This means, that probability of three conditions simultaneously { h/ h,, c / h,,, }, will be , = This means, that only one from 1,7 million will be with height greater, than 38, h, crest greater than 0, 65 h and steepnessδ > 05,. This value is the lower limit of probability ε, i.e., probability of freak in a specific point not greater than %. Estimate of ε, based on the measurements, is about 10 8, i.e., one from 10 8 s may be freak. If the short-term interval duration is 1000 s and field consist from 100 points, then freak may arise in one of 10 3 short-term ranges. In the long-term interval wind is stochastic process modulated by synoptic, annual and year-to-year variability. This means, that system of random values Ξ with mean ξ has long-term distribution Φ ξ ( ) and the climatic ensemble is approximated by multivariate combined distribution. 4.2 Spatial shapes of freak s Presented results based on the measurements at a point. In reality any has at least three dimensions: height, length, and crest length. The last parameter in mean is 3 times greater than length. This circumstance formally is not crucial for applied investigations, as ships and drilling units are point objects and cross the field. Meanwhile any information about three dimensional s is of interest, as such measurements are unique. Direct fixing of such s had been made by stereo photography in sixties. It known only three or four projects SWOP in USA (Cote et al., 1960) and in Russia (Davidan et al., 1978). Figs. 8 & 9 shows some results of unique stereo measurements in the South Pacific not far from continent Antarctica (57 S, 159E) in April 1956 (Album 1960, Lopatoukhin & Boukhanovsky 2008). Originality of this data is as there fixed the as high as 24.9 m (up to recant time the highest measured in the World Ocean). Moreover this may be regarded as freak due to unusual combination of parameters. Ψ Ξ Ξ (, ) Φ ξ ( ξ ) (3) Apparently the probability to occur the freak anywhere in the sea is higher, than to occur 42

9 Figure 8. Initial view of with the height 24.9 m fixed at April 2 in It is worth to mention, that, any extreme has its own unique shape. 5 CONCLUDING REMARKS Figure 9. Reconstruction of spatial shape of freak in South Pacific. (Red line is zero level). it in the fixed point. This effect is valid for all the scales of variability. From the Figures 8 & 9 some interesting details of form are seen. Namely: The is vertically asymmetric height is 24.9 m with crest 18.2, i.e., (c/h) = By this parameter may be regarded as freak. The is horizontally symmetric: windward and leeward slopes are almost equal (172 and 182 m). By this parameter not a freak. Crest of has two hills with a minor trough between. Crest length is at least twice as high as length. The handbooks of a new generation are the results of realization of a concept of climate calculations for regions without measurements. A set of statistics presented in these handbooks allow contributing various requirements arising in shipbuilding and offshore activity. Among a set of statistics there are some unique, mainly, climatic two-dimensional spectra, joint extremes, freak parameters. The pointed approach approved and used in design of drilling units for gas and oil fields of Barents, Kara, Baltic, Okhotsk, Caspian Seas and some other basins. REFERENCES Album of s stereophotgraphs in Antarctica. Hydrometeorological edition (In Russian). Boukhanovsky, A.V., Lopatoukhin, L.J. & Guedes Soares C Spectral climate of the North Sea. Applied Ocean Research. N Buckley, W.H October. Design Wave Climates for the World Wide Operations of Ships. Part 1: Establishments of Design Wave Climate. Int. Maritime Organisation (IMO), Selected Publications. Cote, L., Davis J. & Marks, W., et al The directional spectrum of wind generated sea as determined from data obtained by stereo observation project SWOP. Meteorological Papers, vol. 2, N. 6, p

10 Davidan, I.N., Lopatoukhin, L.I. & Rozhkov, V.A s as stochastic hydrodynamic process. L. Gidrometeorological Edition, p (In Russian). Department of energy, Offshore installations: Guidance on design, Construction and Certification Environmental Considerations. HMSO, London. Divinsky, B.V., Levin, B.V., Lopatoukhin, L.J., Pelinovsky, E.N. & Slyunaev, A.V A freak in the Black Sea: observations and simulations. Proceedings of Earth Science, vol. 395 A, N. 3, pp Global Wave Statistics Published by British Maritime Technology. Unwin Brothers. London. Gulev, S., Grigorieva, V. & Sterl, A Global Atlas of ocean s, based on VOS observations. (CD version). Lopatoukhin, L. & Boukhanovsky, A Freak generation and their probability. International Shipbuilding Progress. 2004, v. 51, N. 2/3, pp Lopatoukhin, L. & Boukhanovsky, A Extreme and freak s. Results of measurements and simulation. Proceeding of ASME. 27th International Conference on Offshore Mechanics and Arctic Engineering OMAE June , Estotril Portugal. Paper OMAE Lopatoukhin, L., Boukhanovsky, A. & Guedes Suares, C Hindcasting and forecasting the probability of freak occurrence. In: Maritime transportation a exploitation of ocean and coastal resources. Ed. C. Guedes Soares, Garbatov & Fonesca. Vol. 2, pp Published by Taylor & Francis. London/Leiden/New York/ Philadelphia /Singapore. Rogue s. Proceedings of a Workshop organized by Ifremer and held in Brest, France November October October Tukey, J.W Exploratory data analysis. Addison Wesley: Reading Mass. p and Wave Atlas of the Mediterranean sea./ Western European Union, 2004 Ed. by NTUA, CSSI, ISMAR- CNR, THETIS Sp.A, SEMANTIC TS, METEO- FRANCE/April, 2004, p and climate handbook. Barents, Okhotsk and Caspian seas /ed. Lopatoukhin, L.I., Boukhanovsky, A.V., Degtjarev A.B., V.A. Rozhkov, V.A./Russian Maritime Register of Shipping. p (In Russian). and climate handbook. Baltic, North, Black, Azov and Mediterranean seas /ed. Lopatoukhi,n L.I., Boukhanovsky, A.V., Ivanov S.V., Chernysheva, E.S./Russian Maritime Register of Shipping. p (In Russian). and climate handbook. Japan and Kara seas /ed. Lopatoukhin, L.I., Boukhanovsky, A.V., Chernysheva, E.S./Russian Maritime Register of Shipping. p (In Russian). and climate handbook. White and Bering seas /ed. Lopatoukhin, L.I., Boukhanovsky, A.V., Chernysheva, E.S./Russian Maritime Register of Shipping. p (In Russian). 44