THE EXPECTED HIGHEST WAVES & DIRECTIONAL SPECTRA AT THE OCEANOGRAPHIC TOWER ACQUA ALTA, VENICE, ITALY

Transcription

1 THE EXPECTED HIGHEST WAVES & DIRECTIONAL SPECTRA AT THE OCEANOGRAPHIC TOWER ACQUA ALTA, VENICE, ITALY Francesco Fedele School of Civil & Environmental Engineering Georgia Institute of Technology, Savannah campus,usa Anthony Yezzi School of Electrical & Computer Engineering Georgia Institute of Technology, Atlanta campus,usa Alvise Benetazzo PROTECNO S.r.l. Padua, ITALY George Z. Forristall Forristall Ocean Engineering, Inc. USA Luigi Cavaleri ISMAR-CNR, Venice, Italy Alessio Boscolo Phoenix S.r.l. Padua, Italy ABSTRACT We propose a novel Wave Acquisition Stereo System (WASS) that exploits new stereo reconstruction techniques for accurate estimates of the spatio-temporal dynamics of ocean waves at the oceanographic tower Acqua Alta, Venice, Italy. WASS has a significant advantage as a low-cost system in both installation and maintenance. A stereo camera view provides three-dimensional data (both in space and time) whose statistical content is richer than that of a time series retrieved from wave gauges, ultrasonic instruments or buoys, the latter being expensive to install and maintain. Indeed, wave spectra and wave statistics can be easily estimated from the multi-dimensional images obtained with WASS.

2 1 INTRODUCTION The prediction of large waves is typically based on the statistical analysis of time series of the wave surface displacement retrieved from wave gauges, ultrasonic instruments or buoys at a fixed point P of the ocean. However, the largest wave crest predicted in time at P underestimates the highest crest expected over the area nearby P. Indeed, large waves travel on top of wave groups, and the probability that the group passes at its apex through P is practically null. The large crest height recorded in time at P is simply due to the dynamical effects of a group that focuses nearby that location forming a larger wave crest. The expected highest wave height over an area is of relevant significance in the offshore industry for a proper design of the air gap under the deck of fixed offshore structures. Localized damages have sometimes been observed on the lower decks of platforms after storms. This may be due to a design that is based on the expected largest crest height at a fixed location nearby the offshore tower that underestimates the expected global maximum, i.e. the largest crest height, over the offshore area local to the tower. The expected highest wave height over an area can be obtained via applications of Piterbarg s results on global maxima of Gaussian fields (Piterbarg 1995), or by the Euler characteristics of excursion sets (Adler 1981, Adler & Taylor 2007). Forristall (2006) applied for the first time Piterbarg's theorem to the air gap problem, and he also showed that it can explain observed damages during hurricanes (Forristall 2007). Offshore industry can thus benefit from technologies that can predict the largest wave expected over a given area and the associated spectral properties. In this project, we address this issue by proposing a video observational technology able to provide a multi-dimensional image of the oceanic state for the monitoring of ocean processes Figure 1: The oceanographic tower Acqua Alta, Venice, Italy. or hydrographic factors around the oceanographic tower Acqua Alta, Venice Italy (see Fig. 1). Specifically, we propose a novel Wave Acquisition Stereo System (WASS) for the reconstruction of the water surface of oceanic sea states. The rich information content of the acquired three-dimensional video data measured by WASS is then exploited to compute reliable estimates of both the directional wave spectrum and the expected global maximum (largest crest height) over an area. 2 PROJECT DESCRIPTION This project is a natural extension of current activities in ocean engineering and instrumentation by Drs. Fedele & Yezzi at Georgia Tech and their collaborators Dr. Alvise Benetazzo of PROTECNO S.r.l. and Dr. Alessio Boscolo of PHOENIX S.r.l, Italy. We have successfully developed WASS (see Fig. 2) for experiments offshore the California Coast and at the Venice coast in Italy (Benetazzo 2006, Gallego et al. 2008). We also supervise a graduate student, Guillermo Gallego, who has extensive experience and excellent training in computer vision applied to stereo reconstructions of ocean waves. Video imagery has a significant advantage as a low-cost system in both installation and maintenance (Holland et al. 1997, Holland & Holman 1997). A stereo camera view provides spatial and temporal data whose statistical content is richer than that of a time series retrieved from a buoy, which is

3 expensive to install and maintain. WASS will process this multi-dimensional image data and obtain a 4- D (space and time) reconstruction of the sea surface. WASS exploits the combination of state-of-the-art of epipolar methods (Benetazzo 2006) and variational partial differential equation techniques (Jin et al. 2005) for the 4-D stereo reconstruction of the spatio-temporal dynamics of ocean waves. We have preliminary results (Gallego et al. 2008) showing that WASS yields accurate estimates of the spatiotemporal ocean dynamics (Figures 3-4), the associated wave spectra (see Figure 5) and wave surface statistics (see Figure 6). We also estimated the largest crest height base Figure 2: WASS set-up. over the reconstructed area via the Euler characteristics of excursion sets (see Figure 7). In collaboration with Dr. Forristall and Dr. Cavaleri of the ISMAR-CNR, Venice Italy, we propose to install and test WASS at the oceanographic tower Acqua Alta. The tower is located in the Northern Adriatic Sea, East of Italy, 16 km off the coastline of Venice, on 16 m of depth (see Fig. 1). It is equipped with 380, 220, 125 VAC 50 Hz, available when personnel are on board. A large set of batteries provides 12 and 24 VDC for occasional measurements and for some basic regular needs. The tower hosts a meteooceanographic station. The data are recorded on board and also sent to land by telemeters. The station includes measurements of wind, temperature, humidity, solar radiation, rain, waves (directional), tides and sea temperature. The water level has been recorded since Two tide gauges of the conventional well type are installed. Wave gauges are also operational and consist of three pressure transducers located on three of the four platform legs at 5 m depth. Continuous recording is performed for 17 min every 3 h. The system, which allows an estimate of the directional wave spectrum, has, with appropriate upgrading, been in operation since An acoustic surface tracking AWAC has been recently installed to measure waves and currents. AWAC is both a current profiler and a wave directional system in one unit. Acqua Alta is thus the perfect site for testing the capabilities of WASS, since the acquired video measurements can be tested and compared against other classical wave measurements. The expected outcomes of this project are: The direct verification of the theory for crest heights over the area of a platform deck (Longuet- Higgins 1963, Forristall 2000, Tayfun & Fedele 2007, Fedele 2008). Full wave-number-frequency spectrum and nonlinear dispersion relation. The prediction of the complete kinematics field from the kinematic boundary condition with no assumption other than that the flow is irrotational. Data assimilation of the video data into a small-scale wave model (1km x1km squares) for more accurate sea state forecasts. 3. PROJECT OBJECTIVES The main objective of this project is the installation of WASS at the oceanographic tower Acqua Alta in Venice Italy to predict the largest wave expected over a given area and the associated spectral properties. The operational capabilities of WASS will be exploited to video monitor an ocean area of 60x60 meter squares from the top of the tower. To do so, the specific tasks of this project are: Phase I (Nov 08-Feb 09): WASS installation & testing at Acqua Alta. WASS will be installed and tested at the oceanographic tower Acqua Alta in Venice Italy. On the roof of the platform (see fig. 1)

4 note a black horizontal structure that can be elongated externally to install instruments that require undisturbed sea surface. We will also install an ultrasonic instrument for point measurements in time of the wave surface. These data along with those from the AWAC acoustic profiler and the pressure gauges, will be used to test the accuracy of the images acquired by WASS. The tower is reached by motor-boat with cabin and by pilot boat, both capable to stand stormy conditions. The travel time between the institute ISMAR and the tower is 80 minutes. Phase II (Feb 09-April 09): Data acquisition during storms. Note that at the tower, the living quarters are on the third floor. They include a 5x5 m living room, a 1x2 m bath, a 2x3 m kitchen, and a 2x2 m room devoted to on board instruments. Cooking and sleeping facilities, taken care by devoted personnel, allow four persons on board for an unlimited period of time. Thus data will be collected before/during and after moderate storm events. We shall need a hard drive of 7-14 Terabyte for hours of data (1 frame = 2 M, 5-10 frames per seconds=10-20 M/s, Gigabytes/hour of data). A proper duty cycle for data acquisition consists of 30 minutes of data every 2 hours during day light with an automatic on/off for no recording during calm water. Phase III (April 09- June 10): Post Processing and data analysis. Video data will be processed for computing wave spectra and statistical properties of the reconstructed sea surface such as the crest, trough and wave height distributions that will be compared with theoretical models. Y Y X X Figure 3. Input stereo pair images to the algorithm (left and center columns). The rectangular domain (8 m x 8.7 m) of the reconstructed surface has been superimposed. The height of the waves is in the range ±0.2 cm. Figure 4. Reconstructed surface from the stereo pairs in Fig. 3.

5 Figure 5. Directional spectrum (left) and wave spectrum S(k) as function of the wave number k computed from the reconstructed wave surface η of Figure p[η=z] Gaussian III Gram-Charlier pdf Tayfun Figure 6. Probability density p(η) of the reconstructed wave surface η in Figure 3: comparisons with theoretical stochastic models for wave height probabilities (Gram-Charlier models from Longuet-Higgings 1963).

6 10 2 VIDEO DATA Gaussian EC Tayfun EC Euler Characteristic EC h/σ Figure 7. Observed Euler Characteristics (EC) and expected EC against the threshold, for the oceanic video data of Fig TIME LINE Design & test VWASS in laboratory Install & test VWASS at Acqua Alta Collect data before/during and after moderate storm events data processing & analysis : spectra and wave statistics Nov Sept Feb Jan 09 April 09 Dec June

7 5. REFERENCES Adler, R.J. 1981, The Geometry of Random Fields, New York: John Wiley. Adler, R.J. & Taylor, J.E Random fields and geometry. Springer Monographs in Mathematics Springer, New York. Benetazzo, A Measurements of short water waves using stereo matched image sequences Coastal Engineering, 53: Fedele F Rogue waves in oceanic turbulence. Physica D (in press) Forristall, G.Z., 2000, Wave Crest Distributions: Observations and Second-Order Theory, Journal of Physical Oceanography 30(8): Forristall, G.Z. 2006, Maximum wave heights over an area and the air gap problem, Proc. OMAE 2006:25th International Conference on Offshore Mechanics and Arctic Engineering, OMAE , Hamburg. Forristall, G.Z. 2007, Wave crest heights and deck damage in Hurricanes Ivan, Katrina and Rita, Offshore Technology Conference Proceedings, OTC 18620, Houston. Gallego G, Benetazzo, A., Yezzi A., Fedele, F. Wave statistics and spectra via a variational Wave Stereo Acquisition System. 27th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Portugal, June Holland, K.T. and R.A. Holman Video estimation of foreshore topography using trinocular stereo. Journal of Coastal Research 13(1): Holland, K.T., R.A. Holman, T.C. Lippmann, J. Stanley, and N. Plant Practical use of video imagery in nearshore oceanographic field studies. IEEE Journal of Oceanic Engineering 22(1): Jin H., Soatto S., Yezzi A., Multi-View Stereo Reconstruction of Dense Shape and Complex Appearance. International Journal of Computer Vision 63(3): (2005). Longuet-Higgins, M.S The effects of non-linearities on statistical distributions in the theory of sea waves. J. Fluid Mech. 17, Piterbarg V Asymptotic Methods in the Theory of Gaussian Processes. American Mathematical Society, ser. Translations of Mathematical Monographs, Vol. 148, 205pp. Tayfun, A., Fedele F Wave height distributions and nonlinear effects. Ocean Engineering 34(11-12):1631,1649. Zakharov VE Statistical theory of gravity and capillary waves on the surface of a finite-depth fluid. European Journal of Mechanics B-fluids 18(3):327-34

8 6. BUDGETS PROTECNO BUDGET WASS + hardware USD 15, Phoenix S.r.l Consultance USD 4, Forristall Consultance USD 10, Alvise Benetazzo Consultance USD 10, Travels USD 10, CNR expenses for Acqua Alta platform USD 63, TOT USD 112, Explanation CNR expenses ($ 63,384.00) for Acqua Alta platform Boat trips / hour hour/trip total trips TOT boat rental ,888 Personnel ,008 Platform / day quantity total days instrumentation space ,200 Personnel (FF, AB, ) ,480 CNR Personnel ,680 Consultant / ora ore Cavaleri 0 TOTAL TOT 42,256 ( 1 =$1.5) $63,384 tower trips 8 days on tower per trip 3 total days 24 trips to go to the tower 8 trips to go back 8 total trips 16 space on tower for instrumentation [days] 150

9 GEORGIA TECH BUDGET Rate Months Year 1 MTDC Calculation Year 1 Fedele 8, ,276 Total Salaries & Fringe 46,625 Yezzi 14, ,492 Travel 6,000 0 Materials & Supplies 0 Total Senior Personnel 21,768 Publication Costs 0 Consultant Services 0 Post Doctoral Associates Computer Services 0 Other Professionals Subawards 0 Graduate Students 1, ,415 Graduate Students Total MTDC 52,625 Undergraduate Students Secretarial - Clerical Other Fringe Benefits Rate 25.00% Total Salaries & Wages 41,183 F & A Rate 55.70% Fringe Benefits 5,442 Cost of Living Increase 3.00% Total Salaries & Fringe 46,625 Equipment > $5,000 per Item 0 Travel - Domestic 2,000 Travel - Foreign 4,000 Other Direct Costs Materials and Supplies 0 Publication Costs 0 Consultant Services 0 Computer Services 0 Subawards 0 Other (Tuition Rate) ,864 Total Other Direct Costs 6,864 Indirect Cost (F&A) 29,312 Total Direct & Indirect Costs 88,801

10 7. BUDGET JUSTIFICATION The total budget consists of $201,185. This amount is split in 2 separate budgets. The first budget of $112,384 is for PROTECNO Srl, Padua, ITALY. This amount includes: 42,256=$63,384 ( current exchange rate 1 =$1.5) for the ISMAR-CNR expenses to use the Acqua Alta tower. These includes: 5,888 for trips to the tower by LITUS boat, a property of ISMAR (16 trips, 4 hours/trip) and 3,008 for boat personnel (16 trips 4 hours/trip), 16,200 for space utilization on the tower (3 months=150 days), 6,480 for 3 people hosted at the tower for 3 days per trip ( 8 trips total ), and 10,680 for CNR personnel. We also account for consultant services for Forristall ($10,000), Benetazzo of Protecno ($10,000), & Boscolo of Phoenix Srl ($4,000). An amount of $15,000 is accounted for the purchase of 14 Terabytes of data storage and 1 high definition camera. Laptops and other supplement materials will be provided by the PI Fedele. An amount of $10,000 is accounted for travels. The second budget of $88,801 is for GEORGIA TECH. This includes: 11 month student stipend and tuition for Guillermo Gallego; 2 month salary support for Fedele, 0.30 month salary support for Yezzi; an amount of $6,000 is accounted for student travels ($4,000 International and $2000 Local). The Fringe benefits rate is 25%. On the above expenses except for student tuition, Georgia Tech charges an overhead at the Facilities & Administrative (F&A) rate of 55.70%.