Mehmet ÖZGER, Zekai ŞEN

Üçlü diyagram yöntemi ile dalga karakteristiklerinin tahmini

Dalga enerjisinin tahmini için belirgin dalga yüksekliği ve ortalama dalga periyotlarının bilinmesi gereklidir. Bu iki değişken aslında feç uzunluğu, rüzgâr esme süresi ve rüzgâr hızına bağlı olarak değerler almaktadır. Belirli bir feç mesafesi boyunca ve belirli bir süre zarfında sabit bir hızda esen rüzgarın ortaya çıkardığı dalga yüksekliği ve periyodunu tahmin etmek için bir çok yaklaşım geliştirilmiştir. Burada ilk defa üçlü diyagram modeli yardımıyla rüzgâr hızı, feç mesafesi ve esme süresi gibi büyüklüklerden dalga yüksekliği ve periyodu tahmin edilmeye çalışılacaktır. Üçlü diyagram yönteminin esası jeoistatistiksel ilkelere dayanmaktadır. Jeoistatistikte yatay ve düşey eksenler konumu belirtirken bunları dik kesen üçüncü eksen ise bölgesel değişkeni göstermektedir. Benzer olarak bu çalışmada yatay ve düşey eksenler modele ait girdi değişkenlerini temsil ederken, bunlara dik olan eksende ise elde edilmek istenen çıktı değişkeni yer almaktadır. Daha sonra bu tahminler kullanılarak dalga enerji miktarları elde edilecektir. Bu yöntem girdi ve çıktı değişkenleri arasında doğrusal olmayan ilişkiler kurabilirken tahmin sonuçlarını oldukça geliştirebilmektedir. Elde edilen sonuçlar literatürde mevcut bulunan JONSWAP formülleri ile karşılaştırılmıştır. Yöntemin uygulanması için Ontario gölünde ölçülmüş saatlik rüzgâr ve dalga verileri düzenlenerek kullanılmıştır. Veriler eğitim ve test verisi olarak iki kısma ayrılmıştır. Önerilen yöntemin dalga karakteristiklerini tahmin etmekte klasik formüle göre çok daha iyi olduğu çeşitli grafik ve nümerik gösterim şekilleri ile ortaya konulmuştur.

Ocean wave characteristics prediction by using triple diagram method

A geostatistical approach was used to express correlation structure between dependent and independent variables of waves and to model prediction uncertainties. This correlation structure is represented by the variography of predicted values in which the distance variable in the variogram is determined by measuring the distance between predictors. This variogram produced from the predictors makes it possible to predict variables as unmeasured points while considering the historic information as measurement points of the field. In fact the method is based on Kriging principles. In order to make optimum interpolation these principles are required. The most important feature is to be applicable for unstationary data. It can relate input variables to output variables in a nonlinear manner. In this study, the method was employed to predict significant wave height and wave period for fetch limited and duration limited cases. Scatter diagram of variables was plotted prior to application of triple diagram method. These diagrams were called as templates where it can be seen that variables are independent from each other. The variation of third variable considered as output variable was investigated in this scatter area. The variogram based on variation of predictors is characterized the features of scatter area. The semi-variograms (SV) were obtained for each case and output variable. The best theoretical SV which fit to experimental SV were searched. The Gaussian type SV was found to be more appropriate for fetch limited case. The variogram value which does not change with distance anymore is called as sill value. This means that variance is fixed after range value that corresponds to sill. It can be seen that nugget effect is zero which means there are no variations for little distances. If there is rapid variation in the SV values while the distances increase very slowly, then it can be concluded that the variation is very high for closer points. The Gaussian type SV was fitted for the duration limited case. It was shown that sill and range values also exist for the duration limited case. This indicates that concerned event is stationary and has constant variance which also means that it has significant covariance. There is a consistency and continuity in data since nugget value is close to zero. The slow variation in the SV values while distances increase shows that points show similar properties with each other. After obtaining the theoretical SV, now one can make optimum interpolation by using Kriging principles. In order to make predictions significant wave height and wave period contour maps were prepared. For fetch limited case while the horizontal axis and vertical axis represent the fetch length and wind speed, the third dimension that perpendicular to those two axis exhibits the wave parameters such as wave height and period. Likewise for duration limited case, blowing duration and wind speed put into horizontal and vertical axes, respectively, as a third axis wave parameters are taken. Triple diagram method outperforms the classical JONSWAP method for both fetch limited and duration limited cases. It is possible to arrive some useful interpretations by using contour maps. The application of this methodology was achieved by using measurements from Ontario Lake. The data obtained from lake was divided into two parts, namely training and testing. Training data were used to set up the model and testing data were employed for validation. Moreover in order to develop the prediction results, adaptive triple diagram method was proposed. This developed method makes it possible to predict errors which come from the triple diagram method and to add the predicted errors to the previous step results. This procedure can be repeated many times until reaching to correct results. However, here satisfactory results were obtained after one step. It is apparent that results were improved much more comparing the triple diagram method.After predicting the wave parameters correctly, these parameters were used to obtain wave power values. Wave power contour maps were constructed using wind properties. It is possible to predict wave power from fetch length, blowing duration and wind speed by employing these maps. It is also concluded that wind speed has a significant effect on the wave power comparing to fetch length and blowing duration. For the small values of fetch length and blowing duration, these parameters loose their effects on wave power.

PDF

___

Agrawal, J.D., Deo, M.C., (2002). On-line wave prediction. Marine Structures, 15, 57–74.
Araghinejad, S., Burn, D.H., ve Karamouz, M., (2006). Long-lead probabilistic of streamflow using ocean atmospheric and hydrological predictors, Water Resources Research, 42, W03431, doi:10.1029/2004WR003853.
ASCE Task Committee on Geostatistical Techniques in Geohydrology of the Ground Water Hydrology Committee of the ASCE Hydraulics Division, (1990a). Review of geostatistics in geohydrology: I. Basic concepts. Journal of Hydraulic Engineering, 116, 5, 612–632.
ASCE Task Committee on Geostatistical Techniques in Geohydrology of the Ground Water Hydrology Committee of the ASCE Hydraulics Division, (1990b). Review of geostatistics in geohydrology: II. Applications. Journal of Hydraulic Engineering, 116, 5, 633–658.
Bishop, C.T., (1983). Comparison of manual wave prediction models, Journal Waterway Port Coast and Ocean Engineering, 109, 1, 1-17.
Bretschneider, C.L., (1970). Wave forecasting relations for wave generation, Look Lab., Hawaii, 1, 31-34.
Bretschneider, C.L., (1973). Prediction of waves and currents, Look Lab., Hawaii, 3, 1-17.
Carter, D.J.C., (1982). Prediction of wave height and period for a constant wind velocity using the JONSWAP results, Ocean Engineering, 9, 1, 17-33.
Clark, I., (1979). Practical Geostatistics, Applied Science Publishers, London, U.K.
Cressie, N., (1985). Fitting variogram models by weighted least squares, Mathematical Geology, 17, 653-702.
Cressie, N., (1993). Statistics for Spatial Data, John Wiley and Sons, New York. Darbyshire, J., (1963). Forecasting wind generated sea waves, Engineering, 195, 482-484.
Deo, M.C., ve Kiran Kumar, N., (2000). Interpolation of wave heights, Ocean Engineering, 27, 9, 907–919.
Deo, M.C., Jagdale, S.S., (2003). Prediction of breaking waves with neural networks. Ocean Engineering, 30, 9, 1163–1178.
Deo, M.C., Jha, A., Chaphekar, A.S., Ravikant, K., (2001). Neural networks for wave forecasting. Ocean Engineering, 28, 7, 889–898.
Donelan, M.A. (1980). Smiliarity theory applied to the forecasting of wave heights, periods and directions, Proceedings of Canadian Coastal Conference, National Reasearch Council of Canada, 47-61.
Donelan, M.A., Hamilton, J., Hui, W.H., (1985). Directional spectra of wind-generated waves, Philosophy Transactions Royal Society. London, A315, 509–562.
Hasselmann, K., T. P. Barnett, E. Bouws, H. Carlson, D. E. Cartwright, K. Enke, J. A. Ewing, H. Gienapp, D. E. Hasselmann, P. Kruseman, A. Meerburg, P. Muller, D. J. Olbers, K. Richter, W. Sell and H. Walden, (1973). Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP), Deut. Hydrogr. Z., A8(12).
Isaaks, E.H. and Srivastava, R.M., (1989). An Introduction to Applied Geostatistics, Oxford Univ. Press, Oxford.
Journel, A., and Huijbregts, A., (1978). Mining Geostatistics, Academic Press, London, UK.
Kazeminezhad, M.H., Etemad-Shahidi, A., ve Mousavi, S.J., (2005). Application of fuzzy inference system in the prediction of wave parameters, Ocean Engineering, 32, 14-15, 1709-1725.
Kriege, D., (1951). A statistical problem to some basic mining valuation problems on the Witwatersand, Journal of the Chemical, Metallurgical and Mining Society of the South Africa, 7, 119-139.
Makarynskyy, O., (2004). Improving wave predictions with artificial neural networks, Ocean Engineering, 31, 5-6, 709–724.
Makarynskyy, O., Pires-Silva, A.A., Makarynska, D., and Ventura-Soares, C., (2005). Artificial neural networks in wave predictions at the west coast of Portugal, Computers Geosciences, 31, 415-424.
Mandal, S., Rao, S., ve Raju, D.H., (2005). Ocean wave parameters estimation using backpropagation neural networks, Marine Structures, 18, 3, 301-318.
Matheron, G., (1963). Principles of geostatistics, Economical Geology., 58, 1246–1266.
Myers, D.E., Begovich, C.L., Butz, T.R. ve Kane, V.E., (1982). Variogram models for regional groundwater chemical data, Mathematical Geology., 14, 629–644.
Nash, J.E. ve Sutcliffe, J.E., (1970). River flow forecasting through conceptual models, Part 1-A discussion of princibles, Journal of Hydrology, 10, 3, 282-290.
Pierson, W. J. ve Moskowitz, L., (1964). A proposed spectral form for fully-developed wind sea based on the similarity law of S. A. Kitaigorodoskii, Journal of Geophysical Research, 69, 5181-5202.
Sırdaş, S. ve Şen, Z., (2003). Spatio-temporal drought analysis in the Trakya region, Turkey, Hydrological Science Journal, 48, 5, 809-820.
Subyani, A. M., (1997). Geostatistical analysis of precipitation in southwest Saudi Arabia, PhD Thesis, Colorado State University.
Subyani, A. M. ve Şen, Z., (1989). Geostatistical modeling of the Wasia aquifer in central Saudi Arabia, Journal of Hydrology, 110, 295-314.
Şen, Z., Altunkaynak, A. ve Özger, M., (2004). El Nino-Southern Oscillation (ENSO) templates and streamflow prediction, Journal of Hydrologic Engineering, 9, 5, 368-374.
Tsai, C.P., Lin, C., Shen, J.-N., (2002). Neural networks for wave forecasting among multi-stations, Ocean Engineering, 29, 13, 1683–1695.