Probabilistic Model for Wind Speed Variability Encountered by a Vessel


As a result of social awareness of air emission due to the use of fossil fuels, the utilization of the natural wind power resources becomes an important option to avoid the dependence on fossil resources in industrial activities. For example, the maritime industry, which is responsible for more than 90% of the world trade transport, has already started to look for solutions to use wind power as auxiliary propulsion for ships. The practical installation of the wind facilities often requires large amount of investment, while uncertainties for the corresponding energy gains are large. Therefore a reliable model to describe the variability of wind speeds is needed to estimate the expected available wind power, coefficient of the variation of the power and other statistics of interest, e.g. expected length of the wind conditions favorable for the wind-energy harvesting. In this paper, wind speeds are modeled by means of a spatio-temporal transformed Gaussian field. Its dependence structure is localized by introduction of time and space dependent parameters in the field. The model has the advantage of having a relatively small number of parameters. These parameters have natural physical interpretation and are statistically fitted to represent variability of observed wind speeds in ERA Interim reanalysis data set.

Share and Cite:

Rychlik, I. and Mao, W. (2014) Probabilistic Model for Wind Speed Variability Encountered by a Vessel. Natural Resources, 5, 837-855. doi: 10.4236/nr.2014.513072.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Dee, D.P., Uppala, S.M., Simmons, A.J., Berrisford, P., Poli, P., Kobayashi, S., Andrae, U., Balmaseda, M.A., Balsamo, G., Bauer, P., Bechtold, P., Beljaars, A.C.M., van de Berg, L., Bidlot, J., Bormann, N., Delsol, C., Dragani, R., Fuentes, M., Geer, A.J., Haimberger, L., Healy, S.B., Hersbach, H., Hólm, E.V., Isaksen, L., Kallberg, P., Kohler, M., Matricardi, M., McNally, A.P., Monge-Sanz, B.M., Morcrette, J.J., Park, B.K., Peubey, C., de Rosnay, P., Tavolato, C., Thépaut, J.N. and Vitart, F. (2011) The ERA-INTERIM Reanalysis: Configuration and Performance of the Data Assimilation System. Quarterly Journal of the Royal Meteorological Society, 137, 553-597.
[2] Baxevani, A., Caires, S. and Rychlik, I. (2008) Spatio-Temporal Statistical Modelling of Significant Wave Height. Environmetrics, 20, 14-31.
[3] Monbet, V., Ailliot, P. and Prevosto, M. (2007) Survey of Stochastic Models for Wind and Sea State Time Series. Probabilistic Engineering Mechanics, 22, 113-126.
[4] Caralis, G., Rados, K. and Zervos, A. (2010) The Effect of Spatial Dispersion of Wind Power Plants on the Curtailment of Wind Power in the Greek Power Supply System. Wind Energy, 13, 339-355.
[5] Kiss, P. and Jánosi, I.M. (2008) Limitations of Wind Power Availability over EUROPE: A Conceptual Study. Nonlinear Processes in Geophysics, 15, 803-813.
[6] Brown, B.G., Katz, R.W. amd Murphy, A.H. (1984) Time Series Models to Simulate and Forecast Wind Speed and Wind Power. Journal of Climate and Applied Meteorology, 23, 1184-1195.<1184:TSMTSA>2.0.CO;2
[7] Longuet-Higgins, M.S. (1957) The Statistical Analysis of a Random, Moving Surface. Philosophical Transactions of the Royal Society A, 249, 321-387.
[8] Baxevani, A., Podgórski, K. and Rychlik, I. (2003) Velocities for Moving Random Surfaces. Probabilistic Engineering Mechanics, 18, 251-271.
[9] Baxevani, A. and Rychlik, I. (2006) Maxima for Gaussian Seas. Ocean Engineering, 33, 895-911.
[10] Podgórski, K., Rychlik, I. and Machado, U.E.B. (2000) Exact Distributions for Apparent Waves in Irregular Seas. Ocean Engineering, 27, 979-1016.
[11] Rychlik, I. and Leadbetter, M.R. (2000) Analysis of Ocean Waves by Crossing and Oscillation Intensities. International Journal of Offshore and Polar Engineering, 10, 282-289.
[12] Rice, S.O. (1944) The Mathematical Analysis of Random Noise Part I and II. Bell System Technical Journal, 23, 282332.
[13] Rychlik, I. (2000) On Some Reliability Applications of Rice Formula for Intensity of Level Crossings. Extremes, 3, 331-348.
[14] Mao, W., Ringsberg, J.W., Rychlik, I. and Storhaug, G. (2010) Development of a Fatigue Model Useful in Ship Routing Design. Journal of Ship Research, 54, 281-293.
[15] Rychlik, I. and Mustedanagic, A. (2013) A Spatial-Temporal Model for Wind Speeds Variability. Department of Mathematical Sciences, Division of Mathematical Statistics, Chalmers University of Technology and University of Gothenbourg, Gothenburg, 1-18.

Copyright © 2021 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.