Tractable analytic expressions for the wind speed probability density functions using expansions of orthogonal polynomials

Journal of Applied Meteorology and Climatology

Volumn 51, Issue 7, 2012, Pages 1310-1320

  Morrissey, Mark L ^a   Greene, J Scott ^a  

^a UNIVERSITY OF OKLAHOMA   (United States)

Author keywords

Numerical weather prediction forecasting; Statistical techniques; Surface observations

Indexed keywords

ANALYTIC EXPRESSIONS; ANALYTICAL EXPRESSIONS; BASIS FUNCTIONS; BASIS WEIGHT; DATA SETS; DOWN-SCALING; NON-PARAMETRIC; NUMERICAL WEATHER PREDICTION; OKLAHOMA; ORTHOGONAL POLYNOMIAL; PARAMETRIC FUNCTIONS; PROBABILITY DENSITY FUNCTION (PDF); SATELLITE WINDS; STATISTICAL TECHNIQUES; SURFACE OBSERVATION; SURFACE WIND SPEED; WEIBULL FUNCTIONS; WIND POWER DENSITY; WIND SPEED;

ESTIMATION; EXPANSION; GRAPHIC METHODS; ORTHOGONAL FUNCTIONS; PARAMETER ESTIMATION; PROBABILITY DENSITY FUNCTION; STATISTICAL METHODS; WEIBULL DISTRIBUTION; WIND POWER;

WIND EFFECTS;

PROBABILITY DENSITY FUNCTION; STATISTICAL ANALYSIS; WEATHER FORECASTING; WEIBULL THEORY; WIND VELOCITY;

OKLAHOMA [UNITED STATES]; UNITED STATES;

EID: 84864843634     PISSN: 15588424     EISSN: 15588432     Source Type: Journal    
DOI: 10.1175/JAMC-D-11-0236.1     Document Type: Article

References (45)

1. Arfken, G. B., and H. J. Weber, 2005: Mathematical Methods for Physicists, Sixth Edition: A Comprehensive Guide. Academic Press, 1200 pp.
2. Baker, R. W., and J. P. Hennessey Jr., 1977: Estimating wind power potential. Power Eng., 81, 56-57.
3. Barthelmie, R. J., and S. C. Pryor, 2003: Can satellite sampling of offshore wind speeds realistically represent wind speed distributions? J. Appl. Meteor., 42, 83-94.
4. Blinnikov, S., and R. Moessner, 1998: Expansion for nearly Gaussian distributions. Astron. Astrophys. Suppl. Ser., 130, 193-205.
5. Brock, F. V., K. C. Crawford, R. L. Elliott, G. W. Cuperus, S. J. Stadler, H. L. Johnson, and M. D. Eilts, 1995: The Oklahoma Mesonet: A technical overview. J. Atmos. Oceanic Technol., 12, 5-19.
6. Bryukhan, F. F., and R. D. Diab, 1993: Decomposition of empirical wind speed distributions by Laguerre polynomials. Wind Eng., 17, 147-151.
7. Cakmur, R. V., and R. L. Miller, 2004: Incorporating the effect of small-scale circulations upon dust emission in an atmospheric general circulation model. J. Geophys. Res., 109, D07201, doi:10.1029/2003JD004067.
8. Capps, S. B., and C. S. Zender, 2008: Observed and CAM3 GCM sea surface wind speed distributions: Characterization, comparison, and bias reduction. J. Climate, 21, 6569-6585.
9. Diggle, P. J., and P. Hall, 1986: The selection of terms in an orthogonal series density estimator. J. Amer. Stat. Assoc., 81, 230-233.
10. Duenas-Osorio, L., and B. Basu, 2008: Unavailability of wind turbines due to wind-induced accelerations. Eng. Struct., 30, 885-893.
11. Feely, R. A., R. Wanninkhof, W. McGillis, M.-E. Carr, and C. E. Cosca, 2004: Effects of wind speed and gas exchange parameterizations on air-sea CO2 fluxes in the equatorial Pacific Ocean. J. Geophys. Res., 109, C08S03, doi:10.1029/2003JC001896.
12. Frech, M., F. Holzapfel, A. Tafferner, and T. Gerz, 2007: Highresolution weather database for the terminal area of Frankfurt airport. J. Appl. Meteor. Climatol., 46, 1913-1932.
13. Gustafson, W. I., Jr., and L. R. Leung, 2007: Regional downscaling for air quality assessment: A reasonable proposition? Bull. Amer. Meteor. Soc., 88, 1215-1227.
14. Hennessey, J. O., 1977: Some aspects of wind power statistics. J. Appl. Meteor., 16, 119-128.
15. Jaramillo, O. A., and M. A. Borja, 2004: Wind speed analysis in La Ventosa, Mexico: A bimodal probability distribution case. Renew. Energy, 29, 1613-1630.
16. Jiang, M., and S. Provost, 2011: Improved orthogonal polynomial density estimates. J. Statist. Comput. Simul., 81, 1495-1516.
17. Johnson, N., S. Kotz, and N. Balakrishnan, 1994: Continuous Univariate Distributions. Vol. 1, 2nd ed., Wiley Series in Probability andMathematical Statistics, JohnWiley and Sons, 756 pp.
18. Juban J., N. Siebert, and G. N. Kariniotakis, 2007: Probabilistic short-term wind power forecasting for the optimal management of wind generation. Proc. PowerTech 2007, Lausanne, Switzerland, IEEE, 683-688.
19. Justus, C. G., W. R. Hargraves, A. Mikhail, and D. Graber, 1978: Methods for estimating wind speed frequency distributions. J. Appl. Meteor., 17, 350-353.
20. Kronmal, R., and M. Tarter, 1968: The estimation of probability densities and cumulatives by Fourier series methods. J. Amer. Stat. Assoc., 63, 925-952.
21. Lackner, M. A., A. L. Rogers, and J. F. Manwell, 2008: Uncertainty analysis in MCP-based wind resource assessment and energy production estimation. J. Sol. Energy Eng., 130, 031006, doi:10.1115/1.2931499.
22. Li, M., and X. Li, 2005: MEP-type distribution function: A better alternative to Weibull function for wind speed distributions. Renew. Energy, 30, 1221-1240.
23. Mearns, L.O., I.Bogardi, F.Giorgi, I.Matyasovszky, andM. Palecki, 1999: Comparison of climate change scenarios generated from regional climatemodel experiments and statistical downscaling. J. Geophys. Res., 104, 6603-6621.
24. Monahan, A. H., 2006a: The probability distribution of sea surface wind speeds. Part I: Theory and sea winds observations. J. Climate, 19, 497-520.
25. Monahan, A. H., 2006b: The probability distribution of sea surface wind speeds. Part II: Dataset intercomparison and seasonal variability. J. Climate, 19, 521-534.
26. Monahan, A. H., 2007: Empirical models of the probability distribution of sea surface wind speeds. J. Climate, 20, 5798-5814.
27. Monahan, A. H., Y. He, N. McFarlane, and A. Dai, 2011: The probability distribution of land surface wind speeds. J. Climate, 24, 3892- 3909.
28. Morrissey, M. L., A. Albers, J. S. Greene, and S. Postawko, 2010a: An isofactorial change-of-scale model for the wind speed probability density function. J. Atmos. Oceanic Technol., 27, 257-273.
29. Morrissey, M. L., W. E. Cook, and J. S. Greene, 2010b: An improved method for estimating the wind power density distribution function. J. Atmos. Oceanic Technol., 27, 1153-1164.
30. Pavia, E. G., and J. J. O'Brien, 1986: Weibull statistics of wind speed over the ocean. J. Climate Appl. Meteor., 25, 1324-1332.
31. Provost, S. B., 2005: Moment-based density approximants. Math. J., 9, 727-756.
32. Pavia, E. G., and M. Jiang, 2012: Orthogonal polynomial density estimates: Alternative representation and degree selection. Int. J. Comput. Math. Sci., 6, 17-24.
33. Pryor, S. C., M. Nielsen, R. J. Barthelmie, and J. Mann, 2004: Can satellite sampling of offshore wind speeds realistically representwind speed distributions? Part II:Quantifying uncertainties associatedwith distribution fittingmethods. J.Appl.Meteor., 43, 739-750.
34. Pryor, S. C.,J. T. Schoof, R. J. Barthelmie, 2005: Empirical downscaling of wind speed probability distributions. J. Geophys. Res., 110, D19110, doi:10.1029/2005JD005899.
35. Ramirez, P., and J. A. Carta, 2005: Influence of the data sampling interval in the estimation of the parameters of the Weibull wind speed probability density distribution: A case study. Energy Convers. Manage., 46, 2419-2438.
36. Silverman, B. W., 1998: Density Estimation. Chapman and Hall, 175 pp.
37. Szego, G., 2003: Orthogonal Polynomials. 4th ed. American Mathematical Society Colloquium Publications, Vol. 23, 432 pp.
38. Tarter, M. E., and R. A. Kronmal, 1976: An introduction to the implementation and theory of nonparametric density estimation. Amer. Stat., 30, 105-112.
39. Veers, P. S., 1983: A general method for fatigue analysis of vertical axis wind turbine blades. Sandia National Laboratories Tech. Rep. SAND82-2543, 12 pp.
40. Vickers, D., and S. Esbensen, 1998: Subgrid surface fluxes in fair weather conditions during TOGA COARE: Observational estimates and parameterizations.Mon.Wea. Rev., 126, 620-633.
41. Wang, C., R. H. Weisberg, and H. Yang, 1998: Effects of the wind speed-evaporation-SST feedback on the El Niño-Southern Oscillation. J. Atmos. Sci., 56, 1391-1403.
42. White, D., 2004: New method for dual-axis fatigue testing of large wind turbine blades using resonance excitation and spectral loading. National Renewable Energy Laboratory Tech. Rep. NREL/TP-500-35268, Golden, CO, 195 pp.
43. Wright, D. G., and K. R. Thompson, 1983: Time-averaged forms of the nonlinear stress law. J. Phys. Oceanogr., 13, 341-345.
44. Yilmaz, V., and H. E. Cxelik, 2008:Astatistical approach to estimate the wind speed distribution: The case of Gelibolu region. Doǧusx Üniv. Derg., 9, 122-132.
45. Zagar, N., M. Zagar, J. Cedilnik, G. Gregoric, and J. Rakovec, 2006: Validation of mesoscale low-level winds obtained by dynamical downscaling of ERA40 over complex terrain. Tellus, 58A, 445-455.