Boundary-Layer Meteorology

, Volume 163, Issue 2, pp 179–201 | Cite as

A Statistical Model for the Prediction of Wind-Speed Probabilities in the Atmospheric Surface Layer

  • G. C. Efthimiou
  • D. Hertwig
  • S. Andronopoulos
  • J. G. Bartzis
  • O. Coceal
Research Article


Wind fields in the atmospheric surface layer (ASL) are highly three-dimensional and characterized by strong spatial and temporal variability. For various applications such as wind-comfort assessments and structural design, an understanding of potentially hazardous wind extremes is important. Statistical models are designed to facilitate conclusions about the occurrence probability of wind speeds based on the knowledge of low-order flow statistics. Being particularly interested in the upper tail regions we show that the statistical behaviour of near-surface wind speeds is adequately represented by the Beta distribution. By using the properties of the Beta probability density function in combination with a model for estimating extreme values based on readily available turbulence statistics, it is demonstrated that this novel modelling approach reliably predicts the upper margins of encountered wind speeds. The model’s basic parameter is derived from three substantially different calibrating datasets of flow in the ASL originating from boundary-layer wind-tunnel measurements and direct numerical simulation. Evaluating the model based on independent field observations of near-surface wind speeds shows a high level of agreement between the statistically modelled horizontal wind speeds and measurements. The results show that, based on knowledge of only a few simple flow statistics (mean wind speed, wind-speed fluctuations and integral time scales), the occurrence probability of velocity magnitudes at arbitrary flow locations in the ASL can be estimated with a high degree of confidence.


Atmospheric surface layer Beta distribution Direct numerical simulation Extreme wind speeds Probability density function Weibull distribution Wind tunnel 



The authors thank Bernd Leitl of the Environmental Wind Tunnel Laboratory at the University of Hamburg for providing access to the reference database (CEDVAL-LES; The authors also thank the Greek Public Power Corporation for providing access to the field measurements. We thank the Walker Institute for a generous Research Development Fund award which enabled collaborative visits by George Efthimiou to the University of Reading. Denise Hertwig is funded as part of the DIPLOS project by the UK Engineering and Physical Sciences Research Council (EPSRC contract number EP/K040707/1). Omduth Coceal gratefully acknowledges ongoing funding from the UK Natural Environment Research Council (NERC) through their National Centre for Atmospheric Science (NCAS) under Grant no. R8/H12/83/002.


  1. Aidan J (2011) Wind speed distribution and performance of some selected wind turbines in Jos, Nigeria. Latin Am J Phys Educ 5:457–460Google Scholar
  2. Bartzis JG, Efthimiou GC, Andronopoulos S (2015) Modelling short term individual exposure from airborne hazardous releases in urban environments. J Hazard Mater 300:182–188CrossRefGoogle Scholar
  3. Bartzis JG, Sfetsos A, Andronopoulos S (2008) On the individual exposure from airborne hazardous releases: the effect of atmospheric turbulence. J Hazard Mater 150:76–82CrossRefGoogle Scholar
  4. Beljaars ACM (1987) The influence of sampling and filtering on measured wind gusts. J Atmos Ocean Technol 4:613–626CrossRefGoogle Scholar
  5. Brabson BB, Palutikof JP (2000) Tests of the generalized Pareto distribution for predicting extreme wind speeds. J Appl Meteorol 39:1627–1640CrossRefGoogle Scholar
  6. Branford S, Coceal O, Thomas TG, Belcher SE (2011) Dispersion of a point-source release of a passive scalar through an urban-like array for different wind directions. Boundary-Layer Meteorol 139:367–394CrossRefGoogle Scholar
  7. Brasseur O (2001) Development and application of a physical approach to estimating wind gusts. Mon Weather Rev 129:5–25CrossRefGoogle Scholar
  8. Carneiro TC, Melo SP, Carvalho PCM, de Braga S (2016) Particle Swarm Optimization method for estimation of Weibull parameters: a case study for the Brazilian northeast region. Renew Energy 86:751–759CrossRefGoogle Scholar
  9. Carta JA, Ramirez P, Velazquez S (2009) A review of wind speed probability distributions used in wind energy analysis case studies in the Canary Islands. Renew Sustain Energy Rev 13:933–955CrossRefGoogle Scholar
  10. Coceal O, Thomas TG, Castro IP, Belcher SE (2006) Mean flow and turbulence statistics over groups of urban-like cubical obstacles. Boundary-Layer Meteorol 121:491–519CrossRefGoogle Scholar
  11. Coceal O, Dobre A, Thomas TG, Belcher SE (2007) Structure of turbulent flow over regular arrays of cubical roughness. J Fluid Mech 589:375–409CrossRefGoogle Scholar
  12. Coceal O, Goulart EV, Branford S, Thomas TG, Belcher SE (2014) Flow structure and near-field dispersion in arrays of building-like obstacles. J Wind Eng Ind Aerodyn 125:52–68CrossRefGoogle Scholar
  13. D’Amico G, Petroni F, Prattico F (2014) Wind speed and energy forecasting at different time scales: a nonparametric approach. Physica A 406:59–66CrossRefGoogle Scholar
  14. Datta D, Datta D (2013) Comparison of Weibull distribution and exponentiated Weibull distribution based estimation of mean and variance of wind data. Int J Energy Inf Commun 4(4):1–11Google Scholar
  15. Efthimiou GC, Bartzis JG (2011) Atmospheric dispersion and individual exposure of hazardous materials. J Hazard Mater 188:375–383CrossRefGoogle Scholar
  16. Efthimiou GC, Bartzis JG (2014) Atmospheric dispersion and individual exposure of hazardous materials. Validation and intercomparison studies. Int J Environ Pollut 55:76–85CrossRefGoogle Scholar
  17. Efthimiou G, Bartzis JG, Andronopoulos S, Sfetsos A (2011a) Air dispersion modelling for individual exposure studies. Int J Environ Pollut 47:302–316CrossRefGoogle Scholar
  18. Efthimiou GC, Bartzis JG, Koutsourakis N (2011b) Modelling concentration fluctuations and individual exposure in complex urban environments. J Wind Eng Ind Aerodyn 99:349–356CrossRefGoogle Scholar
  19. Efthimiou GC, Berbekar E, Harms F, Bartzis JG, Leitl B (2015) Prediction of high concentrations and concentration distribution of a continuous point source release in a semi-idealized urban canopy using CFD-RANS modeling. Atmos Environ 100:48–56CrossRefGoogle Scholar
  20. Fischer R, Bastigkeit I, Leitl B, Schatzmann M (2010) Generation of spatio-temporally high resolved datasets for the validation of LES-models simulating flow and dispersion phenomena within the lower atmospheric boundary layer. In: CWE2010, Chapel-Hill, NC, 23–27 May 2010Google Scholar
  21. Francisco-Fernández M, Quintela-del-Río A (2013) Nonparametric analysis of high wind speed data. Clim Dyn 40:429. doi: 10.1007/s00382-011-1263-2 CrossRefGoogle Scholar
  22. Gupta AK, Nadarajah S (2004) Handbook of beta distribution and its applications. Marcel Dekker, New YorkGoogle Scholar
  23. He Y, Monahan AH, Jones CG, Dai A, Biner S, Caya D, Winger K (2010) Probability distributions of land surface wind speeds over North America. J Geophys Res. doi: 10.1029/2008JD010708
  24. Hertwig D, Efthimiou GC, Bartzis JG, Leitl B (2012) CFD-RANS model validation of turbulent flow in a semi idealized urban canopy. J Wind Eng Ind Aerodyn 111:61–72CrossRefGoogle Scholar
  25. Holmes JD, Moriarty WW (1999) Application of the generalized Pareto distribution to extreme value analysis in wind engineering. J Wind Eng Ind Aerodyn 83:1–10CrossRefGoogle Scholar
  26. Indhumathy D, Seshaiah CV, Sukkiramathi K (2014) Estimation of Weibull parameters for wind speed calculation at Kanyakumari in India. Int J Innovat Res Sci Eng Technol 3:8340–8345CrossRefGoogle Scholar
  27. Janssen WD, Blocken B, van Hooff T (2014) Computational evaluation of pedestrian wind comfort and wind safety around a high-rise building in an urban area. In: 7th international congress on environmental modelling and software, San Diego, CA, 15–19 June 2014Google Scholar
  28. Karthikeya BR, Negi PS, Srikanth N (2016) Wind resource assessment for urban renewable energy application in Singapore. Renew Energy 87:403–414CrossRefGoogle Scholar
  29. Kidmo DK, Danwe R, Doka SY, Djongyang N (2015) Statistical analysis of wind speed distribution based on six Weibull methods for wind power evaluation in Garoua, Cameroon. Rev Energ Renouv 18:105–125Google Scholar
  30. Kollu R, Rayapudi SR, Narasimham SVL, Pakkurthi KM (2012) Mixture probability distribution functions to model wind speed distributions. Int J Energy Environ Eng 3:27CrossRefGoogle Scholar
  31. Koutsourakis N, Hertwig D, Efthimiou GC, Venetsanos AG, Bartzis JG, Leitl B (2012) Evaluation of the ADREA-HF LES code for urban air quality assessment, using the CEDVAL LES wind tunnel database. In: 8th international conference on air quality—science and application, Athens, 19–23 March 2012Google Scholar
  32. Kristensen L, Casanova M, Courtney MS, Troen I (1991) In search of a gust definition. Boundary-Layer Meteorol 55:91–107CrossRefGoogle Scholar
  33. Masseran N, Razali AM, Ibrahim K (2013) The probability distribution model of wind speed over east Malaysia. Res J Appl Sci Eng Technol 6:1774–1779Google Scholar
  34. Men Z, Yee E, Lien FS, Chen DWY (2016) Short-term wind speed and power forecasting using an ensemble of mixture density neural networks. Renew Energy 87:203–211CrossRefGoogle Scholar
  35. Morgan EC, Lackner M, Vogel RM, Baise LG (2011) Probability distributions for offshore wind speeds. Energy Convers Manag 52:15–26CrossRefGoogle Scholar
  36. Nemeş CM (2013) Statistical analysis of wind speed profile: a case study from Iasi region, Romania. Int J Energy Eng 3:261–268CrossRefGoogle Scholar
  37. Odo FC, Offiah SU, Ugwuoke PE (2012) Weibull distribution-based model for prediction of wind potential in Enugu, Nigeria. Adv Appl Sci Res 3:1202–1208Google Scholar
  38. Palutikof JP, Brabson BB, Lister DH, Adcock ST (1999) A review of methods to calculate extreme wind speeds. Meteorol Appl 6:119–132CrossRefGoogle Scholar
  39. Petkovic’ D (2015) Adaptive neuro-fuzzy approach for estimation of wind speed distribution. Elect Power Energy Syst 73:389–392CrossRefGoogle Scholar
  40. Rozas-Larraondo P, Inza I, Lozano JA (2014) A method for wind speed forecasting in airports based on nonparametric regression. Weather Forecast 29(6):1332–1342CrossRefGoogle Scholar
  41. Sallis PJ, Claster W, Hernandez S (2011) A machine-learning algorithm for wind gust prediction. Comput Geosci 37:1337–1344CrossRefGoogle Scholar
  42. Sarkar A, Singh S, Mitra D (2011) Wind climate modeling using Weibull and extreme value distribution. Int J Eng Sci Technol 3:100–106CrossRefGoogle Scholar
  43. Simiu E, Heckert NA, Filliben JJ, Johnson SK (2001) Extreme wind load estimates based on the Gumbel distribution of dynamic pressures: an assessment. Struct Saf 23:221–229CrossRefGoogle Scholar
  44. Steinkohl C, Davis RA, Kluppelberg C (2010) Extreme value analysis of multivariate high frequency wind speed data. Working Paper. University of Munich and Columbia UniversityGoogle Scholar
  45. van Donk SJ, Wagner LE, Skidmore EL, Tatarko J (2005) Comparison of the Weibull model with measured wind speed distributions for stochastic wind generation. Trans ASAE 48:503–510CrossRefGoogle Scholar
  46. Waewsak J, Chancham C, Landry M, Gagnon Y (2011) An analysis of wind speed distribution at Thasala, Nakhon Si Thammarat, Thailand. J Sustain Energy Environ 2:51–55Google Scholar
  47. Yao YF, Thomas TG, Sandham ND, Williams JJR (2001) Direct numerical simulation of turbulent flow over a rectangular trailing edge. Theor Comput Fluid Dyn 14:337–358CrossRefGoogle Scholar
  48. Zhang J, Wang P, Zheng X (2013) A prediction model for simulating near-surface wind gusts. Eur Phys J E 36:51CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Environmental Research Laboratory, INRASTESNCSR DemokritosAgia ParaskeviGreece
  2. 2.Department of MeteorologyUniversity of ReadingReadingUK
  3. 3.Department of Mechanical EngineeringUniversity of Western MacedoniaKozaniGreece
  4. 4.Department of Meteorology, National Centre for Atmospheric ScienceUniversity of ReadingReadingUK

Personalised recommendations