Wind Field Diagnostic Model

  • Eduardo RodríguezEmail author
  • Gustavo Montero
  • Albert Oliver
Part of the Green Energy and Technology book series (GREEN)


This chapter describes Wind3D, a mass-consistent diagnostic model with an updated vertical wind profile and atmospheric parameterization. First, a description of Wind3D is provided, along with their governing equations. Next, the finite element formulation of the model and the description of the solver of the corresponding linear system are presented. The model requires an initial wind field, interpolated from data obtained in a few points of the domain. It is constructed using a logarithmic wind profile that considers the effect of both stable boundary layer (SBL) and the convective boundary layer (CBL). One important aspect of mass-consistent models is that they are quite sensitive to the values of some of their parameters. To deal with this problem, a strategy for parameter estimation based on a memetic algorithm is presented. Finally, a numerical experiment over complex terrain is presented along with some concluding remarks.


  1. 1.
    Burlando M, Georgieva E, Ratto CF (2007) Parameterisation of the planetary boundary layer for diagnostic wind models. Bound-Lay Meteorol 125:389–397. Scholar
  2. 2.
    Montero G, Montenegro R, Escobar JM (1998) A 3-D diagnostic model for wind field adjustment. J Wind Eng Ind Aerod 74–76:249–261. Scholar
  3. 3.
    Sherman CA (1978) A mass-consistent wind model for wind fields over complex terrain. J Appl Meteorol 17(3):312–319CrossRefGoogle Scholar
  4. 4.
    Wagenbrenner NS, Forthofer JM, Lamb BK, Shannon KS, Butler BW (2016) Downscaling surface wind predictions from numerical weather prediction models in complex terrain with windninja. Atmos Chem Phys 16(8):5229–5241., Scholar
  5. 5.
    Mortensen NG, Landberg L, Troen I, Petersen EL (1993) Wind atlas analysis and application program (WAsP), vol 2: Users guide. Riso National Laboratory, Roskilde, DenmarkGoogle Scholar
  6. 6.
    Walmsley JL, Taylor PA, Keith T (1986) A simple model of neutrally stratified boundary layer flow over complex terrain with surface roughness modulations (ms3djh/3r). Bound-Lay Meteorol 36(1–2):157–186. Scholar
  7. 7.
    Lopes AMG (2003) Windstation a software for the simulation of atmospheric flows over complex topography. Environ Model Softl 18(1):81–96. Scholar
  8. 8.
    Barnard JC (1991) An evaluation of three models designed for siting wind turbines in areas of complex terrain. Sol Energy 46(3):283–294. Scholar
  9. 9.
    Walmsley JL, Troen IB, Demetrius P, Lalas DP, Mason PJ (1990) Surface-layer flow in complex terrain: comparison of models and full-scale observations. Bound-Lay Meteorol 52(3):259–281. Scholar
  10. 10.
    Homicz GF (2002) Three-dimensional wind field modeling: a review. SAND Report 2597. Technical Report, Sandia National Laboratories, Albuquerque, NMGoogle Scholar
  11. 11.
    Apsley DD, Castro IP (1997) Flow and dispersion over hills: comparison between numerical predictions and experimental data. J Wind Eng Ind Aerod 67–68:375–386. Scholar
  12. 12.
    Maurizi A, Palma JMLM, Castro FA (1998) Numerical simulation of the atmospheric flow in a mountainous region of the north of portugal. J Wind Eng Ind Aerod 74–76:219–228. Scholar
  13. 13.
    Uchida T, Ohya Y (1999) Numerical simulation of atmospheric flow over complex terrain. J Wind Eng Ind Aerod 81(1–3):283–293. Scholar
  14. 14.
    Montavon C (1998) Validation of a non-hydrostatic numerical model to simulate stratified wind fields over complex topography. J Wind Eng Ind Aerod 74–76:273–282CrossRefGoogle Scholar
  15. 15.
    Dong Z, Gao S, Fryrear DW (2001) Drag coefficients, roughness length and zero-plane displacement height as disturbed by artificial standing vegetation. J Arid Environ 49(3):485–505. Scholar
  16. 16.
    Abtew W, Gregory JM, Borrelli J (1989) Wind profile: estimation of displacement height and aerodynamic roughness. Trans ASAE 32(2):0521–0527.
  17. 17.
    Ferragut L, Montenegro R, Montero G, Rodríguez E, Asensio MI, Escobar JM (2010) Comparison between 2.5-D and 3-D realistic models for wind field adjustment. J Wind Eng Ind Aerod 98(10–11):548–558 (2010). Scholar
  18. 18.
    Montero G, Rodríguez E, Montenegro R, Escobar JM, González-Yuste JM (2005) Genetic algorithms for an improved parameter estimation with local refinement of tetrahedral meshes in a wind model. Adv Eng Softw 36(1):3–10. Scholar
  19. 19.
    Winter G, Montero G, Ferragut L, Montenegro R (1995) Adaptive strategies using standard and mixed finite elements for wind field adjustment. Sol Energy 54(1):49–56. Scholar
  20. 20.
    Hestenes MR, Stiefel E (1952) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49(6):409–436MathSciNetCrossRefGoogle Scholar
  21. 21.
    Montero G, Montenegro R, Escobar J, Rodríguez E (2004) Resolution of sparse linear systems of equations: the rpk strategy. In: Topping B, Soares CM (eds) Progress in engineering computational technology, Chap 5. Saxe-Coburg Publications, Stirlingshire, UK, pp 81–109CrossRefGoogle Scholar
  22. 22.
    Suárez A, Sarmiento H, Flórez E, García M, Montero G (2011) Updating incomplete factorization preconditioners for shifted linear systems arising in a wind model. J Comput Appl Math 235(8):2640–2646., Scholar
  23. 23.
    Zilitinkevich SS, Johansson PE, Mironov DV, Baklanov A (1998) A similarity-theory model for wind profile and resistance law in stably stratified planetary boundary layers. J Wind Eng Ind Aerod 74–76:209–218CrossRefGoogle Scholar
  24. 24.
    Zilitinkevich SS, Tyuryakov SA, Troitskaya YI, Mareev EA (2012) Theoretical models of the height of the atmospheric boundary layer and turbulent entrainment at its upper boundary. Atmos Ocean Phys 48(1):150–160. Scholar
  25. 25.
    Zilitinkevich SS, Fedorovich EE, Shabalova MV (1992) Numerical model of a non-steady atmospheric planetary boundary layer, based on similarity theory. Bound-Lay Meteorol 59:387–411CrossRefGoogle Scholar
  26. 26.
    Montero G, Rodríguez E, Montenegro R, Escobar J, González-Yuste J (2005) Genetic algorithms for an improved parameter estimation with local refinement of tetrahedral meshes in a wind model. Adv Eng Softw 36(1):3–10., Evolutionary Optimization of Engineering ProblemsCrossRefGoogle Scholar
  27. 27.
    Oliver A, Rodríguez E, Escobar JM, Montero G, Hortal M, Calvo J, Cascón JM, Montenegro R (2015) Wind forecasting based on the harmonie model and adaptive finite elements. Pure Appl Geophys 172(1):109–120. Scholar
  28. 28.
    Storn R, Price K: Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359.
  29. 29.
    Greiner D, Emperador JM, Winter G (2004) Single and multiobjective frame optimization by evolutionary algorithms and the auto-adaptive rebirth operator. Comput Methods Appl Mech Engrg 193(33–35):3711–3743. Scholar
  30. 30.
    Byrd RH, Lu P, Nocedal J, Zhu C (1995) A limited memory algorithm for bound constrained optimization. SIAM J Sci Comput 16(5):1190–1208. Scholar
  31. 31.
    Mohan M, Siddiqui TA (1998) Analysis of various schemes for the estimation of atmospheric stability classification. Atmos Environ 32(21):3775–3781. Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Eduardo Rodríguez
    • 1
    Email author
  • Gustavo Montero
    • 1
  • Albert Oliver
    • 1
  1. 1.University Institute for Intelligent Systems and Numerical Applications in Engineering, University of Las Palmas de Gran CanariaLas Palmas de Gran CanariaSpain

Personalised recommendations