Vertical Profiles Over Flat Terrain

  • Stefan Emeis
Part of the Green Energy and Technology book series (GREEN)


This chapter is going to introduce the basic laws for the shape of the vertical profiles of wind speed and turbulence in a flat, horizontally homogeneous atmospheric boundary layer (ABL) over land because this is the simplest surface type.


  1. Allnoch, N.: Windkraftnutzung im nordwestdeutschen Binnenland: Ein System zur Standortbewertung für Windkraftanlagen. Geographische Kommission für Westfalen, Münster, ARDEY-Verlag, 160 pp. (1992).Google Scholar
  2. Arnfield A.J.: Two Decades of urban climate research: a review of turbulence, exchanges of energy and water, and the urban heat island. Int. J. Climatol. 23, 1–26 (2003).Google Scholar
  3. Arnqvist, J., A. Segalini, E. Dellwik, H. Bergström: Wind statistics from a forested landscape. Bound.-Lay. Meteorol. 156, 53–71 (2015).Google Scholar
  4. Arya, S.P.: Atmospheric boundary layer and its parameterization. In: Cermak, J.E. et al. (Eds.) Wind Climate in Cities. Kluwer, Dordrecht. 41–66 pp. (1995).Google Scholar
  5. Atkinson B.W.: Numerical modelling of urban heat-island intensity. Bound.-Lay. Meteorol. 109, 285–310 (2003).Google Scholar
  6. Baas P., Bosveld F.C., Klein Baltink H., Holtslag A.A.M.: A climatology of nocturnal low-level jets at Cabauw. J. Appl. Meteor. Climatol., 48, 1627–1642 (2009).Google Scholar
  7. Banta, R.M., Y.L. Pichugina, W.A. Brewer: Turbulent velocity-variance profiles in the stable boundary layer generated by a nocturnal low-level jet. J. Atmos. Sci., 63, 2700–2719 (2006).Google Scholar
  8. Barlow, J., M. Best, S. Bohnenstengel, P. Clark, S. Grimmond, H. Lean, A. Christen, S. Emeis, M. Haeffelin, I. Harman, A. Lemonsu, A. Martilli, E. Pardyjak, M. Rotach, S. Ballard, I. Boutle, A. Brown, X. Cai, M. Carpentieri, O. Coceal, B. Crawford, S. Di Sabatino, J. Dou, D. Drew, J. Edwards, J. Fallmann, K. Fortuniak, J. Gornall, T. Gronemeier, C. Halios, D. Hertwig, K. Hirano, A. Holtslag, Z. Luo, G. Mills, M. Nakayoshi, K. Pain, K. Schlünzen, S. Smith, L. Soulhac, G. Steeneveld, T. Sun, N. Theeuwes, D. Thomson, J. Voogt, H. Ward, Z. Xie, and J. Zhong: Developing a research strategy to better understand, observe and simulate urban atmospheric processes at kilometre to sub-kilometre scales. Bull. Amer. Meteor. Soc., 98, ES261-ES264 (2017).Google Scholar
  9. Batchvarova E., Gryning S.-E.: Progress in urban dispersion studies. Theor. Appl. Climatol. 84, 57–67 (2006).Google Scholar
  10. Blackadar, A.K.: Boundary layer wind maxima and their significance for the growth of nocturnal inversions. Bull. Amer. Meteorol. Soc., 38, 283–290 (1957).Google Scholar
  11. Blackadar, A.K.: The Vertical Distribution of Wind and Turbulent Exchange in a Neutral Atmosphere. J. Geophys. Res. 67, 3095–3102 (1962).Google Scholar
  12. Brümmer, B., M. Schultze: Analysis of a 7-year low-level temperature inversion data set measured at the 280 m high Hamburg weather mast. Meteorol. Z., 24, 481–494 (2015).Google Scholar
  13. Businger, J.A., J.C. Wyngaard, Y. Izumi, E.F. Bradley: Flux profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28, 181–189 (1971).Google Scholar
  14. CERC: Cambridge Environmental Research Consultants, ADMS dispersion model. (2001)
  15. Cermak, J.E., A.G. Davenport, E.J. Plate, D.X. Viegas (Eds): Wind Climate in Cities. NATO ASI Series E277, Kluwer Acad Publ, Dordrecht, 772 pp. (1995).Google Scholar
  16. Chougule, A., J. Mann, A. Segalini, E. Dellwik: Spectral tensor parameters for wind turbine load modeling from forested and agricultural landscapes. Wind Energy, 18, 469–481 (2015).Google Scholar
  17. Chow, W.T.L., Roth, M.: Temporal dynamics of the urban heat island of Singapore. Int. J. Climatol. 26, 2243–2260 (2006).Google Scholar
  18. Clarke, R.H., Dyer, A.J., Brooks, R.R., Reid, D.G., and Troup, A.J.: The Wangara Experiment: Boundary-Layer Data, Technical Paper,No. 19. Division of Meteorological Physics, CSIRO, Aspendale, Australia, 340 pp. (1971).Google Scholar
  19. Counihan, J.: Simulation of an adiabatic urban boundary layerurban boundary layer in a wind tunnel. Atmos. Environ. 7, 673–689 (1973).Google Scholar
  20. Crutzen, P.J.: New Directions: The growing urban heat and pollution ‘‘island’’ effect – impact on chemistry and climate. Atmos. Environ. 38, 3539–3540 (2004).Google Scholar
  21. Davis, F.K., H. Newstein: The Variation of Gust Factors with Mean Wind Speed and with Height. J. Appl. Meteor. 7, 372–378 (1968).Google Scholar
  22. Dyer, A.J.: A review of flux-profile relations. Bound.-Lay. Meteorol. 7, 363–372 (1974).Google Scholar
  23. Emeis, S.: Vertical variation of frequency distributions of wind speed in and above the surface layer observed by sodar. Meteorol. Z. 10, 141–149 (2001).Google Scholar
  24. Emeis, S.: Vertical wind profiles over an urban area. Meteorol. Z. 13, 353–359 (2004).Google Scholar
  25. Emeis, S.: How well does a Power Law Fit to a Diabatic Boundary-Layer Wind Profile? DEWI Magazine No. 26, 59–62 (2005).Google Scholar
  26. Emeis, S.: Measurement Methods in Atmospheric Sciences. In situ and remote. Series: Quantifying the Environment Vol. 1. Borntraeger Stuttgart. XIV + 257 pp. (2010).Google Scholar
  27. Emeis, S.: Wind speed and shear associated with low-level jets over Northern Germany. Meteorol. Z., 23, 295–304 (2014).Google Scholar
  28. Emeis, S.: Upper limit for wind shear in stably stratified conditions expressed in terms of a bulk Richardson number. Meteorol. Z., 26, 421–430 (2017).Google Scholar
  29. Emeis, S., Jahn, C., Münkel, C., Münsterer, C., Schäfer, K.: Multiple atmospheric layering and mixing-layer height in the Inn valley observed by remote sensing. Meteorol. Z. 16, 415–424 (2007a).Google Scholar
  30. Emeis, S., K. Baumann-Stanzer, M. Piringer, M. Kallistratova, R. Kouznetsov, V. Yushkov: Wind and turbulence in the urban boundary layer – analysis from acoustic remote sensing data and fit to analytical relations. Meteorol. Z. 16, 393–406 (2007b).Google Scholar
  31. Etling, D.: Theoretische Meteorologie Eine Einführung. 2nd edition, Springer, Berlin, Heidelberg, New York. (2002).Google Scholar
  32. Farell, C., Iyengar, A.K.S.: Experiments on the wind tunnel simulation of atmospheric boundary layers. J. Wind Eng. Indust. Aerodyn. 79, 11–35 (1999).Google Scholar
  33. Fiedler, F., H.A. Panofsky: The geostrophic drag coefficient and the ‘effective’ roughness length. Quart. J. Roy. Meteor. Soc., 98, 213–220 (1972).Google Scholar
  34. Floors, R., S.-E. Gryning, A. Peña, E. Batchvarova: Analysis of diabatic flow modification in the internal boundary layer. Meteorol. Z. 20, 649–659 (2011).Google Scholar
  35. Foken, T.: Application of Footprint Models for the Fine-Tuning of Wind Power Locations on Inland Areas. DEWI Mag. 40, 51–54 (2012).Google Scholar
  36. Garratt, J.R.: The atmospheric boundary layer. Cambridge University Press. 334 pp. (1992).Google Scholar
  37. Gerstengarbe, F.-W., P.C. Werner, U. Rüge (Eds.): Katalog der Großwetterlagen Europas (1881 –1998). Nach Paul Hess und Helmuth Brezowsky. 5th edition. German Meteorological Service, Potsdam/Offenbach a. M. (1999) (available from: lexikon/download.php?file = Grosswetterlage.pdf or gwl/gwl.pdf).
  38. Grimmond, C.S.B.: Progress in measuring and observing the urban atmosphere. Theor. Appl. Climatol. 84, 3–22 (2006).Google Scholar
  39. Gryning, S.-E., Batchvarova, E., Brümmer, B., Jørgensen, H., Larsen, S.: On the extension of the wind profile over homogeneous terrain beyond the surface layer. Bound.-Lay. Meteorol. 124,251–268 (2007).Google Scholar
  40. Hellmann, G.: Über die Bewegung der Luft in den untersten Schichten der Atmosphäre. Meteorol. Z. 32, 1–16 (1915).Google Scholar
  41. Hidalgo, J., Masson, V., Baklanov, A., Pigeon, G., Gimeno, L.: Advances in Urban Climate Modeling. Ann. N.Y. Acad. Sci. 1146, 354–374 (2008).Google Scholar
  42. Högström, U., Bergström, H., Smedman, A.-S., Halldin, S., Lindroth, A.: Turbulent exchange above a pine forest, I: Fluxes and gradients. Bound.-Lay. Meteorol. 49, 197–217 (1989).Google Scholar
  43. Högström, U.: Non-dimensional wind and temperature profiles in the atmospheric surface layer: a re-evaluation. Bound.-Lay. Meteorol., 42, 55–78 (1988).Google Scholar
  44. Holtslag, A.A.M., H.A.R. de Bruin: Applied modeling of the nighttime surface energy balance over land. J. Appl. Meteor., 27, 689–704 (1988).Google Scholar
  45. Justus, C.G., W.R. Hargraves, A. Mikhail, D. Graber: Methods for Estimating Wind Speed Frequency Distributions. J. Appl. Meteor. 17, 350–353 (1978).Google Scholar
  46. Kaimal, J.V., J.C. Wyngaard, Y. Izumi, O.R. Coté: Spectral characteristics of surface-layer turbulence. Quart. J. Roy. Meteorol. Soc. 98, 563–589 (1972).Google Scholar
  47. Kanani, F., K. Träumner, B. Ruck, S. Raasch: What determines the differences found in forest edge flow between physical models and atmospheric measurements? – An LES study. Meteorol. Z., 23, 33–49 (2014).Google Scholar
  48. Kanda, M.: Progress in Urban Meteorology: A Review. J. Meteor. Soc. Jap. 85B, 363–383 (2007).Google Scholar
  49. Kraus, H.: Grundlagen der Grenzschicht-Meteorologie. Springer, 214 pp. (2008).Google Scholar
  50. Lampert, A., B.B. Jimenez, G. Gross, D. Wulff, T. Kenull: One-year observations of the wind distribution and low-level jet occurrence at Braunschweig, North German Plain. Wind Energy, 19, 1807–1817 (2016).Google Scholar
  51. Larsén, X,G., S.E. Larsen, E.L. Petersen: Full-Scale Spectrum of Boundary-Layer Winds. Bound.-Lay. Meteorol., 159, 349–371 (2016).Google Scholar
  52. Lettau, H.: Graphs and Illustrations of Diverse Atmospheric States and Processes Observed During the Seventh Test Period of the Great Plains Turbulence Field Program. Occasional Report 1, Atmospheric Analysis Laboratory, Air Force Cambridge Research Center, Mass. (1954).Google Scholar
  53. Lokoshchenko, M.A., M.A., Yavlyaeva, E.A.: Wind Profiles in Moscow city by the Sodar Data.14th International Symposium for the Advancement of Boundary Layer Remote Sensing. IOP Conf. Series: Earth and Environmental Science 1, 012064. (2008).
  54. Mahrt, L.: Modelling the depth of the nocturnal boundary layer. Bound.-Lay. Meteorol., 21, 3–19 (1981).Google Scholar
  55. Mahrt, L., R.C. Heald, D.H. Lenschow, B.B. Stankov, I. Troen: An observational study of the structure of the nocturnal boundary layer. Bound.-Lay. Meteorol., 17, 247–264 (1979).Google Scholar
  56. Miao, S., F. Shen, M.A. LeMone, M. Tewari, Q. Li, Y. Wang: An Observational and Modeling Study of Characteristics of Urban Heat Island and Boundary Layer Strutures in Beijing. J. Appl. Meteor. Climatol. 48, 484–501 (2009).Google Scholar
  57. Miyake, M.: Transformation of the atmospheric boundary layer over inhomogeneous surfaces. Univ. of Washington, Seattle, unpubl. MSc-thesis, Sci. Rep. 5R-6. (1965).Google Scholar
  58. Optis, M., A. Monahan, F. C. Bosveld: Moving Beyond Monin–Obukhov Similarity Theory in Modelling Wind-Speed Profiles in the Lower Atmospheric Boundary Layer under Stable Stratification. Boundary-Layer Meteorol., 153, 497–514 (2014).Google Scholar
  59. Optis, M., Monahan, A., Bosveld, F.C.: Limitations and breakdown of Monin–Obukhov similarity theory for wind profile extrapolation under stable stratification. Wind Energy, 19, 1053–1072 (2016).Google Scholar
  60. Panofsky, H.A., H. Tennekes, D.H. Lenschow, J.C. Wyngaard: The characteristics of turbulent velocity components in the surface layer under convective conditions. Bound.-Lay. Meteorol., 11, 355–361 (1977).Google Scholar
  61. Paulson, C.A.: The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J. Appl. Meteorol. 9, 857–861 (1970).Google Scholar
  62. Peña, A., S.-E. Gryning, J. Mann, C.B. Hasager: Length Scales of the Neutral Wind Profile over Homogeneous Terrain. J. Appl. Meteor. Climatol., 49, 792–806 (2010a).Google Scholar
  63. Peña, A., S.-E. Gryning, C. Hasager: Comparing mixing-length models of the diabatic wind profile over homogeneous terrain. Theor. Appl. Climatol., 100, 325–335 (2010b).Google Scholar
  64. Peppler, A.: Windmessungen auf dem Eilveser Funkenturm. Beitr. Phys. fr. Atmosph. 9, 114–129 (1921).Google Scholar
  65. Piringer, M., Joffre, S., Baklanov, A., Christen, A., Deserti, M., de Ridder, K., Emeis, S., Mestayer, P., Tombrou, M., Middleton, D., Baumann-Stanzer, K., Dandou, A., Karppinen, A., Burzynski, J.: The surface energy balance and the mixing height in urban areas – activities and recommendations of COSTAction 715. Bound.-Lay. Meteorol. 124, 3–24 (2007).Google Scholar
  66. Plate, E.J.: Urban Climates and Urban ClimateModelling: An Introduction. – In: Cermak, J.E. et al. (Eds.) Wind Climate in Cities. NATO ASI Series E277, Kluwer Acad Publ, Dordrecht, 23–39. (1995).Google Scholar
  67. Raupach, M.R.: Anomalies in flux-gradient relationships over forest. Bound.-Lay. Meteorol. 16, 467–486 (1979).Google Scholar
  68. Rotach, M.W.: On the influence of the urban roughness sublayer on Turbulence and dispersion. Atmos. Environ. 33, 4001–4008 (1999).Google Scholar
  69. Roth, M.: Review of atmospheric turbulence over cities. Quart. J. Roy. Meteor. Soc. 126, 941–990 (2000).Google Scholar
  70. Sathe, A., S.-E. Gryning, A. Peña: Comparison of the atmospheric stability and wind profiles at two wind farm sites over a long marine fetch in the North Sea. Wind Energy 14, 767–780 (2011).Google Scholar
  71. Savelyev, S.A., P.A. Taylor: Internal Boundary Layers: I. Height Formulae for Neutral and Diabatic Flows. Bound.-Lay. Meteorol. 115, 1–25 (2005).Google Scholar
  72. Schatzmann, M., Leitl, B.: Validation and application of obstacle-resolving urban dispersion models. Atmos. Environ. 36, 4811–4821 (2002).Google Scholar
  73. Schmid, H.P.: Footprint modeling for vegetation atmosphere exchange studies: a review and perspective. Agric. Forest Meteorol. 113, 159–183 (2002).Google Scholar
  74. Schmid, H.P.: Source areas for scalars and scalar fluxes. Bound.-Lay. Meteorol. 67, 293–318 (1994).Google Scholar
  75. Schroers, H., H. Lösslein, K. Zilich: Untersuchung der Windstruktur bei Starkwind und Sturm. Meteorol. Rdsch. 42, 202–212 (1990).Google Scholar
  76. Sedefian, L.: On the vertical extrapolation of mean wind power density. J. Appl. Meteor. 19, 488–493 (1980).Google Scholar
  77. Shreffler, J.H.: Detection of Centripetal Heat Island Circulations from Tower Data in St. Louis. Bound.-Lay. Meteorol. 15, 229–242 (1978).Google Scholar
  78. Shreffler, J.H.: Heat Island Convergence in St. Louis during Calm Periods. J. Appl. Meteorol. 18, 1512–1520 (1979).Google Scholar
  79. Smedman, A.-S., M. Tjernström, U. Högström: Analysis of the turbulent structure of a marine low-level jet. Bound.-Lay. Meteorol., 66, 105–126 (1993).Google Scholar
  80. Stull, R.: An Introduction to Boundary-Layer Meteorology. Kluwer Academic Publishers, Dordrecht. 666 pp. (1988).Google Scholar
  81. Taylor, P.A.: Comments and further analysis on effective roughness lengths for use in numerical three-dimensional models. – Bound.-Layer Meteor. 39, 403–418 (1987).Google Scholar
  82. Teunissen, H.W.: Structure of mean winds and turbulence in the planetary boundary layer over rural terrain. Bound.-Lay. Meteorol. 19, 187–221 (1980).Google Scholar
  83. Troen, I., E.L. Petersen: European Wind Atlas. Risø National Laboratory, Roskilde, Denmark. 656 pp. (1989).Google Scholar
  84. Türk, M., K. Grigutsch, S. Emeis: The Wind Profile Above the Sea – Investigations Basing on Four Years of FINO 1 Data. DEWI Mag., 33, 12–16 (2008).Google Scholar
  85. Türk, M., S. Emeis: The dependence of offshore turbulence on wind speed. J. Wind Eng. Ind. Aerodyn., 98, 466–471 (2010).Google Scholar
  86. Van der Hoven, I.: Power spectrum of horizontal wind speed in the frequency range from 0.0007 to 900 cycles per hour. J. Meteorol., 14, 160–164 (1957).Google Scholar
  87. Van de Wiel, B.J.H., A.F. Moene, G.J. Steeneveld, P. Baas, F.C. Bosveld, A.A.M. Holtslag: A Conceptual View on Inertial Oscillations and Nocturnal Low-Level Jets. J. Atmos. Sci., 67, 2679–2689 (2010).Google Scholar
  88. Velasco, E., Márquez, C., Bueno, E., Bernabé, R.M., Sánchez, A., Fentanes, O., Wöhrnschimmel, H., Cárdenas, B., Kamilla, A.,Wakamatsu, S., Molina, L.T.: Vertical distribution of ozone and VOCs in the low boundary layer of Mexico City. Atmos. Chem. Phys. Discuss. 7, 12751–12779 (2007).Google Scholar
  89. Wieringa, J.: Gust factors over open water and built-up country. Bound.-Lay. Meteorol. 3, 424–441 (1973).Google Scholar
  90. Wieringa, J.: Shapes of annual frequency distributions of wind speed observed on high meteorological masts. Bound.-Lay.Meteorol. 47, 85–110 (1989).Google Scholar
  91. Wittich, K.-P., R. Roth: A case study of nocturnal wind and temperature profiles over the inhomogeneous terrain of Northern Germany with some considerations of turbulent fluxes. Bound.-Lay. Meteor., 28, 169–186 (1984).Google Scholar
  92. Wittich, K.-P., J. Hartmann, R. Roth: Analytical Shear Statistics Based on Nocturnal Wind Profiles. J. Climate Appl. Meteorol., 25, 1507–1517 (1986).Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Meteorologie und KlimaforschungKarlsruher Institut für TechnologieGarmisch-PartenkirchenGermany

Personalised recommendations