Basic Equations of Atmospheric Turbulence

  • Thomas Foken


Before starting the derivation of the equations for the turbulent fluxes of momentum, heat and trace gases, we present a short introduction into the basic equations. These include the equations of mean and turbulent motions, describing the transport and for energy and matter, and the conservation equation for the turbulence kinetic energy. To illustrate the importance of micrometeorological equations and parameterizations for modelling on all scales, different closure techniques of the turbulent differential equations are described.


Atmospheric Boundary Layer Latent Heat Flux Friction Velocity Roughness Length Vertical Wind 
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  1. Amiro BD (1990) Comparison of turbulence statistics within three boreal forest canopies. Boundary-Layer Meteorol. 51:99–121.Google Scholar
  2. Andreas EL (1989) Two-wavelength method of measuring path-averaged turbulent surface heat fluxes. J Atm Oceanic Techn. 6:280–292.Google Scholar
  3. Andreas EL (2002) Parametrizing scalar transfer over snow and ice: A review. J Hydrometeorol. 3:417–432.Google Scholar
  4. Andreas EL, Claffey KJ, Fairall CW, Grachev AA, Guest PS, Jordan RE and Persson POG (2004) Measurements of the von Kármán constant in the atmospheric surface layer - further discussions. 16th Conference on Boundary Layers and Turbulence, Portland ME2004. Am. Meteorol. Soc., pp. 1–7, paper 7.2.Google Scholar
  5. Arya SP (1999) Air Pollution Meteorology and Dispersion. Oxford University Press, New York, Oxford, 310 pp.Google Scholar
  6. Arya SP (2001) Introduction to Micrometeorology. Academic Press, San Diego, 415 pp.Google Scholar
  7. Beljaars ACM (1995) The parametrization of surface fluxes in large scale models under free convection. Quart J Roy Meteorol Soc. 121:255–270.Google Scholar
  8. Berkowicz R and Prahm LP (1984) Spectral representation of the vertical structure of turbulence in the convective boundary layer. Quart J Roy Meteorol Soc. 110:35–52.Google Scholar
  9. Bernhardt K-H (1995) Zur Interpretation der Monin-Obuchovschen Länge. Meteorol Z. 4:81–82.Google Scholar
  10. Bernhardt K (1970) Der ageostrophische Massenfluß in der Bodenreibungsschicht bei beschleunigungsfreier Strömung. Z Meteorol. 21:259–279.Google Scholar
  11. Bernhardt K (1972) Vorlesung ‘Dynamik der Atmosphäre’. Humboldt-Universität zu BerlinGoogle Scholar
  12. Bernhardt K (1975) Some characteristics of the dynamic air-surface interaction in Central Europe. Z Meteorol. 25:63–68.Google Scholar
  13. Bernhardt K (1980) Zur Frage der Gültigkeit der Reynoldsschen Postulate. Z Meteorol. 30:361–368.Google Scholar
  14. Beyrich F (1997) Mixing height estimation from sodar data — A critical discussion. Atmos Environm. 31:3941–3953.Google Scholar
  15. Beyrich F, Kouznetsov RD, Leps J-P, Lüdi A, Meijninger WML and Weisensee U (2005) Structure parameters for temperature and humidity from simultaneous eddy-covariance and scintillometer measurements. Meteorol Z. 14:641–649.Google Scholar
  16. Beyrich F and Leps J-P (2012) An operational mixing height data set from routine radiosoundings at Lindenberg: Methodology. Meteorol Z. 21:337–348.Google Scholar
  17. Blackadar AK and Tennekes H (1968) Asymptotic similarity in neutral barotropic planetary boundary layers. J Atmos Sci. 25:1015–1020.Google Scholar
  18. Blackadar AK (1997) Turbulence and Diffusion in the Atmosphere. Springer, Berlin, Heidelberg, 185 pp.Google Scholar
  19. Boussinesq J (1877) Essai sur la théorie des eaux courantes. Mem Savants Etrange. 23:46 pp.Google Scholar
  20. Bowen IS (1926) The ratio of heat losses by conduction and by evaporation from any water surface. Phys Rev. 27:779–787.Google Scholar
  21. Brocks K and Krügermeyer L (1970) Die hydrodynamische Rauhigkeit der Meeresoberfläche. Ber Inst Radiometeorol Marit Meteorol. 14:55 pp.Google Scholar
  22. Buckingham E (1914) On physically similar systems; illustrations of the use of dimensional equations. Phys Rev. 4:345–376.Google Scholar
  23. Busch NE, Chang SW and Anthes RA (1976) A Multi-Level Model of the Planetary Boundary Layer Suitable for Use with Mesoscale Dynamic Models. J Appl Meteorol. 15:909–919.Google Scholar
  24. Businger JA and Yaglom AM (1971) Introduction to Obukhov’s paper “Turbulence in an atmosphere with a non-uniform temperature”. Boundary-Layer Meteorol. 2:3–6.Google Scholar
  25. Businger JA, Wyngaard JC, Izumi Y and Bradley EF (1971) Flux-profile relationships in the atmospheric surface layer. J Atmos Sci. 28:181–189.Google Scholar
  26. Businger JA (1982) Equations and concepts. In: Nieuwstadt FTM and Van Dop H (eds.), Atmospheric turbulence and air pollution modelling: A course held in The Hague, 21–25 September 1981. D. Reidel Publ. Co., Dordrecht, 1–36.Google Scholar
  27. Businger JA (1986) Evaluation of the accuracy with which dry deposition can be measured with current micrometeorological techniques. J Appl Meteorol. 25:1100–1124.Google Scholar
  28. Businger JA (1988) A note on the Businger-Dyer profiles. Boundary-Layer Meteorol. 42:145–151.Google Scholar
  29. Charnock H (1955) Wind stress on water surface. Quart J Roy Meteorol Soc. 81:639–642.Google Scholar
  30. Cheng Y and Bruntseart W (2005) Flux-profile relationships for wind speed and temperature in the stable atmospheric boundary layer. Boundary-Layer Meteorol. 114:519–538.Google Scholar
  31. Clarke RH (1970) Observational studies in the atmospheric boundary layer. Quart J Roy Meteorol Soc. 96:91–114.Google Scholar
  32. Clarke RH and Hess GD (1974) Geostrophic departure and the functions A and B of Rossby-number similarity theory. Boundary-Layer Meteorol. 7:267–287.Google Scholar
  33. Corrsin S (1951) On the spectrum of isotropic temperature fluctuations in an isotropic turbulence. J Appl Phys. 22:469–473.Google Scholar
  34. Csanady GT (1967) On the “resistance law” of a turbulent Ekman-Layer. J Atmos Sci. 24:467–471.Google Scholar
  35. Davenport AG, Grimmond CSB, Oke TR and Wieringa J (2000) Estimating the roughness of cities and shelterred country. 12th Conference on Applied Climatology, Ashville, NC2000. American Meteorological Society, pp. 96–99.Google Scholar
  36. Deardorff JW (1966) The counter-gradient heat flux in the lower atmosphere and in the laboratory. J Atmos Sci. 23:503–506.Google Scholar
  37. Deardorff JW (1970) Convective Velocity and Temperature Scales for the Unstable Planetary Boundary Layer and for Rayleigh Convection. J Atmos Sci. 27:1211–1213.Google Scholar
  38. Dyer AJ (1974) A review of flux-profile-relationships. Boundary-Layer Meteorol. 7:363–372.Google Scholar
  39. ESDU (1972) Characteristics of wind speed in the lowest layers of the atmosphere near the ground: strong winds. Engl. Sci. Data Unit Ltd. Regent St., London, 35 pp.Google Scholar
  40. Etling D (2008) Theoretische Meteorologie. Springer, Berlin, Heidelberg, 376 pp.Google Scholar
  41. Foken T (1990) Turbulenter Energieaustausch zwischen Atmosphäre und Unterlage - Methoden, meßtechnische Realisierung sowie ihre Grenzen und Anwendungsmöglichkeiten. Ber Dt Wetterdienstes. 180:287 pp.Google Scholar
  42. Foken T, Skeib G and Richter SH (1991) Dependence of the integral turbulence characteristics on the stability of stratification and their use for Doppler-Sodar measurements. Z Meteorol. 41:311–315.Google Scholar
  43. Foken T, Jegede OO, Weisensee U, Richter SH, Handorf D, Görsdorf U, Vogel G, Schubert U, Kirzel H-J and Thiermann V (1997) Results of the LINEX-96/2 Experiment. Dt Wetterdienst, Forsch. Entwicklung, Arbeitsergebnisse. 48:75 pp.Google Scholar
  44. Foken T (2006) 50 years of the Monin-Obukhov similarity theory. Boundary-Layer Meteorol. 119:431–447.Google Scholar
  45. Garratt JR (1992) The Atmospheric Boundary Layer. Cambridge University Press, Cambridge, 316 pp.Google Scholar
  46. Gryning S-E, Batchvarova E, Brümmer B, Jørgensen H and Larsen S (2007) On the extension of the wind profile over homogeneous terrain beyond the surface boundary layer. Boundary-Layer Meteorol. 124:251–268.Google Scholar
  47. Handorf D, Foken T and Kottmeier C (1999) The stable atmospheric boundary layer over an Antarctic ice sheet. Boundary-Layer Meteorol. 91:165–186.Google Scholar
  48. Hantel M (2013) Einführung Theoretische Meteorologie. Springer Spektrum, Berlin, Heidelberg, 430 pp.Google Scholar
  49. Hasager CB and Jensen NO (1999) Surface-flux aggregation in heterogeneous terrain. Quart J Roy Meteorol Soc. 125:2075–2102.Google Scholar
  50. Helmis CG, Sgouros G, Tombrou M, Schäfer K, Münkel C, Bossioli E and Dandou A (2012) A comparative study and evaluation of mixing-height estimation based on sodar-RASS, ceilometer data and numerical model simulations. Boundary-Layer Meteorol. 145:507–526.Google Scholar
  51. Hill RJ, Clifford SF and Lawrence RS (1980) Refractive index and absorption fluctuations in the infrared caused by temperature, humidity and pressure fluctuations. J Opt Soc Am. 70:1192–1205.Google Scholar
  52. Högström U (1974) A field study of the turbulent fluxes of heat water vapour and momentum at a ‘typical’ agricultural site. Quart J Roy Meteorol Soc. 100:624–639.Google Scholar
  53. Högström U (1985) Von Kármán constant in atmospheric boundary flow: Reevaluated. J Atmos Sci. 42:263–270.Google Scholar
  54. Högström U (1988) Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Boundary-Layer Meteorol. 42:55–78.Google Scholar
  55. Högström U (1990) Analysis of turbulence structure in the surface layer with a modified similarity formulation for near neutral conditions. J Atmos Sci. 47:1949–1972.Google Scholar
  56. Högström U (1996) Review of some basic characteristics of the atmospheric surface layer. Boundary-Layer Meteorol. 78:215–246.Google Scholar
  57. Högström U, Hunt JCR and Smedman A-S (2002) Theory and measurements for turbulence spectra and variances in the atmospheric neutral surface layer. Boundary-Layer Meteorol. 103:101–124.Google Scholar
  58. Højstrup J (1981) A simple model for the adjustment of velocity spectra in unstable conditions downstream of an abrupt change in roughness and heat flux. Boundary-Layer Meteorol. 21:341–356.Google Scholar
  59. Holzworth GC (1964) Estimates of mean maximum mixing depth in the contiguous United States. Monthly Weather Review. 92:235–242.Google Scholar
  60. Holzworth GC (1967) Mixing depths, wind speeds and air pollution potential for selected locations in the United States. J Appl Meteorol. 6:1039–1044.Google Scholar
  61. Jacobson MZ (2005) Fundamentals of Atmospheric Modelling. Cambridge University Press, Cambridge, 813 pp.Google Scholar
  62. Johansson C, Smedman A, Högström U, Brasseur JG and Khanna S (2001) Critical test of Monin-Obukhov similarity during convective conditions. J Atmos Sci. 58:1549–1566.Google Scholar
  63. Kader BA and Yaglom AM (1972) Heat and mass transfer laws for fully turbulent wall flows. Int J Heat Mass Transfer. 15:2329–2350.Google Scholar
  64. Kaimal JC, Wyngaard JC, Izumi Y and Coté OR (1972) Spectral characteristics of surface layer turbulence. Quart J Roy Meteorol Soc. 98:563–589.Google Scholar
  65. Kaimal JC and Finnigan JJ (1994) Atmospheric Boundary Layer Flows: Their Structure and Measurement. Oxford University Press, New York, NY, 289 pp.Google Scholar
  66. Kantha LH and Clayson CA (2000) Small scale processes in geophysical fluid flows. Academic Press, San Diego, 883 pp.Google Scholar
  67. Kazanski AB and Monin AS (1960) A turbulent regime above the surface atmospheric layer (in Russian). Izv AN SSSR, ser Geofiz. 1:165–168.Google Scholar
  68. Kazanski AB and Monin AS (1961) On the dynamical interaction between the atmosphere and the Earth’s surface (in Russian). Izv AN SSSR, ser Geofiz. 5:786–788.Google Scholar
  69. Kitajgorodskij SA and Volkov JA (1965) O rascete turbulentnych potokov tepla i vlagi v privodnom sloe atmosfery (The calculation of the turbulent fluxes of temperature and humidity in the atmosphere near the water surface) Izv AN SSSR, Fiz Atm Okeana. 1:1317–1336.Google Scholar
  70. Kitajgorodskij SA (1976) Die Anwendung der Ähnlichkeitstheorie für die Bearbeitung der Turbulenz in der bodennahen Schicht der Atmosphäre. Z Meteorol. 26:185–204.Google Scholar
  71. Kohsiek W (1982) Measuring CT2, CQ2, and CTQ in the unstable surface layer, and relations to the vertical fluxes of heat and moisture. Boundary-Layer Meteorol. 24:89–107.Google Scholar
  72. Kolmogorov AN (1941a) Rassejanie energii pri lokolno-isotropoi turbulentnosti (Dissipation of energy in locally isotropic turbulence). Dokl AN SSSR. 32:22–24.Google Scholar
  73. Kolmogorov AN (1941b) Lokalnaja struktura turbulentnosti v neschtschimaemoi schidkosti pri otschen bolschich tschislach Reynoldsa (The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers). Dokl AN SSSR. 30:299–303.Google Scholar
  74. Kondo J and Sato T (1982) The determination of the von Kármán constant. J Meteor Soc Japan. 60:461–471.Google Scholar
  75. Kramm G and Herbert F (2009) Similarity hypotheses for the atmospheric surface layer expressed by non-dimensional characteristic invariants – A review Open Atmos Sci J. 3:48–79.Google Scholar
  76. Kraus H (2004) Die Atmosphäre der Erde. Springer, Berlin, Heidelberg, 422 pp.Google Scholar
  77. Kraus H (2008) Grundlagen der Grenzschichtmeteorologie. Springer, Berlin, Heidelberg, 211 pp.Google Scholar
  78. Lettau HH (1957) Windprofil, innere Reibung und Energieumsatz in den untersten 500 m über dem Meer. Beitr Phys Atm. 30:78–96.Google Scholar
  79. Lumley JL and Panofsky HA (1964) The structure of atmospheric turbulence. Interscience Publishers, New Yotk, 239 pp.Google Scholar
  80. Monin AS and Obukhov AM (1954) Osnovnye zakonomernosti turbulentnogo peremesivanija v prizemnom sloe atmosfery (Basic laws of turbulent mixing in the atmosphere near the ground). Trudy Geofiz inst AN SSSR. 24 (151):163–187.Google Scholar
  81. Monin AS and Yaglom AM (1973) Statistical Fluid Mechanics: Mechanics of Turbulence, Volume 1. MIT Press, Cambridge, London, 769 pp.Google Scholar
  82. Monin AS and Yaglom AM (1975) Statistical Fluid Mechanics: Mechanics of Turbulence, Volume 2. MIT Press, Cambridge, London, 874 pp.Google Scholar
  83. Münkel C, Eresmaa N, Räsänen J and Karppinen A (2007) Retrieval of mixing height and dust concentration with lidar ceilometer. Boundary-Layer Meteorol. 124:117–128.Google Scholar
  84. Obukhov AM (1946) Turbulentnost’ v temperaturnoj - neodnorodnoj atmosfere (Turbulence in an atmosphere with a non-uniform temperature). Trudy Inst Theor Geofiz AN SSSR 1:95–115.Google Scholar
  85. Obukhov AM (1949) Struktura temperaturnogo polja v turbulentnom potoke (Structure of the temperature field in the turbulent stream). Izv AN SSSR, ser geogr geofiz. 13:58–69.Google Scholar
  86. Oncley SP, Friehe CA, Larue JC, Businger JA, Itsweire EC and Chang SS (1996) Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions. J Atmos Sci. 53:1029–1054.Google Scholar
  87. Paeschke W (1937) Experimentelle Untersuchungen zum Rauhigkeitsproblem in der bodennahen Luftschicht. Z Geophys. 13:14–21.Google Scholar
  88. Pandolfo JP (1966) Wind and temperature profiles for constant-flux boundary layers in lapse conditions with a variable eddy conductivity to eddy viscosity ratio. J Atmos Sci. 23:495–502.Google Scholar
  89. Panofsky HA (1963) Determination of stress from wind and temperature measurements. Quart J Roy Meteorol Soc. 89:85–94.Google Scholar
  90. Panofsky HA, Tennekes H, Lenschow DH and Wyngaard JC (1977) The characteristics of turbulent velocity components in the surface layer under convective conditions. Boundary-Layer Meteorol. 11:355–361.Google Scholar
  91. Panofsky HA and Dutton JA (1984) Atmospheric Turbulence - Models and Methods for Engineering Applications. John Wiley and Sons, New York, 397 pp.Google Scholar
  92. Paulson CA (1970) The mathematical representation of wind speed and temperature profiles in the unstable atmospheric surface layer. J Climate Appl Meteorol. 9:857–861.Google Scholar
  93. Peltier LJ, Wyngaard JC, Khanna S and Brasseur JG (1996) Spectra in the unstable surface layer. J Atmos Sci. 53:49–61.Google Scholar
  94. Peña A, Gryning S-E and Hasager C (2010) Comparing mixing-length models of the diabatic wind profile over homogeneous terrain. Theor Appl Climat. 100:325–335.Google Scholar
  95. Prandtl L (1925) Bericht über Untersuchungen zur ausgebildeten Turbulenz. Z Angew Math Mech. 5:136–139.Google Scholar
  96. Pruitt WO, Morgan DL and Lourence FJ (1973) Momentum and mass transfer in the surface boundary layer. Quart J Roy Meteorol Soc. 99:370–386.Google Scholar
  97. Reithmaier LM, Göckede M, Markkanen T, Knohl A, Churkina G, Rebmann C, Buchmann N and Foken T (2006) Use of remotely sensed land use classification for a better evaluation of micrometeorological flux measurement sites. Theor Appl Climat. 84:219–233.Google Scholar
  98. Roll HU (1948) Wassernahes Windprofil und Wellen auf dem Wattenmeer. Ann Meteorol. 1:139–151.Google Scholar
  99. Salby ML (2012) Physics of the Atmosphere and Climate. Cambridge University Press, Cambridge, 666 pp.Google Scholar
  100. Schlichting H and Gersten K (2003) Boundary-Layer Theory. McGraw Hill, New York, XXIII, 799 pp.Google Scholar
  101. Schmitz-Peiffer A, Heinemann D and Hasse L (1987) The ageostrophic methode - an update. Boundary-Layer Meteorol. 39:269–281.Google Scholar
  102. Seibert P, Beyrich F, Gryning S-E, Joffre S, Rasmussen A and Tercier P (2000) Review and intercomparison of operational methods for the determination of the mixing height. Atmos Environm. 34:1001–1027.Google Scholar
  103. Skeib G (1980) Zur Definition universeller Funktionen für die Gradienten von Windgeschwindigkeit und Temperatur in der bodennahen Luftschicht. Z Meteorol. 30:23–32.Google Scholar
  104. Smedman A-S (1991) Some turbulence characteristics in stable atmospheric boundary layer flow. J Atmos Sci. 48:856–868.Google Scholar
  105. Sonntag D (1990) Important new values of the physical constants of 1986, vapour pressure formulations based on the ITC-90, and psychrometer formulae. Z Meteorol. 40:340–344.Google Scholar
  106. Sorbjan Z (1989) Structure of the Atmospheric Boundary Layer. Prentice Hall, New York, 317 pp.Google Scholar
  107. Sorbjan Z (2008) Gradient-based similarity in the atmospheric boundary layer. Acta Geophys. 56:220–233.Google Scholar
  108. Sreenivasan KR (1995) On the universality of the Kolmogorov constant. Phys Fluids. 7:2778–2784.Google Scholar
  109. Sreenivasan KR (1996) The passive scalar spectrum and the Obukhov–Corrsin constant. Phys Fluids. 8:189–196.Google Scholar
  110. Stull RB (1984) Transilient turbulence theorie, Part 1: The concept of eddy mixing across finite distances. J Atmos Sci. 41:3351–3367.Google Scholar
  111. Stull RB (1988) An Introduction to Boundary Layer Meteorology. Kluwer Acad. Publ., Dordrecht, Boston, London, 666 pp.Google Scholar
  112. Stull RB (2000) Meteorology for Scientists and Engineers. Brooks/Cole, Pacific Grove, 502 pp.Google Scholar
  113. Tatarski VI (1961) Wave Propagation in a Turbulent Medium. McGraw-Hill, New York, 285 pp.Google Scholar
  114. Taylor GI (1938) The spectrum of turbulence. Proceedings Royal Society London. A 164:476–490.Google Scholar
  115. Tennekes H (1982) Similarity relations, scaling laws and spectral dynamics. In: Nieuwstadt FTM and Van Dop H (eds.), Atmospheric turbulence and air pollution modelling. D. Reidel Publ. Comp., Dordrecht, Boston, London, 37–68.Google Scholar
  116. Thomas C and Foken T (2002) Re-evaluation of integral turbulence characteristics and their parameterisations. 15th Conference on Turbulence and Boundary Layers, Wageningen, NL, 15–19 July 2002. Am. Meteorol. Soc., pp. 129-132.Google Scholar
  117. Tillman JE (1972) The indirect determination of stability, heat and momentum fluxes in the atmospheric boundary layer from simple scalar variables during dry unstable conditions. J Climate Appl Meteorol. 11:783–792.Google Scholar
  118. Troen I and Lundtang Peterson E (1989) European Wind Atlas. Risø National Laboratory, Roskilde, 656 pp.Google Scholar
  119. Troen IB and Mahrt L (1986) A simple model of the atmospheric boundary layer; sensitivity to surface evaporation. Boundary-Layer Meteorol. 37:129–148.Google Scholar
  120. Wieringa J (1980) A revaluation of the Kansas mast influence on measurements of stress and cup anemometer over speeding. Boundary-Layer Meteorol. 18:411–430.Google Scholar
  121. Wieringa J (1992) Updating the Davenport roughness classification. J Wind Eng Industry Aerodyn. 41:357–368.Google Scholar
  122. Wippermann F and Yordanov D (1972) A note on the Rossby similarity for flows of barotropic planetary boundary layers. Beitr Phys Atm. 45:66–71.Google Scholar
  123. Wyngaard JC, Coté OR and Izumi Y (1971a) Local free convection, similarity and the budgets of shear stree and heat flux. J Atmos Sci. 28:1171–1182.Google Scholar
  124. Wyngaard JC and Coté OR (1971) The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J Atmos Sci. 28:190–201.Google Scholar
  125. Wyngaard JC, Izumi Y and Collins SA (1971b) Behavior of the refractive-index-structure parameter near the ground. J Opt Soc Am. 61:1646–1650.Google Scholar
  126. Wyngaard JC (1973) On surface layer turbulence. In: Haugen DH (ed.), Workshop on Micrometeorology. Am. Meteorol. Soc., Boston, 101–149.Google Scholar
  127. Wyngaard JC (2010) Turbulence in the Atmosphere. Cambridge University Press, Cambridge, 393 pp.Google Scholar
  128. Yaglom AM (1977) Comments on wind and temperature flux-profile relationships. Boundary-Layer Meteorol. 11:89–102.Google Scholar
  129. Yaglom AM (1979) Similarity laws for constant-pressure and pressure-gradient turbulent wall flow. Ann Rev Fluid Mech. 11:505–540.Google Scholar
  130. Zilitinkevich SS and Tschalikov DV (1968) Opredelenie universalnych profilej skorosti vetra i temperatury v prizemnom sloe atmosfery (Determination of universal profiles of wind velocity and temperature in the surface layer of the atmosphere). Izv AN SSSR, Fiz Atm Okeana. 4:294–302.Google Scholar
  131. Zilitinkevich SS (1969) On the computation of the basic parameters of the interaction between the atmosphere and the ocean. Tellus. 21:17–24.Google Scholar
  132. Zilitinkevich SS (1970) Dinamika pogranichnogo sloia atmosfery (Dynamics of the atmospheric boundary layer). Gidrometeorologicheskoe Izdatelstvo, Leningrad pp.Google Scholar
  133. Zilitinkevich SS (1975) Resistance laws and prediction equations for the depth of the planetary boundary layer. J Atmos Sci. 32:741–752.Google Scholar
  134. Zilitinkevich SS, Perov VL and King JC (2002) Near-surface turbulent fluxes in stable stratification: Calculation techniques for use in general circulation models. Quart J Roy Meteorol Soc. 128:1571–1587.Google Scholar

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Authors and Affiliations

  1. 1.Bayreuth Center of Ecology and Environmental Research (BayCEER)University of BayreuthBayreuthGermany
  2. 2.BischbergGermany

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