Modeling of the Energy and Matter Exchange

  • Thomas Foken


Within micrometeorology the term modeling is not uniquely defined. It refers to various methods covering a range of complexity extending from simple regressions up to complicated numerical models . In applied meteorology (agro meteorology and hydro meteorology) simple analytical models are very common. Modeling of evaporation is particularly important but sophisticated numerical methods are not yet widely used in this research area. The following chapter describes different types of models and their limitations beginning with simple analytical methods up to numerical models of near-surface energy and matter transport. The application of models in heterogeneous terrain receives special attention and related flux averaging approaches are addressed in a separate subchapter.


Atmospheric Boundary Layer Roughness Length Wind Profile Grid Element Buoyancy Flux 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Albertson JD and Parlange MB (1999) Natural integration of scalar fluxes from complex terrain. Adv Water Res. 23:239–252.Google Scholar
  2. Allen RG, Pereira LS, Raes D and Smith M (1998) Crop evaporation. FAO Irrigation Drainage Pap. 56:XXVI + 300 pp.Google Scholar
  3. Allen RG, Walter IA, Elliott R, Howell T, Itenfisu D and Jensen M (2005) The ASCE standardized reference evapotranspiration equation. Environmental and Water Resources Institute of the American Society of Civil Engineers, X + 59 pp.Google Scholar
  4. Arya SP (2001) Introduction to Micrometeorology. Academic Press, San Diego, 415 pp.Google Scholar
  5. Avissar R and Pielke RA (1989) A parametrization of heterogeneous land surface for atmospheric numerical models and its impact on regional meteorology. Monthly Weather Review. 117:2113–2136.Google Scholar
  6. Baldocchi D (1988) A multi-layer model for estimating sulfor dioxid deposition to a deciduous oke forest canopy. Atmos Environm. 22:869–884.Google Scholar
  7. Baldocchi D, Hicks BB and Camara P (1987) A canopy stomatal resistance model for gaseous deposition to vegetated surfaces. Atmos Environm. 21:91–101.Google Scholar
  8. Ball JT, Woodrow IE and Berry JA (1987) A model predicting stomatal conductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggens J (ed.), Progress in Photosynthesis Research. Vol. IV. Martinus Nijhoff Publisher, Dordrecht, IV.5.221–IV.5.224.Google Scholar
  9. Batchvarova E and Gryning S-E (1991) Applied model for the growth of the daytime mixed layer. Boundary-Layer Meteorol. 56:261–274.Google Scholar
  10. Behrens J, Rakowsky N, Hiller W, Handorf D, Läuter M, Päpke J and Dethloff K (2005) amatos: parallel adaptive mesh generator for atmospheric and oceanic simulation. Ocean Modelling. 10:171–183.Google Scholar
  11. 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
  12. Beljaars ACM and Holtslag AAM (1991) Flux parametrization over land surfaces for atmospheric models. J Appl Meteorol. 30:327–341.Google Scholar
  13. Beljaars ACM and Viterbo P (1998) Role of the boundary layer in a numerical weather prediction model. In: Holtslag AAM and Duynkerke PG (eds.), Clear and Cloudy Boundary Layers, vol VNE 48. Royal Netherlands Academy of Arts and Sciences, Amsterdam, 287–304.Google Scholar
  14. Best MJ, Beljaars A, Polcher J and Viterbo P (2004) A proposed structure for coupling tiled surfaces with the planetary boundary layer. J Hydrometeorol. 5:1271–1278.Google Scholar
  15. Biermann T, Babel W, Ma W, Chen X, Thiem E, Ma Y and Foken T (2014) Turbulent flux observations and modelling over a shallow lake and a wet grassland in the Nam Co basin, Tibetan Plateau. Theor Appl Climat. 116:301–316.Google Scholar
  16. Bjutner EK (1974) Teoreticeskij rascet soprotivlenija morskoj poverchnosti (Theoretical calculation of the resistance at the surface of the ocean). In: Dubov AS (ed.), Processy perenosa vblizi poverchnosti razdela okean - atmosfera (Exchange processes near the ocean - atmosphere interface). Gidrometeoizdat, Leningrad, 66–114.Google Scholar
  17. Blackadar AK (1997) Turbulence and Diffusion in the Atmosphere. Springer, Berlin, Heidelberg, 185 pp.Google Scholar
  18. Blümel K (1998) Estimation of sensible heat flux from surface temperature wave and one-time-of-day air temperature observations. Boundary-Layer Meteorol. 86:193–232.Google Scholar
  19. Blyth EM (1995) Comments on ‘The influence of surface texture on the effective roughness length’ by H. P. Schmid and D. Bünzli (1995, 121, 1–21). Quart J Roy Meteorol Soc. 121:1169–1171.Google Scholar
  20. Brötz B, Eigenmann R, Dörnbrack A, Foken T and Wirth V (2014) Early-morning flow transition in a valley in low-mountain terrain. Boundary-Layer Meteorol. 152:45–63.Google Scholar
  21. Brutsaert WH (1982) Evaporation into the atmosphere: Theory, history and application. D. Reidel, Dordrecht, 299 pp.Google Scholar
  22. Burridge DM and Gadd AJ (1977) The Meteorological Office operational 10-level numerical weather prediction model (December 1975). Meteorological Office Technical Notes. 34:39 pp.Google Scholar
  23. Csanady GT (2001) Air-sea interaction, Laws and mechanisms. Cambridge University Press, Cambridge, New York, 239 pp.Google Scholar
  24. Davidan IN, Lopatuhin LI and Rogkov VA (1985) Volny v okeane (Waves in the ocean). Gidrometeoizdat, Leningrad, 256 pp.Google Scholar
  25. Deardorff JW (1972) Numerical investigation of neutral und unstable planetary boundary layer. J Atmos Sci. 29:91–115.Google Scholar
  26. DeBruin HAR (1983) A model for the Priestley–Taylor parameter α. J Climate Appl Meteorol. 22:572–578.Google Scholar
  27. DeBruin HAR and Holtslag AAM (1982) A simple parametrization of the surface fluxes of sensible and latent heat during daytime compared with the Penman–Monteith concept. J Climate Appl Meteorol. 21:1610–1621.Google Scholar
  28. Dommermuth H and Trampf W (1990) Die Verdunstung in der Bundesrepublik Deutschland, Zeitraum 1951-1980, Teil 1. Deutscher Wetterdienst, Offenbach, 10 pp.Google Scholar
  29. Doorenbos J and Pruitt WO (1977) Guidelines for predicting crop water requirements. FAO Irrigation Drainage Pap. 24, 2nd ed.:145 pp.Google Scholar
  30. DVWK (1996) Ermittlung der Verdunstung von Land- und Wasserflächen. DVWK-Merkblätter zur Wasserwirtschaft. 238:134 pp.Google Scholar
  31. Falge EM, Ryel RJ, Alsheimer M and Tenhunen JD (1997) Effects on stand structure and physiology on forest gas exchange: A simulation study for Norway spruce. Trees. 11:436–448.Google Scholar
  32. Farquhar GD, von Caemmerer S and Berry JA (1980) A biochemical of photosynthetic CO2 assimilation in leaves of C3 species. Planta. 149:78–90.Google Scholar
  33. Foken T (1978) The molecular temperature boundary layer of the atmosphere over various surfaces. Archiv Meteorol Geophys Bioklim, Ser. A. 27:59–67.Google Scholar
  34. Foken T (1984) The parametrisation of the energy exchange across the air-sea interface. Dynamics Atm Oceans. 8:297–305.Google Scholar
  35. Foken T (1986) An operational model of the energy exchange across the air-sea interface. Z Meteorol. 36:354–359.Google Scholar
  36. Foken T (1996) Turbulenzexperiment zur Untersuchung stabiler Schichtungen. Ber Polarforschung. 188:74–78.Google Scholar
  37. Foken T (2002) Some aspects of the viscous sublayer. Meteorol Z. 11:267–272.Google Scholar
  38. Foken T (2016) Angewandte Meteorologie. Springer-Spektrum, Berlin, Heidelberg, 394 pp.Google Scholar
  39. Foken T, Kitajgorodskij SA and Kuznecov OA (1978) On the dynamics of the molecular temperature boundary layer above the sea. Boundary-Layer Meteorol. 15:289–300.Google Scholar
  40. Foken T, Dlugi R and Kramm G (1995) On the determination of dry deposition and emission of gaseous compounds at the biosphere-atmosphere interface. Meteorol Z. 4:91–118.Google Scholar
  41. Friedrich K, Mölders N and Tetzlaff G (2000) On the influence of surface heterogeneity on the Bowen-ratio: A theoretical case study. Theor Appl Climat. 65:181–196.Google Scholar
  42. Garratt JR (1992) The Atmospheric Boundary Layer. Cambridge University Press, Cambridge, 316 pp.Google Scholar
  43. Geernaert GL (ed) (1999) Air-Sea Exchange: Physics, Chemistry and Dynamics. Kluwer Acad. Publ., Dordrecht, 578 pp.Google Scholar
  44. Göckede M and Foken T (2001) Ein weiterentwickeltes Holtslag-van Ulden-Schema zur Stabilitätsparametrisierung in der Bodenschicht. Österreichische Beiträge zu Meteorologie und Geophysik. 27:(Extended Abstract and pdf-file on CD) 210.Google Scholar
  45. Göckede M, Markkanen T, Mauder M, Arnold K, Leps JP and Foken T (2005) Validation of footprint models using natural tracer measurements from a field experiment. Agrical Forest Meteorol. 135:314–325.Google Scholar
  46. Grimmond CSB, King TS, Roth M and Oke TR (1998) Aerodynamic roughness of urban areas derived from wind observations. Boundary-Layer Meteorol. 89:1–24.Google Scholar
  47. Groß G (1993) Numerical Simulation of Canopy Flows. Springer, Berlin, Heidelberg pp.Google Scholar
  48. 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
  49. Gusev EM and Nasonova ON (2010) Modelirovanie teplo- i vlagoobmena poverchnosti sushi s atmosferoj (Modelling of the heat and moisture exchange of land surfaces with the atmosphere). Nauka, Moskva, 327 pp.Google Scholar
  50. 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
  51. Hasager CB and Jensen NO (1999) Surface-flux aggregation in heterogeneous terrain. Quart J Roy Meteorol Soc. 125:2075–2102.Google Scholar
  52. Hasager CB, Nielsen NW, Jensen NO, Boegh E, Christensen JH, Dellwik E and Soegaard H (2003) Effective roughness calculated from satellite-derived land cover maps and hedge-information used in a weather forecasting model. Boundary-Layer Meteorol. 109:227–254.Google Scholar
  53. Haude W (1955) Bestimmung der Verdunstung auf möglichst einfache Weise. Mitt Dt Wetterdienst. 11:24 pp.Google Scholar
  54. Herzog H-J, Vogel G and Schubert U (2002) LLM - a nonhydrostatic model applied to high-resolving simulation of turbulent fluxes over heterogeneous terrain. Theor Appl Climat. 73:67–86.Google Scholar
  55. Hess GD (2004) The neutral, barotropic planetary layer capped by a low-level inversion. Boundary-Layer Meteorol. 110:319–355.Google Scholar
  56. Hicks BB, Baldocchi DD, Meyers TP, Hosker jr. RP and Matt DR (1987) A preliminary multiple resistance routine for deriving dry deposition velocities from measured quantities. Water, Air and Soil Pollution. 36:311–330.Google Scholar
  57. Hillel D (1980) Applications of Soil Physics. Academic Press, New York, 385 pp.Google Scholar
  58. 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
  59. Holtslag AAM and van Ulden AP (1983) A simple scheme for daytime estimates of the surface fluxes from routine weather data. J Climate Appl Meteorol. 22:517–529.Google Scholar
  60. Houghton JT (2015) Global Warming, The complete Briefing. Cambridge University Press, Cambridge, 396 pp.Google Scholar
  61. Inclán MG, Forkel R, Dlugi R and Stull RB (1996) Application of transilient turbulent theory to study interactions between the atmospheric boundary layer and forest canopies. Boundary-Layer Meteorol. 79:315–344.Google Scholar
  62. Jacobs AFG, Heusinkveld BG and Nieveen JP (1998) Temperature behavior of a natural shallow water body during a summer periode. Theor Appl Climat. 59:121–127.Google Scholar
  63. Jacobson MZ (2005) Fundamentals of Atmospheric Modelling. Cambridge University Press, Cambridge, 813 pp.Google Scholar
  64. Jarvis PG (1976) The interpretation of the variations in leaf water potential and stomatal conductance found in canopies in the field. Phil Trans Roy. Soc London B: Biolog Sci. 273:593–610.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. Kanani-Sühring F and Raasch S (2015) Spatial variability of scalar concentrations and fluxes downstream of a clearing-to-forest transition: A Large-Eddy Simulation study. Boundary-Layer Meteorol. 155:1–27.Google Scholar
  67. Kantha LH and Clayson CA (2000) Small scale processes in geophysical fluid flows. Academic Press, San Diego, 883 pp.Google Scholar
  68. 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
  69. Klaassen W, van Breugel PB, Moors EJ and Nieveen JP (2002) Increased heat fluxes near a forest edge. Theor Appl Climat. 72:231–243.Google Scholar
  70. Kramm G and Foken T (1998) Ucertainty analysis on the evaporation at the sea surface. Second Study Conference on BALTEX, Juliusruh, 25–29 May 1998. BALTEX Secretariat, pp. 113–114.Google Scholar
  71. Kramm G, Foken T, Molders N, Muller H and Paw U KT (1996a) The sublayer-Stanton numbers of heat and matter for different types of natural surfaces. Contr Atmosph Phys. 69:417–430.Google Scholar
  72. Kramm G, Beier M, Foken T, Müller H, Schröder P and Seiler W (1996b) A SVAT-skime for NO, NO2, and O3 - Model description and test results. Meteorol Atmos Phys. 61:89–106.Google Scholar
  73. Kramm G, Dlugi R and Mölders N (2002) Sublayer-Stanton numbers of heat and matter for aerodynamically smooth surfaces: basic considerations and evaluations. Meteorol Atmos Phys. 79:173–194.Google Scholar
  74. Landau LD and Lifschitz EM (1987) Fluid Mechanics. Butterworth-Heinemann, Oxford, 539 pp.Google Scholar
  75. Leclerc MY and Foken T (2014) Footprints in Micrometeorology and Ecology. Springer, Heidelberg, New York, Dordrecht, London, XIX, 239 pp.Google Scholar
  76. Letzel MO, Krane M and Raasch S (2008) High resolution urban large-eddy simulation studies from street canyon to neighbourhood scale. Atmos Environm. 42:8770–8784.Google Scholar
  77. Leuning R (1995) A critical appraisal of a combined stomatal-photosynthesis model for C3 plants. Plant, Cell & Environment. 18:339–355.Google Scholar
  78. Lilly DK (1967) The representation of small-scale turbulence in numerical simulation experiments. In: Goldstein HH (ed). IBM Scientific Computing Symposium on Environmental Science, Yorktown Heights, N.Y., November 14-16, 1966 1967, pp. IBM Form No. 320-1951, 1195–1210.Google Scholar
  79. Louis JF (1979) A parametric model of vertical fluxes in the atmosphere. Boundary-Layer Meteorol. 17:187–202.Google Scholar
  80. Louis JF, Tiedtke M and Geleyn JF (1982) A short history of the PBL parametrization at ECMWF. Workshop on Boundary Layer parametrization, Reading1982. ECMWF, pp. 59–79.Google Scholar
  81. Lüers J and Bareiss J (2010) The effect of misleading surface temperature estimations on the sensible heat fluxes at a high Arctic site – the Arctic Turbulence Experiment 2006 on Svalbard (ARCTEX-2006). Atmos Chem Phys. 10:157–168.Google Scholar
  82. Mahrt L (1996) The bulk aerodynamic formulation over heterogeneous surfaces. Boundary-Layer Meteorol. 78:87–119.Google Scholar
  83. Mallick K, Boegh E, Trebs I, Alfieri JG, Kustas WP, Prueger JH, Niyogi D, Das N, Drewry DT, Hoffmann L and Jarvis AJ (2015) Reintroducing radiometric surface temperature into the Penman–Monteith formulation. Water Resources Res. 51:6214–6243.Google Scholar
  84. Mangarella PA, Chambers AJ, Street RL and Hsu EY (1972) Laboratory and field interfacial energy and mass flux and prediction equations. J Geophys Res. 77:5870–5875.Google Scholar
  85. Mangarella PA, Chambers AJ, Street RL and Hsu EY (1973) Laboratory studies of evaporation and energy transfer through a wavy air-water interface. J. Phys. Oceanogr. 3:93–101.Google Scholar
  86. Mengelkamp H-T, Warrach K and Raschke E (1999) SEWAB a parameterization of the surface energy and water balance for atmospheric and hydrologic models. Adv Water Res. 23:165–175.Google Scholar
  87. Meyers TP and Paw U KT (1986) Testing a higher-order closure model for modelling airflow within and above plant canopies. Boundary-Layer Meteorol. 37:297–311.Google Scholar
  88. Meyers TP and Paw U KT (1987) Modelling the plant canopy microenvironment with higher-order closure principles. Agrical Forest Meteorol. 41:143–163.Google Scholar
  89. Mix W, Goldberg V and Bernhardt K-H (1994) Numerical experiments with different approaches for boundary layer modelling under large-area forest canopy conditions. Meteorol Z. 3:187–192.Google Scholar
  90. Moene AF and van Dam JC (2014) Transport in the Atmosphere-Vegetation-Soil Continuum. Cambridge University Press, Cambridge, 436 pp.Google Scholar
  91. Moeng C-H (1998) Large eddy simulation of atmospheric boundary layers. In: Holtslag AAM and Duynkerke PG (eds.), Clear and cloudy boundary layers, vol VNE 48. Royal Netherlands Academy of Arts and Science, Amsterdam, 67–83.Google Scholar
  92. Moeng C-H and Wyngaard JC (1989) Evaluation of turbulent transport and dissipation closure in second-order modelling. J Atmos Sci. 46:2311–2330.Google Scholar
  93. Moeng C-H, Sullivan PP and Stevens B (2004) Large-eddy simulation of cloud-topped mixed layers. In: Fedorovich Eet al (eds.), Atmospheric Turbulence and mesoscale Meteorology. Cambridge University Press, Cambridge, 95–114.Google Scholar
  94. Mölders N (2001) Concepts for coupling hydrological and meteorological models. Wiss. Mitt. aus dem Inst. für Meteorol. der Univ. Leipzig und dem Institut für Troposphärenforschung e. V. Leipzig. 22:1–15.Google Scholar
  95. Mölders N (2012) Land-Use and Land-Cover Changes, Impact on climate and air quality. Springer, Dordrecht, Heidelberg, London, New York, 189 pp.Google Scholar
  96. Mölders N and Kramm G (2014) Lectures in Meteorology. Springer, Cham Heidelberg New York Dordrecht London XIX, 591 pp.Google Scholar
  97. Mölders N, Raabe A and Tetzlaff G (1996) A comparison of two strategies on land surface heterogeneity used in a mesoscale ß meteorological model. Tellus. 48A:733–749.Google Scholar
  98. Monson R and Baldocchi D (2014) Terrestrial Biosphere-Atmosphere Fluxes. Cambridge University Press, New York, XXI, 487 pp.Google Scholar
  99. Monteith JL (1965) Evaporation and environment. Symp Soc Exp Biol. 19:205–234.Google Scholar
  100. Montgomery RB (1940) Observations of vertical humidity distribution above the ocean surface and their relation to evaporation. Pap Phys Oceanogr Meteorol. 7:1–30.Google Scholar
  101. Müller C (1999) Modelling Soil-Biosphere Interaction. CABI Publishing, Wallingford, 354 pp.Google Scholar
  102. Ohmura A, Steffen K, Blatter H, Greuell W, Rotach M, Stober M, Konzelmann T, Forrer J, Abe-Ouchi A, Steiger D and Neiderbäumer G (1992) Greenland Expedition, Progress Report No. 2, April 1991 to Oktober 1992. Swiss Federal Institute of Technology, Zürich, 94 pp.Google Scholar
  103. Owen PR and Thomson WR (1963) Heat transfer across rough surfaces. J Fluid Mech. 15:321–334.Google Scholar
  104. Panin GN (1985) Teplo- i massomen meszdu vodoemom i atmospheroj v estestvennych uslovijach (Heat- and mass exchange between the water and the atmosphere in the nature). Nauka, Moscow, 206 pp.Google Scholar
  105. Panin GN, Nasonov AE and Souchintsev MG (1996a) Measurements and estimation of energy and mass exchange over a shallow see. In: Donelan M (ed.), The air-sea interface, Miami, 489–494.Google Scholar
  106. Panin GN, Tetzlaff G, Raabe A, Schönfeld H-J and Nasonov AE (1996b) Inhomogeneity of the land surface and the parametrization of surface fluxes - a discussion. Wiss Mitt Inst Meteorol Univ Leipzig und Inst Troposphärenforschung Leipzig. 4:204–215.Google Scholar
  107. Panin GN, Nasonov AE, Foken T and Lohse H (2006) On the parameterization of evaporation and sensible heat exchange for shallow lakes. Theor Appl Climat. 85:123–129.Google Scholar
  108. Panofsky HA (1973) Tower micrometeorology. In: Haugen DA (ed.), Workshop on Micrometeorology. American Meteorological Society, Boston, 151–176.Google Scholar
  109. 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
  110. Penman HL (1948) Natural evaporation from open water, bare soil and grass. Proceedings Royal Society London. A193:120–195.Google Scholar
  111. Priestley CHB and Taylor JR (1972) On the assessment of surface heat flux and evaporation using large-scale parameters. Monthly Weather Review. 100:81–92.Google Scholar
  112. Pyles RD, Weare BC and Paw U KT (2000) The UCD Advanced Canopy-Atmosphere-Soil Algorithm: comparisons with observations from different climate and vegetation regimes. Quart J Roy Meteorol Soc. 126:2951–2980.Google Scholar
  113. Raasch S and Schröter M (2001) PALM - A large-eddy simulation model performing on massively parallel computers. Meteorol Z. 10:363–372.Google Scholar
  114. Reichardt H (1951) Vollständige Darstellung der turbulenten Geschwindigkeitsverteilung in glatten Röhren. Z angew Math Mech. 31:208–219.Google Scholar
  115. Richter D (1977) Zur einheitlichen Berechnung der Wassertemperatur und der Verdunstung von freien Wasserflächen auf statistischer Grundlage. Abh Meteorol Dienstes DDR. 119:35 pp.Google Scholar
  116. Rigby JR, Yin J, Albertson J and Porporato A (2015) Approximate Analytical Solution to Diurnal Atmospheric Boundary-Layer Growth Under Well-Watered Conditions. Boundary-Layer Meteorol. 156:73–89.Google Scholar
  117. Roll HU (1948) Wassernahes Windprofil und Wellen auf dem Wattenmeer. Ann Meteorol. 1:139–151.Google Scholar
  118. Rutgersson A and Sullivan PP (2005) Investigating the effects of water waves on the turbulence structure in the atmosphere using direct numerical simulations. Dynamics Atm Oceans. 38:147–171.Google Scholar
  119. Schädler G, Kalthoff N and Fiedler F (1990) Validation of a model for heat, mass and momentum exchange over vegetated surfaces using LOTREX-10E/HIBE88 data. Contr Atmosph Phys. 63:85–100.Google Scholar
  120. Schlegel F, Stiller J, Bienert A, Maas H-G, Queck R and Bernhofer C (2015) Large-Eddy Simulation study of the effects on flow of a heterogeneous forest at sub-tree resolution. Boundary-Layer Meteorol. 154:27–56.Google Scholar
  121. Schlichting H and Gersten K (2006) Grenzschicht-Theorie. Springer, Berlin, Heidelberg, 799 pp.Google Scholar
  122. Schmid HP and Bünzli D (1995a) The influence of the surface texture on the effective roughness length. Quart J Roy Meteorol Soc. 121:1–21.Google Scholar
  123. Schmid HP and Bünzli D (1995b) Reply to comments by E. M. Blyth on ‘The influence of surface texture on the effective roughness length’. Quart J Roy Meteorol Soc. 121:1173–1176.Google Scholar
  124. Schmidt H and Schumann U (1989) Coherent structures of the convective boundary layer derived from large eddy simulations. J Fluid Mech. 200:511–562.Google Scholar
  125. Schrödter H (1985) Verdunstung, Anwendungsorientierte Meßverfahren und Bestimmungsmethoden. Springer, Berlin, Heidelberg, 186 pp.Google Scholar
  126. Schumann U (1989) Large-eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmos Environm. 23:1713–1727.Google Scholar
  127. 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
  128. Sellers PJ and Dorman JL (1987) Testing the simple biospere model (SiB) for use in general circulation models. J Climate Appl Meteorol. 26:622–651.Google Scholar
  129. Shukauskas A and Schlantschiauskas A (1973) Teploodatscha v turbulentnom potoke shidkosti (Heat exchange in the turbulent fluid). Izd. Mintis, Vil’njus, 327 pp.Google Scholar
  130. Smagorinsky J (1963) General circulation experiments with the primitive equations: I. The basic experiment. Monthly Weather Review. 91:99–164.Google Scholar
  131. Smith SD, Fairall CW, Geernaert GL and Hasse L (1996) Air-sea fluxes: 25 years of progress. Boundary-Layer Meteorol. 78:247–290.Google Scholar
  132. Sodemann H and Foken T (2004) Empirical evaluation of an extended similarity theory for the stably stratified atmospheric surface layer. Quart J Roy Meteorol Soc. 130:2665–2671.Google Scholar
  133. Sponagel H (1980) Zur Bestimmung der realen Evapotranspiration landwirtschaftlicher Kulturpflanzen. Geologisches Jahrbuch. F9:87 pp.Google Scholar
  134. Staudt K, Serafimovich A, Siebicke L, Pyles RD and Falge E (2011) Vertical structure of evapotranspiration at a forest site (a case study). Agrical Forest Meteorol. 151:709–729.Google Scholar
  135. Stull RB (1988) An Introduction to Boundary Layer Meteorology. Kluwer Acad. Publ., Dordrecht, Boston, London, 666 pp.Google Scholar
  136. Stull R and Santoso E (2000) Convective transport theory and counter-difference fluxes. 14th Symposium on Boundary Layer and Turbulence, Aspen, CO., 7.-11. Aug. 2000. Am. Meteorol. Soc., Boston, pp. 112–113.Google Scholar
  137. Sverdrup HU (1937/38) On the evaporation from the ocean. J. Marine Res. 1:3–14.Google Scholar
  138. Taylor PA (1987) Comments and further analysis on the effective roughness length for use in numerical three-dimensional models: A research note. Boundary-Layer Meteorol. 39:403–418.Google Scholar
  139. Tennekes H (1973) A Model for the Dynamics of the Inversion Above a Convective Boundary Layer. J Atmos Sci. 30:558–567.Google Scholar
  140. Troen I and Lundtang Peterson E (1989) European Wind Atlas. Risø National Laboratory, Roskilde, 656 pp.Google Scholar
  141. Turc L (1961) Évaluation des besoins en eau d’irrigation évapotranspiration potentielle. Ann Agron. 12:13–49.Google Scholar
  142. van Bavel CHM (1986) Potential evapotranspiration: The combination concept and its experimental verification. Water Resources Res. 2:455–467.Google Scholar
  143. Vollmer L, van Dooren M, Trabucchi D, Schneemann J, Steinfeld G, Witha B, Trujillo J and Kühn M (2015) First comparison of LES of an offshore wind turbine wake with dual-Doppler lidar measurements in a German offshore wind farm. J Phys: Conf Ser. 625:012001.Google Scholar
  144. von Kármán T (1934) Turbulence and skin friction. J. Aeronautic Sci. 1:1–20.Google Scholar
  145. Wendling U, Schellin H-G and Thomä M (1991) Bereitstellung von täglichen Informationen zum Wasserhaushalt des Bodens für die Zwecke der agrarmeteorologischen Beratung. Z Meteorol. 41:468–475.Google Scholar
  146. Yokoyama O, Gamo M and Yamamoto S (1979) The vertical profiles of the turbulent quantities in the atmospheric boundary layer. J Meteor Soc Japan. 57:264–272.Google Scholar
  147. Zilitinkevich SS and Calanca P (2000) An extended similarity theory for the stably stratified atmospheric surface layer. Quart J Roy Meteorol Soc. 126:1913–1923.Google Scholar
  148. Zilitinkevich SS and Esau IN (2005) Resistance and heat transfer laws for stable and neutral planetary layers: Old theory advanced and re-evaluated. Quart J Roy Meteorol Soc. 131:1863–1892.Google Scholar
  149. Zilitinkevich SS and Mironov DV (1996) A multi-limit formulation for the equilibrium depth of a stable stratified atmospheric surface layer. Boundary-Layer Meteorol. 81:325–351.Google Scholar
  150. 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

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

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

Personalised recommendations