Numerical modeling of heat and water vapor transport through the interfacial boundary layer into a turbulent atmosphere

  • A. S. M. Gieske
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 11)


A stochastic numerical model is developed to simulate heat and water vapor transfer from a rough surface through a boundary layer into the fully turbulent atmosphere. The so-called interfacial boundary layer is conceptualized as a semi-stagnant layer of air in the roughness cavities at the surface into which the smallest eddies penetrate to random approach distances and with random inter-arrival times, carrying away energy, molecules, or any other scalar admixture. The model makes use of the one-dimensional transient heat conduction equation where the boundary conditions are updated in time and space by random deviates from a general gamma distribution. The one-dimensional transfer equation is solved by the implicit finite difference method which allows conversion to a standard tridiagonal matrix equation.


Friction Velocity Roughness Length Heat Conduction Equation Turbulent Atmosphere Water Vapor Transport 
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  1. [1]
    Brutsaert W (1975) A theory for local evaporation from rough and smooth surfaces at ground level, Water Resour Res 11(4): 543–550Google Scholar
  2. [2]
    Brutsaert W (1979) Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness, Bnd-Layer Met. 16:365–388CrossRefGoogle Scholar
  3. [3]
    Brutsaert W (1982) Evaporation into the atmosphere. Reidel Pub Co, Dordrecht, The NetherlandsGoogle Scholar
  4. [4]
    Brutsaert W (1965) A model for evaporation as a molecular diffusion process into a turbulent atmosphere. J Geophys Res 70(20): 5017–5024Google Scholar
  5. [5]
    Harriott P (1962a) A random eddy modification of the penetration theory. Chemical Engineering Science 17:149–154.CrossRefGoogle Scholar
  6. [6]
    Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number. J Fluid Mech 13:82–85CrossRefGoogle Scholar
  7. [7]
    Obukhov AM (1971) Turbulence in an atmosphere with a non-uniform temperature. Bnd-Layer Met. 2:7–29CrossRefGoogle Scholar
  8. [8]
    Kays WM, Crawford ME (1993) Convective heat and mass transfer. McGraw-Hill, USAGoogle Scholar
  9. [9]
    Carslaw HS, Jaeger JC (1986) Conduction of Heat in Solids. Oxford University Press, UKGoogle Scholar
  10. [10]
    Trombetti F, Caporaloni M, Tampieri F (1978) Bulk transfer velocity to and from natural and artificial surfaces. Bnd-Layer Met. 14: 585–595CrossRefGoogle Scholar
  11. [11]
    Kustas WP, Humes KS, Norman JM, Moran MS (1996) Single-and Dual-Source Modeling of Energy Fluxes with Radiometric Surface Temperature. J Appl Meteor 35: 110–121CrossRefGoogle Scholar
  12. [12]
    Su Z (2005) Estimation of the surface energy balance. In: Encyclopedia of hydrological sciences: 5 Volumes. / ed. by M.G. Anderson and J.J. McDonnell. Chichester Wiley & Sons 2:731–752Google Scholar
  13. [13]
    Harriott P (1962b) A review of Mass Transfer to Interfaces. Can J Chem Eng 4:60–69Google Scholar
  14. [14]
    Thomas LC, Fan LT (1971) Adaptation of the surface rejuvenation model to turbulent heat and mass transfer at a solid-fluid interface. Ind Eng Chem Fundam 10(1): 135–139CrossRefGoogle Scholar
  15. [15]
    Wang HF, Anderson MP (1982) Introduction to Groundwater Modeling, Finite Difference and Finite Element Methods. W.H. Freeman and Company. San Francisco, USAGoogle Scholar
  16. [16]
    Press WH, Flannery BP, Teukolsky SA, Vetterling WT (1986) Numerical Recipes, The Art of Scientific Computing. Cambridge University PressGoogle Scholar
  17. [17]
    Crago R, Hervol N, Crowley R (2005) A complementary evaporation approach to the scalar roughness length. Water Res. Res. 41: W06117CrossRefGoogle Scholar
  18. [18]
    Verhoef A, De Bruin HAR, Van den Hurk BJJM (1997) Some practical notes on the parameter kB-1 for sparse vegetation. J Appl Met 36: 560CrossRefGoogle Scholar
  19. [19]
    Bird RB, Stewart WE, Lightfoot EN (1960) Transport Phenomena. Wiley and Sons, USAGoogle Scholar
  20. [20]
    Owen PR, Thomson WR (1962) Heat transfer across rough surfaces. Journal Fluid Mech 15: 321–334CrossRefGoogle Scholar
  21. [21]
    Chamberlain (1968) Transport of gases to and from surfaces with bluff and wave-like roughness elements. Quart J. Royal Met Soc 94: 318–332CrossRefGoogle Scholar
  22. [22]
    Dipprey DF, Sabersky RH (1963) Heat and momentum transfer in smooth and rough tubes at various Prandtl numbers. Int Journal Heat Mass Transfer 6:329–353CrossRefGoogle Scholar

Copyright information

© Springer 2007

Authors and Affiliations

  • A. S. M. Gieske
    • 1
  1. 1.Water Resources DivisionInternational Institute for Geo-Information Science and Earth Observation (ITC)EnschedeThe Netherlands

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