Boundary-Layer Meteorology

, Volume 16, Issue 2, pp 155–167 | Cite as

Theoretical studies of the parameterization of the non-neutral surface boundary layer

Part I: governing physical concepts
  • Fritz Herbet
  • Walter-Georg Panhans


The parameterization of the non-neutral atmospheric surface layer has been reexamined using the basic principles of small-scale energetics and thermodynamics. On the basis of this more complete treatment, theK-parameterization has been reformulated. It is found that the linear regression laws between fluxes and driving gradient forces of the turbulent heat and humidity exchanges in the surface layer can be derived in a much more comprehensive manner than by using the commonly used K-theory.

With respect to stationary conditions and in the context of similarity concepts, a system of algebraic equations has been formulated which provides reasonable estimates of the distributions of the dimension less rates of viscous energy dissipation as well as turbulent kinetic and thermal-diffusive energy transport as functions of the variablez/L. Quantitative calculations have been performed using the scaling height formulations of Takeuchi and Yokoyama, Prandtl, and von Kârmân as closure conditions of the equations.


Boundary Layer Surface Layer Energy Dissipation Surface Boundary Closure Condition 
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List of Symbols

û = (û,\(\hat v\), ŵ)

wind speed vector

ûh = (û,\(\hat v\))

horizontal wind speed vector


vertical wind speed

u″, u″h, w″

turbulent deviations of û, û h ŵ


internal energy (per unit mass)

\(\hat k\)

eddy-kinetic energy (per unit mass)

\(\bar p\)


\(\bar \rho \), ρ

density (of the total system)


density of dry air


characteristic density, e.g. =p0/{R a [1 + (Rν/R a − 1)mν0]T0}

\(\bar T\),T

temperature [K]

\(\bar \theta \), Θ

potential temperature [K]

\(\hat m\)ν,mν

vapor mass fraction (specific humidity)


water vapor, dry air gas constants


specific heat of dry air at constant pressure


fixed pressure-value (e.g. 1000 mb)

\(\bar \pi = (\bar p/p_o )^{R_a /c_{p_a } } \)T0,mν0

temperature, humidity corresponding top0


earth-gravity acceleration


von Kármán factor


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  1. Businger, J. A., Wyngaard, J. C., Izumi, Y., and Bradley, E. F.: 1971, ‘Flux Profile Relationships in the Atmospheric Surface Layer’,J. Atmos. Sci. 28, 181–189.Google Scholar
  2. Clarke, R. H.: 1970, ‘Recommended Methods for the Treatment of the Boundary Layer in Numerical Models’,Austr. Meteorol. Mag. 18, 51–73.Google Scholar
  3. De Groot, S. R. and Mazur, P.: 1969, ‘Non-equilibrium Thermodynamics’, North-Holland Publishing Company, 510 pp.Google Scholar
  4. Delsol, F., Miyakoda, K., and Clarke, R. H.: 1971, ‘Parameterized Processes in the Surface Boundary Layer of an Atmospheric Circulation Model’,Quart. J. Roy. Meteorol. Soc. 97, 181–208.CrossRefGoogle Scholar
  5. Estoque, M. A.: 1963, ‘A Numerical Model of the Atmospheric Boundary Layer’,J. Geophys. Res. 68, 1103–1113Google Scholar
  6. Fortak, H.: 1969, ‘Zur Energetik der Planetarischen Grenzschicht’,Ann. Met. (Neue Folge) 4, 157–162.Google Scholar
  7. Gyarmati, I.: 1970,Non-equilibrium Thermodynamics, Science Library, Springer, 184 pp.Google Scholar
  8. Herbert, F.: 1975, ‘Irreversible Prozesse in der Atmosphäre — Teil 3’,Contr. Atm. Phys. 48, 1–29.Google Scholar
  9. Lumley, J. L., Panofsky, H. A.: 1964,The Structure of Atmospheric Turbulence, Interscience, 239 pp.Google Scholar
  10. Pandolfo, J. P.: 1966, ‘Wind and Temperature Profiles for Constant Flux Boundary Layer’,J. Atm. Sc. 23, 495–502.Google Scholar
  11. Takeuchi, K. and Yokoyama, O.: 1963, ‘The scale of Turbulence and the Wind Profile in the Surface Boundary Layer’,J. Meteorol. Soc. Japan, Ser. II,41, 108–117.Google Scholar
  12. van Mieghem, J.: 1973, ‘Atmospheric Energetics’, Clarendon Press (Oxford) 306 pp.Google Scholar
  13. Weisman, R. N.: 1975, ‘A Developing Boundary Layer Over an Evaporating Surface’,Boundary Layer Metereol. 8, 437–445.Google Scholar
  14. Wyngaard, J. G. and Coté, O. R.: 1971, ‘The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’,J. Atmos. Sci. 28, 190–201.Google Scholar
  15. Zilitinkevich, S. S.: 1966, ‘Effects of Humidity Stratification on Hydrostatic Stability’,Izv. ANSSR, Atm. and oc. Phys. 655–658.Google Scholar

Copyright information

© D. Reidel Publishing Company 1979

Authors and Affiliations

  • Fritz Herbet
    • 1
  • Walter-Georg Panhans
    • 2
  1. 1.Eidgenössische Technische Hochschule, Atmosphärenphysik ETHZürichSwitzerland
  2. 2.Zentralamt des Deutschen WetterdienstesOffenbachFRG

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