Boundary-Layer Meteorology

, Volume 96, Issue 1–2, pp 107–142 | Cite as

Equilibrium Evaporation and the Convective Boundary Layer

  • M. R. Raupach

Abstract

A theory is developed for surface energy exchanges in well-mixed, partlyopen systems, embracing fully open and fully closed systems as limits.Conservation equations for entropy and water vapour are converted intoan exact rate equation for the potential saturation deficit D in a well-mixed, partly open region. The main contributions to changes in D arise from (1) the flux of D at the surface, dependent on a conductance gq that is a weighted sum of the bulk aerodynamic and surface conductances; and (2) the ‘exchange’ flux of D with the external environment by entrainment or advection, dependent on a conductance ge that is identifiable with the entrainment velocity when the partly open region is a growing convective boundary layer (CBL). The system is fully open when ge/gq → ∞, and fully closed when ge/gq → 0. The equations determine the steady state surface energy balance (SEB) in a partly open system, the associated steady-state deficit, and the settling time scale needed to reach the steady state. The general result for the steady-state SEB corresponds to the equations of conventional combination theory for the SEB of a vegetated surface, with the surface-layer deficit replaced by the external deficit and with gq replaced by the series sum (gq-1 + ge-1)-1. In the fully open limit D is entirely externally prescribed, while in the fully closed limit, D is internally determined and the SEB approaches thermodynamic equilibrium energy partition. In the case of the CBL, the conductances gq and ge are themselves functions of D through short-term feedbacks, induced by entrainment in the case of ge and by both physiological and aerodynamic (thermal stability) processes in the case of gq. The effects of these feedbacks are evaluated. It is found that a steady-state CBL is physically achievable only over surfaces with at least moderate moisture availability; that entrainment has a significant accelerating effect on equilibration; that the settling time scale is well approximated by h/(gq + ge), where h is the CBL depth; and that this scale is short enough to allow a steady state to evolve within a semi-diurnal time scale only when h is around 500 m or less.

Equilibrium evaporation Equilibrium energy partition Convective boundary layer Combination equation Penman–Monteith equation 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ayotte, K. W., Sullivan, P. P., Andren, S. C., Doney, S. C., Holtslag, A. A. M., Large, W. G., McWilliams, J. C., Moeng, C.-H., Otte, M. J., Tribbia, J. J., and Wyngaard, J. C.: 1996, 'An Evaluation of Neutral and Convective Planetary Boundary Layer Parameterizations Relevant to Large Eddy Simulations', Boundary-Layer Meteorol. 79, 131–175.Google Scholar
  2. Ball, F. K.: 1960, 'Control of Inversion Height by Surface Heating', Quart. J. Roy. Meteorol. Soc. 86, 483–494.Google Scholar
  3. Betts, A. K.: 1973, 'Non-Precipitating Cumulus Convection and its Parameterisation', Quart. J. Roy. Meteorol. Soc. 99, 178–196.Google Scholar
  4. Betts, A. K.: 1992, 'FIFE Atmospheric Boundary Layer Budget Methods', J. Geophys. Res. 97, 18523–18531.Google Scholar
  5. Betts, A. K.: 1994, 'Relation between Equilibrium Evaporation and the Saturation Pressure Budget', Boundary-Layer Meteorol. 71, 235–245.Google Scholar
  6. Carson, D. J.: 1973, 'The Development of a Dry Inversion-Capped Convectively Unstable Boundary Layer', Quart. J. Roy. Meteorol. Soc. 99, 450–467.Google Scholar
  7. Culf, A. D.: 1994, Equilibrium Evaporation beneath a Growing Convective Boundary Layer', Boundary-Layer Meteorol. 70, 37–49.Google Scholar
  8. de Bruin, H. A. R.: 1983, 'A Model for the Priestley-Taylor Parameter α. J. Clim. Appl. Meteorol. 22, 572–578.Google Scholar
  9. de Bruin, H. A. R. and Jacobs, C. M. J.: 1993, 'Impact of CO2 on the Regional Evapotranspiration of Agro-Ecosystems: A Theoretical and Numerical Modelling Study', Vegetatio 104/105, 307–318.Google Scholar
  10. Drazin, P. G.: 1992, Nonlinear Systems, Cambridge University Press, Cambridge, U.K., 317 pp.Google Scholar
  11. Driedonks, A. G. M.: 1982a, 'Sensitivity Analysis of the Equations for a Convective Mixed Layer', Boundary-Layer Meteorol. 22, 475–480.Google Scholar
  12. Driedonks, A. G.M.: 1982b, 'Models and Observations of the Growth of the Atmospheric Boundary Layer', Boundary-Layer Meteorol. 23, 283–306.Google Scholar
  13. Hutjes, R. W. A., Kabat, P., Running, S. W., Shuttleworth, W.J., Field, C. B., Bass, B., Assunçao da Silva Dias, M., Avissar, R., Becker, A., Claussen, M., Dolman, A. J., Feddes, R. A., Fosberg, M., Fukushima, Y., Gash, J. H. C., Guenni, L., Hoff, H., Jarvis, P. G., Kayane, I., Krenke, A. N., Liu, Changming, Meybeck, M., Nobre, C. A., Oyebande, L., Pitman, A., Pielke, R. A., Raupach, M. R., Saugier, B., Schulze, E. D., Sellers, P. J., Tenhunen, J. D., Valentini, R., Victoria, R. L., and Vörösmarty, C. J.: 1998, 'Biospheric Aspects of the Hydrological Cycle', J. Hydrol. 213, 1–21.Google Scholar
  14. Jacobs, C. M. J. and de Bruin, H. A. R.: 1992, 'The Sensitivity of Regional Transpiration to Land-Surface Charactereistics: Significance of Feedback', J. Climate 5, 683–698.Google Scholar
  15. Jacobs, C. M. J. and de Bruin, H. A. R.: 1997, 'Predicting Regional Transpiration at Elevated Atmospheric CO2: Influence of the PBL-Vegetation Interaction', J. Appl. Meteorol. 36, 1663–1675.Google Scholar
  16. Leuning, R.: 1995, 'A Critical Appraisal of a Combined Stomatal-Photosynthesis Model for C3 Plants', Plant Cell Environ. 18, 339–355.Google Scholar
  17. McNaughton, K. G.: 1976a, 'Evaporation and Advection I: Evaporation from Extensive Homogeneous Surfaces', Quart. J. Roy. Meteorol. Soc. 102, 181–191.Google Scholar
  18. McNaughton, K. G.: 1976b, 'Evaporation and Advection II: Evaporation Downwind of a Boundary Separating Regions Having Different Surface Resistances and Available Energies', Quart. J. Roy. Meteorol. Soc. 102, 193–202.Google Scholar
  19. McNaughton, K. G. and Jarvis, P. G.: 1983, 'Predicting the Effects of Vegetation Changes on Transpiration and Evaporation', in T. T. Kozlowski (ed.), Water Deficits and Plant Growth, Vol. VII, Academic Press, New York, pp. 1–47.Google Scholar
  20. McNaughton, K. G. and Spriggs, T. W.: 1986, 'A 'Mixed-Layer Model for Regional Evaporation', Boundary-Layer Meteorol. 34, 243–262.Google Scholar
  21. McNaughton, K. G. and Spriggs, T. W.: 1989, 'An Evaluation of the Priestley and Taylor Equation and the Complementary Relationship Using Results from a Mixed-Layer Model of the Convective Boundary Layer', in T. A. Black, D. L. Spittlehouse, M. D. Novak, and D. T. Price (eds.), Estimation of Areal Evapotranspiration, IAHS Press, Wallingford, U.K. IAHS Publication No. 177, pp. 89–104.Google Scholar
  22. McNaughton, K. G. and Raupach, M. R.: 1996, 'Responses of the Convective Boundary Layer and the Surface Energy Balance to Large-Scale Heterogeneity', in J. B. Stewart, E. T. Engman, R. A. Feddes, and Y. Kerr (eds.), Scaling Up in Hydrology Using Remote Sensing, Wiley, Chichester, U.K., pp. 171–182.Google Scholar
  23. Mellor, G. L. and Yamada, T.: 1982, 'Development of a Turbulence Closure Model for Geophysical Fluid Problems', Rev. Geophys. Space Phys. 20, 851–875.Google Scholar
  24. Moeng, C-H.: 1984, 'A Large-Eddy-Simulation Model for the Study of Planetary Boundary-Layer Turbulence', J. Atmos. Sci. 41, 2052–2062.Google Scholar
  25. Monteith, J. L.: 1995, 'Accommodation between Transpiring Vegetation and the Convective Boundary Layer', J. Hydrol. 166, 251–263.Google Scholar
  26. Perrier, A.: 1980, 'Etude micro-climatique des relations entre les propriétés de surface et les caractéristiques de l'air: Application aux échanges régionaux', Météor Environ., EVRY, France.Google Scholar
  27. Pielke, R. A.: 1984, Mesoscale Meteorological Modeling, Academic Press, San Diego. 612 pp.Google Scholar
  28. Pielke, R. A., Avissar, R., Raupach, M. R., Dolman, H., Zeng, X., and Denning, S.: 1998, 'Interactions between the Atmosphere and Terrestrial Ecosystems: Influence on Weather and Climate', Global Change Biol. 4, 461–475.Google Scholar
  29. Priestley, C. H. B. and Taylor, R. J.: 1972, 'On the Assessment of Surface Heat Flux and Evaporation using Large-Scale Parameters', Mon. Wea. Rev. 100, 81–92.Google Scholar
  30. Raupach, M. R.: 1991, 'Vegetation-Atmosphere Interaction in Homogeneous and Heterogeneous Terrain: Some Implications of Mixed-Layer Dynamics', Vegetatio 91, 105–120.Google Scholar
  31. Raupach, M. R.: 1998, 'Radiative, Physiological, Aerodynamic and Boundary-Layer Feedbacks on the Terrestrial Surface Energy Balance', Global Change Biol. 4, 477–494.Google Scholar
  32. Raupach, M. R. and Finnigan, J. J.: 1995, 'Scale Issues in Boundary Layer Meteorology: Surface Energy Balances in Heterogeneous Terrain', Hydrol. Processes 9, 589–612.Google Scholar
  33. Raupach, M. R., Baldocchi, D. D., Bolle, H.-J., Dümenil, L., Eugster, W., Meixner, F. X., Olejnik, J. A., Pielke, R. A., Tenhunen, J. D., and Valentini, R.: 1999, 'How Is the Atmospheric Coupling of Land Surfaces Affected by Topography, Complexity in Landscape Patterning, and the Vegetation mosaic?', in J. D. Tenhunen and P. Kabat (eds.), Integrating Hydrology, Ecosystem Dynamics and Biogeochemistry in Complex Landscapes, Dahlem Workshop No. 82, pp. 177–196.Google Scholar
  34. Rayner, K. N. and Watson, I. D.: 1991, 'Operational Prediction of Daytime Mixed-Layer Heights for Dispersion Modelling', Atmos. Environ. 25A, 1427–1436.Google Scholar
  35. Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, Kluwer Academic Publishers, Dordrecht, 666 pp.Google Scholar
  36. Tennekes, H.: 1973, 'A Model for the Dynamics of the Inversion above a Convective Boundary Layer', J. Atmos. Sci. 30, 558–567.Google Scholar
  37. Troen, I. and Mahrt, L.: 1986, 'A Simple Model of the Atmospheric Boundary Layer: Sensitivity to Surface Evaporation', Boundary-Layer Meteorol. 37, 129–148.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • M. R. Raupach
    • 1
  1. 1.CSIRO Land and WaterCanberraAustralia

Personalised recommendations