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Boundary-Layer Meteorology

, Volume 38, Issue 1–2, pp 159–184 | Cite as

A theory for the scalar roughness and the scalar transfer coefficients over snow and sea ice

  • Edgar L. Andreas
Article

Abstract

Although the bulk aerodynamic transfer coefficients for sensible (C H ) and latent (C E ) heat over snow and sea ice surfaces are necessary for accurately modeling the surface energy budget, they have been measured rarely. This paper, therefore, presents a theoretical model that predicts neutral-stability values of C H and C E as functions of the wind speed and a surface roughness parameter. The crux of the model is establishing the interfacial sublayer profiles of the scalars, temperature and water vapor, over aerodynamically smooth and rough surfaces on the basis of a surface-renewal model in which turbulent eddies continually scour the surface, transferring scalar contaminants across the interface by molecular diffusion. Matching these interfacial sublayer profiles with the semi-logarithmic inertial sublayer profiles yields the roughness lengths for temperature and water vapor. When coupled with a model for the drag coefficient over snow and sea ice based on actual measurements, these roughness lengths lead to the transfer coefficients. C E is always a few percent larger than CH. Both decrease monotonically with increasing wind speed for speeds above 1 m s−1, and both increase at all wind speeds as the surface gets rougher. Both, nevertheless, are almost always between 1.0 × 10−3 and 1.5 × 10−3.

Keywords

Wind Speed Water Vapor Transfer Coefficient Drag Coefficient Energy Budget 
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.

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Reference

  1. Abramowitz, M. and Stegun, I. A. (eds.): 1965, Handbook of Mathematical Functions, Dover, New York, 1046 pp.Google Scholar
  2. Andreas, E. L.: 1986, ‘A New Method of Measuring the Snow-Surface Temperature’, Cold Regions Sci. Technol. 12, 139–156.Google Scholar
  3. Andreas, E. L. and Murphy, B.: 1986, ‘Bulk Transfer Coefficients for Heat and Momentum over Leads and Polynyas’, J. Phys. Oceanogr., in press.Google Scholar
  4. Arya, S. P. S.: 1973, ‘Contribution of Form Drag on Pressure Ridges to the Air Stress on Arctic Ice’, J. Geophys. Res. 78, 7092–7099.Google Scholar
  5. Arya, S. P. S.: 1975, ‘A Drag Partition Theory for Determining the Large-Scale Roughness Parameter and Wind Stress on Arctic Pack Ice’, J. Geophys. Res. 80, 3447–3454.Google Scholar
  6. Banke, E. G., Smith, S. D., and Anderson, R. J.: 1980, ‘Drag Coefficients at AIDJEX from Sonic Anemometer Measurements’, R. S. Pritchard (ed.), in Sea Ice Processes and Models, University of Washington Press, Seattle, 430–442.Google Scholar
  7. Bradley, E. F.: 1972, ‘The Influence of Thermal Stability on a Drag Coefficient Measured Close to the Ground’, Agric. Meteorol. 9, 183–190.Google Scholar
  8. Brutsaert, W.: 1975a, ‘A Theory for Local Evaporation (or Heat Transfer) from Rough and Smooth Surfaces at Ground Level’, Water Resour. Res. 11, 543–550.Google Scholar
  9. Brutsaert, W.: 1975b, ‘The Roughness Length for Water Vapor, Sensible Heat, and Other Scalars’, J. Atmos. Sci. 32, 2028–2031.Google Scholar
  10. Businger, J. A.: 1973, ‘Turbulent Transfer in the Atmospheric Surface Layer’, D. A. Haugen (ed.), in Workshop on Micrometeorology, American Meteorological Society, Boston, 67–100.Google Scholar
  11. 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
  12. Chamberlain, A. C.: 1966, ‘Transport of Gases to and from Grass and Grass-Like Surfaces’, Proc. Roy. Soc. London A290, 236–265.Google Scholar
  13. Chamberlain, A. C.: 1968, ‘Transport of Gases to and from Surfaces with Bluff and Wave-Like Roughness’, Quart. J. Roy. Meteorol. Soc. 94, 318–332.Google Scholar
  14. Chamberlain, A. C.: 1983, ‘Roughness Length of Sea, Sand, and Snow’, Boundary-Layer Meteorol. 25, 405–409.Google Scholar
  15. Charnock, H.: 1955, ‘Wind Stress on Water: An Hypothesis’, Quart. J. Roy. Meteorol. Soc. 81, 639.Google Scholar
  16. Colbeck, S. C.: 1976, ‘An Analysis of Water Flow in Dry Snow’, Water Resour. Res. 12, 523–527.Google Scholar
  17. Colbeck, S. C. and Anderson, E. A.: 1982, ‘The Permeability of a Melting Snow Cover’, Water Resour. Res. 18, 904–908.Google Scholar
  18. Danckwerts, P. V.: 1951, ‘Significance of Liquid-Film Coefficients in Gas Absorption’, Industr. Engng. Chem. 43, 1460–1467.Google Scholar
  19. Danckwerts, P. V.: 1970, Gas-Liquid Reactions, McGraw-Hill, New York, 276 pp.Google Scholar
  20. Deardorff, J. W.: 1968, ‘Dependence of Air-Sea Transfer Coefficients on Bulk Stability’, J. Geophys. Res. 73, 2549–2557.Google Scholar
  21. Dennery, P. and Krzywicki, A.: 1967, Mathematics for Physicists, Harper and Row, New York, 384 pp.Google Scholar
  22. Dipprey, D. F. and Sabersky, R. H.: 1963, ‘Heat and Momentum Transfer in Smooth and Rough Tubes at Various Prandtl Numbers’, Int. J. Heat Mass Transfer 6, 329–353.Google Scholar
  23. Duff, G. F. D. and Naylor, D.: 1966, Differential Equations of Applied Mathematics, John Wiley and Sons, New York, 423 pp.Google Scholar
  24. Dyer, A. J.: 1974, ‘A Review of Flux-Profile Relationships’, Boundary-Layer Meteorol. 7, 363–372.Google Scholar
  25. Garratt, J. R. and Hicks, B. B.: 1973, ‘Momentum, Heat and Water Vapour Transfer to and from Natural and Artificial Surfaces’, Quart. J. Roy. Meteorol. Soc. 99, 680–687.Google Scholar
  26. Goldstein, S., ed.: 1965, Modern Developments in Fluid Dynamics, Dover, New York, 702 pp.Google Scholar
  27. Grass, A. J.: 1971, ‘Structural Features of Turbulent Flow over Smooth and Rough Boundaries’, J. Fluid Mech. 50, 233–255.Google Scholar
  28. Hibler, W. D., III: 1980, ‘Modeling a Variable Thickness Sea Ice Cover’, Mon. Wea. Rev. 108, 1943–1973.Google Scholar
  29. Hicks, B. B. and Martin, H. C.: 1972, ‘Atmospheric Turbulent Fluxes over Snow’, Boundary-Layer Meteorol. 2, 496–502.Google Scholar
  30. Hill, R. J.: 1978, ‘Spectra of Fluctuations in Refractivity, Temperature, Humidity, and the Temperature-Humidity Cospectrum in the Inertial and Dissipation Ranges’, Radio Sci. 13, 953–961.Google Scholar
  31. Kestin, J. and Persen, L. N.: 1962, ‘The Transfer of Heat across a Turbulent Boundary Layer at Very High Prandtl Numbers’, Int. J. Heat Mass Transfer 5, 355–371.Google Scholar
  32. Khundzhua, G. G. and Andreyev, Ye. G.: 1974, ‘An Experimental Study of Heat Exchange between the Ocean and the Atmosphere in Small-Scale Interaction’, Izv., Atmos. Oceanic Phys. 10, 685–687.Google Scholar
  33. Kim, H. T., Kline, S. J., and Reynolds, W. C.: 1971, ‘The Production of Turbulence near a Smooth Wall in a Turbulent Boundary Layer’, J. Fluid Mech. 50, 133–160.Google Scholar
  34. Kind, R. J.: 1976, ‘A Critical Examination of the Requirements for Model Simulation of Wind-Induced Erosion/Deposition Phenomena such as Drifting Snow’, Atmos. Environ. 10, 219–227.Google Scholar
  35. Kondo, J.: 1975, ‘Air-Sea Bulk Transfer Coefficients in Diabatic Conditions’, Boundary-Layer Meteorol. 9, 91–112.Google Scholar
  36. Kondo, J. and Yamazawa, H.: 1986, ‘Bulk Transfer Coefficient over a Snow Surface’, Boundary-Layer Meteorol. 34, 125–135.Google Scholar
  37. Large, W. G. and Pond, S.: 1982, ‘Sensible and Latent Heat Flux Measurements over the Ocean’, J. Phys. Oceanogr. 12, 464–482.Google Scholar
  38. Leavitt, E., Bell, D., Clarke, M., Anderson, R., and Paulson, C: 1977, ‘Computation of Air Stress and Sensible Heat Fluxes from Surface Layer Profile Data, AIDJEX, 1975’, AIDJEX Bull. 36, 157–174.Google Scholar
  39. Lettau, H. H.: 1979, ‘Wind and Temperature Profile Prediction for Diabatic Surface Layers including Strong Inversion Cases’, Boundary-Layer Meteorol. 17, 443–464.Google Scholar
  40. Liu, W. T. and Businger, J. A.: 1975, ‘Temperature Profile in the Molecular Sublayer near the Interface of a Fluid in Turbulent Motion’, Geophys. Res. Letters 2, 403–404.Google Scholar
  41. Liu, W. T., Katsaros, K. B., and Businger, J. A.: 1979, ‘Bulk Parameterization of Air-Sea Exchanges of Heat and Water Vapor including the Molecular Constraints at the Interface’, J. Atmos. Sci. 36, 1722–1735.Google Scholar
  42. Mangarella, P. A., Chambers, A. J., Street, R. L., and Hsu, E. Y.: 1973, ‘Laboratory Studies of Evaporation and Energy Transfer Through a Wavy Air-Water Interface’, J. Phys. Oceanogr. 3, 93–101.Google Scholar
  43. Maykut, G. A.: 1978, ‘Energy Exchange over Young Sea Ice in the Central Arctic’, J. Geophys. Res. 83, 3646–3658.Google Scholar
  44. Monin, A. S. and Yaglom, A. M.: 1971, Statistical Fluid Mechanics: Mechanics of Turbulence, Vol. 1, MIT Press, Cambridge, Mass., 769 pp.Google Scholar
  45. Owen, P. R. and Thomson, W. R.: 1963, ‘Heat Transfer across Rough Surfaces’, J. Fluid Mech. 15, 321–334.Google Scholar
  46. Parkinson, C. L. and Washington, W. M.: 1979, ‘A Large-Scale Numerical Model of Sea Ice’, J. Geophys. Res. 84, 311–337.Google Scholar
  47. Paulson, C. A.: 1970, ‘The Mathematical Representation of Wind Speed and Temperature Profiles in the Unstable Atmospheric Surface Layer’, J. Appl. Meteorol. 9, 857–861.Google Scholar
  48. Pruppacher, H. R. and Klett, J. D.: 1978, Microphysics of Clouds and Precipitation, D. Reidel, Publ. Co., Dordrecht, Holland, 714 pp.Google Scholar
  49. Schlichting, H.: 1968, Boundary-Layer Theory, 6th ed., J. Kestin (trans.), McGraw-Hill, New York, 748 pp.Google Scholar
  50. Schmidt, R. A.: 1982, ‘Vertical Profiles of Wind Speed, Snow Concentration, and Humidity in Blowing Snow’, Boundary-Layer Meteorol. 23, 223–246.Google Scholar
  51. Shirasawa, K.: 1981, ‘Studies on Wind Stress on Sea Ice’, Low Temp. Sci. A40, 101–118.Google Scholar
  52. Tennekes, H. and Lumley, J. L.: 1972, A First Course in Turbulence, MIT Press, Cambridge, Mass., 300 pp.Google Scholar
  53. Thorpe, M. R., Banke, E. G., and Smith, S. D.: 1973, ‘Eddy Correlation Measurements of Evaporation and Sensible Heat Flux over Arctic Sea Ice’, J. Geophys. Res. 78, 3573–3584.Google Scholar
  54. Untersteiner, N. and Badgley, F. I.: 1965, ‘The Roughness Parameter of Sea Ice’, J. Geophys. Res. 70, 4573–4577.Google Scholar

Copyright information

© D. Reidel Publishing Company 1987

Authors and Affiliations

  • Edgar L. Andreas
    • 1
  1. 1.U.S. Army Cold Regions Research and Engineering LaboratoryHanoverUSA

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