Abstract
The question whether two different scalars have the same behaviour in the surface layer under stable conditions is investigated. “Similarity” of two scalars is defined in terms of the equality of their corresponding dimensionless Monin-Obukhov similarity functions. Previous theoretical and experimental results concerning the issue are briefly reviewed: they are found to be contradictory. An analytical derivation of the square of the correlation coefficient between two scalars is obtained based on the correlation structure of the turbulent dissipation functions for stable conditions, when it can be assumed that the divergence of the vertical transport of scalar variance/covariance is negligible. The resulting expression elucidates some earlier conflicting results, and helps to establish the equality of the similarity functions for all scalars in the stable surface layer. A statistical analysis in the time domain is also performed using temperature and humidity turbulence data measured in nocturnal stable conditions during FIFE-89. Our results, both from the analytical derivation and the statistical analysis of turbulence data, confirm that under validity of the Monin-Obukhov similarity theory assumptions, the corresponding similarity functions for temperature and humidity are equal to within the statistical uncertainty of the measurements. An important consequence is that the eddy diffusivities of temperature and humidity are also equal.
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Benjamin, J. R. and Cornell, C. A.: 1970, Probability, Statistics and Decision for Civil Engineers, McGraw-Hill.
Bertela, M.: 1989, ‘Inconsistent Flux Partitioning by the Bowen Ratio Method’, Boundary-Layer Meteorol. 49, 149–167.
Bradley, E. F., Antonia, R. A., and Chambers, A. J.: 1981, ‘Temperature Structure in the Atmospheric Surface Layer. I — The Budget of Temperature Variance’, Boundary-Layer Meteorol. 20, 275–292.
Brost, R. A.: 1979, ‘Some Comments on the “Turbulent Exchange Coefficients for Sensible Heat and Water vapour Under Advective Conditions”’, J. Appl. Meteorol. 18, 378–380.
De Bruin, H. A. R., Bink, N. J., and Kroon, L. J. M.: 1991, ‘Fluxes in the Surface Layer under Advective Conditions’, in Schmugge and Andre (eds.), Land Surface Evaporation. Measurments and Parameterization, pp. 151–171.
De Bruin, H. A. R., Kohsiek, W., and Van der Hurk, B. J. J. M.: 1993, ‘A Verification of Some Methods to Determine the Fluxes of Momentum, Sensible Heat and Water vapour using Standard Deviation and Structure Parameter of Scalar Meteorological Quantities’, Boundary-Layer Meteorol. 63, 231–257.
Dias, N. L.: 1994, The Structure of Temperature and Humidity Fluctuations in the Stable Surface Layer, Ph.D. Thesis, Cornell University.
Dias, N. L., Brutsaert, W., and Wesely, M. L.: 1995, ‘Z-Less Stratification under Stable Conditions’, Submitted to Boundary-Layer Meteorol..
Dyer, A. J.: 1967, ‘The Turbulent Transport of Heat and Water Vapor in an Unstable Atmosphere’, Quart. J. Roy. Meteorol. Soc. 102, 501–508.
Fairall, C. W. and Larsen, S. E.: 1986, ‘Inertial-Dissipation Methods and Turbulent Fluxes at the Air-Ocean Interface’, Boundary-Layer Meteorol. 34, 287–301.
Hicks, B. B. (1981), ‘An Examination of Turbulence Statistics in the Surface Boundary Layer’, Boundary-Layer Meteorol. 21 389–402.
Hicks, B. B. and Everett, R. G.: 1979, ‘Comments on “Turbulent Exchange Coefficients for Sensible Heat and Water vapour under Advective Conditions”’, J. Appl. Meteorol. 18, 381–382.
Hill, R. J.: 1989, ‘Implications of Monin-Obukhov Similarity Theory for Scalar Quantities’, J. Atmos. Sci. 46, 2236–2244.
Kohsiek, W.: 1982, ‘Measuring C T 2,C Q 2and C tQ in the Unstable Surface Layer, and Relations to the Vertical Fluxes of Heat and Moisture’, Boundary-Layer Meteorol. pp2489-107.
Lang, A. R. G., McNaughton, K. G., Chen, F., Bradley, E. F., and Ohtaki, E.: 1983a, ‘Inequality of Eddy Transfer Coefficients for Vertical Transport of Sensible and Latent Heats During Advective Inversions’, Boundary-Layer Meteorol. 25, 25–41.
Lang, A. R. G., McNaughton, K. G., Chen, F., Bradley, E. F., and Ohtaki, E.: 1983b, ‘An Experimental Appraisal of the Terms in the Heat and Moisture Flux Equations for Local Advection’, Boundary-Layer Meteorol. 25, 89–102.
Launder, B. E.: 1975, ‘On the Effects of a Gravitational Field on the Turbulent Transport of Heat and Momentum’, J. Fluid Mech. 67, 569–581.
Leclerc, M. V. and Thurtell, G. W.: 1990, ‘Footprint Prediction of Scalar Fluxes using a Markovian Analysis’, Boundary-Layer Meteorol. 52, 247–258.
McBean, G. A. and Elliot, J. A.: 1981, ‘Pressure and Humidity Effects on Optical Refractive-Index Fluctuations’, Boundary-Layer Meteorol. 20, 101–109.
Moncrieff, J. B., Verma, S. B. and Cook, D. R.: 1992, ‘Intercomparison of Eddy Correlation Carbon Dioxide Sensors during FIFE-89’, J. Geophys. Res. 94 D17, 18,725–18,730.
Ohtaki, E.: 1985, ‘On the Similarity in Atmospheric Fluctuations of Carbon Dioxide, Water vapour and Temperature over Vegetated Fields’, Boundary-Layer Meteorol. 32, 25–37.
Phelps, G. T. and Pond, S.: 1971, ‘Spectra of the Temperature and Humidity Fluctuations and of Fluxes of Moisture and Heat in the Marine Boundary Layer’, J. Atmos. Sci. 28, 918–928.
Priestley, J. T. and Hill, R. J.: 1985, ‘Measuring High-Frequency Humidity, Temperature and Radio Refractive Index in the Surface Layer’, J. Atmos. Ocean. Technol. 2, 233–251.
Roth, M. and Oke, T. R.: 1993, ‘Turbulent Transfer Relationships over an Urban Surface. I: Spectral Characteristics’, Quart. J. Roy. Meteorol. Soc. 119, 1071–1104.
Roth, M. and Oke, T. R.: 1995, ‘Relative Efficiencies of Turbulent Transfer of Heat, Mass and Momentum over a Patchy Urban Surface’, J. Atmos. Sci. 52, 1863–1874.
Sellers, P. J., Hall, F. G., Asrar, G., Strebel, D. E., and Murphy, R. E.: 1992, ‘An Overview of the First International Satellite Land Surface Climatology Project ISLSCP Field Experiment (FIFE)’, J. Geophys. Res. 97 D17, 18,345–18,371
Stannard, D. I. and Rosenberry, D. O. (1991), ‘A Comparison of Short-Term Measurements of Lake Evaporation using Eddy-Correlation and Energy Budget Methods’, J. Hydrol. 122, 15–22.
Stull, R. B.: 1988, An Introduction to Boundary Layer Meteorology, D. Reidel, 666 pp.
Swinbank, W. C. and Dyer, A. J.: 1963, ‘An Experimental Study in Micrometeorology’, Quart. J. Roy. Meteorol. Soc. 102, 494–500.
Tillman, J. E.: 1972, ‘The Indirect Determination of Stability, Heat and Momentum Fluxes in the Atmospheric Boundary Layer from Simple Scalar Variables during Dry Unstable Conditions’, J. Appl. Meteorol. 11, 783–792.
Verma, S. B., Rosenberg, N. J., and Blad, B. L.: 1978, ‘Turbulent Exchange Coefficients for Sensible Heat and Water vapour under Advective Conditions’, J. Appl. Meteorol. 17, 330–338.
Warhaft, Z.: 1976, ‘Heat and Moisture Flux in the Stratified Boundary Layer’, Quart. J. Roy. Meteorol. Soc. 102, 703–707.
Wesely, M. L.: 1988, ‘Use of Variance Techniques to Measure Dry Air-Surface Exchange Rates’, Boundary-Layer Meteorol. 44, 13–31.
Wesely, M. L. and Hicks, B. B.: 1978, ‘High-Frequency Temperature and Humidity Correlation above a Warm Wet Surface’, J. Appl. Meteorol. 17, 123–128.
Wylie, R. G. and Lalas, T.: 1992, ‘Measurement of Temperature and Humidity’, World Meteorological Organization, Technical note 194, Geneva.
Wyngaard, J. C.: 1973, ‘On Surface-Layer Turbulence’, in D. A. Haugen (ed.), Workshop on Micrometeorology, American Meteorological Society, Boston.
Wyngaard, J. C., Coté, O. R., and Izumi, Y.: 1971, ‘Local Free Convection Similarity and the Budgets of Shear Stress and Heat Flux’, J. Atmos. Sci. 28, 1171–1182.
Wyngaard, J. C. and Brost, R. A.: 1984, ‘Top-Down and Bottom-Up Diffusion of a Scalar in the Convective Boundary Layer’, J. Atmos. Sci. 41, 102–112.
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Now at SIMEPAR — Sistema Meteorológico do Paraná and UFPR — Universidade Federal do Paraná, Caixa Postal 318 CEP 80001-970, Curitiba PR Brazil.
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Dias, N.L., Brutsaert, W. Similarity of scalars under stable conditions. Boundary-Layer Meteorol 80, 355–373 (1996). https://doi.org/10.1007/BF00119423
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DOI: https://doi.org/10.1007/BF00119423