Abstract
The flux of sensible heat from the land surface is related to the average rate of dissipation of temperature fluctuations in the atmospheric surface layer through the temperature variance budget equation. In many cases it is desirable to estimate the heat flux from measurement or inference of the dissipation rate. Here we study how the dissipation rate scales with atmospheric stability, using three inertial range methods to calculate the dissipation rate: power spectra, second order structure functions, and third order structure functions. Experimental data are analyzed from a pair of field experiments, during which turbulent fluctuations of velocity and temperature were measured over a broad range of neutral and unstable atmospheric flows. It is shown that the temperature dissipation rate scales with a single convective power law continuously from near-neutral to strongly unstable stratification. The dissipation scaling is found to nearly match production in the near-neutral region, but to be consistently lower than production in the more convective regimes. The convective scaling is shown to offer a simplified means of computing sensible heat flux from the dissipation rate of temperature variance.
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Albertson, J. D., Parlange, M. B., Katul, G. G., Chu, C.-R., Stricker, H. and Tyler, S.: 1995a, ‘Sensible Heat Flux from Arid Regions: A Simple Flux-Variance Method’, Water Resour. Res. 31, 969–973.
Albertson, J. D., Kiely, G., Parlange, M. B. and Eichinger, W. E.: 1995b, ‘The Average Dissipation Rate of Turbulent Kinetic Energy in the Neutral and Unstable Atmospheric Surface Layer’, J. Geophys. Res. submitted.
Andreas, E. L.: 1998, ‘Using Scintillation at Two Wavelengths to Measure Path-Averaged Heat Fluxes in Free Convection’, Boundary-Layer Meteorol. 54, 167–182.
Antonia, R. A., Chambers, A. J., Phong-Anant, D. and Rajagopalan, S.: 1979, ‘Properties of Spatial Temperature Derivatives in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 17, 101–118.
Betchov, R. and Yaglom, A. M.: 1971, ‘Comments on the Theory of Similarity as Applied to Turbulence in an Unstably Stratified Fluid’, Izv., Atmos. Ocean. Phys. 7, 1270–1279, (829–834 in English translation).
Bradley, E. F., Antonia, R. A. and Chambers, A. J.: 1981, ‘Temperature Structure in the Atmospheric Surface Layer’, Boundary-Layer Meteorol. 20, 275–292.
Brutsaert, W.: 1982, Evaporation Into the Atmosphere, 299 pp., Kluwer Academic Publishers.
Brutsaert, W.: 1992, ‘Stability Correction Functions for the Mean Wind Speed and Temperature in the Unstable Surface Layer’, Geophys. Res. Letters, 19, 469–472.
Champagne, F. H., Friehe, C. A., LaRue, J. C. and Wyngaard, J. C.: 1977, ‘Flux Measurements, Flux Estimation Techniques, and Fine-Scale Turbulence Measurements in the Unstable Surface Layer over Land’, J. Atmos. Sci. 34, 515–530.
Corrsin, S.: 1951, ‘On the Spectrum of Isotropic Temperature Fluctuations in an Isotropic Turbulence’, J. Appl. Phys. 22, 469–473.
DeLeonibus, P. S. and Simpson, L. S.: 1987, ‘Dissipation Observations of Drag Coefficients Over the Open Ocean’, IEEE J. Oceanic Eng. OE-12, 296–300.
Edson, J. B., Fairall, C. W., Mestayer, P. G. and Larssen, S. E.: 1991, ‘A Study of the Inertial-Dissipation Method for Computing Air-Sea Fluxes’, J. Geophys. Res. 96C, 10689–10711.
Eichinger, W. E., Cooper, D. I., Holtkamp, D. B., Karl Jr., R. R., Quick, C. R. and Till, J. J.: 1993, ‘Derivation of Water Vapour Fluxes from Lidar Measurements’, Boundary-Layer Meteorol. 63, 39–64.
Fairall, C. W., Edson, J. B., Larsen, S. E. and Mestayer, P. G.: 1990, ‘Inertial-dissipation Air-Sea Measurements: a Prototype System Using Realtime Spectral Computations’, J. Atmos. Ocean. Tech. 7, 425–453.
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.
Feynman, R. P., Leighton, R. B. and Sands, M.: 1963, The Feynman Lectures on Physics, Vol. 1, Addison-Wesley.
Hill, R. G., Ochs, G. R. and Wilson, J. J.: 1992, ‘Measuring Surface Layer Fluxes of Heat and Momentum Using Optical Scintillation’, Boundary-Layer Meteorol. 58, 391–408.
Högström, U.: 1988, ‘Non-Dimensional Wind and Temperature Profiles’, Boundary-Layer Meteorol. 42, 55–78.
Högström, U.: 1990, ‘Analysis of Turbulence Structure in the Surface Layer with a Modified Similarity Formulation for near Neutral Conditions’, J. Atmos. Sci. 47, 1949–1972.
Kader, B. A.: 1988, ‘Three-Level Structure of an Unstably Stratified Atmospheric Surface Layer’, Izv. Atmos. Ocean. Phys. 24, 907–919 (English translation).
Kader, B. A.: 1992, ‘Determination of Turbulent Momentum and Heat Fluxes by Spectral Methods’, Boundary-Layer Meteorol. 61, 323–347.
Kader, B. A. and Perepelkin, V. G.: 1984, ‘Profiles of the Wind Velocity and Temperature in the Near-Surface Layer of the Atmosphere under Conditions of Neutral and Unstable Stratification’, Izv. Atmos. Ocean. Phys. 20, 112–119, (English translation).
Kader, B. A. and Perepelkin, V. G.: 1989, ‘Effect of Unstable Stratification on the Wind Speed and Temperature Profiles in the Surface Layer’, Izv. Atmos. Ocean. Phys. 25, 583–588, (English translation).
Kader, B. A. and Yaglom, A. M.: 1990, ‘Mean Fields and Fluctuation Moments in Unstably Stratified turbulent Boundary Layers’, J. Fluid Mech. 212, 637–662.
Kaimal, J. C. and Finnigan, J. J.: 1994, Atmospheric Boundary Layer Flows. Their Structure and Measurement, Oxford University Press, 289p.
Katul, G. G., Chu, C.-R., Parlange, M. B., Albertson, J. D. and Ortenburger, T. A.: 1995, ‘Low-Wavenumber Spectral Characteristics of Velocity and Temperature in the Atmospheric Surface Layer Flows’, J. Geophys. Res. 100, 1424–14255.
Kolmogorov, A. N.: 1941, ‘The Local Structure of Turbulence in Incompressible Viscous Fluid for very Large Reynolds Number’, Dokl. Akad. Nauk. SSSR, 30, 301–303.
Lumley, J. L. and Panofsky, H. A.: 1964, ‘The Structure of Atmospheric Turbulence’, Wiley Interscience, New York, 239 pp.
Monin, A. A. and Yaglom, A. M.: 1975, Statistical Fluid Mechanics. Vol. II, J. Lumley (ed.), MIT Press, 874 pp.
Monji, N.: 1973, ‘Budgets of Turbulent Energy and Temperature Variance in the Transition Zone from Forced to Free Convection’, J. Meteorol. Soc. Japan 51, 133–145.
Obukhov, A. M.: 1949, ‘Structure of the Temperature Field in a Turbulent Flow’, Izv. Akad. Nauk. SSSR, Ser. Georgr. i. Grofiz. 13, 58–69.
Skupniewicz, C. E. and Davidson, K. L.: 1991, ‘Hot-Film Measurements from a Small Buoy: Surface Wind Estimates Using the Inertial Dissipation Method’, J. Atmos. Ocean. Tech. 8, 309–322.
Taylor, G. I.: 1938, ‘The Spectrum of Turbulence’, Proc. Roy. Soc., A, CLXIV, 476–490.
Tennekes, H. and Lumley, J.: 1972, A First Course in Turbulence, MIT Press, 300 pp.
Wyngaard, J. C. and Cotè, O. R.: 1971, ‘The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer’, J. Atmos. Sci. 28, 190–201.
Yaglom, A. M.: 1949, ‘Homogeneous and Isotropic Turbulence in a Viscious Compressible Fluid’, Izv. Akad. Nauk SSSR Ser. Georg, i Geofiz. 12, 501–522.
Zilitinkevich, S. S. and Chalikov, D. V.: 1968, ‘Determining the Universal Wind-Velocity and Temperature Profiles in the Atmospheric Boundary Layer’, Izv. Atmos. Ocean. Phys. 4, 294–302 (English Translation, pp. 165–170).
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Also at Johns Hopkins University, Baltimore, Maryland
Also at Los Alamos National Laboratory, Los Alamos, New Mexico.
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Kiely, G., Albertson, J.D., Parlance, M.B. et al. Convective scaling of the average dissipation rate of temperature variance in the atmospheric surface layer. Boundary-Layer Meteorol 77, 267–284 (1996). https://doi.org/10.1007/BF00123528
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DOI: https://doi.org/10.1007/BF00123528