• Andreas, E. L. 1987. On the Kolmogorov constants for the temperature-humidity cospectrum and the refractive index spectrum. J. Atmos. Sci. 44:23992406.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L. 1988a. Estimating averaging times for point and path-averaged measurements of turbulence spectra. J. Appl. Meteor. 27:295304.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L. 1988b. Estimating C2 n over snow and sea ice from meteorological data. J. Opt. Soc. Amer. 5A:481495.

  • Andreas, E. L. 1989a. The refractive index structure parameter, C2 n, for a year over the frozen Beaufort Sea. Radio Sci. 24:667679.

  • Andreas, E. L. 1989b. Two-wavelength method of measuring path-averaged turbulent surface heat fluxes. J. Atmos. Oceanic Technol. 6:280292.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L. 1990. Selected Papers on Turbulence in a Refractive Medium. Society of Photo-Optical Instrumentation Engineers Milestone Series, Vol. 25, SPIE, 693 pp.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L. 1992. Uncertainty in a path-averaged measurement of the friction velocity u∗. J. Appl. Meteor. 31:13121321.

  • Andreas, E. L. 2002. Parameterizing scalar transfer over snow and ice: A review. J. Hydrometeor. 3:417432.

  • Andreas, E. L., and B. A. Cash. 1996. A new formulation for the Bowen ratio over saturated surfaces. J. Appl. Meteor. 35:12791289.

  • Andreas, E. L., , C. W. Fairall, , P. S. Guest, , and P. O. G. Persson. 1999. An overview of the SHEBA atmospheric surface flux program. Preprints, Fifth Conf. on Polar Meteorology and Oceanography, Dallas, TX, Amer. Meteor. Soc., 411–416.

    • Search Google Scholar
    • Export Citation
  • Andreas, E. L., , C. W. Fairall, , P. O. G. Persson, , and P. S. Guest. 2000. Probability distributions for scintillometer-derived values of the inner scale and the refractive index structure parameter and their implications for averaging. Preprints, 14th Symp. on Boundary Layers and Turbulence, Aspen, CO, Amer. Meteor. Soc., 19–22.

    • Search Google Scholar
    • Export Citation
  • Arya, S. P. 1988. Introduction to Micrometeorology. Academic Press, 307 pp.

  • Ben-Yosef, N., and E. Goldner. 1988. Splitting-source model for the statistics of irradiance scintillations. J. Opt. Soc. Amer. 5A:126131.

    • Search Google Scholar
    • Export Citation
  • Businger, J. A., , J. C. Wyngaard, , Y. Izumi, , and E. F. Bradley. 1971. Flux-profile relationships in the atmospheric surface layer. J. Atmos. Sci. 28:181189.

    • Search Google Scholar
    • Export Citation
  • Chernov, L. A. 1967. Wave Propagation in a Random Medium. Dover, 168 pp.

  • De Bruin, H. A. R., , B. J. J. M. van den Hurk, , and W. Kohsiek. 1995. The scintillation method tested over a dry vineyard area. Bound.-Layer Meteor. 76:2540.

    • Search Google Scholar
    • Export Citation
  • De Bruin, H. A. R., , W. M. L. Meijninger, , A-S. Smedman, , and M. Magnusson. 2002. Displaced-beam small aperture scintillometer test. Part I: The WINTEX data-set. Bound.-Layer Meteor. 105:129148.

    • Search Google Scholar
    • Export Citation
  • Dyer, A. J., and E. F. Bradley. 1982. An alternative analysis of flux-gradient relationships at the 1976 ITCE. Bound.-Layer Meteor. 22:319.

    • Search Google Scholar
    • Export Citation
  • Edson, J. B., and C. W. Fairall. 1998. Similarity relationships in the marine atmospheric surface layer for terms in the TKE and scalar variance budgets. J. Atmos. Sci. 55:23112328.

    • Search Google Scholar
    • Export Citation
  • Fairall, C. W., and S. E. Larsen. 1986. Inertial-dissipation methods and turbulent fluxes at the air-ocean interface. Bound.-Layer Meteor. 34:287301.

    • Search Google Scholar
    • Export Citation
  • Frederickson, P. A., , K. L. Davidson, , C. R. Zeisse, , and C. S. Bendall. 2000. Estimating the refractive index structure parameter (C2 n) over the ocean using bulk methods. J. Appl. Meteor. 39:17701783.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R. G. 1988. Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance. Appl. Opt. 27:21942198.

    • Search Google Scholar
    • Export Citation
  • Frehlich, R. G. 1992. Laser scintillation measurements of the temperature spectrum in the atmospheric surface layer. J. Atmos. Sci. 49:14941509.

    • Search Google Scholar
    • Export Citation
  • Gray, D. A., and A. T. Waterman Jr.. 1970. Measurement of fine-scale atmospheric structure using an optical propagation technique. J. Geophys. Res. 75:10771083.

    • Search Google Scholar
    • Export Citation
  • Green, A. E., , K. J. McAneney, , and M. S. Astill. 1994. Surface-layer scintillation measurements of daytime sensible heat and momentum fluxes. Bound.-Layer Meteor. 68:357373.

    • Search Google Scholar
    • Export Citation
  • Gurvich, A. S., , N. S. Time, , L. S. Turovtseva, , and V. F. Turchin. 1974. Reconstruction of the temperature fluctuation spectrum of the atmosphere from optical measurements. Izv., Atmos. Oceanic Phys. 10:292297.

    • Search Google Scholar
    • Export Citation
  • Harr, M. E. 1987. Reliability-Based Design in Civil Engineering. McGraw-Hill, 543 pp.

  • Hartogensis, O. K., , H. A. R. De Bruin, , and B. J. H. Van de Wiel. 2002. Displaced-beam small aperture scintillometer test. Part II: CASES-99 stable boundary-layer experiment. Bound.-Layer Meteor. 105:149176.

    • Search Google Scholar
    • Export Citation
  • Haugen, D. A., , J. C. Kaimal, , and E. F. Bradley. 1971. An experimental study of Reynolds stress and heat flux in the atmospheric surface layer. Quart. J. Roy. Meteor. Soc. 97:168180.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J. 1997. Algorithms for obtaining atmospheric surface-layer fluxes from scintillation measurements. J. Atmos. Oceanic Technol. 14:456467.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J., and S. F. Clifford. 1978. Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation. J. Opt. Soc. Amer. 68:892899.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J., and R. G. Frehlich. 1997. Probability distribution of irradiance for the onset of strong scintillation. J. Opt. Soc. Amer. 14A:15301540.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J., , R. A. Bohlander, , S. F. Clifford, , R. W. McMillan, , J. T. Priestley, , and W. P. Schoenfeld. 1988. Turbulence-induced millimeter-wave scintillation compared with micrometeorological measurements. IEEE Trans. Geosci. Remote Sens. 26:330342.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J., , G. R. Ochs, , and J. J. Wilson. 1992a. Measuring surface-layer fluxes of heat and momentum using optical scintillation. Bound.-Layer Meteor. 58:391408.

    • Search Google Scholar
    • Export Citation
  • Hill, R. J., , G. R. Ochs, , and J. J. Wilson. 1992b. Surface-layer fluxes measured using the C2 T-profile method. J. Atmos. Oceanic Technol. 9:526537.

    • Search Google Scholar
    • Export Citation
  • Högström, U. 1988. Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation. Bound.-Layer Meteor. 42:5578.

    • Search Google Scholar
    • Export Citation
  • Holtslag, A. A. M., and H. A. R. De Bruin. 1988. Applied modeling of the nighttime surface energy balance over land. J. Appl. Meteor. 27:689704.

    • Search Google Scholar
    • Export Citation
  • Kiehl, J. T., and K. E. Trenberth. 1997. Earth's annual global mean energy budget. Bull. Amer. Meteor. Soc. 78:197208.

  • Kohsiek, W., and M. H. A. J. Herben. 1983. Evaporation derived from optical and radio-wave scintillation. Appl. Opt. 22:25662570.

  • Lenschow, D. H., , J. Mann, , and L. Kristensen. 1994. How long is long enough when measuring fluxes and other turbulence statistics? J. Atmos. Oceanic Technol. 11:661673.

    • Search Google Scholar
    • Export Citation
  • Lumley, J. L., and H. A. Panofsky. 1964. The Structure of Atmospheric Turbulence. Interscience, 239 pp.

  • Mahrt, L. 1998. Flux sampling errors for aircraft and towers. J. Atmos. Oceanic Technol. 15:416429.

  • Mitchell, J. F. B. 1989. The “greenhouse” effect and climate change. Rev. Geophys. 27:115139.

  • Nieveen, J. P., and A. E. Green. 1999. Measuring sensible heat flux density over pasture using the C2 T-profile method. Bound.-Layer Meteor. 91:2335.

    • Search Google Scholar
    • Export Citation
  • Oncley, S. P., , C. A. Friehe, , J. C. Larue, , J. A. Businger, , E. C. Itsweire, , and S. S. Chang. 1996. Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions. J. Atmos. Sci. 53:10291044.

    • Search Google Scholar
    • Export Citation
  • Persson, P. O. G., , C. W. Fairall, , E. L. Andreas, , P. S. Guest, , and D. K. Perovich. 2002. Measurements near the Atmospheric Surface Flux Group tower at SHEBA: Near-surface conditions and surface energy budget. J. Geophys. Res. 107:8045, doi:10.1029/2000JC000705.

    • Search Google Scholar
    • Export Citation
  • Sreenivasan, K. R., , A. J. Chambers, , and R. A. Antonia. 1978. Accuracy of moments of velocity and scalar fluctuations in the atmospheric surface layer. Bound.-Layer Meteor. 14:341359.

    • Search Google Scholar
    • Export Citation
  • Strohbehn, J. W. 1970. The feasibility of laser experiments for measuring the permittivity spectrum of the turbulent atmosphere. J. Geophys. Res. 75:10671076.

    • Search Google Scholar
    • Export Citation
  • Tatarskii, V. I. 1961. Wave Propagation in a Turbulent Medium. Dover, 285 pp.

  • Tatarskii, V. I. 1971. The Effects of the Turbulent Atmosphere on Wave Propagation. Israel Program for Scientific Translations, 472 pp.

  • Thiermann, V. 1992. A displaced-beam scintillometer for line-averaged measurements of surface layer turbulence. Preprints, 10th Symp. on Turbulence and Diffusion, Portland, OR, Amer. Meteor. Soc., 244–247.

    • Search Google Scholar
    • Export Citation
  • Thiermann, V., and H. Grassl. 1992. The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation. Bound.-Layer Meteor. 58:367389.

    • Search Google Scholar
    • Export Citation
  • Uttal, T. Coauthors,. 2002. Surface Heat Budget of the Arctic Ocean. Bull. Amer. Meteor. Soc. 83:255275.

  • Wesely, M. L. 1976. The combined effect of temperature and humidity fluctuations on refractive index. J. Appl. Meteor. 15:4349.

  • Wesely, M. L., and E. C. Alcarez. 1973. Diurnal cycles of the refractive index structure function coefficient. J. Geophys. Res. 78:62246232.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C. 1973. On surface-layer turbulence. Workshop on Micrometeorology, D. A. Haugen, Ed., Amer. Meteor. Soc., 101–149.

  • Wyngaard, J. C., and O. R. Coté. 1971. The budgets of turbulent kinetic energy and temperature variance in the atmospheric surface layer. J. Atmos. Sci. 28:190201.

    • Search Google Scholar
    • Export Citation
  • Wyngaard, J. C., and S. F. Clifford. 1978. Estimating momentum, heat and moisture fluxes from structure parameters. J. Atmos. Sci. 35:12041211.

    • Search Google Scholar
    • Export Citation
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Probability Distributions for the Inner Scale and the Refractive Index Structure Parameter and Their Implications for Flux Averaging

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  • a U.S. Army Cold Regions Research and Engineering Laboratory, Hanover, New Hampshire
  • | b NOAA/Environmental Technology Laboratory, Boulder, Colorado
  • | c Cooperative Institute for Research in Environmental Sciences, University of Colorado, Boulder, Colorado
  • | d Naval Postgraduate School, Monterey, California
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Abstract

Defining the averaging time required for measuring meaningful turbulence statistics is a central problem in boundary layer meteorology. Path-averaging scintillation instruments are presumed to confer some time-averaging benefits when the objective is to measure surface fluxes, but that hypothesis has not been tested definitively. This study uses scintillometer measurements of the inner scale (l0) and the refractive index structure parameter (C2n) to investigate this question of required averaging time. The first conclusion is that the beta probability distribution is useful for representing C2n and l0 measurements. Consequently, beta distributions are used to set confidence limits on C2n and l0 values obtained over various averaging periods. When the C2n and l0 time series are stationary, a short-term average of C2n or l0 can be as accurate as a long-term average. However, as with point measurements, when time series of path averaged C2n or l0 values are nonstationary, turbulent surface fluxes inferred from these C2n and l0 values can be variable and uncertain—problems that path averaging was presumed to mitigate. Because nonstationarity is a limiting condition, the last topic is quantifying the nonstationarity with a published nonstationarity ratio and also by simply counting zero crossings in the time series.

Corresponding author address: Dr. Edgar L Andreas, U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755-1290. eandreas@crrel.usace.army.mil

Abstract

Defining the averaging time required for measuring meaningful turbulence statistics is a central problem in boundary layer meteorology. Path-averaging scintillation instruments are presumed to confer some time-averaging benefits when the objective is to measure surface fluxes, but that hypothesis has not been tested definitively. This study uses scintillometer measurements of the inner scale (l0) and the refractive index structure parameter (C2n) to investigate this question of required averaging time. The first conclusion is that the beta probability distribution is useful for representing C2n and l0 measurements. Consequently, beta distributions are used to set confidence limits on C2n and l0 values obtained over various averaging periods. When the C2n and l0 time series are stationary, a short-term average of C2n or l0 can be as accurate as a long-term average. However, as with point measurements, when time series of path averaged C2n or l0 values are nonstationary, turbulent surface fluxes inferred from these C2n and l0 values can be variable and uncertain—problems that path averaging was presumed to mitigate. Because nonstationarity is a limiting condition, the last topic is quantifying the nonstationarity with a published nonstationarity ratio and also by simply counting zero crossings in the time series.

Corresponding author address: Dr. Edgar L Andreas, U.S. Army Cold Regions Research and Engineering Laboratory, 72 Lyme Road, Hanover, NH 03755-1290. eandreas@crrel.usace.army.mil

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