Probability Distributions for the Inner Scale and the Refractive Index Structure Parameter and Their Implications for Flux Averaging

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 in...

[1]  Richard A. Silverman,et al.  Wave Propagation in a Random Medium , 1960 .

[2]  R. A. Silverman,et al.  Wave Propagation in a Turbulent Medium , 1961 .

[3]  John L. Lumley,et al.  The structure of atmospheric turbulence , 1964 .

[4]  J. Strohbehn.  The feasibility of laser experiments for measuring the permittivity spectrum of the turbulent atmosphere , 1970 .

[5]  D. A. Gray,et al.  Measurement of fine‐scale atmospheric structure using an optical propagation technique , 1970 .

[6]  V. I. Tatarskii.  The effects of the turbulent atmosphere on wave propagation , 1971 .

[7]  E. F. Bradley,et al.  Flux-Profile Relationships in the Atmospheric Surface Layer , 1971 .

[8]  J. Wyngaard,et al.  The Budgets of Turbulent Kinetic Energy and Temperature Variance in the Atmospheric Surface Layer , 1971 .

[9]  D. A. Haugen,et al.  An experimental study of Reynolds stress and heat flux in the atmospheric surface layer , 1971 .

[10]  M. L. Wesely,et al.  Diurnal cycles of the refractive index structure function coefficient , 1973 .

[11]  M. Wesely,et al.  The Combined Effect of Temperature and Humidity Fluctuations on Refractive Index , 1976 .

[12]  K. Sreenivasan,et al.  Accuracy of moments of velocity and scalar fluctuations in the atmospheric surface layer , 1978 .

[13]  S. Clifford,et al.  Modified spectrum of atmospheric temperature fluctuations and its application to optical propagation , 1978 .

[14]  J. Wyngaard,et al.  Estimating Momentum, Heat and Moisture Fluxes from Structure Parameters , 1978 .

[15]  E. F. Bradley,et al.  An alternative analysis of flux-gradient relationships at the 1976 ITCE , 1982 .

[16]  M. Herben,et al.  Evaporation derived from optical and radio-wave scintillation. , 1983, Applied optics.

[17]  C. W. Fairall,et al.  Inertial-dissipation methods and turbulent fluxes at the air-ocean interface , 1986 .

[18]  Milton E. Harr,et al.  Reliability-Based Design in Civil Engineering , 1987 .

[19]  E. L. Andreas.  On the Kolmogorov Constants for the Temperature-Humidity Cospectrum and the Refractive Index Spectrum , 1987 .

[20]  N. Ben-yosef,et al.  Splitting-source model for the statistics of irradiance scintillations , 1988 .

[21]  U. Högström.  Non-dimensional wind and temperature profiles in the atmospheric surface layer: A re-evaluation , 1988 .

[22]  Edgar L. Andreas,et al.  Estimating Cn 2 over snow and sea ice from meteorological data , 1988 .

[23]  R. Frehlich,et al.  Estimation of the parameters of the atmospheric turbulence spectrum using measurements of the spatial intensity covariance. , 1988, Applied optics.

[24]  R. A. Bohlander,et al.  Turbulence-induced millimeter-wave scintillation compared with micrometeorological measurements , 1988 .

[25]  A. Holtslag,et al.  Applied Modeling of the Nighttime Surface Energy Balance over Land , 1988 .

[26]  S. P. S. Arya,et al.  Introduction to micrometeorology , 1988 .

[27]  Edgar L. Andreas.  Estimating Averaging Times for Point and Path-Averaged Measurements of Turbulence Spectra , 1988 .

[28]  John F. B. Mitchell,et al.  THE "GREENHOUSE" EFFECT AND CLIMATE CHANGE , 1989 .

[29]  E. L. Andreas.  The refractive index structure parameter, C2n, for a year over the frozen Beaufort Sea , 1989 .

[30]  Edgar L. Andreas,et al.  Two-Wavelength Method of Measuring Path-Averaged Turbulent Surface Heat Fluxes , 1989 .

[31]  Edgar L. Andreas.  Selected papers on turbulence in a refractive medium , 1990 .

[32]  V. Thiermann,et al.  The measurement of turbulent surface-layer fluxes by use of bichromatic scintillation , 1992 .

[33]  G. R. Ochs,et al.  Measuring surface-layer fluxes of heat and momentum using optical scintillation , 1992 .

[34]  E. L. Andreas.  Uncertainty in a Path-averaged Measurement of the Friction Velocity u* , 1992 .

[35]  G. R. Ochs,et al.  Surface-Layer Fluxes Measured Using the CT2-Profile Method , 1992 .

[36]  Rod Frehlich,et al.  Laser Scintillation Measurements of the Temperature Spectrum in the Atmospheric Surface Layer. , 1992 .

[37]  A. E. Green,et al.  Surface-layer scintillation measurements of daytime sensible heat and momentum fluxes , 1994 .

[38]  D. Lenschow,et al.  How long is long enough when measuring fluxes and other turbulence statistics , 1994 .

[39]  B. Hurk,et al.  The scintillation method tested over a dry vineyard area , 1995 .

[40]  Edgar L. Andreas,et al.  A New Formulation for the Bowen Ratio over Saturated Surfaces , 1996 .

[41]  John C. LaRue,et al.  Surface-layer fluxes, profiles, and turbulence measurements over uniform terrain under near-neutral conditions , 1996 .

[42]  K. Trenberth,et al.  Earth's annual global mean energy budget , 1997 .

[43]  Reginald J. Hill,et al.  Algorithms for Obtaining Atmospheric Surface-Layer Fluxes from Scintillation Measurements , 1997 .

[44]  R. Hill,et al.  Probability distribution of irradiance for the onset of strong scintillation , 1997 .

[45]  Christopher W. Fairall,et al.  Similarity Relationships in the Marine Atmospheric Surface Layer for Terms in the TKE and Scalar Variance Budgets , 1998 .

[46]  Larry Mahrt,et al.  Flux Sampling Errors for Aircraft and Towers , 1998 .

[47]  A. E. Green,et al.  Measuring Sensible Heat Flux Density over Pasture Using the ct2-Profile Method , 1999 .

[48]  E. L. Andreas.  Probability distributions for scintillometer-derived values of the inner scale and the refractive index structure parameter and their implications for averaging , 2000 .

[49]  Kenneth L. Davidson,et al.  Estimating the Refractive Index Structure Parameter () over the Ocean Using Bulk Methods. , 2000 .

[50]  P. Guest,et al.  Measurements near the Atmospheric Surface Flux Group tower at SHEBA: Near‐surface conditions and surface energy budget , 2002 .

[51]  E. L. Andreas.  Parameterizing Scalar Transfer over Snow and Ice: A Review , 2002 .

[52]  J. Curry,et al.  Surface Heat Budget of the Arctic Ocean , 2002 .

[53]  O. Hartogensis,et al.  Displaced-Beam Small Aperture Scintillometer Test. Part Ii: Cases-99 Stable Boundary-Layer Experiment , 2002 .

[54]  A. Smedman,et al.  Displaced-Beam Small Aperture Scintillometer Test. Part I: The Wintex Data-Set , 2002 .