Local and global statistics of clear‐air Doppler radar signals

[1] A refined theoretical analysis of the clear-air Doppler radar (CDR) measurement process is presented. The refined theory builds on the Fresnel-approximated (as opposed to Fraunhofer-approximated) radio wave propagation theory, and turbulence statistics like locally averaged velocities, local velocity variances, local dissipation rates, and local structure parameters are allowed to vary randomly within the radar's sampling volume and during the dwell time. A local version of the moments theorem and the random Taylor hypothesis are used to derive first-principle formulations of all higher moments of the Doppler cross-spectrum. The mth moment is written as a convolution integral of a spectral sampling function and a generalized, mth-order refractive-index spectrum or, alternatively, as a convolution integral of a lag-space sampling function and a spatial cross-covariance function of the local refractive-index fluctuations and their local mth-order time derivatives. Closed-form expressions of the first three moments (i.e., m = 0, 1, 2) of the Doppler spectrum for the monostatic, single-signal case are derived. This refined theory, or “local sampling theory,” enables one to correctly interpret CDR observations that are collected under conditions where the applicability of the traditional “global sampling theory” is questionable. The commonly used global sampling assumptions (Bragg-isotropy, homogeneity, and stationarity of all turbulence statistics within the sampling volume and during the dwell time) may be invalid for small-scale intermittency in the mixed layer, for refractive-index sheets corrugated by gravity waves or instabilities, and for layered turbulence in the stably stratified atmosphere.

[1]  A. S. Gurvich,et al.  The Backscattering from Anisotropic Turbulent Irregularities , 1992 .

[2]  T. Tsuda,et al.  Azimuth angle variations of specular reflection echoes in the lower atmosphere observed with the MU radar , 1997 .

[3]  D. Zrnic,et al.  Doppler Radar and Weather Observations , 1984 .

[4]  K. Gage,et al.  Recent Developments in Observation, Modeling, and Understanding Atmospheric Turbulence and Waves , 2003 .

[5]  W. Neff,et al.  The fine structure of elevated refractive layers: Implications for over‐the‐horizon propagation and radar sounding systems , 1984 .

[6]  Kenneth E. Gilbert,et al.  Electromagnetic wave propagation through simulated atmospheric refractivity fields , 1999 .

[7]  David Atlas,et al.  Microscale ordered motions and atmospheric structure associated with thin echo layers in stably stratified zones , 1973 .

[8]  K. S. Gage,et al.  Vertical profiles of refractivity turbulence structure constant: Comparison of observations by the Sunset Radar with a new theoretical model , 1978 .

[9]  Shoichiro Fukao,et al.  A frequency domain radar interferometric imaging (FII) technique based on high-resolution methods , 2001 .

[10]  R. Jenny,et al.  Fundamentals of Optics , 2001 .

[11]  E. Praskovskaya,et al.  Structure‐function‐based approach to analyzing received signals for spaced antenna radars , 2003 .

[12]  meeting summary: Future Directions for Research on Meter- and Submeter-Scale Atmospheric Turbulence , 2001 .

[13]  A. Obukhov.  Some specific features of atmospheric turbulence , 1962 .

[14]  B. B. Balsley,et al.  On the Use of Radars for Operational Wind Profiling , 1982 .

[15]  A. Muschinski.  Possible Effect of Kelvin-Helmholtz Instability on VHF Radar Observations of the Mean Vertical Wind , 1996 .

[16]  H. Luce,et al.  Temperature sheets and aspect sensitive radar echoes , 2001 .

[17]  Earl E. Gossard,et al.  Radar observation of clear air and clouds , 1983 .

[18]  Joseph Werne,et al.  Stratified shear turbulence: Evolution and statistics , 1999 .

[19]  E. Gledzer,et al.  The sweeping decorrelation hypothesis and energy–inertial scale interaction in high Reynolds number flows , 1993, Journal of Fluid Mechanics.

[20]  D. Dudley,et al.  Ultra‐wideband electromagnetic pulse propagation in a homogeneous, cold plasma , 1997 .

[21]  Jürgen Röttger,et al.  Partial reflection and scattering of VHF radar signals from the clear atmosphere , 1978 .

[22]  Christopher W. Fairall,et al.  A Stochastic Model of Gravity-Wave-Induced Clear-Air Turbulence , 1991 .

[23]  Prakash Vedula,et al.  Random Taylor hypothesis and the behavior of local and convective accelerations in isotropic turbulence , 2001 .

[24]  D. A. Carter,et al.  The effect of gravity waves on specular echoes observed by the Poker Flat MST Radar , 1981 .

[25]  Andreas Muschinski,et al.  First In Situ Evidence for Coexisting Submeter Temperature and Humidity Sheets in the Lower Free Troposphere , 1998 .

[26]  P. Chilson,et al.  First observations of Kelvin‐Helmholtz billows in an upper level jet stream using VHF frequency domain interferometry , 1997 .

[27]  D. Zrnic,et al.  Reflection and scatter formula for anisotropically turbulent air , 1984 .

[28]  Richard J. Lataitis,et al.  Space and Time Filtering of Remotely Sensed Velocity Turbulence , 1999 .

[29]  R. Palmer,et al.  Atmospheric radar imaging using multiple‐receiver and multiple‐frequency techniques , 2001 .

[30]  S. Clifford,et al.  A Study of Convection Capped by a Stable Layer Using Doppler Radar and Acoustic Echo Sounders , 1974 .

[31]  S. Fukao,et al.  An investigation of tilted aspect‐sensitive scatterers in the lower atmosphere using the MU and Aberystwyth VHF radars , 1999 .

[32]  S. Fukao,et al.  Kelvin‐Helmholtz instability around the tropical tropopause observed with the Equatorial Atmosphere Radar , 2003 .

[33]  V. R. Kuznetsov,et al.  Fine-scale turbulence structure of intermittent hear flows , 1992, Journal of Fluid Mechanics.

[34]  Shiyi Chen,et al.  Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 1. Velocity field , 1996, Journal of Fluid Mechanics.

[35]  B. Bénech,et al.  Comparison of Radar Reflectivity and Vertical Velocity Observed with a Scannable C-Band Radar and Two UHF Profilers in the Lower Troposphere , 2003 .

[36]  Donald H. Lenschow,et al.  First synthesis of wind‐profiler signals on the basis of large‐eddy simulation data , 1999 .

[37]  Robert E. McIntosh,et al.  Local Structure of the Convective Boundary Layer from a Volume-Imaging Radar. , 2000 .

[38]  G. J. Phillips,et al.  The Analysis of Observations on Spaced Receivers of the Fading of Radio Signals , 1950 .

[39]  Ronald F. Woodman,et al.  Radar Observations of Winds and Turbulence in the Stratosphere and Mesosphere. , 1974 .

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

[41]  J. Röttger.  Investigations of lower and middle atmosphere dynamics with spaced antenna drifts radars , 1981 .

[42]  Jean Vernin,et al.  Direct Evidence of “Sheets” in the Atmospheric Temperature Field , 1994 .

[43]  A. M. Oboukhov.  Some specific features of atmospheric tubulence , 1962, Journal of Fluid Mechanics.

[44]  Kenneth S. Gage,et al.  Radar Observations of the Free Atmosphere: Structure and Dynamics , 1990 .

[45]  Phillip B. Chilson,et al.  Range imaging using frequency diversity , 1999 .

[46]  James M. Wilczak,et al.  Ground-based remote sensing of the atmospheric boundary layer: 25 years of progress , 1996 .

[47]  A. Leonard.  Energy Cascade in Large-Eddy Simulations of Turbulent Fluid Flows , 1975 .

[48]  D. W. van de Kamp,et al.  Data processing algorithms used by NOAA’s wind profiler demonstration network , 1994 .

[49]  W. Hocking,et al.  The structure of turbulence in the middle and lower atmosphere seen by and deduced from MF, HF and VHF radar, with special emphasis on small-scale features and anisotropy , 2001 .

[50]  Kenneth E. Gilbert,et al.  Concepts, observations, and simulation of refractive index turbulence in the lower atmosphere , 2001 .

[51]  Roger M. Wakimoto,et al.  Radar and Atmospheric Science: A Collection of Essays in Honor of David Atlas , 2003 .

[52]  J. Moum,et al.  Anisotropy of turbulence in stably stratified mixing layers , 2000 .

[53]  Ronald F. Woodman,et al.  ASPECT SENSITIVITY MEASUREMENTS OF VHF BACKSCATTER MADE WITH THE CHUNG-LI RADAR - PLAUSIBLE MECHANISMS , 1989 .

[54]  B. Stevens,et al.  Observations, experiments, and large eddy simulation , 2001 .

[55]  N. L. Abshire,et al.  Preliminary Evaluation of the First NOAA Demonstration Network Wind Profiler , 1990 .

[56]  B. Balsley,et al.  Interpretation of angle‐of‐arrival measurements in the lower atmosphere using spaced antenna radar systems , 1998 .

[57]  Andreas Muschinski,et al.  A similarity theory of locally homogeneous and isotropic turbulence generated by a Smagorinsky-type LES , 1996, Journal of Fluid Mechanics.

[58]  J. Röttger,et al.  UHF/VHF radar techniques for atmospheric research and wind profiler applications , 1990 .

[59]  W. Hocking,et al.  Absolute reflectivities and aspect sensitivities of VHF radio wave scatterers measured with the SOUSY radar , 1986 .

[60]  S. Fukao,et al.  Coherent radar imaging using Capon's method , 1998 .

[61]  Manfred Wendisch,et al.  A New Tethered Balloon-Borne Payload for Fine-Scale Observations in the Cloudy Boundary Layer , 2003 .

[62]  G. R. Stitt,et al.  Frequency domain interferometry: A high resolution radar technique for studies of atmospheric turbulence , 1987 .

[63]  P. Chilson,et al.  Implementation and Validation of Range Imaging on a UHF Radar Wind Profiler , 2003 .

[64]  Douglas C. Engelbart,et al.  Performance of the first European 482 MHz Wind Profiler Radar with RASS under operational conditions;Leistungsvermögen des ersten Europäischen 482 MHz Windprofiler Radar mit RASS unter operationellen Bedingungen , 1998 .

[65]  J. Wyngaard,et al.  Structure–Function Parameters in the Convective Boundary Layer from Large-Eddy Simulation , 1995 .

[66]  Yannick Meillier,et al.  Turbulence Measurements with the CIRES Tethered Lifting System during CASES-99: Calibration and Spectral Analysis of Temperature and Velocity , 2003 .

[67]  S. Kern,et al.  First Frequency-Domain Interferometry Observations of Large-Scale Vertical Motion in the Atmosphere , 1999 .

[68]  Richard J. Lataitis,et al.  Cross correlations and cross spectra for spaced antenna wind profilers: 1. Theoretical analysis , 1996 .

[69]  R. A. Antonia,et al.  THE PHENOMENOLOGY OF SMALL-SCALE TURBULENCE , 1997 .

[70]  Earl E. Gossard.  Radar Research on the Atmospheric Boundary Layer , 1990 .

[71]  A. S. Monin,et al.  The Structure of Atmospheric Turbulence , 1958 .

[72]  D. Fritts,et al.  Direct numerical simulation of VHF radar measurements of turbulence in the mesosphere , 2000 .

[73]  Peter T. May,et al.  An Examination of Wind Profiler Signal Processing Algorithms , 1989 .

[74]  U. Görsdorf,et al.  Enhanced Accuracy of RASS-Measured Temperatures Due to an Improved Range Correction , 2000 .

[75]  A. Kolmogorov.  A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high Reynolds number , 1962, Journal of Fluid Mechanics.

[76]  H. Óttersten.  Mean Vertical Gradient of Potential Refractive Index in Turbulent Mixing and Radar Detection of CAT , 1969 .

[77]  Gerd Teschke,et al.  Wavelet based methods for improved wind profiler signal processing , 2001 .

[78]  G. D. Nastrom,et al.  Mean Vertical Motions Seen by Radar Wind Profilers , 1994 .

[79]  Ulrich Schumann,et al.  Coherent structure of the convective boundary layer derived from large-eddy simulations , 1989, Journal of Fluid Mechanics.

[80]  S. Grossmann.  The Spectrum of Turbulence , 2003 .

[81]  Yannick Meillier,et al.  Extreme Gradients in the Nocturnal Boundary Layer: Structure, Evolution, and Potential Causes , 2003 .

[82]  B. Balsley,et al.  Bias in Mean Vertical Wind Measured by VHF Radars: Significance of Radar Location Relative to Mountains , 2000 .

[83]  J. G. Brasseur,et al.  Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. Part 2. Passive scalar field , 1999, Journal of Fluid Mechanics.

[84]  A. Muschinski.  The First Moments of the Variance- and Cross-spectra of Standard and Interferometric Clean-air-Doppler-radar Signals , 1998 .

[85]  B. B. Balsley,et al.  Doppler Radar Probing of the Clear Atmosphere , 1978 .

[86]  H. Tennekes,et al.  Eulerian and Lagrangian time microscales in isotropic turbulence , 1975, Journal of Fluid Mechanics.

[87]  T. Tsuda,et al.  Zenith-angle dependence of VHF specular reflection echoes in the lower atmosphere , 1997 .

[88]  Wayne M. Angevine,et al.  Errors in Mean Vertical Velocities Measured by Boundary Layer Wind Profilers , 1997 .

[89]  J. B. Mead,et al.  A Volume-Imaging Radar Wind Profiler for Atmospheric Boundary Layer Turbulence Studies , 1998 .

[90]  Andreas Muschinski,et al.  Fine-Scale Measurements Of Turbulence In The Lower Troposphere: An Intercomparison Between A Kite- And Balloon-Borne, And A Helicopter-Borne Measurement System , 2001 .

[91]  Andreas Muschinski,et al.  The difference between Doppler velocity and real wind velocity in single scattering from refractive index fluctuations , 2001 .

[92]  R. Frehlich,et al.  The Use of State-of-the-Art Kites for Profiling the Lower Atmosphere , 1998 .

[93]  P. E. Johnston,et al.  Range Errors in Wind Profiling Caused by Strong Reflectivity Gradients , 2002 .

[94]  James N. Moum,et al.  Length scales of turbulence in stably stratified mixing layers , 2000 .

[95]  V. I. Tatarskii.  Theory of single scattering by random distributed scatterers , 2003 .

[96]  K. S. Gage,et al.  Evidence for specular reflection from monostatic VHF radar observations of the stratosphere , 1978 .

[97]  Frank D. Eaton,et al.  A new frequency‐modulated continuous wave radar for studying planetary boundary layer morphology , 1995 .

[98]  W. Singer,et al.  Scattering properties of PMSE irregularities and refinement of velocity estimates , 2001 .

[99]  M. Alexander,et al.  Gravity wave dynamics and effects in the middle atmosphere , 2003 .

[100]  Andreas Muschinski,et al.  Turbulence and gravity waves in the vicinity of a midtropospheric warm front: A case study using VHF echo‐intensity measurements and radiosonde data , 1997 .

[101]  K. Lilly.  The representation of small-scale turbulence in numerical simulation experiments , 1966 .

[102]  Warner L. Ecklund,et al.  A UHF Wind Profiler for the Boundary Layer: Brief Description and Initial Results , 1988 .