Proceedings with Extended Abstracts (single PDF file) - Radio ...

FAST AND ACCURATE CALCULATION OF SPECTRAL BEAM-BROADENING FOR TURBULENCE STUDIESW.K. HockingDept. of Physics and Astronomy, University of Western Ontario, London, Ontario. Canada.Abstract.A method is described which allows modern VHF radars to be used to quickly and accuratelydetermine spectral beam-broadening, and hence to determine atmospheric turbulencestrengths by spectral width methods. This method is superior to procedures which assumeconstant winds, or assume constant winds plus a linear wind-shear, and can be carried outquickly and efficiently on modern computers.Introduction.For the last 20 years, the techniques for measurement of atmospheric turbulence by spectralwidth methods using windprofiler radars have been well known. A very general formalismwas demonstrated by Hocking (1983), which could be applied even for complicated polardiagrams, variable wind speeds, and different pulse lengths. However, despite the generalityof this formula, it has not been properly applied over much of the recent past. Often it isassumed that the wind shows no height variation across the radar pulse, and in other cases itis assumed that the wind varies linearly with height. There are many situations in whichneither assumption is valid, and estimates of the broadening due to horizontal motion of thescatterers can be in error. This has been recognized by Nastrom (1997) and VanZandt et al.,(2002), and the latter paper has introduced an alternative “dual beam” method whichsomewhat mitigates inaccuracies in estimates of the beam-broadening effects. However, suchprocedures are still limited in that they do not properly consider the effects of the radar pulselengths, layer thickness, and so forth.Many of problems in estimation of the turbulent energy dissipation rates disappear if thespectral beam-broadening can be properly determined. A very accurate formula which maybe used for this calculation was given by Hocking (1983), and we present it again below,with an additional term which we have added to accommodate scatterer anisotropy, viz.P(f) ∝ ∫ P(θ,φ) [σ/r 2 ⊗ g(r) ] exp{ -(sin 2 (θ)/sin2(θ s )} dΩwhere P(f) represents the power spectral density as a function of frequency f, P(θ,φ) is theradar polar diagram, (θ,φ) are the polar coordinates of the scattering point, σ is thebackscatter cross-section for isotropic scatter, g(r) describes the pulse as a function of ranger, θ s is the anisotropy parameter, and dΩ is the solid angle, = sinθ dθ dφ. The symbol ⊗represents a convolution. In addition we may use the extra relation that dΩ = tan(θ)dVdφ/cos(φ –φ 0 ), where V = v r /V mag , φ 0 is the azimuthal direction of the wind, and V mag is thewind speed. The frequency f is found as f = 2/λ v r .The integration actually takes place on contours of constant radial velocity, which aregenerally hyperbolae, as shown in fig. 1. In the case that vertical velocities becomeimportant, these hyperbolae become ellipses at angles close to vertical (e.g., see Chu, 2002)but in the main they are hyperbolae.214