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

than the SA-produced σ w; the latter values are unaffected by the beam broadening. TheSTARS-measured standard deviations σ u, σv, and the horizontal momentum flux uv arealso presented in Fig. 2; these characteristics cannot be measured by other SA techniques.The STARS results show strong anisotropy of turbulence at all studied heights. One shouldnote that, independent of a specific measurement technique, caution is needed in theinterpretation of the radar-produced characteristics of turbulence; e.g., Briggs (1980),Hocking et al. (1989), Doviak et al. (1996), Praskovsky and Praskovskaya (2003a, b).Good agreement between STARS and HAD in measuring the mean winds and intensity ofthe vertical turbulent velocity seems to be expected because the considered SA techniques arerelated to each other. Let us consider the standard complex signals from two receivers E1(t)and E2( t)where t is time. The second order cross CF and SF, respectively, can be defined inthe standard way as follows (Tatarskii, 1971, chap. 1A):* *22C12( τ) = E1 () tE2 ( t+ τ) E1 () tE1() t , D12( τ) = [ S1() t − S2( t+ τ) ] ⎡⎣ S1() t − S1()t ⎤⎦Here S ( t)= E(t)E * ( t)is the instantaneous signal power, τ is the temporal separation, thebrackets denote the ensemble averages, and the superscript * denotes the complexconjugation. The auto CF and SF are particular cases of the cross functions at E1(t)= E2( t).2As shown in Praskovsky et al. (2003), D12 ( τ ) = 2 − 2 C12( τ ) . However, the CF and SFbasedSA techniques are conceptually different in spite of being formally related to eachother for a particular case of the second order functions.CF can be applied to globally statistically stationary random processes while only localstationarity is sufficient for applying SF. Physical processes in the atmosphere are almostnever globally statistically stationary while practically any process can be safely consideredas locally stationary; e.g., Tatarskii (1971, chap. 1A). Only τ → 0 is considered in STARS;the small parameter always simplifies a physical task. In particular, STARS requires asmaller number of less restrictive assumptions for deriving operational equations for σu, σv,σw, and uv than HAD needs for the only characteristic σw.154The major difference between CF and SF-based SA techniques is in the physical conceptunderlying the techniques. As a mathematical tool, the cross-CF describes the similaritybetween signals from two receivers E1(t)and E2( t + τ ) at all temporal separations− ∞ < τ < ∞ . The physical concept underlying all CF-based techniques is the tracking of thediffraction pattern and its changes, hence the tracking of a scattering medium and its changesin the illuminated volume. The cross-SF as a mathematical tool describes the differencebetween the signals S1(t)and S2 ( t + τ ) at very smallτ→ 0 ; the SF-based techniques areintrinsically differential. The physical concept underlying the techniques is the evaluation ofthe rates of spatial and temporal changes in the diffraction pattern, hence evaluation of therates of spatial and temporal changes in a scattering medium in the illuminated volume. Theoptimal spatial and temporal increments for CF methods are therefore much larger than thosesuitable for SF methods, which might lead to the preferential use of one or other method for agiven observed diffraction pattern. Due to this difference, the SF-based methods are morestrongly affected by noise with small temporal scales than the CF-based techniques, whilenoise with a large temporal scale, such as ground clutter, affects CF more strongly than SF.The difference also leads to slightly smaller values of σ wproduced by STARS than thoseproduced by HAD.