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

• the power method: the two dissipation rates are inferred from the reflectivity, i.e. C 2 n.• the variance method: the KE dissipation rate is inferred from the turbulent KE.3.1 The “power” methodThe received power is related to the atmospheric reflectivity η (m 2 /m 3 ) [Probert-Jones, (1964),Doviak and Zrnic’, (1984)] By assuming that the refractive index irregularities are caused byinertial turbulence (Tatarskii, 1961; Ottersten, 1969b).η = 0.38Cn/λ 2 1/3 where Cn 2 = a 2 ɛ nɛ 1/3(7)kThese assumptions were confirmed by direct reconstructions of radar reflectivity profiles fromhigh resolution in-situ measurements (Luce et al., 1996).Refractive index fluctuations δn are induced by vertical displacements δz, that is δn =Mδz, where M is the gradient of generalised potential refractive index (Tatarskii, 1961; Ottersten,1969b). Cn 2 can therefore be expressed as a function of one or the other dissipationrates:Cn 2 = a ( ) 2 M 2 ɛ pN ɛ 1/3k⎧⎨⎩Cn 2 = γa ( ) 2 M 2 2/3N ɛk(8)Cn 2 = γ 1/3 a ( ) 2 M 2 2/3N ɛ p= F T Cn, 2 where F T is the turbu-The radar estimate of Cn 2 is a volume average, i.e. 〈Cn〉 2 Vlent fraction within the radar sampling volume. Taking into account the turbulent fraction F T(VanZandt et al, 1978, Gage et al, 1980):ɛ k = 1 ( ) 3 ( ) N 1 < C2 3/2n > Ra 3 M γ 3/2 F Tɛ p = 1 a 3 ( NM3.2 The “spectral width” method) 31γ 1/2 ( < C2n > RF T) 3/2(9)The turbulent velocities induce a spectral broadening of the backscattered echo, (e.g. Frisch andClifford, 1974; Sato and Woodman, 1982; Hocking, 1983, 1986; Nastrom and Eaton, 1997).Other non-turbulent processes may also contribute to the observed spectral width: (1) beam andshear broadening and (2) wave and 2D turbulence broadening, The causes of spectral broadeningbeing a priori independent one from the other:∆f 2 = ∆f 2 T + ∆f 2 (B+S) + +∆f 2 W (10)where ∆f (Hz) is the half-power half width of the power spectrum, the subscripts indicatingthe various contributions.• Beam and shear broadening can be evaluated knowing the beam geometry and the mean windprofile (e.g. Hocking, 1983, 1997). An alternative method for evaluating the (beam + shear)broadening by using two beam-widths was recently proposed by VanZandt et al. (2002).• The wave contribution can be reduced by short integration time or can be subtracted by usinga wave model (e.g. Nastrom and Eaton, 1997).After corrections, the turbulent velocity variance is simply related to the Doppler width:( ) 2 λrv ′ 2 = ∆fT 2 /(2 ln 2) (11)2Several others methods exist for estimating the turbulent velocity variance, mostly from MFradars (FCA, IDI).196