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

4 Estimation of the momentum fluxesThe momentum fluxes u' w' and v' w'are deduced from the Doppler spectra width ofthe four oblique beams of the UHF profiler. Each components of the momentum fluxes isestimated from the difference of the variances of two pairs of opposite oblique beams:⎛v2v2 ⎞ ⎛ϕ v2v2 ⎞⎛⎜ ' 1 − ' 2 ⎟sin1 − ⎜ ' 3 − ' 4 ⎟sinϕ3v2v2 ⎞ ⎛ϕ v2v2 ⎞⎜ ' 1 − ' 2 ⎟ cos 1 − ⎜ ' 3 − ' 4 ⎟ cosϕ3u'w'=⎝ ⎠ ⎝ ⎠ and v'w'=⎝ ⎠ ⎝ ⎠2sin 2ϕs2sin 2ϕswith ϕ I the azimuth angle and ϕ s the elevation angle of the UHF beam. As an example, theestimation of the momentum fluxes, deduced from the UHF measurements made duringTRAC experiment (case of the 19/06/98), is presented in Figure 2 with normalized height.Compared to aircraft measurement, there is an underestimation for the UHF method but thetwo vertical evolutions are very similar.5 Estimation of the virtual sensible heat fluxesThe sensible heat fluxes can be deduced from the turbulent kinetic energy equation in usingthe UHF profiler data. The turbulent kinetic equation given below:⎛ ' ' ⎞∂e ct ∂ ⎜ ' ' w P ∂e ct ⎟ ⎛ ' ' u ' ' v ⎞w e ? u w v w ßw'?'ct⎜∂ ∂= −⎟ + v − et z⎜ + + −? 0 z⎟+∂z z,∂ ∂⎝ ∂ ∂⎝⎠⎠for a stationary and horizontally homogeneous flow, becomes:' ' ∂u∂v− (u w + v ' w') + ßw'?'− e = 0 ,∂z∂z1,21UHFaircraftNormalized height (Z/Zi)0,80,60,40,20-10 10 30 50 70 90Sensible heat fluxes (W m-2)Figure 3: sensible heat fluxes deduced from the UHF data and compared with theaircraft data: (a) dynamical production term, (b) thermal production term and (c)comparison of the sensible heat fluxes with aircraft measurements.The sensible heat flux can be estimated in these cases from the algebric sum (i) of theturbulent dissipation rate deduced from the Doppler spectra of the vertical velocity and (ii) ofthe dynamical production term including the momentum fluxes and the vertical gradient of thehorizontal velocity. Figure 3 presents a vertical profile of the sensible heat fluxes deducedfrom this method and compared with the aircraft data. The UHF profile overestimates theaircraft data but maintains the same vertical evolution. This overestimation can be due to theunderestimation of the momentum fluxes presented above.312