# Three-Dimensional Wind Measurements with the Fibered Airborne Coherent Doppler Wind Lidar LIVE
## 2 Experiments
### Lidar Signal Processing  
Lidar raw data are first processed into spectrograms which show power spectral density as a function of lidar range on one axis and Doppler frequency on the other axis. Within a short time (0.3 s), called the line of sight time, the motion of the laser beam (\(6^{\circ}\)) is considered small enough to be neglected. All computed spectrograms within this line of sight time are averaged in order to reduce noise. This task is made in real time using GPU (Graphics Processing Unit) computing. Such averaged spectrograms are computed for every line of sight of a full 360\({}^{\circ}\) scan. Thus, after a full scan, spectrogram data show power spectral density as a function of line of sight angle, lidar range and Doppler frequency. From this stage, real time processing and post processing will differ. The aim of real time processing is to quickly deliver information about lidar measurement. The carrier to noise ratio (CNR) and radial wind speed are computed from spectrogram data at all lidar ranges and line of sight angles, using fast computing moments estimators along the Doppler frequency dimension. This CNR and radial wind speed data (functions of line of sight angle and lidar range) are displayed in real time by the lidar interface for monitoring purposes. The aim of post processing is to offer the best performance. Since the aircraft will operate above the planetary boundary layer (PBL), the backscatter coefficient is expected to be a hundred times lower than usual at ground level. Therefore, the best low CNR estimators must be used for wind vector retrieval. According to [15], the usual algorithms such as velocity azimuth display (VAD) are limited at low CNRs; in essence, these algorithms use radial velocity data computed from the spectrogram in a way that is similar to real time processing. The limitation at low CNRs lies in the fact that each column of the spectrogram (along the Doppler frequency dimension) has been computed within a short time (of a line of sight). Thus, retrieving information at a column scale is not efficient in terms of low CNR performance. A more efficient algorithm would work with spectrogram data as a whole along the line of sight angle dimension. According again to [15], two algorithms show excellent low CNR performance: the maximum of the function of the accumulated spectra (MFAS) and the wind vector maximum likelihood (WVML). For each lidar range, both algorithms compute the wind speed vector directly from spectrogram data along the Doppler frequency dimension and line of sight angle dimension. Both algorithms are complementary and are applied to our data during post processing. The MFAS is, in essence, well suited for signal detection. Figure 4 shows an example of low CNR spectrogram data obtained at high altitude (first range gate from the aircraft), which at first sight seems to contain only noise. The MFAS algorithm has detected the lidar signal, and its presence is highlighted by a trail of black dots. Lidar signal center frequency as a function of scan angle has a sinusoidal shape due to the projection of a constant wind vector on laser beam direction with conical motion. The phase of the sinusoidal shape is the direction of horizontal wind, its amplitude is proportional to the modulus of horizontal wind, and its offset from zero Doppler frequency is proportional to vertical wind. The MFAS algorithm makes rough assumptions about the value of horizontal wind (within the range of expected values). There is a sinusoidal shape for each assumption. As shown in Figure 5 on the left hand side, the MFAS algorithm shifts the spectrogram data of frequency in order to compensate for lidar signal center frequency dependence on scan angle. Then, the MFAS algorithm averages the compensated spectrogram data over all scan angle values, as shown in Figure 5 on the right hand side. If the assumption is roughly equal to the real value of horizontal wind, the accumulated spectra will exhibit a signal peak.