# Multi-LEO Satellite Stereo Winds
## 4 Discussion
### Validation
#### 4.1.2 LiDAR Layer Heights
It shows two examples of LiDAR versus stereo height for 21 December 2021: an LWIR case over the Arctic and a visible case over the Antarctic. Both show large populations of differences near zero. The LWIR case has more of a positive bias in the central part of its histogram but both cases show asymmetry to the positive side. This is to be expected, since LiDAR may identify a layer height at an optical depth less than that of the imagery. While LiDAR provides a precision measurement of a layer height at an optical thickness that may be thinner than that of the imagery, the cloud top is not necessarily the relevant height for the wind assignment. The stereo method uses a pattern that may contain objects with a diverse set of heights and the retrieval is based on how that pattern appears \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & \multicolumn{3}{c}{**Stereo-Wind Case**} & \multicolumn{3}{c}{**Ground Points**} & \multicolumn{3}{c}{**CALIOP**} \\
**Case** & **Pole** & **Date** & **Band** & \(N\) & **u(lb)** & **\(\sigma\)(lb)** & **u(lb)** & **u(lb)** & **\(\sigma\)(lb)** \\ \hline
3A & N & 21 December 2021 & LWIR & 24,702 & \(-1.6\) & 206.0 & 339 & 322.6 & 459.4 \\
3B & N & 21 December 2021 & LWIR & 44,317 & 12.3 & 153.7 & 417 & 240.3 & 415.3 \\
3A & S & 21 December 2021 & LWIR & 15,252 & \(-0.9\) & 275.9 & 276 & 114.6 & 501.5 \\
3B & S & 21 December 2021 & LWIR & 26,308 & 21.0 & 170.4 & 647 & \(-\)28.0 & 463.4 \\
3A & N & 9 July 2021 & LWIR & 772.6 & 2.3 & 236.0 & 514 & 53.5 & 469.7 \\
3B & N & 9 July 2021 & LWIR & 17,451 & 24.4 & 163.5 & 299 & 10.1 & 420.4 \\
3A & S & 9 July 2021 & LWIR & 23,501 & 0.4 & 251.5 & 88 & 352.0 & 549.5 \\
3B & S & 9 July 2021 & LWIR & 31,642 & \(-\)0.52 & 197.0 & 242 & 364.4 & 355.9 \\
3B & S & 21 December 2021 & VIS & 63,943 & 8.3 & 145.4 & 746 & \(-\)31.5 & 435.2 \\
3B & N & 21 December 2021 & MWIR & 36,547 & 8.5 & 170.5 & 284 & 189.1 & 413.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Ground-point statistics and CALIOP LiDAR comparisons. The height (\(l\)) difference means \(\mu\) and standard deviations \(\sigma\) of each population \(N\) are reported for the indicated case. Figure 12: Collocated CALIOP–stereo height differences for 21 December 2021 over the Arctic in LWIR (**a**) and Antarctic in VIS (**b**). The mean differences between the collocated LiDAR and stereo heights are estimated for each stereo-wind site using the MAD method. to translate in time and with changing viewing perspectives. The height and wind velocity are therefore effective ones that are characteristic of the pattern. Moreover, in low wind shear conditions within an atmospheric layer, either a height assigned based on cloud tops or a pattern height would apply equally well and a difference between the two is not a wind height assignment error. A similar analysis using the Aeolus Doppler wind LiDAR could also be attempted; however, its requirement to observe the dark side of the terminator will limit the opportunities to collocate with MODIS near the poles. The LiDAR standard deviations in Table 2 are consistently larger than those of the ground points, but this may overestimate the stereo-wind errors.