# Multi-LEO Satellite Stereo Winds
## 4 Discussion
### Validation  
#### 4.1.1 Clear-Sky Terrain Features  
Patterns that represent terrain features under clear skies are entirely satisfactory for the application of the stereo method [53]. Their retrieved wind speeds should be zero and their heights above the terrain surface should be zero. Deviations from ideal are indicative of the accuracy of the retrievals. In general, one finds numerous ground points on each polar overpass and both their retrieved heights and speeds can have noticeable biases. Ground-point retrievals are readily identified by K-means clustering in speed-height space as the cluster with the least height-speed combination. We use the time difference between the two satellites as the time scale to convert speed to distance units, before quadratically combining it with the height and sorting the clusters. The clustering population is restricted to heights above ground level less than 2 km and speeds less than 1 m/s. We can see in Figure 7, where the ground-point retrieval statistics have been plotted for each polar overpass during a one-day period, that there is a noticeable bias in all height retrievals after a first pass of processing. It is interesting to look at the disparities for the ground points, which are plotted in Figure 8. Ideally, these disparities should all cluster at the origin, since all the imagery is registered to the terrain surface; however, Figure 8 shows a clear mean offset between the SLSTR nadir and the oblique scenes and the MODIS reference that is indicative of a deregistration between the SLSTR imagery and MODIS. Figure 7: Ground-point retrieval statistics for 14 Antarctic overpasses on 21 December 2021 show biases in the retrieved heights and speeds for each overpass. The coordinate directions (\(u\), \(v\)) are oriented along the cardinal directions and remain well-defined as the swaths never include the exact location of either North or South Pole. Because the retrieval algorithm is very sensitive to small relative registration errors between SLSTR and MODIS, it is useful to conduct a second retrieval pass that reprocesses the disparities after being compensated by the means of the errors observed in the first-pass ground points. This is functionally equivalent to using ground control points from MODIS to reregister the SLSTR nadir and oblique scenes to MODIS. Like GOES-R, the MODIS registration to the terrain surface is very accurate (within 60 m [54]). SLSTR data product quality reports are published for each 27-day orbital cycle [55]. Registration errors are typically larger for the oblique view, as is the case for Figure 8.  
Figure 9 shows the ground-point retrieval statistics after the second processing pass. The compensation is carried out independently for each polar overpass whenever there is an adequate population of ground points to be found. Figure 10 shows the compensations for each overpass of a full day (14 orbits). Even if no ground points can be found on a given overpass, it could still be useful to compensate for the registration errors using the compensation from a previous orbit. The overall bias in the retrieved heights seen in Figure 7 has been effectively compensated in Figure 9 after the second processing pass. Similarly, the means for the ground-point velocities are closer to zero. It is also interesting to observe that the standard deviations of the ground-point velocities in Figure 9 are smallest when the absolute values of the SLSTR-MODIS time differences are largest. The time difference for the first overpass is \(-29\) min and increases by about 2 min per overpass until it reaches \(-1\) min for overpass 14. The approach just described shares similarities with [PERSON] and [PERSON] [56], where the registration between the forward and nadir views of ATSR was modeled from tie-point measurements. Figure 8: A population of LWIR ground-point disparities for a Terra-S3B overpass (21 December 2021 19:14Z) clearly shows the relative registration error between the SLSTR nadir and the oblique scenes and MODIS.