Identify the shared satellite–satellite representativeness error

Determine the shared satellite–satellite representativeness-error variance in the triple-collocation decomposition of stereo winds, operational atmospheric-motion vectors, and radiosonde observations, which is not identifiable from three systems and four unknowns.

Background

The paper applies triple collocation to estimate the intrinsic errors of stereo wind retrievals, operational atmospheric motion vectors, and radiosonde observations. However, the two satellite systems track the same cloud and moisture features and therefore may share a representativeness error relative to the point-measuring radiosonde.

The authors introduce the shared representativeness-error variance as an additional unknown. Because the three observing systems provide insufficient independent information to estimate four variance terms, the shared component cannot be uniquely recovered, and the reported satellite and radiosonde error estimates are interpreted as bounds rather than exact values.

References

With three systems and four unknowns, $\sigma2_{\mathrm{rep}}$ is not identifiable.

— Distilling deep optical flow stereo methods to retrieve dense three-dimensional wind fields  (2609.03100 - Vandal et al., 2 Sep 2026) in Section 4, subsection “Triple collocation”