Distilling deep optical flow stereo methods to retrieve dense three-dimensional wind fields

1. Introduction

• Operational AMV height assignment depends on NWP background states, a coupling found to contribute up to 70% of overall AMV uncertainty.Stereo parallax offers a geometric alternative to NWP-dependent height assignment.Source: §1 · pp. 3–4
• Window-based normalized cross-correlation is computationally expensive and can fail to track low-texture features, motivating optical flow for stereo matching.Optical flow can generate denser flow vectors efficiently using accelerated computing.Source: §1 · p. 4
• The paper introduces WindFlow for GEO-GEO stereo retrieval, using a cross-satellite geometric solver to estimate wind heights.The solver uses tracked displacements from same- and cross-satellite image pairs.Source: Figure 1 · p. 5, §1 · p. 6
• Triple collocation found optical flow improved water vapor bands by 0.5 m s−1 but was less accurate on long-wave infrared; radiosonde fine-tuning reduced RMSVD by 18% across five GEO infrared bands.The best fine-tuning performance was on water vapor bands.Source: §1 · p. 6
• The single-satellite student expands retrieval from 33% coverage to full-disk, with an RMSVD degradation of 1.34 m s−1.The stereo model supplies the teacher winds for student training.Source: §1 · p. 6

2. Background

• Same-satellite disparities constrain motion, while cross-satellite parallax encodes height; the stereo formulation combines both to retrieve winds and height.The parallax sensitivity varies mildly with height, so it is re-evaluated iteratively during retrieval.Source: §2 · pp. 7–8
• Four two-dimensional disparity fields provide eight observations for a per-pixel weighted least-squares estimate of five states: height, position correction, and horizontal velocity.At least one cross-satellite pair must provide nonzero parallax; formal covariance supplies uncertainty estimates used for quality screening and student targets.Source: §2 · p. 8
• Deep optical flow tracks apparent pixel motion across image frames, and prior WindFlow work applied a RAFT backbone to geostationary imagery.That earlier WindFlow reproduced NOAA AMV winds but did not include tracer height, motivating this study.Source: §2 · p. 9
• Because radiosonde labels are sparse, the paper uses stereo teacher outputs to train a single-satellite student for full-disk geostationary winds.The teacher-generated dense dataset comes from overlapping satellite coverage.Source: §2 · pp. 9–10

Method overview

• The fine-tuned stereo model generates dense overlapping-domain training data for a single-satellite student that uses three consecutive geostationary frames.The study uses GOES-16/18/19 ABI imagery; ABI data are the only required input for winds and heights.Source: §3 · p. 10

Radiosonde data

• IGRA profiles are collocated to ABI scenes within ±30 minutes and paired with GEO triplets; training spans 15 months, with October–November 2025 held out for validation.Balloon drift, which can exceed 50 km during upper-tropospheric ascent, is a stated source of uncertainty.Source: §3 · p. 11

Evaluation datasets

• Evaluation includes NOAA DMWV, ERA5, and EarthCARE cloud profiles, but ERA5 is not statistically independent because it ingests both DMWV and IGRA.DMWV uses window-based feature tracking and NWP background states for height assignment.Source: §3 · p. 11

3b. Deep optical flow GEO-GEO stereo winds

• Four same- and cross-satellite optical-flow disparities feed a per-pixel weighted least-squares solve for horizontal winds and height.The solver uses column scaling and a small Tikhonov ridge to address poor conditioning.Source: §3 · pp. 11–12
• Height-dependent parallax vectors are recalculated at each estimate; full-disk median updates typically meet the 50 m stopping tolerance within two to three iterations.Updates at deep convective tops can remain larger after termination and contribute to height uncertainty.Source: §3 · pp. 12–13

3c. Tuning stereo winds with radiosondes

• Fine-tuning reduces geometric chi-squared residuals and aligns retrieved winds with radiosondes, while leaving heights unlabeled and geometrically determined.The differentiable stereo solver propagates state-space loss gradients back into the optical-flow model.Source: §3 · p. 13, 1) Differentiable solver and gradient… · p. 14

Self-supervised geometric residual

• The reduced chi-squared loss provides dense self-supervision by driving RAFT toward disparity fields jointly explainable by one state per pixel.It measures the fit of the recovered state to the observed disparity components and requires no external labels.Source: 3) Loss · pp. 14–15

Sparse radiosonde wind supervision

• Sparse radiosonde winds are matched to the retrieved-height interpolation of sonde profiles with a per-component Huber loss, indirectly providing a height signal without height labels.The sonde loss is differentiable with respect to height, but offers little height constraint where winds vary slowly with altitude.Source: 3) Loss · p. 15

Height anchor against the pretrained reference

• Without a height constraint, fine-tuning can collapse water-vapor tracer heights toward 3 km; a frozen pretrained RAFT reference and Gaussian-KL regularizer anchor height while leaving winds free to change.The collapse arises because the geometric residual can be minimized by reducing predicted displacement; only height is anchored so radiosonde supervision can correct winds.Source: 3) Loss · pp. 15–16

3d. Single satellite knowledge distillation

• To remove the stereo method’s overlap requirement, the student learns from a single-satellite temporal triplet to reproduce the teacher’s dense state and uncertainty without parallax at inference.The teacher supplies supervision unavailable directly to the student; the student mapping predicts wind, height, uncertainty, and a quality scalar.Source: 4) Optimization · pp. 16–17

1) Pseudo-label generation

• Teacher pseudo-labels are filtered by overlap validity, a chi-squared ceiling, and a physical-height bracket; their uncertainties both weight noisy labels and train student confidence estimates.The existing collocation and temporal hold-outs are retained to prevent test-region or test-month labels leaking through the teacher.Source: 1) Pseudo-label generation · p. 17

Single-satellite student model

• The student combines a RAFT optical-flow encoder for motion with a spatial-context head for height and uncertainty, and Gaussian-KL matching distills the teacher’s per-pixel predictive distribution.Inputs comprise 53 channels: three frames of 10 infrared channels, forward/backward flow for five bands, ground footprint, and satellite zenith.Source: 2) Student architecture · pp. 17–18, 3) Distillation loss · p. 18

4) Optimization and inference

• The student learns a reliability field for quality assurance analogous to the stereo teacher’s χ².At inference, its learned height-uncertainty and χ² fields support per-pixel masking at user-selectable thresholds without stereo geometry.Source: 3) Distillation loss · p. 18, 4) Optimization and inference · p. 19
• Student training uses dense teacher pseudo-labels rather than collocated radiosondes, providing a substantially larger effective training volume.Training uses AdamW with cosine annealing on 512×512 patches from bands C08, C09, C10, C12, and C14.Source: 4) Optimization and inference · pp. 18–19
• The single-sensor infrared-band representation is designed to transfer to GK2A and SEVIRI, extending three-dimensional wind retrieval across the full geostationary ring.The input bands are shared across sensors, and the full-ring capability is the goal of distillation.Source: 4) Optimization and inference · p. 19

1) Consistency with Normalized Correlation Coefficient Feature Tracking

• WindFlow produced 5.3 million quality-controlled pixels versus NCC’s 25,498 vectors, roughly 208 times the density, while resolving the same synoptic structure.The fine-tuned model yielded 5.6 million pixels.Source: Figure 2 · p. 20, 1) Consistency with Normalized… · pp. 20–21
• Retrieved heights matched with a −0.12 km bias, 1.20 km RMS difference, and 0.93 correlation, demonstrating that optical-flow disparities preserve the sub-pixel parallax signal.Height in both pipelines is determined geometrically from cross-satellite parallax.Source: Figure 2 · p. 20, 1) Consistency with Normalized… · p. 21

2) Radiosonde fine-tuning

• 18.9%: fine-tuning reduced aggregate vector RMS difference from 7.25 to 5.88 m s−1 across 1,320 held-out radiosonde collocations, with component correlations rising to 0.83 for u and 0.90 for v.The comparison scores each retrieval at its own assigned altitude.Source: Figure 3 · p. 22, 2) Radiosonde fine-tuning · p. 23
• χ2 ≤ 0.1 screening reduced RMSVD from 11.3 to 7.5 m s−1 and moved speed bias from +1.0 to −0.5 m s−1 while retaining 40% of retrievals.The χ2 ≤ 0.2 threshold used for triple collocation retains 62% of the data.Source: Figure 4 · p. 23, 2) Radiosonde fine-tuning · p. 24
• Speed bias shifted from an underestimate of 2.13 m s−1 to −0.21 m s−1, while zonal bias moved from −0.46 to +1.30 m s−1 despite reduced zonal RMS difference.The fine-tuning therefore removes the systematic slow speed bias but trades a modest mean offset in u for lower random error.Source: 2) Radiosonde fine-tuning · pp. 23–24
• RMSVD fell 46% on C08 (6.2 μm), 23% on C09 (6.9 μm), and 35% on C10 (7.3 μm), versus 2% on C12 and 6% on C14.The largest gains occur in water-vapor bands, where fine-tuning addresses the pretrained tracker’s out-of-distribution behavior rather than uniformly inflating skill.Source: 2) Radiosonde fine-tuning · p. 24

1) Triple collocation against operational AMVs

• Fine-tuning labeled only winds; heights remained unlabeled geometric WLS outputs constrained by an anchor regularizer, preserving NWP-independent height retrieval.The height validation uses independent active-sensor observations.Source: 2) Radiosonde fine-tuning · pp. 24–25
• Shared satellite representativeness error makes triple-collocation satellite variances lower bounds, but leaves within-band stereo-versus-AMV rankings unchanged; ERA5 is excluded as non-independent.Radiosonde intrinsic errors are an upper bound that absorbs unidentifiable shared error; ERA5 assimilates both AMVs and sondes and is shown only for reference.Source: 2) Radiosonde fine-tuning · pp. 25–26, Table 1 · p. 26
• Triple collocation favors stereo over operational AMVs on water-vapor bands C08, C09, and C10, but AMVs lead on long-wave C14.Stereo intrinsic error versus operational AMV intrinsic error is 3.31 versus 3.76 m s−1 on C08 (6.2 μm), 4.82 versus 5.17 m s−1 on C09 (6.9 μm), and 4.77 versus 5.28 m s−1 on C10 (7.3 μm); on C14 (11.2 μm), AMVs achieve 3.04 m s−1 versus stereo at 4.17 m s−1.Source: Figure 5 · p. 27, 1) Triple collocation against… · pp. 27–28

4c. Single-satellite student against the stereo teacher

• The student's learned quality gate provides standalone geometry-free QA, but is band-dependent, conservative, and not calibrated to geometric χ².At the strict learned threshold χ̂² ≤0.2, it admits 3,781 collocations versus the teacher’s 19,881 and prunes hardest on water-vapor bands, with C08 retaining essentially no common points; the figure instead uses χ̂² ≤0.5 to populate all bands.Source: 1) Triple collocation against… · pp. 28–29
• 4.84 m s−1 (teacher) versus 6.18 m s−1 (student) aggregate vector RMS difference against sondes means single-satellite distillation costs 1.34 m s−1 across 5,234 collocations.Component RMS differences rise from 3.58 to 4.72 m s−1 in u and from 3.25 to 4.00 m s−1 in v.Source: Figure 6 · p. 29, 1) Triple collocation against… · p. 30
• Student component biases are +0.01 m s−1 in u and +0.07 m s−1 in v, but its slow speed bias is larger than the teacher’s.The student’s speed bias is −1.52 versus −0.93 m s−1 for the teacher, consistent with variance-reducing distribution-matching distillation.Source: 1) Triple collocation against… · p. 30

• RMSVD was 23% on C08, 37% on C09, 50% on C10, 17% on C12, and 21% on C14, with the largest values on water vapor bands and the smallest on ozone and window channels.This ordering reverses the fine-tuning gains; the proposed geometric explanation is presented as an interpretation, not a demonstrated attribution.Source: 1) Triple collocation against… · pp. 30–31
• A single-satellite student runs on any satellite triplet and extends retrieval beyond stereo overlap, with a 1.34 m s−1 aggregate RMSVD increase against radiosondes and a quality field for screening.The coverage comparison is quantified in Figure 7; the student makes retrievals available over the full geostationary ring.Source: 1) Triple collocation against… · p. 31

4d. EarthCARE height validation

• At EarthCARE, the stereo teacher recovers opposing flow in upper and lower layers, while the student reproduces the upper layer but retrieves the lower layer sparsely.The upper tracer layer is near 11–13 km and the lower convective layer is between 2–5 km; the student’s sparse lower-layer retrieval is consistent with weaker height inference for low, optically thin features.Source: 1) Triple collocation against… · pp. 31, 33
• In the window band, the teacher’s vector train beyond the cirrus deck is judged spurious: RAFT can yield self-consistent disparities and low χ2 without tracking a physical feature.The paper identifies window-band cloud-edge extrapolation as a failure that geometric residuals alone do not catch, motivating band-aware screening; this judgment does not extend to clear-sky water vapor tracers.Source: 1) Triple collocation against… · pp. 32–33
• Where both systems retrieve vectors, NOAA AMVs agree with the stereo teacher in direction and height, while the teacher provides denser, more vertically complete coverage.Both products also corroborate the lower convective-layer flow where AMV coverage permits comparison.Source: 1) Triple collocation against… · p. 33
• ERA5 fills the domain with a smooth wind field but does not represent cloud structure and averages across the sharp directional shear resolved by the observational systems.Source: 1) Triple collocation against… · p. 33

5. Discussion and Conclusion

• Radiosonde tuning reduced aggregate RMSVD by 18%, while retrieved heights remained tracer heights paired with winds and independent of NWP.The differentiable optical-flow retrieval replaces window-based feature tracking in the GEO-GEO stereo framework.Source: §5 · pp. 33–34
• Stereo intrinsic errors are below operational AMVs on all three water-vapor bands, with the ordering reversed on the long-wave window band.The authors view stereo optical-flow winds as complementary to the operational chain, with the largest impact in moisture channels.Source: §5 · p. 34
• The stereo teacher was distilled into a single-satellite student that extends retrieval from overlap regions to full-disk GEO imagery.The student reports quality assurance itself, at a cost of 1.34 m s−1 RMSVD.Source: §5 · p. 34
• Optical-flow winds inherit brightness-constancy limits: condensation, evaporation, and convection can change brightness and mix feature growth with advection.At 10-minute full-disk cadence, features can evolve between frames; shorter mesoscale cadence would reduce evolution but shrink displacement signals toward the sub-pixel noise floor.Source: §5 · p. 34
• The five-state solve assumes one tracer per pixel, so multilayer scenes inflate χ² and become coverage gaps rather than layered retrievals.Self-consistent disparities can return low χ² that quality control misses; formal height uncertainty, disparity coherence, and window-band texture masks are proposed screening priorities.Source: §5 · pp. 34–35
• WindFlow pretraining used 7-km, 30-minute nature-run water-vapor fields at single levels, unlike ABI bands integrating emission across weighting functions and often containing superposed flows.Fine-tuning corrected part of the mismatch; the authors suggest synthetic ABI radiances with native cadence and multilevel structure as a path to improvement.Source: §5 · p. 34
• The student is trained from a teacher available only in the GOES-East/West overlap, and transfer to GK2A or SEVIRI remains untested.The authors identify multi-pair training as a direct path toward globally trustworthy geometric output.Source: §5 · p. 35
• Stereo heights are tracer heights self-consistent with winds and independent of NWP; accelerated optical flow removes a computational barrier to operational AMV production.The authors note that temporal tracer-height sequences could provide information about vertical motion, a wind component no current AMV product provides.Source: §5 · p. 35