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REVIEW 4 major objections 8 minor 92 references

Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching

T0 review · 4 major / 8 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read A single frozen weather-video prior performs filtering, smoothing, and forecasting by changing only which frames are observed.

desk verdict A serious, well-ablated empirical study of latent video flow-matching for atmospheric DA; the unified-prior claim mostly holds, but the posterior approximation is never checked against a reference and the GraphDOP comparison is curve-extracted. read the letter →

arxiv 2608.05103 v1 pith:IW2ZU27A submitted 2026-08-05 cs.LG math-phmath.MPphysics.ao-phphysics.flu-dyn

Dibyajyoti Chakraborty , Romit Maulik This is my paper
classification cs.LGmath-phmath.MPphysics.ao-phphysics.flu-dyn
keywords latentvideoflow-matchingdataassimilationgenerativepriorsERA5reanalysisposteriorsamplingobservation-to-forecastensembleuncertaintyquantificationatmosphericstatereconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to show that a single pretrained generative model of global weather videos can replace the numerical forecast model in data assimilation. The authors train a latent flow-matching prior on 8-day windows of ERA5 reanalysis, then condition it on real observations through posterior sampling. They claim that because the prior generates a continuous trajectory, information propagates between observed and unobserved frames, so filtering, smoothing, and fixed-interval reconstruction are just different choices of which frames are observed. They further claim that sparse in-situ observations alone can produce full-state ensemble forecasts competitive with an observation-to-forecast model trained on much more data. If true, one frozen video prior would serve as both a background model and a forecast model for a family of assimilation tasks.

What carries the argument

The central object is the latent video flow-matching prior: a TrigFlow model (spherical interpolation between latent and Gaussian noise, $z_t = \cos(t) z_0 + \sin(t) \varepsilon$) trained on 128-channel autoencoder latents of 32-frame, 8-day ERA5 windows. At sampling time, a guided TrigFlow sampler combines the learned velocity with a DPS-style likelihood gradient evaluated at the Tweedie estimate of the clean latent, annealed by an SDA coefficient, plus a low-noise Langevin corrector, to draw posterior samples. The measurement operator $A$ (grid subsampling, bilinear interpolation at stations, or super-obbing) is the only thing that changes across tasks.

What would settle it

Run a classical ensemble or variational assimilation system (e.g., an ensemble Kalman filter or 4D-Var) on the same ERA5 truth and the same sparse IGRA/ISD observations, and compare RMSE and ensemble calibration on the withheld-station test; if the classical system beats the posterior at comparable or lower compute, the DPS-style likelihood approximation would be in doubt.

Watch

Extended reading notes

Core claim

The paper's central claim is that temporal consistency is internal to the prior: a latent video flow-matching model trained unconditionally on ERA5 windows propagates information from observed frames to unobserved frames, so the classical data-assimilation regimes (filtering, smoothing, fixed-interval reconstruction) reduce to choosing which temporal frames are observed. With real radiosonde (IGRA), surface station (ISD), and ship/buoy (ICOADS) observations, the same frozen prior reconstructs the full 69-variable atmospheric state and produces ensemble forecasts directly from observations, competitive at longer leads with GraphDOP, an observation-to-forecast system trained on a broader observing network. The authors also report that posterior samples remain geostrophically and hypsometrically consistent, and that ensemble spread is reasonably calibrated when the corrector noise is retained.

Load-bearing premise

The posterior sampler approximates the observation likelihood score using the gradient at the denoised (Tweedie) estimate with a hand-tuned annealing strength, and the paper never checks this approximation against a classical data-assimilation baseline.

Editorial extensions

If this is right

  • The same frozen prior can realize the classical DA regimes—filter (leading frames observed), smoother (middle frames observed), and fixed-interval reconstruction—with no retraining, simply by changing the observed-frame mask.
  • Full-state ensemble forecasts can be generated directly from sparse real observations, with six-day forecast skill comparable to GraphDOP at long leads and better for 2 m temperature.
  • The prior's internal temporal propagation replaces the separate emulator or numerical forecast model used in earlier snapshot-based generative DA.
  • Ensemble spread from posterior draws provides uncertainty quantification, with SSR values 0.72–0.85 across tasks, underdispersed but in the right direction for operational inflation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to treat the observation mask as a user input, turning the same prior into an interactive tool for observing-system design: one could ask which frames or stations most reduce posterior spread. The paper does not test this.
  • Because the likelihood operator is differentiable and the prior is video-based, the framework could in principle ingest future satellite radiances through a differentiable radiative-transfer operator, which the authors note is left to future work.
  • The fact that observed-window length barely changed forecast skill (Appendix C) suggests the prior's internal dynamics, not the conditioning window, dominate the forecast; a testable implication is that even shorter windows than one frame may suffice for some applications.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 8 minor

Summary. This paper trains a 3D autoencoder and a latent video flow-matching prior (TrigFlow with a DiT3D backbone) on 69-variable ERA5 windows of 32 six-hourly frames, then uses a guided sampler with a DPS-style likelihood and SDA annealing to condition this frozen prior on observations. The authors demonstrate super-resolution from coarse grids, data fusion from real IGRA and ISD station data, filtering/smoothing/fixed-interval regimes obtained by changing only which frames are observed, and direct observation-to-forecast for 2020, including a Hurricane Laura case study. The central claim is that one frozen generative video prior can act as the forecast model and likelihood in several classical DA configurations, with uncertainty quantified by the spread of posterior draws.

Significance. If the posterior samples are faithful, this is a substantial empirical contribution: a single generative prior supports multiple DA geometries and produces physically consistent states, with extensive ablations, held-out station verification, and released code. The authors are unusually transparent about limitations, including the absence of an end-to-end operational comparison and the explicitly illustrative Aardvark experiment (Appendix D). The main caveats are that the likelihood approximation is not validated against a reference posterior and that the GraphDOP comparison is not a same-protocol rerun; these issues are fixable and do not erase the value of the empirical study.

major comments (4)
  1. [Sec. 2.2-2.3, Eq. (6)-(7), Algorithm 1] The likelihood is not fully specified as a Bayesian posterior. The observation noise scale σ_y is introduced but never assigned a value; the guidance scale is task-dependent (e.g., scale 4.0 for SR vs 0.5 for station tasks in Table 13) and γ is tuned. In Algorithm 1 the gradient is multiplied by this hand-set scale, effectively tempering the likelihood. Because the abstract's core claim is that this is 'Bayesian inference' and 'posterior sampling', the paper should either report σ_y and a sensitivity analysis for the tuned constants, or validate the approximation against a reference posterior/classical DA scheme (e.g., an ensemble Kalman filter, a particle filter on a reduced problem, or a variational method). The comparisons in App. A.5 are against other approximate samplers (DAPS, DiffPIR, PnP-DM, STeP-HMC), none of which is a reference posterior. This is load-bearing for the headline claim of a unified DA approach.
  2. [Table 3] The calibration results show SSR 0.72-0.85 and empirical coverage around 0.77 versus the Gaussian target of 0.954 for 8-member ensembles. This is direct evidence that the posterior spread is overconfident, which weakens the claim that the method provides calibrated uncertainty quantification through ensemble spread. The authors note that an inflation-style correction would be needed, but the main text should either include such a correction and report the resulting SSR/coverage, or substantially qualify the UQ claims. As written, the uncertainty quantification contribution is only partially supported.
  3. [Sec. 4.4, Fig. 16] The GraphDOP and IFS skill curves are extracted from a published figure rather than obtained by running those models under the same protocol. The text states this, but the quantitative claims of being 'competitive with state-of-the-art observation-to-forecast models' and having 'clear advantages over GraphDOP at longer leads' rest on that extraction. There are no error bars or uncertainty estimates for the extracted curves, and GraphDOP uses a broader observing system. A same-protocol rerun (at least for GraphDOP) or a clearly labelled qualitative comparison with softened claims is needed.
  4. [Table 6] In the held-out station verification for IGRA, the reconstruction RMSE is consistently higher than ERA5 at the same withheld stations (e.g., t2m 3.16 vs 2.91 K, z500 165 vs 155 m2/s2, t300 1.42 vs 1.19 K, u200 3.77 vs 2.95 m/s). The sentence that the reconstruction 'closely tracks that of ERA5' understates this gap. The claim that the reconstruction is competitive with ERA5 in observation space should be revised or quantified, for example with ratios or confidence intervals.
minor comments (8)
  1. [Eq. (7)] Please state the value of σ_y used in each experiment; it is introduced as the observation noise standard deviation but no value is reported anywhere in the paper.
  2. [Fig. 16] Add a caption note stating that the GraphDOP and IFS curves are digitized from Ref. [28] and describe the extraction procedure so readers can assess the accuracy of the comparison.
  3. [Table 13] Report the guidance scale and γ values used for the station and observation-to-forecast tasks, not only for the SR sweep.
  4. [Introduction] The statement in Sec. 5 that 'an end-to-end comparison with operational assimilation is beyond our scope' is a useful caveat; consider moving it to the introduction so readers do not over-interpret the DA claims.
  5. [Appendix D] The Aardvark experiment is already flagged as illustrative, but the figure caption should also clearly say it uses a training-period observation and is not a held-out test.
  6. [App. A.5] The sentence that baseline performance 'reflects our implementations rather than the methods in general' is honest; please release the exact configurations for these baselines in the code repository to support reproducibility.
  7. [Fig. 1 caption] The phrase 'The latent video looks like Gaussian noise visually; however, it has some small structures' is informal; rephrase it in a more precise way.
  8. [Keywords] There is a missing space in 'KeywordsGenerative' at the start of the keyword line.

Circularity Check

1 steps flagged · score 2.0 of 10

The main DA chain is self-contained and non-circular; the only reduction found is a disclosed in-sample Aardvark illustration, which is minor and not load-bearing.

  1. other [Appendix D (Forecasting from the Aardvark latent observations), Fig. 27]
    "The public Aardvark release contains only one observation data point, on 2018-08-18, (which falls within our training period). A held-out, multiple initial conditions test would require an extended observation-assembly pipeline, which we leave for future work. In this simplified experiment, we observe that the Aardvark latent lowers the forecast errors, with some variables performing better than GraphDOP."

    This experiment feeds a latent observation from 2018-08-18, a date inside the 1979-2018 ERA5 training window, into the frozen prior and then verifies the resulting forecast against ERA5 for the same date. Because the prior was trained on ERA5 windows that include that date, the 'forecast' is not a strictly out-of-sample prediction; it could be produced by recall of seen states rather than by the claimed generalization of the latent video prior. The paper itself labels it 'just an illustration, not a rigorous test case benchmark' and does not use it to support the central observation-to-forecast comparisons, which are based on thirty-two disjoint 2020 initial conditions. The step is therefore a disclosed in-sample illustration rather than a load-bearing circular result.

full rationale

The paper's central derivation is not circular by construction. A frozen latent video prior is trained on ERA5 windows from 1979-2018, and all headline DA experiments condition on external observations via the likelihood of Eq. (6) and the annealed variance of Eq. (7); the observations enter through the measurement operator A, and the scoring is against held-out ERA5 frames or withheld station observations. The DPS-style likelihood at the Tweedie estimate is an approximation, and the paper does not validate it against a reference posterior, but that is a correctness and calibration concern, not a circular reduction. No fitted parameter is renamed as a prediction: the sampler hyperparameters are tuned on validation windows and applied to disjoint test initial conditions, and the GraphDOP comparison uses an external published benchmark. The only genuine reduction to training inputs is the Appendix D Aardvark forecast, which uses a training-period observation date and is explicitly described by the authors as an illustration, not a rigorous test; the main observation-to-forecast results in Sec. 4.4 are independent of it. Self-citations are present but not load-bearing: the cited prior work [22] is used only to contrast the snapshot approach with the present video prior. Overall, the derivation chain stands on its own, with one minor disclosed in-sample experiment preventing a zero score.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim depends on the trained video prior, the DPS approximation, and evaluation against ERA5. The free-parameter count is dominated by sampler hyperparameters tuned on validation data; no new physical entities are introduced.

free parameters (6)
  • guidance scale (SR) = 4.0
    Tuned by ablation on validation windows (Appendix A.4, Table 13); scales the likelihood gradient in Algorithm 1.
  • guidance scale (station tasks) = 0.5 with DSG
    Re-selected for IGRA, ISD, and joint tasks via validation sweeps (Table 14); DSG unit-normalizes the gradient.
  • SDA annealing coefficient gamma = 0.1
    Swept in Table 13; controls how quickly likelihood guidance weakens at high noise in Eq. 7.
  • corrector activation threshold sigma_c_max = 3 or 5
    Chosen in efficiency ablations (Tables 8, 9, 11); gates the Langevin corrector to low noise levels.
  • corrector noise scale lambda = 0 or 1
    Selected by calibration and accuracy ablations (Tables 3, 10, 11); lambda=1 for calibrated spread, lambda=0 for mean-seeking.
  • log-noise training distribution = ln sigma ~ N(0,1.5^2), sigma in [0.002,80]
    Hyperparameter of the TrigFlow training loss, chosen rather than derived (Sec. 3.3).
assumptions (6)
  • standard math TrigFlow spherical interpolation, Tweedie estimate, and DPM-Solver++ rotation update are valid.
    Used in Eqs. 1-2 and Algorithm 1; these are established mathematical results.
  • ad hoc to paper The DPS likelihood gradient evaluated at the Tweedie estimate is a faithful approximation to the true posterior score for the measurement operators used.
    Eq. 6 and the annealed variance Eq. 7 are approximations, not derived exactly; their validity is assumed across tasks.
  • domain assumption Observation errors are Gaussian, independent, with known sigma_y, and the measurement operator A is differentiable.
    All likelihoods use Eqs. 6-7; no treatment of correlated or non-Gaussian observation errors.
  • domain assumption ERA5 reanalysis is an acceptable ground truth for evaluation.
    All headline RMSE metrics compare to ERA5, which is also the training target of the prior (Sec. 3.1, 3.4).
  • domain assumption The frozen autoencoder decoder faithfully reconstructs all 69 physical variables from latents.
    Guidance is backpropagated through D; decoder error (AE floor in Table 8) bounds achievable accuracy.
  • domain assumption The learned 32-frame video distribution generalizes to the 2020 test period.
    Training 1979-2018, validation 2019, testing 2020; distribution shift from climate variability is assumed small.

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Cite this review

Pith. "Pith review of Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching." pith.science (2026). https://pith.science/paper/IW2ZU27A

@misc{pith2026260805103,
  author       = {Pith},
  title        = {Pith review of: Multimodal Spatiotemporal Atmospheric Data Assimilation with Latent Flow-matching},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/IW2ZU27A}},
  note         = {Machine review of arXiv:2608.05103}
}
read the original abstract

Data assimilation (DA) uses Bayesian inference to update the state of a numerical forecast model with observed data. In this study, we propose a fundamentally different, unified approach to atmospheric data assimilation. We use latent video flow-matching to sample temporally consistent trajectories from a prior trained using ERA5 reanalysis (69 variables over an 8-day window). We also use posterior sampling to assimilate real observation sources, such as those from the NOAA Integrated Global Radiosonde Archive and the Integrated Surface Database. Because the prior generates a continuous trajectory, it naturally propagates information between observed and unobserved frames. Therefore, we can perform various DA tasks, such as filtering and smoothing, simply by changing the observed frames. Moreover, we generate full-state ensemble forecasts directly from sparse observations, achieving performance competitive with state-of-the-art observation-to-forecast models.

Figures

Figures reproduced from arXiv: 2608.05103 by the authors.

Figure 1
Figure 1. Overview of the proposed method. An autoencoder [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Super-resolution reconstruction on an observed frame for the surface variables: the low-resolution observation [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Super-resolution uncertainty quantification: posterior ensemble mean (left), signed error of the mean from [PITH_FULL_IMAGE:figures/full_fig_p010_3.png] view at source ↗
Figures from the paper (39 more)
Figure 4
Figure 4. Figure 4: Zonal power spectra. The posterior sampling recovers the correct spectral slope up to high wavenumbers [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Longitudinal traces at 40.4 ◦N: ERA5 truth vs. the posterior ensemble mean with a ±2σ band [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Reconstruction scatter: ensemble mean vs. ERA5 truth at observed (red) and unobserved (grey) pixels. Points [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: SR per-frame physical RMSE per variable (six panels: t2m, u10m, v10m, q1000, z500, t850). Vertical shading [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: The two real observation sources IGRA and ISD (union of reporting sites across the eight observed frames [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: IGRA radiosonde data-fusion surface fields: ERA5 truth, posterior ensemble mean, and signed error. [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: IGRA radiosonde data fusion uncertainty quantification: ensemble mean (left) and standard deviation (right). [PITH_FULL_IMAGE:figures/full_fig_p015_10.png]
Figure 11
Figure 11. Figure 11: IGRA reconstruction vs ERA5 scatter plots for three observed variables (t2m, u10m, z500). [PITH_FULL_IMAGE:figures/full_fig_p016_11.png]
Figure 12
Figure 12. Figure 12: 2 m-temperature signed error by assimilation modality. Among the real-observations data-fusion, the joint [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: ISD surface reconstruction vs ERA5 scatter plots for three observed variables (t2m, u10m, MSLP). [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: The three temporal observation geometries over the 32-frame window, each observing 8 frames: smoother [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]
Figure 15
Figure 15. Figure 15: DA experiments: per-frame physical RMSE per variable (six panels: t2m, u10m, v10m, q1000, z500, t850) [PITH_FULL_IMAGE:figures/full_fig_p018_15.png]
Figure 16
Figure 16. Figure 16: Observations-to-forecast skill. Latitude-weighted RMSE against ERA5 versus lead over thirty-two initial [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]
Figure 17
Figure 17. Figure 17: Hurricane Laura case study: actual track (ERA5, black; minimum-MSLP) versus the sixteen individual [PITH_FULL_IMAGE:figures/full_fig_p020_17.png]
Figure 18
Figure 18. Figure 18: Hurricane Laura case study: the window starts Aug 21 00Z and the first three days are observed as Laura [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]
Figure 19
Figure 19. Figure 19: Distribution of the 10 m zonal wind u near the Laura region: ERA5 (black) against the posterior ensemble for two, three, and four days of observations. Aug 21 00Z, observing the three days in which Laura crosses the Lesser Antilles, Puerto Rico, and Hispaniola, follow…
Figure 20
Figure 20. Figure 20: Hindcast of Hurricane Laura (10 m wind speed): ERA5 (top row), two individual posterior members, the ensemble mean, and the ensemble spread (standard deviation across members, bottom row) on the four inferred days Aug 21-24 00Z. Black contours are each field’s own MSL…
Figure 21
Figure 21. Figure 21: Hindcast of Hurricane Laura’s precursor (mean sea-level pressure). Individual members develop a closed [PITH_FULL_IMAGE:figures/full_fig_p023_21.png]
Figure 22
Figure 22. Figure 22: Distribution of the 10 m zonal wind u inside the box for the hindcast, split into the observed segment (Aug 25-28, green) and the inferred precursor (Aug 21-24, red); ERA5 solid, posterior dashed. 24 [PITH_FULL_IMAGE:figures/full_fig_p024_22.png]
Figure 23
Figure 23. Figure 23: On SR, the reduced-step DPS+corr (N25) matches the 50-step DPS baseline with fewer steps and less wall time, and adding more corrector steps improves accuracy consistently. The IGRA radiosondes show a similar same ordering ( [PITH_FULL_IMAGE:figures/full_fig_p031_23.png]
Figure 23
Figure 23. Figure 23: SR sampler efficiency: SR physical RMSE per variable (six panels: t2m, u10m, v10m, q1000, z500, t850) [PITH_FULL_IMAGE:figures/full_fig_p032_23.png]
Figure 24
Figure 24. Figure 24: Physical RMSE per variable (six panels: t2m, u10m, v10m, q1000, z500, t850) vs. wall-time per draw; [PITH_FULL_IMAGE:figures/full_fig_p032_24.png]
Figure 25
Figure 25. Figure 25: Effect of grid-cell super-obbing on forecast skill: the raw clustered observations versus one super-observation [PITH_FULL_IMAGE:figures/full_fig_p039_25.png]
Figure 26
Figure 26. Figure 26: Observed-window ablation for the in-situ obs [PITH_FULL_IMAGE:figures/full_fig_p040_26.png]
Figure 27
Figure 27. Figure 27: Forecast using a single (train-period) latent observation of Aardvark (2018-08-18). GraphDOP and IFS as [PITH_FULL_IMAGE:figures/full_fig_p041_27.png]
Figure 28
Figure 28. Figure 28: Surface variables: ERA5 truth, 8-member ensemble mean, and signed error (mean [PITH_FULL_IMAGE:figures/full_fig_p043_28.png]
Figure 29
Figure 29. Figure 29: Geopotential (per pressure level), part 1/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p044_29.png]
Figure 30
Figure 30. Figure 30: Geopotential (per pressure level), part 2/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p045_30.png]
Figure 31
Figure 31. Figure 31: Zonal wind u (per pressure level), part 1/2; same panel layout as [PITH_FULL_IMAGE:figures/full_fig_p046_31.png]
Figure 32
Figure 32. Figure 32: Zonal wind u (per pressure level), part 2/2; same panel layout as [PITH_FULL_IMAGE:figures/full_fig_p047_32.png]
Figure 33
Figure 33. Figure 33: Meridional wind v (per pressure level), part 1/2; same panel layout as [PITH_FULL_IMAGE:figures/full_fig_p048_33.png]
Figure 34
Figure 34. Figure 34: Meridional wind v (per pressure level), part 2/2; same panel layout as [PITH_FULL_IMAGE:figures/full_fig_p049_34.png]
Figure 35
Figure 35. Figure 35: Temperature (per pressure level), part 1/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p050_35.png]
Figure 36
Figure 36. Figure 36: Temperature (per pressure level), part 2/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p051_36.png]
Figure 37
Figure 37. Figure 37: Specific humidity (per pressure level), part 1/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p052_37.png]
Figure 38
Figure 38. Figure 38: Specific humidity (per pressure level), part 2/2; same panel layout as Fig. 28. [PITH_FULL_IMAGE:figures/full_fig_p053_38.png]
Figure 39
Figure 39. Figure 39: IGRA: ERA5 truth vs. reconstruction at the radiosonde station locations, for a representative subset of the 63 [PITH_FULL_IMAGE:figures/full_fig_p054_39.png]
Figure 40
Figure 40. Figure 40: IGRA: ERA5 truth vs. reconstruction at off-station grid points, for the same representative subset of the 63 [PITH_FULL_IMAGE:figures/full_fig_p055_40.png]
Figure 41
Figure 41. Figure 41: ISD surface observations: ERA5 truth vs. reconstruction at stations (top) and off-station grid points (bottom), [PITH_FULL_IMAGE:figures/full_fig_p055_41.png]

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