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arxiv: 2607.05207 · v1 · pith:C2LYQBQK · submitted 2026-07-06 · cs.CV · cs.LG

Probing Geospatial SSL Representations with Environmental Signals

Rohita Mocharla , Vishal M. Patel This is my paper

Reviewed by Pith T0 review T1 audit T2 compute T3 formal T4 kernel 2026-07-07 23:24 UTCglm-5.2pith:C2LYQBQKrecord.jsonopen to challenge →

classification cs.CV cs.LG
keywords self-supervised learningremote sensingERA5 reanalysisrepresentation probingsatellite imageryenvironmental variablesgeospatial foundation modelsrepresentation geometry
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The pith

Satellite AI models silently encode weather and climate data

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

This paper investigates whether self-supervised learning models trained on satellite imagery absorb physically meaningful environmental information — temperature, precipitation, solar radiation, surface pressure, and soil water — despite never being explicitly trained to predict these variables. The authors probe frozen representations from several geospatial foundation models using co-located ERA5 reanalysis data as ground truth, testing both linear and nonlinear decodability. They find that models with nearly identical downstream task performance can encode vastly different amounts of environmental signal, and that the degree to which these signals are linearly accessible from the representation correlates with performance on environmentally dependent tasks such as agriculture and disaster mapping. The authors also apply intrinsic geometric diagnostics — uniformity, effective rank, alignment, and off-diagonal covariance — and find that some of these properties, particularly uniformity and effective rank, are associated with environmental signal accessibility. The paper releases an extended dataset pairing ERA5 variables with the SSL4EO satellite imagery dataset to support future physically grounded evaluation.

Core claim

The central discovery is that self-supervised representations of satellite imagery encode physically meaningful environmental variables (temperature, precipitation, solar radiation, surface pressure, soil water) that were never part of the training objective, and that the linear accessibility of these signals — not merely their presence — is associated with downstream task performance on environmentally dependent domains like agriculture and disaster response. This holds across both controlled models trained identically on the same data (DINO, MAE, MoCo) and publicly available geospatial foundation models. The finding that linear decodability matters more than mere encoding suggests that how

What carries the argument

The central mechanism is the probing protocol: frozen encoder embeddings from satellite imagery models are fed to ridge regression (linear) and MLP (nonlinear) probes trained to predict co-located ERA5 reanalysis variables. Probe selectivity is verified against randomly permuted targets. Intrinsic representation metrics — alignment, uniformity, effective rank, and off-diagonal covariance — characterize the geometry of the embedding space independently of any task. Spearman correlations between probe R², intrinsic metrics, and downstream PANGAEA benchmark scores (broken into agriculture, disaster, marine, and urban domains) establish the associative relationships.

If this is right

  • If environmental signal accessibility predicts downstream performance on agriculture and disaster tasks, future SSL pretraining objectives could be designed to explicitly preserve linear accessibility of environmental variables, potentially improving transfer to these domains.
  • The finding that models with similar benchmark scores differ substantially in environmental encoding suggests current geospatial benchmarks are blind to representation properties that matter for real-world environmental applications.
  • The released ERA5-annotated dataset extension enables a new evaluation axis for geospatial foundation models — physical grounding — that complements task-driven benchmarks and could become standard in model comparison.
  • The weak association between representation metrics and out-of-distribution robustness, while preliminary, suggests that environmental probing and intrinsic geometry may not be sufficient predictors of robustness, leaving open what representation properties do govern generalization under distribution shift.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If linear accessibility of environmental signals is more predictive of downstream utility than their mere presence, this implies that SSL objectives that produce geometrically uniform, high-rank representations may be preferable for environmental applications — even if nonlinear probes show equivalent total information content.
  • The observation that DINOv3 Sat achieves strong ERA5 probe performance from RGB-only input, outperforming multispectral models, raises the question of whether environmental signals are encoded indirectly through surface features (vegetation, terrain, atmospheric visibility) rather than through direct spectral sensitivity, which could be tested by probing individual spectral bands.
  • The domain-specific associations (strongest for agriculture and disaster, weaker for marine and urban) suggest that environmental signal encoding may be a proxy for whether the representation captures land-surface processes, which are most relevant to agriculture and disaster tasks — implying that different environmental variables might better predict performance in marine or urban domains.

Load-bearing premise

The paper assumes that ERA5 reanalysis variables are physically related to what Sentinel-1 and Sentinel-2 sensors record, so that high probe scores indicate genuine environmental signal encoding rather than spurious statistical correlations. The authors do not provide a quantitative physical model linking specific ERA5 variables to sensor measurements, leaving open the possibility that probe performance reflects confounded correlations with land cover or seasonal patterns.

What would settle it

If a model trained on imagery from regions where ERA5 variables are decorrelated from surface reflectance (e.g., persistently cloud-covered areas where atmospheric variables vary independently of surface observations) still achieves high ERA5 probe R², this would suggest the probe is learning spurious geographic or seasonal correlations rather than genuine environmental signal encoding.

Figures

Figures reproduced from arXiv: 2607.05207 by Rohita Mocharla, Vishal M. Patel.

Figure 1
Figure 1. Figure 1: Overview of the proposed evaluation framework. Frozen encoders pretrained on large-scale Earth observation data produce fixed embeddings that are evaluated along two complementary axes: (1) ERA5 [12] probes measuring the linear and nonlinear accessibility of physically grounded environmental variables, and (2) intrinsic representation diagnostics (Uniformity [35], Effective Rank [28], Align￾ment [35], and … view at source ↗
Figure 2
Figure 2. Figure 2: Probe selectivity analysis for the control models. Both the linear and MLP probes exhibit high selectivity for DINO, in￾dicating that ERA5 environmental information is encoded in the representation. MAE [11] and MoCo [10] show slight improve￾ment on ground-truth targets compared to randomized targets. For comparison between the SSL4EO [36] control mod￾els and geospatial foundation models, ridge regression … view at source ↗
Figure 3
Figure 3. Figure 3: Relationship between diagnostic metrics and probe performance. To identify the relationship between diagnostic metrics and probe performance we calculate the Spearman coefficient for the evaluated models. Metrics that show a relationship to ERA5 probe performance are outlined in red. We observe an association between eRank and the linear (ρlinear = 0.42) and MLP probe (ρMLP = 0.40). We observe a moderate a… view at source ↗
Figure 4
Figure 4. Figure 4: Relationship between ERA5 probe performance and downstream task performance across PANGAEA [21] application domains. Domain performance is measured as the mean mIoU across datasets within each domain: agriculture (PATIS [7, 8], Crop Type Mapping [29, 38], AI4Farms [22]), disaster (Sen1Fl11 [25], HLS BurnScar [15]), marine (MADOS [17]), and urban (Five Billion Pixels [33], DynamicEarthNet [32], SpaceNet 7 [… view at source ↗
Figure 5
Figure 5. Figure 5: Relationship between task performance and diagnos￾tic metrics. We use the same task breakdown as [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: Spatial distribution of ERA5 variables for S-2 and S￾1. The spatial graph shows both the training and test set combined, showcasing the global coverage of the dataset [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Distribution of ERA5 variables for split training and test sets for S2 and S1. The two figures show the distribution of each of the ERA5 variables for train (blue) and test (orange) sub￾sets. The figure on the top is the S-2 co-locate ERA5 distribution and the figure on the bottom is the S-1 co-locate ERA5 variables. 11 [PITH_FULL_IMAGE:figures/full_fig_p011_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Probe performance as a function of training set size. Saturation experiment used to determine the probe training subset size. Ridge regression (left) exhibits little improvement beyond approximately 50K training samples. The MLP probe (right) is trained using a fixed optimization budget of 8K gradient steps; consequently, larger training sets receive fewer effective training epochs. Based on these results,… view at source ↗
Figure 10
Figure 10. Figure 10: MLP hyperparameter search. We perform a grid search over learning rate, hidden dimension, and dropout rate. The selected configuration corresponds to the highest mean validation R 2 across the five ERA5 prediction tasks. The top graph shows the results for the MoCo objective, while the bottom graph shows the results for the MAE objective. The DINO objective is omitted because it showed minimal variation a… view at source ↗
Figure 11
Figure 11. Figure 11: Ridge regression hyperparameter search. We sweep the regularization parameter, α, for each SSL objective. Each panel summarizes the highest validation R 2 obtained for every ERA5 prediction task together with its corresponding optimal value of α. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Preliminary OOD analysis. The heatmap summarizes the correlation between the four intrinsic metrics and the five dis￾tribution shifts evaluated by EarthShift [4]. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_12.png] view at source ↗
read the original abstract

Self-supervised learning (SSL) is designed to learn generic, transferable representations rather than representations optimized for a single task. Most geospatial benchmarks evaluate representations solely through downstream tasks, providing limited insight into the information encoded within the representation itself. We ask a different question: do SSL representations of satellite imagery preserve statistical associations with environmental variables that co-vary with the imaging process? To answer this question, we probe SSL representations using co-located ERA5 reanalysis variables, a global dataset of physically consistent environmental variables, including temperature, precipitation, surface solar radiation, surface pressure, and volumetric soil water. These variables are physically related to the spectral reflectance and radar backscatter recorded by Sentinel-1 and Sentinel-2, making them meaningful evaluation targets despite not being used during SSL pretraining. We complement this probing analysis with intrinsic representation metrics to characterize representation geometry and investigate how these properties relate to downstream performance and the encoding of environmental signals. Using DINO, MAE, and MoCo models trained under identical conditions, we show that representation-level metrics distinguish models with similar downstream benchmark performance, providing complementary information beyond task-driven benchmarks. We further find that the linear accessibility of environmental signals is associated with performance on environmentally dependent tasks in the PANGAEA benchmark. Finally, we release ERA5 annotations co-located with the SSL4EO dataset to enable physically grounded representation evaluation for future geospatial foundation models.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 7 minor

Summary. This paper introduces a representation-level evaluation protocol for geospatial SSL models that combines (1) probing with co-located ERA5 reanalysis variables (temperature, precipitation, solar radiation, surface pressure, soil water) to measure environmental signal accessibility, and (2) intrinsic representation diagnostics (alignment, uniformity, effective rank, off-diagonal covariance). The authors evaluate three SSL4EO control models (DINO, MAE, MoCo) trained under identical conditions, plus nine publicly available geospatial foundation models. Key findings include: (a) models with similar downstream PANGAEA performance encode substantially different amounts of ERA5-recoverable environmental information; (b) linear accessibility of ERA5 variables is associated with performance on environmentally dependent downstream tasks (agriculture: ρ_linear=0.75, disaster: ρ_linear=0.68); (c) uniformity and effective rank show moderate associations with probe performance. The authors release ERA5 annotations co-located with SSL4EO to enable future evaluation. The experimental design is reasonable: controlled SSL4EO models trained under identical conditions, selectivity analysis following Hewitt and Liang to rule out memorization, and hyperparameter sweeps for probe design.

Significance. The paper addresses a genuine gap: existing geospatial benchmarks (Geo-Bench, PANGAEA, EarthShift, NeuCo-Bench) evaluate representations solely through downstream task performance, offering limited insight into what information is encoded. The ERA5-SSL4EO co-located dataset release is a tangible community contribution. The selectivity control (Figure 2) following Hewitt and Liang is a methodological strength. The finding that linear (not MLP) probe performance correlates with downstream task utility is interesting and suggests that accessibility, not mere presence, matters. The work is exploratory and associative rather than causal, which the authors acknowledge. The stress-test concern about geographic/seasonal confounds is the most substantive issue: ERA5 variables are largely determined by location and season, so a representation encoding landscape identity could trivially predict them. This is a real concern that the paper does not address, though it does not invalidate the contribution entirely—the dataset release and the probing protocol remain useful even if the interpretation of results requires refinement.

major comments (3)
  1. Section 4.2 and Figure 2: The selectivity control only checks against randomly permuted ERA5 labels. It does not control for the possibility that the probe is recovering geographic location or season rather than environmental physics per se. ERA5 variables (temperature, precipitation, solar radiation, soil water, pressure) are strongly determined by latitude, longitude, and day-of-year. Any representation encoding landscape identity (desert vs. tundra vs. rainforest) will trivially predict these variables. The paper's seasonal alignment metric (Section 3.2) shows awareness of seasonal confounds but uses it only as a diagnostic, not as a control in the probing experiments. This is load-bearing because the central claim—that 'SSL representations encode physically meaningful environmental signals'—could be reduced to 'SSL representations encode geographic identity,' which is much less novel
  2. Figure 4 and Section 5: The Spearman correlations between ERA5 probe R² and downstream task performance (agriculture: ρ_linear=0.75, disaster: ρ_linear=0.68) are computed over n=11 models (Table 2). With this sample size, the statistical significance of ρ=0.75 is marginal (p≈0.008 for a one-tailed test, but the paper does not report p-values or confidence intervals). More importantly, if both ERA5 probe R² and downstream agriculture/disaster performance are proxies for 'how well the model encodes where and when the image was taken,' the correlation becomes trivially explained. The paper should at minimum report p-values and discuss whether the correlation survives after partialing out geographic/seasonal confounds
  3. Table 2: Several models show negative R² values (ScaleMAE: Linear R²=-0.44, MLP R²=-0.17; SSL4EO MAE: Linear R²=-0.43, MLP R²=-0.18; SSL4EO MoCo: Linear R²=-0.07, MLP R²=-0.07). Negative R² means the probe performs worse than predicting the mean. The paper does not discuss what negative R² implies about the representation or the probe. Are these models actively encoding anti-correlated information, or is the probe failing to converge? This affects interpretation of the Spearman correlations in Figure 4, where these negative-R² models serve as data points
minor comments (7)
  1. Section 4.3: The MLP probe is trained with a fixed optimization budget of 8K gradient steps regardless of training set size (Figure 9 caption), meaning larger training sets receive fewer effective epochs. This confounds training set size with optimization budget. The paper should clarify whether the 50K subset choice is affected by this interaction
  2. Table 2: The 'Bold refers to best performing model for that metric' caption is ambiguous—should specify whether bolding is per-column
  3. Section 7.3: The OOD analysis uses n=5 models, which the authors acknowledge is exploratory. Consider stating this limitation more prominently in the main text (Section 5) rather than only in the appendix
  4. Figure 3: The Spearman coefficients (ρ_linear=0.42, ρ_MLP=0.40, ρ_linear=0.44) are described as showing 'association' but the strength is weak-to-moderate. Consider using more precise language (e.g., 'weak positive association')
  5. Section 4.4: The paper states inputs are preprocessed using each model's normalization statistics and spectral bands, but all models are evaluated using Sentinel-2 imagery only. Models pretrained with multispectral data (CROMA, DOFA) may be disadvantaged. This should be noted as a limitation
  6. Table 3: The cardinality counts for S-1 and S-2 differ slightly (867216 vs 867164). Clarify whether this reflects missing ERA5 data for specific observations or a processing artifact
  7. Section 1: The phrase 'directly influence the spectral reflectance and radar backscatter' overstates the physical link. Temperature, for instance, influences vegetation phenology which affects reflectance, but the link is indirect. Consider softening to 'are statistically associated with'

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for a careful and constructive review. The referee correctly identifies that the geographic/seasonal confound is the most substantive limitation of the current manuscript, and we agree that additional controls are needed. We address each comment below.

read point-by-point responses

  1. Referee: Section 4.2 and Figure 2: The selectivity control only checks against randomly permuted ERA5 labels. It does not control for the possibility that the probe is recovering geographic location or season rather than environmental physics per se. ERA5 variables are strongly determined by latitude, longitude, and day-of-year. Any representation encoding landscape identity will trivially predict these variables. The central claim could be reduced to 'SSL representations encode geographic identity,' which is much less novel.

    Authors: We agree this is the most important limitation of the current manuscript. The selectivity control following Hewitt and Liang rules out probe memorization but does not rule out the possibility that the probe is recovering geographic or seasonal identity rather than environmental physics per se. This is a genuine concern because ERA5 variables are strongly determined by location and time of year. We will address this in the revision by adding a location/season baseline probe: we will train a ridge regression probe using only (latitude, longitude, day-of-year) as inputs to predict ERA5 variables on the same evaluation split. This establishes the performance ceiling achievable from geographic identity alone. If SSL representations exceed this baseline, it provides evidence that they encode environmental information beyond what is recoverable from location and season. We will also report partial Spearman correlations between ERA5 probe R² and downstream task performance after controlling for a geographic/seasonal proxy (e.g., the R² of the location-only baseline). We acknowledge that even this control is imperfect—geographic identity and environmental physics are not fully separable—but it meaningfully strengthens the interpretation beyond the current manuscript. We will revise the claims in Sections 4.2 and 5 to explicitly state this caveat and frame the contribution as 'SSL representations encode environmental signals, some of which exceed what is recoverable from geographic identity alone,' rather than making the stronger unqualified claim. revision: yes

  2. Referee: Figure 4 and Section 5: The Spearman correlations between ERA5 probe R² and downstream task performance are computed over n=11 models. With this sample size, the statistical significance of ρ=0.75 is marginal. The paper does not report p-values or confidence intervals. More importantly, if both ERA5 probe R² and downstream agriculture/disaster performance are proxies for 'how well the model encodes where and when the image was taken,' the correlation becomes trivially explained. The paper should at minimum report p-values and discuss whether the correlation survives after partialing out geographic/seasonal confounds.

    Authors: The referee is correct on both points. We will add p-values and bootstrap 95% confidence intervals for all reported Spearman correlations in the revised manuscript. For the agriculture correlation (ρ_linear=0.75, n=11), the two-tailed p-value is approximately 0.008, which is significant at conventional thresholds but should be interpreted with caution given the small sample size. We agree that the confound concern applies here as well: if both ERA5 probe performance and downstream agriculture/disaster performance partly reflect how well the model encodes geographic and seasonal information, the correlation could be inflated. We will address this by reporting partial Spearman correlations after controlling for the location-only baseline R² (as described in our response to the first comment). If the correlation survives partialing, it strengthens the claim; if it attenuates substantially, we will report this honestly and adjust our interpretation accordingly. We will also add an explicit discussion of this limitation in Section 5 and the Conclusion. revision: yes

  3. Referee: Table 2: Several models show negative R² values (ScaleMAE: Linear R²=-0.44, MLP R²=-0.17; SSL4EO MAE: Linear R²=-0.43, MLP R²=-0.18; SSL4EO MoCo: Linear R²=-0.07, MLP R²=-0.07). Negative R² means the probe performs worse than predicting the mean. The paper does not discuss what negative R² implies about the representation or the probe. Are these models actively encoding anti-correlated information, or is the probe failing to converge? This affects interpretation of the Spearman correlations in Figure 4, where these negative-R² models serve as data points.

    Authors: We thank the referee for raising this point, which we should have discussed explicitly. Negative R² in this context does not indicate that the representation encodes anti-correlated information. Rather, it indicates that the probe's predictions on the held-out validation set are worse than predicting the per-variable mean of the training set. This can occur when the representation contains little linearly decodable environmental signal and the probe overfits to noise in the training set, producing predictions that are systematically miscalibrated on the validation distribution. For the linear probe specifically, the fixed regularization parameter (α=10,000) used for cross-model comparison may be suboptimal for models whose representations are poorly conditioned (e.g., ScaleMAE's high off-diagonal covariance of 401.76), leading to poor generalization. We note that for the SSL4EO control models, the selectivity analysis (Figure 2) used independently optimized regularization and showed that MAE and MoCo still performed near the randomized baseline, consistent with the negative R² values in Table 2. We will add a paragraph in Section 5 discussing negative R² values, their likely causes (probe overfitting on representations with low environmental signal content, combined with fixed regularization for cross-model consistency), and their implications for the Spearman correlations. We note that including or excluding the negative-R² models from the correlation analysis does not qualitatively change the direction of the association, but we will report both versions in the revision for transparency. revision: yes

Circularity Check

0 steps flagged

No circularity found: probing targets (ERA5), intrinsic metrics, and downstream benchmarks are all external to the SSL pretraining and to each other.

full rationale

The paper's central claim is that SSL representations encode physically meaningful environmental signals (measured by ERA5 probing) and that linear accessibility of these signals correlates with downstream task performance (PANGAEA). Walking the derivation chain: (1) ERA5 reanalysis variables are external data from Hersbach et al. [12], never used during SSL pretraining, so probing them is not circular. (2) Intrinsic metrics (alignment, uniformity, eRank, offDiag) are computed directly from frozen representations using standard definitions from Wang & Isola [35], Roy & Vetterli [28], and Bardes et al. [2] — no fitting to the target result. (3) The Spearman correlations between ERA5 probe R² and PANGAEA downstream mIoU connect two independently measured quantities (probe performance vs. external benchmark performance), so the correlation is not forced by construction. (4) The selectivity control (Figure 2) uses randomly permuted ERA5 labels as a null baseline, which is a standard non-circular control. (5) The SSL4EO dataset [36] is cited for training data, but the authors are not the primary authors of that dataset (Wang et al. is a different group), so even this citation is not self-citation. The paper does not fit a parameter to a subset of data and then predict a closely related quantity. It does not invoke a self-authored uniqueness theorem. The metrics and targets are independently defined and externally sourced. The skeptic's concern about geographic/seasonal confounds is a validity threat (correctness risk), not a circularity issue — the ERA5 variables are genuinely external targets regardless of whether they proxy for location. No step in the derivation chain reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

6 free parameters · 3 axioms · 0 invented entities

The paper introduces no new entities (particles, forces, dimensions). The free parameters are standard hyperparameters for probing and intrinsic metrics, selected via search or following prior work. The axioms are domain assumptions about the physical link between ERA5 and satellite observations, and standard statistical assumptions about probing and correlation.

free parameters (6)
  • Ridge regression regularization alpha = 10000
    Fixed regularization parameter for foundation model comparison (Section 4.3). Selected to ensure consistent evaluation, though optimized independently for selectivity analysis.
  • MLP probe hidden dimension = 256
    Chosen via hyperparameter search (Section 4.3, Appendix 7.2).
  • MLP probe dropout rate = 0.1
    Chosen via hyperparameter search (Section 4.3, Appendix 7.2).
  • Probe training subset size = 50000
    Selected through saturation experiments (Section 4.1, Appendix 7.2).
  • Alignment metric alpha = 2
    Exponent for Euclidean distance in alignment metric, following Wang and Isola (Section 3.2).
  • Uniformity metric temperature t = 2
    Temperature parameter for uniformity metric, following Wang and Isola (Section 3.2).
axioms (3)
  • domain assumption ERA5 reanalysis variables are physically related to the spectral reflectance and radar backscatter recorded by Sentinel-1 and Sentinel-2.
    Invoked in Section 1 and Section 4.2 to justify ERA5 as probing targets. The paper asserts this physical relationship but does not derive it quantitatively.
  • standard math Probe performance on true ERA5 labels exceeding randomized baseline indicates information encoded in the representation rather than probe memorization.
    Invoked in Section 3.1 and Section 4.3, following Hewitt and Liang [13]. This is a standard assumption in probing literature.
  • domain assumption Spearman correlation over the evaluated model set is a valid measure of association between representation properties and task performance.
    Used throughout Section 5. The small sample size (n=11 for main results, n=5 for OOD) limits statistical power, which the paper partially acknowledges.

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