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Recoverable Geographic Location Information in Earth-Observation Embeddings

Peiwen Zhang, Kristie Hu, Jovana Knezevic, Shunde Yin, Kyle Gao

arXiv:2609.29151v1cs.CV

TL;DR

Downstream accuracy does not reveal whether EO foundation-model embeddings retain geographic information, which can matter for location-aware applications and geography-invariant representations. This study tests distance association and predicts locations from three models using quality-checked European solar farms. All three embeddings retain recoverable geographic information, with AlphaEarth showing the strongest distance association and lowest prediction error among the tested representations.

  • Problem

    Downstream accuracy does not reveal how strongly EO embeddings encode location, leaving the recoverability of geographic information from general-purpose embeddings without coordinate inputs unquantified.

    Source: §1 · p. 1

  • Method

    The study assesses cosine–geodesic distance association and spatially held-out coordinate prediction from three EO-model embeddings using a controlled solar-farm dataset.

    Source: §1 · p. 1, §2 · p. 1

  • Results

    All three EO foundation-model embeddings contain recoverable geographic information; AlphaEarth has the strongest distance association and lowest location-prediction error, while errors generally rise as nearby training farms are excluded.

    Source: §3.3 · pp. 3–4, §4 · p. 4

  • Takeaways & Limitations

    Geographic information content is a proposed additional criterion for auditing EO embeddings alongside downstream performance, with its desirability depending on the downstream task.

    Source: §4 · p. 4

    The findings’ generalizability is limited by uneven geographic coverage, including 81.3% of farms in Spain, and location predictability may partly reflect country- or dataset-specific patterns rather than fine-grained geographic information.

    Source: §4 · p. 4

Abstract

from arXiv · show

Earth-observation (EO) foundation models provide reusable embeddings, yet downstream task accuracy does not reveal whether these representations encode geographic information, which may be beneficial for location-aware applications but potentially detrimental when representations invariant to geographic location are desired. We therefore evaluate the geographic coordinate robustness of Tessera v1, Tessera v1.1, and AlphaEarth by testing whether coordinates can be predicted from the embedding representations using 284 quality-verified European solar farms from 2024. We assessed geographic information content information through the association between cosine and geodesic distances and through prediction of projected coordinates in EPSG:3035. Embeddings from all three EO foundation models contain recoverable geographic information. All prediction models significantly outperform training-range uniform random sampling baselines, with AlphaEarth exhibiting the strongest distance association and lowest mean geodesic error. Both Tessera variants also yielded higher geographic distance correlations than the Sentinel-2 controls. These findings motivate geographic information content as an additional criterion for auditing EO foundation models.

1. INTRODUCTION

The introduction asks whether geographic location remains recoverable from general-purpose EO embeddings, since downstream accuracy alone does not reveal geographic content. It proposes a controlled comparison of distance association and coordinate prediction across three models.

1. INTRODUCTION

  • Downstream task accuracy does not reveal how strongly EO embeddings encode location, which may help location-aware tasks but be undesirable when geography-agnostic representations are required.The study asks whether coordinates can be predicted from Tessera v1, Tessera v1.1, and AlphaEarth embeddings within the solar-farm class.Source: §1 · p. 1
  • Prior work uses geographic information as a training signal, but how much location remains recoverable from general-purpose EO embeddings without coordinate inputs is unquantified.The introduction also notes that spatial dependence and train–test separation matter, motivating spatial folds and resampling dependency groups rather than treating 40,186 farm pairs as independent.Source: §1 · p. 1
  • The contribution is a controlled assessment of embedding geometry and coordinate sensitivity through cosine–geodesic distance association and spatially held-out coordinate probes.The probes are compared against appearance-based and random baselines.Source: §1 · p. 1

2. DATA AND METHODOLOGY

The methodology uses visually checked, same-class solar farms to compare geographic information across EO embeddings. It combines spatially held-out coordinate prediction with distance-association tests and evaluates results against appearance and random baselines.

2. DATA AND METHODOLOGY

  • The dataset comprises 284 visually and coverage-checked solar farms from eight countries, with valid 2024 coverage in all three EO embeddings.Spain accounts for 231 farms, or 81.3% of the sample.Source: §2 · pp. 1–2
  • Pixel-level embeddings were aggregated by component-wise medians, and Sentinel-2 center-pixel and 3 × 3 patch features served as appearance-based controls.The controls provide a comparison with geographic information recoverable from local multispectral features.Source: §2 · p. 2
  • Coordinate prediction used linear and ridge regression plus MLPs with 2, 4, 6, or 8 hidden layers, evaluated with five-fold spatial cross-validation.Farms within 25 km were grouped into dependency components that could not be split across folds; ridge and MLP parameters were selected using spatial validation within the training data.Source: §2 · p. 2
  • Prediction error was measured as geodesic distance and compared with a uniform random baseline sampling latitude and longitude within training-farm ranges.Confidence intervals were estimated by resampling spatial blocks, and model comparisons used the same test farms.Source: §2 · p. 2
  • The study varied the training exclusion distance from 25 to 100 km in 5 km increments and also evaluated predictions with an entire country held out.Test farms and fold assignments remained fixed across the distance sweep; the country holdout used linear regression, ridge regression, and 8-layer MLPs.Source: §2 · p. 2

3. RESULTS

Across distance associations, spatial cross-validation, exclusion-distance sweeps, and country holdouts, all three EO foundation-model embeddings support coordinate recovery. Performance varies by representation, predictor, and geography.

3.1. Embedding distance follows physical distance

  • Both Tessera variants had higher correlation point estimates than Sentinel-2 controls; permutation tests for Spearman correlation and Ridge regression yielded p = 0.001.Source: §3.1 · p. 2
  • Spearman ρ was 0.751 [0.664, 0.808] for AlphaEarth, exceeding Tessera v1.1 at 0.424 [0.344, 0.514] and v1 at 0.386 [0.308, 0.492].Source: §3.1 · p. 2, Table 1 · p. 3

3.2. Farm location prediction from embeddings

  • AlphaEarth had 168–193 km mean errors versus TESSERA’s 225–308 km across predictors; all three beat the 1,350.5 km uniform-random baseline and Sentinel-2 controls.Source: Figure 2 · p. 3, §3.2 · p. 3

3.3. Location prediction becomes less accurate as spatial separation increases

  • Prediction errors generally increased as training exclusion distance rose from 25 to 100 km; ordinary linear regression increased more for TESSERA and Sentinel-2 3 × 3 features than ridge and the 8-layer MLP.Source: §3.3 · pp. 3–4, Figure 3 · p. 4

3.4. Location-prediction performance varies across held-out countries.

  • Under leave-one-country-out testing, AlphaEarth errors were 157–189 km in the UK and 217–294 km in Ireland, versus TESSERA’s 466–700 km and 435–643 km.Source: Figure 4 · p. 4, §3.4 · p. 4
  • For AlphaEarth, MLP-8 beat linear and ridge in Spain (232 versus 633 and 372 km) but lost to both in Romania (1,515 versus 884 and 1,058 km).Portugal and Romania each had only two farms, so country-level comparisons warrant caution.Source: Figure 4 · p. 4, §3.4 · p. 4

4. DISCUSSION AND CONCLUSION

All three EO foundation-model embeddings contain recoverable geographic information, with AlphaEarth showing the strongest distance association and lowest location-prediction error. The findings are limited by uneven geographic coverage and are relevant differently depending on whether downstream tasks need location information.

  • In the evaluated solar-farm dataset, all three EO foundation-model embeddings contained recoverable geographic information; AlphaEarth had the strongest distance association and lowest prediction errors, while Tessera versions were comparable.Source: §4 · p. 4
  • Prediction errors generally increased when nearby training farms were excluded, and performance varied across held-out countries.Source: §4 · p. 4
  • Geographic coverage was uneven, with 81.3% of farms in Spain; geographic dependence may help location-sensitive tasks but be undesirable for global similarity search.Source: §4 · p. 4
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