Physically Typed and Geometry-Aware Representations for Earth Foundation Models

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.

Earth observation foundation models encode land surface information into dense embedding vectors, yet the geometric structure of these representations and its implications for downstream reasoning remain underexplored. We characterize the manifold geometry of Google AlphaEarth's 64-dimensional embeddings across 12.1 million Continental United States samples (2017--2023) and develop an agentic system that leverages this geometric understanding for environmental reasoning. The manifold is non-Euclidean: effective dimensionality is 13.3 (participation ratio) from 64 raw dimensions, with local intrinsic dimensionality of approximately 10. Tangent spaces rotate substantially, with 84% of locations exceeding 60\textdegree{} and local-global alignment (mean$|\cosθ| = 0.17$) approaching the random baseline of 0.125. Supervised linear probes indicate that concept directions rotate across the manifold, and compositional vector arithmetic using both PCA-derived and probe-derived directions yields poor precision. Retrieval instead produces physically coherent results, with local geometry predicting retrieval coherence ($R^2 = 0.32$). Building on this characterization, we introduce an agentic system with nine specialized tools that decomposes environmental queries into reasoning chains over a FAISS-indexed embedding database. A five-condition ablation (120 queries, three complexity tiers) shows that embedding retrieval dominates response quality ($μ= 3.79 \pm 0.90$ vs.\ $3.03 \pm 0.77$ parametric-only; scale 1--5), with peak performance on multi-step comparisons ($μ= 4.28 \pm 0.43$). A cross-model benchmark show that geometric tools reduce Sonnet 4.5's score by 0.12 points but improve Opus 4.6's by 0.07, with Opus achieving higher geometric grounding (3.38 vs.\ 2.64), suggesting that the value of geometric characterization scales with the reasoning capability of the consuming model.

Large foundation models (FMs) are transforming Earth science by integrating heterogeneous multimodal data, such as multi-platform imagery, gridded reanalysis data, diverse geophysical and geochemical observations, and domain-specific text, to support tasks ranging from basic perception to advanced scientific discovery. This paper provides a unified review of Earth science foundation models (Earth FMs) through two complementary dimensions: depth, which traces the evolution of model capabilities from perception to multimodal reasoning and agentic scientific workflows, and breadth, which summarizes their expanding applications across the atmosphere, hydrosphere, lithosphere, biosphere, anthroposphere, and cryosphere, as well as coupled Earth system processes. Using this framework, we review representative multimodal Earth foundation models and compile more than 200 datasets and benchmarks spanning diverse Earth science tasks and modalities. We further discuss key challenges in multimodal data heterogeneity, scientific reliability and continual updating, scalability and sustainability, and the transition from foundation models to agentic and embodied Earth intelligence, and outline future directions toward more integrated, trustworthy, and actionable AI Earth scientists. Overall, this paper offers a structured roadmap for understanding the development of Earth foundation models from both capability depth and application breadth.