Characterizing AlphaEarth Embedding Geometry for Agentic Environmental Reasoning

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.

Physically Interpretable AlphaEarth Foundation Model Embeddings Enable LLM-Based Land Surface Intelligence

Satellite foundation models produce dense embeddings whose physical interpretability remains poorly understood, limiting their integration into environmental decision systems. Using 12.1 million samples across the Continental United States (2017--2023), we first present a comprehensive interpretability analysis of Google AlphaEarth's 64-dimensional embeddings against 26 environmental variables spanning climate, vegetation, hydrology, temperature, and terrain. Combining linear, nonlinear, and attention-based methods, we show that individual embedding dimensions map onto specific land surface properties, while the full embedding space reconstructs most environmental variables with high fidelity (12 of 26 variables exceed $R^2 > 0.90$; temperature and elevation approach $R^2 = 0.97$). The strongest dimension-variable relationships converge across all three analytical methods and remain robust under spatial block cross-validation (mean $ΔR^2 = 0.017$) and temporally stable across all seven study years (mean inter-year correlation $r = 0.963$). Building on these validated interpretations, we then developed a Land Surface Intelligence system that implements retrieval-augmented generation over a FAISS-indexed embedding database of 12.1 million vectors, translating natural language environmental queries into satellite-grounded assessments. An LLM-as-Judge evaluation across 360 query--response cycles, using four LLMs in rotating generator, system, and judge roles, achieved weighted scores of $μ= 3.74 \pm 0.77$ (scale 1--5), with grounding ($μ= 3.93$) and coherence ($μ= 4.25$) as the strongest criteria. Our results demonstrate that satellite foundation model embeddings are physically structured representations that can be operationalized for environmental and geospatial intelligence.