Emergent Sparsity: How Many Effective Variables Survive Coarse-Graining in AlphaEarth Embeddings?

Geospatial foundation models generate high-dimensional embeddings that achieve strong predictive performance, yet their internal organization remains obscure, limiting their scientific use. Recent interpretability studies relate Google AlphaEarth Foundations (GAEF) embeddings to continuous environmental variables, but it is still unclear whether the embedding space exhibits a functional or hierarchical organization, in which some dimensions act as specialized representations while others encode shared or broader geospatial structure. In this work, we propose a functional interpretability framework that reverse-engineers the role of embedding dimensions by characterizing their contribution to land cover structure from observed classification behavior. The approach combines large-scale experimentation with a structural analysis of embedding-class relationships based on feature importance patterns and progressive ablation. Our results show that embedding dimensions exhibit consistent and non-uniform functional behavior, allowing them to be categorized along a hierarchical functional spectrum: specialist dimensions associated with specific land cover classes, low- and mid-generalist dimensions capturing shared characteristics between classes, and highgeneralist dimensions reflecting broader environmental gradients. Critically, we find that accurate land cover classification (98% of baseline performance) can be achieved using as few as 2 to 12 of the 64 available dimensions, depending on the class. This demonstrates substantial redundancy in the embedding space and offers a pathway toward significant reductions in computational cost. Together, these findings reveal that AlphaEarth embeddings are not only physically informative, but also functionally organized into a hierarchical structure, providing practical guidance for dimension selection in operational classification tasks.

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.

Earth observation is moving from foundation models that users must run themselves toward embedding products that package model feature outputs as reusable data without needing to download and process the imagery used to generate them. Earth embeddings are vectors that summarize locations, image patches, or pixels, letting users analyze compact features instead of repeatedly training or running large models on raw satellite imagery. This chapter explains the main types of Earth embeddings, from implicit location encoders to explicit patch and pixel products, and compares their coverage, resolution, dimensionality, storage cost, licenses, and reproducibility. We review their use in land cover and crop mapping, ecological and hazard modeling, socioeconomic prediction, and semantic search, with evidence on when embeddings improve on conventional features and when pooling, fusion, or spatial transfer limit performance. Two case studies show practical workflows for similarity search and land cover mapping. We close with guidance for choosing, evaluating, storing, compressing, and publishing embeddings, and with open problems in oceanic and atmospheric coverage, uncertainty, and benchmarking.