Better Together: Evaluating the Complementarity of Earth Embedding Models

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.

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.

Geospatial and urban applications increasingly require models to compare heterogeneous evidence across street-view imagery, remote-sensing observations, text descriptions, region proposals, and temporal change cues. However, existing multimodal embedding models and benchmarks are still largely designed and evaluated around general-purpose image-text matching, leaving unclear whether unified embedding space can support heterogeneous geospatial tasks involving spatial relationships, fine-grained semantics, and temporal changes. To address this gap, we make three key contributions. First, we introduce GeoMEB, a large-scale multimodal embedding benchmark that standardizes 45 urban evaluation tasks across retrieval, visual question answering, change detection, classification, and visual grounding, together with training collections comprising 1.32M examples and 286K evaluation queries. Second, we present Geo-Embed, a unified embedding model that adapts a shared vision-language backbone to instruction-conditioned query-target matching over heterogeneous geospatial inputs, including single images, multiple images, text, regions, and masks. On GeoMEB, Geo-Embed achieves the strongest overall performance among representative multimodal embedders, with a 15.3% relative improvement over the strongest baseline. These results motivate future geospatial embedders that organize training and evaluation around explicit query-target relations, including semantic, cross-view, region-level, and temporal correspondence.