Evaluating AlphaEarth Embeddings for Crop Classification: Separability, Temporal Dynamics, and Cross-Regional Transferability

Earth Observation (EO)-based agricultural monitoring is shifting from pixel-level spectral analysis toward representation-driven modeling, yet systematic evaluation of learned representations across spatial, temporal, and domain-generalization dimensions remains limited. Geospatial foundation models generate high-dimensional embeddings encoding spatio-temporal land-surface properties, but their utility for agricultural applications remains insufficiently understood. This study presents a representation-agnostic evaluation framework integrating geometric separability, temporal dynamics, spatial robustness, and cross-regional generalisation. A 64-dimensional AlphaEarth embedding space is benchmarked against Sentinel-2 reflectance, NDVI-derived phenology, and harmonic features using field-scale data from the Conterminous United States (CONUS; 2017-2023) and Northern India (2021). Traditional features achieve strong linear separability (Fisher ratio), while embeddings provide superior distribution-aware separation -- Bhattacharyya and Mahalanobis distances up to an order of magnitude higher for spectrally similar pairs (e.g. Corn/Soybeans: 3.9 vs. 0.10). Embeddings uniquely capture multi-year crop rotation dynamics, reaching a separability ratio of 1.784 versus a maximum of 1.003 across all engineered features, and exhibit lower residual spatial autocorrelation of errors (mean Moran's $I \approx 0.17$). However, harmonic and NDVI features show stronger cross-continental transferability (US $\to$ India Macro F1: 0.493 vs. 0.326 for embeddings), reflecting better distributional alignment. The combined feature space yields balanced performance, supporting hybrid modeling. These findings reveal a fundamental trade-off between representational richness and cross-region transferability, providing a structured framework for feature selection in large-scale crop classification.