When local gains fail to transfer: Frozen Earth-observation embeddings across wildfires

Frozen Earth-observation embeddings are judged almost entirely by spatially blocked cross-validation inside one study region. We show that this number does not predict accuracy in a new region; we show why; and we show the one setting in which such a model does keep working, using a protocol that needs only a linear probe and labels one already has. The testbed is wildfire, with Copernicus burned-area maps of six fires in Greece and Spain and descriptors from the year before each fire, comparing TESSERA and AlphaEarth with ESA WorldCover classes and annual Sentinel-2 index summaries. Inside a fire, the embeddings identify the burned land 0.05 to 0.13 ROC AUC better than the index summaries, and repeated fold allocations, spatial buffers, a block bootstrap, and gradient-boosted trees leave that margin unchanged. On a fire in another region, they lose 0.15 to 0.18 AUC, and the index summaries lose 0.06, so the three end within a few hundredths of each other. The representation is not the cause. Eight labelled blocks from the new region restore the embedding advantage and give a higher AUC than 59,000 labelled pixels from other regions, and the weight vector fitted in one region is nearly orthogonal to the vector fitted in the others, so the part that carries across regions is small and low-dimensional. Forecasting within a region is a different matter. Fitted on a fire that burned in 2023 and applied to a fire twelve kilometres away that burned in 2024, where nothing used postdates the target fire, TESSERA reaches 0.772 AUC and loses 0.04 against a classifier fitted inside the 2024 fire, while classifiers fitted in other regions lose 0.09 to 0.18. A region with one mapped fire can therefore forecast susceptibility for later fires there; a region without one cannot borrow a model from elsewhere, and every evaluation of a frozen embedding should report a held-out region.