Cost-aware evaluation of time-series foundation models for urban air-quality and temperature forecasting

Cities with the greatest need for hyper-local air-quality and weather forecasts often have the shortest data records and the tightest compute budgets. The usual responses, searching for a tiny architecture or transferring from data-rich cities, assume foundation models are too heavy, an assumption more often adopted than tested. Across 29 cities and two domains (hourly PM2.5 and 2 m temperature), under pre-specified protocols with measured energy and a cost-adjusted decision rule, we compare all three. On PM2.5 three zero-shot foundation models spanning two families and a 4.3-fold size range are statistically indistinguishable from the tuned specialist in mean absolute scaled error (MASE 0.659-0.662 vs. 0.692 under deployable causal covariates) and formally equivalent to one another. The specialist’s apparent temperature edge (0.533 vs. 0.792) depends heavily on covariate timing: 0.638 with covariates carrying measured 24-h forecast error, 0.745 with only values knowable at the forecast origin. Perfect foresight therefore distorts the cross-domain comparison, as it can in any benchmark using future covariates. Transfer learning never significantly beats zero-shot at any budget. Under frequent retraining the untrained model uses roughly ten times less measured energy, though a once-trained specialist eventually amortizes. Where models are refreshed often, downloading one now matches training one.