PermaCP: Depth-Conditional Conformal Calibration for Permafrost Borehole Temperature

Forecasts of ground temperature in permafrost boreholes can carry a trustworthy error bar around them. Deciding when to evacuate an Alpine valley or close a mountain road, as the frozen ground beneath it thaws, means weighing a false alarm against acting too late, and that error bar matters more for the call than the predicted temperature alone. The standard way of calibrating it fails. PermaCP, a small and open method, calibrates the error bar separately at each depth and corrects for the slow warming. Shallow ground swings widely with the seasons while the deeper layers under foundations warms slowly and steadily, so one calibration is overconfident near the surface and needlessly wide at depth. Across 25 boreholes of the Swiss permafrost network, logged daily for 12 to 36 years, PermaCP restores error bars that hold at every depth: a 90\% interval contains the true temperature about 90\% of the time, including on hot days and near the thaw threshold where the standard approach misses, though the deepest bands fall short at higher confidence levels. The result is a dependable uncertainty that Alpine hazard and infrastructure decisions rest on, and the same fix extends to grounds that warm out of step with its surface, from Arctic pipelines to the Qinghai-Tibet railway. The code is available at: https://github.com/redshoe47-cmyk/perma-cp.