Shrinking Freezing Seasons and Frost Design Depth: Air Freezing Indices at Ten Northern US Stations, 1951-2025, with Stefan-Solution Bounds

The air freezing index, the accumulated degree-days of freezing in a winter, sets the design frost depth for foundations, pavements and buried pipes in cold regions. I compute it for 75 freezing seasons, 1950-51 to 2024-25, at ten first-order weather stations in the northern United States from NOAA GHCN-Daily data. I derive the Stefan solution for frost penetration, which makes depth proportional to the square root of the index; it follows that the exact percentage change in depth is the square root of one plus the change in the index, minus one, which is always below half the change, and that the depth computed from the mean index exceeds the mean depth by Jensen's inequality. All ten stations show a downward trend (Mann-Kendall p below 0.05 at all ten, and at nine after prewhitening); the median fall in the 30-year mean index between 1951-1980 and 1996-2025 is 27.1%, and the regional mean declines by 50.8 degree-days per decade. The design index, the mean of the three coldest seasons in 30 years, falls by less, 5.0% to 23.5%, so the Stefan design depth falls by only 2.5% to 12.6%. Because cold winters still occur while mild ones have become common, frost design should continue to rest on cold extremes, not on the shrinking average.