The single-pair unwrapping ceiling is a property of the track, not of the radar

Ajay Kumar Sah 

The half-fringe limit of a repeat-pass interferogram is quoted as a property of the sensor: a quarter wavelength of line-of-sight displacement per pair. On a slope it is not. Sensitivity to downslope motion is f = |m · u|, and at a mountain source f varies with the track, with the site, and across the source itself. We compute f per pixel over 500 m source discs at two rock–ice avalanche sources, Langtang Lirung (Nepal, 2026) and Ronti Peak (India, 2021), on four Sentinel-1 relative orbits, from a 30 m DEM, look azimuths measured from product footprints, and incidence angles measured directly from on-demand interferometric products. Expressed as a downslope rate, the single-pair ceiling is 0.46 m/yr on Langtang descending and 2.77 m/yr on Langtang ascending: a factor of 6.0 between two geometries of the same sensor, over the same source, in the same week. At Ronti the same comparison gives 1.25. How track-dependent the ceiling is, is itself site-dependent. Within a single 500 m disc, f spans 1.3× on Langtang descending and 13.6× on Langtang ascending, so on most geometries the ceiling is not a value for the source but a distribution across it. This accounts physically for a result previously reported as an empirical curiosity — that the best-covered geometry measures worst — because near-normal incidence is simultaneously the condition for full coverage, for insensitivity to downslope motion, and for the widest internal spread in sensitivity. We then measure the other instrument's limit at the same source: the detection floor of single-pair optical pixel-offset tracking, from 28 Sentinel-2 pairs against a prespecified stable-ground control. That floor does not improve with separation (sigma ~ T^0.25) and is set instead by scene-pair condition, which the quantity most easily computed before processing, tile cloud cover, fails to predict. Joint screening on snow and cloud over the source area halves the spread and halves the median floor, and roughly doubles the number of pairs in which a published pre-failure rate of 9.6 m/yr downslope would have been detectable. The floor reproduces at the second site, 5.77 against 5.55 m/yr, once pairs spanning that site's own failure are removed — those decorrelate the control area itself, at twenty-five times the dispersion of a same-separation pair that does not span it. Neither instrument detects the published rate in a single routine product on any geometry examined. A null from a 12-day pair is uninterpretable without the projected ceiling for that specific track, and λ/4 is not sufficient.