Making Ice Under a Clear Night Sky: A Radiative-Cooling Yield Bound and a Shallow-Pond Design for Arid Climates

A water surface under a clear night sky radiates heat to the cold sky and can freeze without any machinery, a method used historically in arid regions but rarely given a quantitative yield bound that a builder can size against. This paper computes that bound from first principles. A shallow layer of water, 0.03 m deep, initially at 10 °C, is exposed for a 10-hour night at an air temperature of 4 °C. The net heat loss is the longwave radiation from the surface, set by an effective sky temperature that depends on humidity, minus the heat convected back from the warmer air, which depends on wind. Under the driest, calmest conditions considered (effective sky temperature −30 °C, convective coefficient 2 W/m²/K) the yield bound is 7.53 kg of ice per square metre per night, a sheet about 8.2 mm thick. Under dry air with light wind (sky −20 °C, coefficient 5 W/m²/K) the yield is 2.65 kg/m² per night. The yield falls to exactly zero in two broad regions: whenever the air is moderately humid or humid, at any wind speed considered, and whenever a fresh breeze blows, even in dry air. A clinic needing 30 kg of ice per day can be supplied by a pond of 11.3 m² in the dry, light-wind case, or 14.2 m² with a 25 percent margin; a household cluster needing 50 kg per day requires 18.9 m², or 23.6 m² with the same margin. The results give a plain siting rule: night-sky ice making is a dry-air, sheltered-site technology, and a site assessment that ignores humidity and wind exposure will predict ice where none forms.