The Humid-Sky Limit of Passive Radiative Cooling: Window Closure by Water Vapour, the Stagnation Temperature from Dry Desert to Humid Tropics, and the Comparison with a Plain White Surface

The humid-sky limit of passive radiative cooling is derived with a two-band atmospheric model in which the hemispherical 8-13 micrometre window transmittance falls with precipitable water vapour W as tau = 0.85 exp(-0.040 W). For an ideal selective emitter (unit emissivity in the window, zero elsewhere, zero solar absorptivity) with parasitic coefficient 6 W/m2/K at 300 K ambient, the cooling power at ambient temperature falls from 125.8 W/m2 dry to 84.3 W/m2 at W = 10 mm, 37.9 W/m2 at 30 mm and 17.0 W/m2 at 50 mm, and the night-time stagnation depression falls from 15.41 K dry to 10.26 K at 10 mm, 4.57 K at 30 mm and 2.05 K at 50 mm; across stated conditions it falls from 12.87 K in a dry desert (35 C, 15% relative humidity, W = 7 mm) to 2.31 K in the humid tropics (30 C, 85%, W = 48 mm). A scan over W = 0 to 80 mm finds no humidity at which a plain white surface (infrared emissivity 0.95, solar absorptivity 0.10) stagnates colder than the selective emitter, by night or by day; but the selective emitter's night-time advantage falls below 1 K at W = 40.2 mm and below 0.5 K at 57.5 mm, while by day the white surface stagnates above ambient beyond about W = 10 mm because it absorbs 85 W/m2 of sunlight. In the humid-tropics condition the dew point is only 2.8 K below ambient, capping any useful depression there regardless of emitter quality. All numbers are produced by the deposited compute.py; the model is simulated, not measured. AI use is disclosed: this paper was produced by Dave, an AI system, at the direction of the author. The author, William Alexander Aldred, directed the work and is sole author of record.