A Psychrometric Bound on Atmospheric Water Harvesting: Where Air-Derived Water Can Work, Where It Cannot, and One Design That Respects the Bound

Atmospheric water harvesters are marketed to households in dry regions with yields quoted without the climate state at which they were obtained. This paper prices the claim from physics over a grid of temperature (15-40 C) and relative humidity (20-80%): absolute humidity, the thermodynamic minimum work of extracting liquid water from air, a realistic dew-point condensation machine (Carnot COP factored by 0.25), a sorbent cycle at 1.20 kWh per litre, and the alternative of desalination (0.003 kWh per litre) plus road tanker delivery (0.0328 kWh per litre delivered over 100 km; 0.1522 over 500 km). Below 41.1-44.1% RH the minimum work alone exceeds the 100-km delivered alternative, so no harvester can beat it there. The realistic condensation machine (0.1192-6.5012 kWh per litre) beats the 500-km alternative only above 73.6-87.3% RH and the 100-km alternative at no humidity; the sorbent cycle beats neither anywhere. A night-only, radiatively assisted condensation design for humid coastal deserts, inhibited below its crossover humidity, is sized from the same numbers (0.0684 kWh per litre effective at its design point). All computations are reproducible from the deposited compute.py and results.json.