A Rain Gauge Made from a Funnel and a Bottle: Reading Resolution, Wetting Loss, and the Evaporation Deadline

A rain gauge improvised from a funnel and a bottle is often dismissed as a toy, but its errors can be computed, and most of them turn out to be small or controllable. This study builds the full error budget of such a gauge from stated assumptions — reading resolution set by the ratio of funnel to vessel diameters, a wetting film of 0.05 mm left on the funnel walls at each event, and evaporation from the stored water at stated open-water rates of 2, 5, and 10 mm per day for cool, warm, and hot arid windy climates, reduced by a sheltering factor of 0.6. For a 200 mm funnel over a 30 mm measuring cylinder (area gain 44.444), one 2 mm graduation corresponds to 0.045 mm of rain, the 95 percent reading half-width is 0.0441 mm, and wetting loss is 0.0707 mm per event, so a 10 mm storm read immediately carries a worst-case error of 0.1148 mm, or 1.15 percent. Evaporation, not resolution, sets the reading deadline, and the deadline depends decisively on the width of the vessel the water waits in: stored in the 30 mm cylinder, the gauge may wait 88.9 hours in the hot climate before evaporation alone reaches 0.5 mm (177.8 hours warm, 444.4 hours cool), but stored in a 70 mm bottle the same 0.5 mm bound is reached in 16.3 hours in the hot climate, and a 10 mm storm left 24 hours in that bottle is wrong by 1.0458 mm, or 10.46 percent. The design-and-use rule follows directly: any funnel of 100 mm or more paired with a vessel no wider than half the funnel diameter reads to 0.5 mm of rain; keep the catch in a narrow cylinder, and read a wide bottle within the same day in warm weather and within about 16 hours in hot arid wind. All values are simulated from stated assumptions, not measured. SIMULATED, NOT MEASURED.