Physics

The rain right now comes from ČHMÚ’s weather radar, a new picture every 5 minutes. The reflectivity in the 3 × 3 km around the window is averaged as power (not in dBZ) and turned into rain on the ground with the same Marshall–Palmer relation ČHMÚ uses. Each 4 dBZ colour class counts at its middle. Without a fresh picture (under 20 minutes old), it is Open-Meteo’s model, whose current values are sums over 15 minutes.

• ČHMÚ, radar data description (2026)
• Open-Meteo forecast API

Drop sizes follow Marshall & Palmer: heavier rain has more drops and bigger ones. Light rain still has over a hundred drops larger than half a millimetre in every cubic metre.

Drops ≥ 0.5 mm per m³: 0.4 mm/h → 134, 5 mm/h → 634, 25 mm/h → 1352.

• Marshall & Palmer (1948), J. Meteorology 5

Every drop falls at the terminal velocity for its size, the Atlas fit to Gunn & Kinzer’s laboratory measurements. Snowflakes fall slower, by the Locatelli & Hobbs fit for unrimed aggregates.

0.5 mm: 2.0 m/s · 1 mm: 4.0 m/s · 2 mm: 6.5 m/s · 3 mm: 8.1 m/s.

• Atlas, Srivastava & Sekhon (1973), Rev. Geophysics 11
• Gunn & Kinzer (1949), J. Meteorology 6
• Locatelli & Hobbs (1974), J. Geophysical Research 79

Each drop has a position in metres and is projected through the camera calibrated from the photo (23 mm lens, pitched 3.2° up). The wind at the window is the 10 m wind on a logarithmic profile over a suburb; its part towards or away from the wall dies out close to the wall, where the air stagnates.

AssumedThe roughness z₀ = 0.5 m for the suburb.

AssumedThe wind towards the wall fades exponentially over 6 m (a simplification of the flow at a facade).

• Blocken & Carmeliet (2004), review of wind-driven rain

A drop shows as a streak: the path it travels while the eye integrates light, about 1/30 s. How strongly it shows depends on the angle it fills against the eye’s resolution of one arcminute. Drops far too small to resolve are “fog-like rain”: they are not drawn as streaks, they dim the view instead. Drops are brighter than what is behind them, because each one refracts a wide view of the sky into the eye. Millions of drops are in view, so a sample is drawn, always the same share.

• Garg & Nayar, Vision and Rain (2007)
• Garg & Nayar, Photometric model of a rain drop (2004)

Rain scatters light, so the far hills fade by how much rain of that strength dims the air. The visibility follows from the extinction by Koschmieder’s law.

0.4 mm/h → 23 km · 5 mm/h → 4.3 km · 30 mm/h → 1.3 km.

• Tremblay et al., Rain rendering for evaluating robustness to bad weather

When the wind blows at the window, the rain it drives onto the facade lands on the glass. Each drop spreads into a bead; beads that touch merge, and once one is about 2.5 mm across the glass can no longer hold it and it runs down, sweeping up the beads in its way. Beads dry slower the more humid the air is.

Assumedα = 0.1 s/m is the upper end of what the standards give for a low wall like this (about 0.02–0.10).

AssumedA drop spreads to 1.8 × its diameter on the glass, and the drying constant k.

• Blocken & Carmeliet (2010), wind-driven rain models compared
• ISO 15927-3:2009 (preview)

A film of water over a rough surface sends part of the light it reflects back down by total internal reflection, so the surface gets another chance to absorb it. Every pixel of the drawing is taken as a dry albedo (in linear light, per colour channel) and turned into a wet one.

Checked against the paper: p = 0.4749. The roofs get 11–14 % darker, the walls about 15 %.

AssumedThe colours of a drawing stand in for real albedos. Mineral refractive index 1.5.

• Lekner & Dorf (1988), Why some things are darker when wet, Applied Optics 27

Each drop spreads on impact to its largest diameter and leaves a wet spot. The spots fall at random, so the wet share of a roof grows as one minus an exponential. The drops carry exactly the rain measured. The walls face the window and get wet only from the rain the wind drives at them.

Roofs 95 % wet after: 0.2 mm/h ~40 min · 1 mm/h ~8 min · 3.5 mm/h ~2.5 min · 10 mm/h ~1 min.

AssumedContact angle θ = 57°, the one measured value for a roofing material found. Anywhere from 20° to 120° changes the time by under ±20 %.

• Pasandideh-Fard et al. (1996), Physics of Fluids 8
• Contact angle of a roofing material, Materials 16 (2023)

Drying follows WETTIME, a model fitted to 132 timed drying tests. After the rain, 5 minutes of runoff; then a mean drying time adjusted for the air, the sun and the wind. In nearly saturated air drying does not start at all, and fog wets everything.

Δ: below 19.7 °C +3.7, above 28 °C −3.0 · humidity under 50 % −4.5, over 82.5 % +6.1 · night or overcast +11.6, clear day −17.2 · wind +11.6 without, −11.6 with (only when the sun’s Δ is positive).

AssumedThe tests were on asphalt and concrete, not clay tiles or render. The 10 m wind stands for the test chamber’s fan.

• Harwood et al. (1988), WETTIME, Transportation Research Record 1172
• Alduchov & Eskridge (1996), J. Applied Meteorology 35

The window faces west-south-west, where most of Prague’s rain comes from, so the wind often blows rain in. The catch ratio η at a window was measured by drop size and wind. Each drop size comes in at its own slope, which gives a simple result: the sill gets the same rain per square metre as open ground, out to a depth that grows with the wind.

0.8 mm/h at 5 m/s: ~30 drops a second, up to 33 cm in. 10 mm/h at 8 m/s: ~440 a second, 61 cm in.

AssumedThe opening is 1.45 m high with a 15 cm outer reveal, until measured.

AssumedDrops are as dense near the wall as in the open.

• Blocken & Carmeliet (2015), wind-driven rain on a window
• Prague wind during rain: LKPR reports 2010–2024 (IEM)

Whether a drop splashes was measured for real water drops at raindrop sizes and speeds. On a dry sill, drops under about 1.5 mm stay; on water, the threshold is about the same. A drop that stays is a bead, a spherical cap at water’s contact angle on PVC. Beads that touch merge.

AssumedThe sill is as smooth as the smoothest surface measured.

• Stow & Hadfield (1980), J. Meteorological Society of Japan 58
• Liang & Mudawar (2016), drop impact on a liquid film (review)
• Contact angle of water on PVC, 81° (Ibrahim et al. 2025)

A drop splashing on water throws up a crown that lasts a few milliseconds, so the eye sees only a faint flash. Then come the secondary droplets: their number and sizes are measured, and each flies with gravity and air drag.

A 2 mm drop: a crown ~6 mm high and ~16 mm wide, gone in ~5 ms.

AssumedThe droplets’ launch speed (0.7 V) and angle (30°) are not measured: they are set so the droplets land as far as measured.

• Stow & Stainer (1977), J. Meteorological Society of Japan 55