True rate 0 mm/hDrops on funnel 0 /sTips 0Gauge 0 mmFPS 0

Drag to orbit, wheel or pinch to zoom. Streaks are a sample of the falling drops (length ~ speed, brightness ~ size). Blue bars inside the seesaw show the water in each bucket; the gauge tips every 0.2 mm of rain. Time runs at 60x real speed.

Tipping-Bucket Rain Gauge: Marshall-Palmer Drop Spectrum, Tip Counts and High-Intensity Undercatch

Every raindrop that lands on the 16 cm funnel is drawn from the Marshall-Palmer size spectrum, added to a bucket, and the seesaw tips each 0.2 mm. See how a few hundred discrete drops per second become a smooth rainfall record, and where the gauge reads too low.

Rain and wind

Spectrum readout

Gauge readout

Cumulative rainfall, true vs gauge (mm)

Rain rate seen by the gauge (tips in the last 10 min)

Drop-size spectrum (share of drops reaching the funnel)

Line: flux-weighted Marshall-Palmer curve, proportional to v(D) exp(-Lambda D). The measured histogram builds up as drops fall; small samples are noisy, and that noise is real.

Experiment: how much does the gauge under-read?

Each row is a separate one-hour synthetic run with the current wind. Predicted = catch ratio x (1 - 0.5 tau r_tip) with tau = 0.3 s; at low rates the 0.2 mm quantisation dominates instead.

Independent numerical checks

Controls

Rain rate sets the nominal Marshall-Palmer rate R (log scale); wind reduces the effective catch area.
Presets jump to a drizzle, steady rain, a downpour or a windy shower. Speed multiplies simulated time; Reset restarts the gauge with the same random seed.
The close-up view shows the seesaw; the field view shows the whole station.

The science

Drop spectrum. Marshall and Palmer (1948) found N(D) = N₀ e^{-Λ D} with N₀ = 8000 m^-3 mm^-1 and Λ = 4.1 R^-0.21 mm^-1 (R in mm/h). It is a long-term average; real showers differ drop by drop.

Terminal speed. The Atlas et al. (1973) fit v(D) = 9.65 - 10.3 e^{-0.6 D} m/s is used (clipped to 0.05 m/s for drops under about 0.3 mm). The number of drops crossing a horizontal surface per second is Φ = ∫ v(D) N(D) dD; larger drops are over-represented because they fall faster, so drops are sampled from the flux-weighted spectrum.

Rain rate. R = 6π 10^-4 ∫ D³ v(D) N(D) dD (mm/h, D in mm). Because the two empirical fits are not exactly consistent, the integral differs from the nominal R by up to about 20 %; the simulation uses the integral as the true rate and the checks show the difference.

Gauge. A drop of diameter D adds π D³/6 to the bucket; dividing by the funnel area (π 80² mm²) gives millimetres of rain. The seesaw tips at 0.2 mm. While it moves (0.3 s, illustrative) half of the inflow drains away, so the gauge under-reads by about 0.5 τ r_tip, a few percent at 200 mm/h. Wind reduces catch by an illustrative factor 1 - 0.011 u^1.3; real undercatch depends on gauge shape and shielding, so this is not a calibration.

Simplifications. No splash, evaporation, wetting loss or turbulence; the wind does not tilt the drops. The 3D streaks are a visual sample, not the counted drops. The Blender model is a stylised cut-away, not a specific instrument.