t 0:00Mode ReflectivityPeak - dBZMax rate - mm/hr_max - kmv_N - m/s-FPS 0

Drag to orbit, wheel or pinch to zoom, tap the ground to pick a point for the time series. The coloured patch is the radar picture painted by the rotating beam (white rings every 20 km); arrows show the wind and are coloured by its radial component.

Weather Radar: Reflectivity, Doppler Velocity and Storm Nowcast Lab

Run a weather radar: send pulses, read echo strength (dBZ) and wind (Doppler), see why range and speed are ambiguous, spot rotation in a storm and forecast where it will be in 10 to 30 minutes.

Display

Radar settings

Storm and rain law

Time

Selected point (tap the ground)

Radar readouts

Selected point: reflectivity and rain rate

Range-velocity dilemma

Nowcast (TREC cross-correlation)

Two radar pictures 5 minutes apart give a motion vector; the latest picture is shifted along it and compared with the simulated truth at the lead time. Needs 5+ minutes of simulated scans.

Independent numerical checks

Controls and what to try

Drag / one finger: orbit; wheel / pinch: zoom; tap the ground: choose the point of the time series.
Display modes: reflectivity, Doppler velocity (green and blue toward the radar, yellow and red away), rain rate from the Z-R law, accumulated rain, nowcast and simulated truth at the lead time.
Raise PRF above about 1500 Hz: the unambiguous range shrinks under 100 km and with range folding on, far storms reappear at the wrong distance; lower PRF and the Nyquist velocity drops, so fast winds alias (turn on Dealias to unfold them).
X-band loses signal behind heavy rain (attenuation shadow), S-band does not; the clutter filter removes ridge echoes but also weak slow weather.
Look for a velocity couplet (blue next to red) in the rotating-storm scenario; the shear readout flags it above 0.01 per second.

The science

Range. A pulse that returns after the delay t_d comes from r = c t_d/2; a pulse of length τ fills a gate Δr = cτ/2 (1 µs = 150 m). The next pulse leaves after 1/PRF, so echoes from beyond r_max = c/(2 PRF) arrive after the next pulse and are drawn at r − r_max (range folding).

Reflectivity. For drops much smaller than the wavelength (Rayleigh) the received power is P_r ∝ |K|² Z / r² with Z = ∫N(D) D⁶ dD (mm⁶ m⁻³) and the logarithmic scale dBZ = 10 log₁₀ Z (+3 dB doubles Z, +10 dB is ten times). Marshall-Palmer drops N(D) = N₀ e^(−ΛD), N₀ = 8000 m⁻³ mm⁻¹, Λ = 4.1 R^−0.21 give Z = 720 N₀/Λ⁷, close to the empirical Z = 200 R^1.6 used to turn echoes into rain rate R (mm/h) and, integrated over time, accumulation.

Doppler. The phase change between pulses gives the radial velocity v_r = (λ/4π) Δφ/Δt; only the component along the beam is seen. It is ambiguous beyond the Nyquist velocity v_N = λ PRF/4, so v_meas = ((v + v_N) mod 2v_N) − v_N. Hence the dilemma r_max v_N = cλ/8: a long range or a large unambiguous speed, not both. A rotating storm shows adjacent toward and away velocities (a couplet); the shear is Δv/Δr.

Beam. With effective Earth radius 4/3 R_E the beam centre height is h = √(r² + R'² + 2 r R' sin θ) − R', R' = 4/3 · 6371 km, and its width is r θ_3dB; far echoes are sampled higher and are smeared, and a beam above the storm top sees nothing.

Attenuation and noise. Two-way loss A = 2∫k dr with k = a_k R (dB/km, strongest at X-band); the minimum detectable signal rises as Z_min(r) = Z_min,100 + 20 log₁₀(r/100 km) and gates close to it carry Gaussian noise of about 4 dB.

Nowcast. The shift (u, v) that maximises the cross-correlation of two pictures is the motion vector; extrapolation is Z(x, t+Δ) = Z(x − uΔ, t). Skill is the critical success index CSI = hits/(hits + misses + false alarms) at 30 dBZ and the RMSE in dBZ. Extrapolation cannot predict growth or decay: cells in the model are born and die on a 10 / 20 / 15 minute cycle, so skill drops with lead time.

Simplifications. Gaussian rain cells with trailing sub-cores instead of full microphysics, one elevation angle, no polarimetry, no beam blockage, stylised ground clutter from the terrain, radar constant and noise floor are model values, wind is uniform steering plus a Rankine vortex. Educational, not an operational forecast. Weather only. Models built with Blender, scene by Three.js.