Date -Sun decl. 0°ITCZ 0°Probe -readyFPS 0

Drag to orbit, wheel or pinch to zoom. Streaks: surface wind (cyan = easterly, orange = westerly, white = mostly north-south). Cyan ring = ITCZ, yellow rings = edges of the Hadley cells, white arrow = wind at the probe. The continents are idealised, not real geography.

Seasonal Wind Belts: ITCZ Migration, Hadley Cell and Coriolis Turning on a Spinning Planet

An idealised planet whose Sun moves between the tropics. Watch the trade winds, westerlies and polar easterlies, the rain belt that lags the Sun, and the way a heated continent turns the flow into a monsoon.

Planet

Calendar

Probe (a place to read the wind)

Live readouts

Zonal-mean surface wind against latitude

Sun declination and ITCZ latitude through the year

Wind at the probe through the year (m/s)

Experiment: how wide is the Hadley cell?

For planets spinning from 0.3 to 3 times as fast as Earth, the model's cell half-width is listed together with the westerly belt it leaves room for. The scaling follows the angular-momentum-conserving Hadley cell: sin φ_H ≈ 0.5 / Ω.

Independent numerical checks

Controls

Drag / one finger: orbit; wheel / pinch: zoom. The clock runs one year in the chosen number of seconds; scrub the date slider to freeze any day.
Axial tilt 0° removes the seasons: the ITCZ stays on the equator. Spin rate scales Earth's rotation: slow planets get one huge Hadley cell, fast ones get narrow cells.
Ocean depth sets how far the ITCZ lags the Sun. Land heating adds thermal lows over the two warm continents (northern: late spring to summer; southern: opposite).
The probe marks a place; the third chart shows its wind through the year, including the monsoon reversal.

The science

Sun and seasons. The subsolar latitude is the declination δ = ε sin(2π (d − 80)/365.25) (ε = axial tilt, 23.44° for Earth). It is compared in the checks with a Kepler-orbit calculation (eccentricity 0.0167, solar longitude λ, sin δ = sin ε sin λ); the two differ by up to 1.4° because the real Sun moves faster near perihelion.

Rain belt lag. A mixed layer of depth H responds to the seasonal forcing as C dT/dt = F − λ T, C = ρ c H (ρc = 4.1×10⁶ J m⁻³ K⁻¹), λ ≈ 30 W m⁻² K⁻¹, so τ = C/λ ≈ 1.6 H days (H in metres). For a sinusoidal forcing the response has amplitude 1/√(1+ω²τ²) and lag atan(ωτ)/ω. The ITCZ is placed at φ_ITCZ = 0.35 δ_lagged; the factor 0.35 is a tuned, illustrative zonal-mean value (real displacements are larger over land).

Cells. The Hadley cell reaches latitude φ_H = asin(0.5/Ω*) from the ITCZ (Ω* = spin / Earth spin; 30° for Earth), the Ferrel cell the next φ_H, and a polar cell the rest. Surface meridional flow is prescribed (toward the ITCZ in the Hadley cell, 3 m/s peak; away in the Ferrel cell, 2 m/s; toward again in the polar cell, 1.5 m/s). These amplitudes are typical, not computed.

Coriolis turning. With f = 2 Ω sin φ and surface friction rate k = 2.5×10⁻⁵ s⁻¹ the steady zonal wind balances k u = f v, soft-limited at 14 m/s: u = U tanh(f v / (k U)). Equatorward flow therefore turns into easterly trade winds, poleward flow into westerlies, and the sign change of f across the equator turns the south-east trades into south-west monsoon-like flow north of it. Without friction a parcel moves in an inertial circle of radius v/f and period 2π/f = π/(Ω sin φ) (23.9 h at 30°), checked numerically.

Land heating. Two Gaussian continents carry a seasonal temperature anomaly ΔT sin(2π(d − 95)/365.25) (northern positive in northern summer, southern opposite). The flow toward the warm (low-pressure) centre is 0.33 m/s per (K/rad) × ∇T, turned by atan(f/5×10⁻⁵ s⁻¹) to the right (north) or left (south). It is a thermal-low caricature, not a pressure solver.

Simplifications and illustrative constants. No zonal asymmetries other than the two land blobs, no ocean currents, topography, eddies, moisture, jets, or Walker circulation; the prescribed cell structure replaces solving the equations of motion. Real winds are far more variable. Models built with Blender, scene by Three.js.