Move a weather station over an idealised continent and read its twelve-month climograph. Which climate does it have, and why?
Upper strip: at sea level. Lower strip: at the real terrain height of this slice. The white tick is the station.
Hint: temperature falls about 6.5 °C per kilometre of height.
Each button changes one variable at the station and reports the climate each time.
The science
Insolation. The daily-mean sunlight at the top of the atmosphere is Q = (S/π)(d0/d)² (h0 sinφ sinδ + cosφ cosδ sin h0) with S = 1361 W/m², latitude φ, solar declination δ = asin(sin 23.44° sin(2π(d-80)/365.25)) and the sunset hour angle cos h0 = -tanφ tanδ (h0 = 0 in polar night, π in polar day). Averaged over the sphere and the year it is S/4 = 340 W/m²; at the pole on the June solstice it is larger than at the equator, but the sun is low and the ground cold, so it does not make a hot pole.
Temperature. The annual mean at sea level uses an illustrative fit T = -20 + 47.5 cos1.2φ (°C), lapse rate 6.5 °C per km, plus your warming. The seasonal cycle follows the insolation with a lag of about one month and an amplitude that grows with distance from the sea (coastal 0.03, interior 0.09 °C per W/m²) and shrinks near the poles. These coefficients are not fitted to data: they make a believable idealised world.
Precipitation. A tropical rain belt that follows the sun (the ITCZ moves about 7° each way with a month's delay), dry subtropics near 28°, storm-track rain near 50°, drier interiors, a mild gain with height, and winter-wet or summer-wet seasonality that depends on latitude and distance from the sea. Parametric, invented for teaching.
Koppen-Geiger. The classification follows Peel et al. (2007): E if the warmest month is under 10 °C; B if annual rain is under 10 × a threshold (2T, 2T+14 or 2T+28 mm depending on when the rain falls; BW below half of it, h or k by 18 °C mean); A if the coldest month is 18 °C or more (Af if the driest month has at least 60 mm, Am, Aw); otherwise C (coldest month above -3 °C) or D, with s, w, f for the dry season and a, b, c, d for summer warmth. The checks run it on nine published station normals.
Simplifications. One idealised continent, no ocean currents, no winds, no rain-shadow modelling beyond a drier interior, no clouds or albedo feedback, relief shown at a quarter of its true height. This is not a climate model; do not read forecasts from it. Assets built with Blender; scene by Three.js.