Date -Rain belt at -Wet-day chance -Rain today -Soil water -fps -

Drag to orbit, wheel or pinch to zoom. The tank on the left is the root-zone soil bucket (full line = field capacity). Dark clouds and rain streaks appear on wet days drawn from the model. Maize turns yellow as water stress builds. Vertical sizes are not to scale.

Tropical Rain Belt and a Maize Field

Twice a year the equatorial rain belt sweeps across the tropics. Where it passes, the chance of a wet day jumps. Random wet and dry days then fill a soil bucket that the crop drinks from, and a long dry spell shows up as water stress and lost yield.

Site and rain belt

Daily weather

Soil and crop

Live readouts

Soil water through the year (mm)

Weekly rain: this year vs model expectation (mm)

Experiment: where on the map does maize fail?

Relative yield against site latitude, averaged over 30 random weather years (carried soil moisture), with the 10th-percentile bad year. Everything else stays as set above.

Independent numerical checks

Controls

Day slider or Play moves through one simulated year. New weather year draws a different random sequence of wet and dry days with the same climate.
Latitudes are positive north. The rain belt follows the Sun with a lag, so it peaks in the north around day 200 (mid-July).

The science

Rain belt. The latitude of the belt is φ_b(d) = φ_c + A cos(2π(d − d_peak)/365). The probability that a day is wet at the site is a Gaussian bump around the belt: p(d) = p_min + (p_max − p_min) exp(−½((φ_site − φ_b)/σ)²). A site near the centre latitude sees the belt pass twice and gets two rainy seasons; a site near the edge of the swing gets one; beyond it, almost none.

Wet-day Markov chain. Rain comes in spells, so today depends on yesterday: P(wet|dry) = p(1−ρ) and P(wet|wet) = p(1−ρ) + ρ, which keeps the long-run wet fraction equal to p and the day-to-day correlation equal to ρ. Wet-day depth is exponential with mean μ, a standard simple weather generator.

Soil bucket (Manabe style). Each day S → S + P − ET − R. Evapotranspiration is ET = PET·min(1, S/(f_w S_fc)) (full rate while the bucket is above fraction f_w of capacity) and any water above capacity S_fc leaves as runoff or drainage R. Mass is conserved exactly.

Yield. Relative yield follows the FAO-33 form Y/Y_max = 1 − K_y(1 − ΣET/ΣPET) over the growing season, with K_y = 1.25 for maize over the whole season (a typical textbook value).

Simplifications, stated honestly. One site, one soil layer, no infiltration limit, interception, snow or irrigation, no sub-seasonal drivers such as monsoon breaks or El Niño, a Gaussian belt of fixed width, and a single crop with no growth stages. The belt latitude range, p_max, depths, PET, bucket size and K_y are illustrative or typical values, not data for a real location.

Made for learning; models are simplified.