🌾 Crop Yield Predictor — Satellite NDVI Meets Weather Data

The band comes from a 24-member Monte Carlo ensemble recomputed at every week: each member replays the real, already-observed weather up to that week, then draws a fresh random weather trajectory (plus its own fixed light-use-efficiency and harvest-index noise) for the remaining unobserved weeks. Early in the season almost the whole season is still unknown, but accumulated biomass is tiny, so absolute spread in tonnes/hectare starts small. As the season progresses, compounding of the per-member efficiency noise against a larger accumulated biomass base widens the absolute spread, even as the number of still-uncertain future weeks shrinks. Near harvest there are almost no unknown weeks left to resample, so the ensemble collapses back toward a single realized outcome — producing the widen-then-narrow shape. This mirrors how real seasonal crop forecasts (which condition on realized weather-to-date and ensemble future weather) genuinely behave.

Every cell in the 10×10 grid shares the exact same rainfall and temperature trajectory (the weather is field-wide), but each cell has its own randomly generated soil quality multiplier that scales its water-holding capacity and starting moisture. Cells with higher soil quality drain more slowly and stay above the water-stress threshold longer during dry spells, so they sustain a higher NDVI and accumulate more biomass. This is exactly why real precision-agriculture platforms overlay satellite NDVI on soil maps: the same weather produces a patchwork of outcomes across a single field because soil, not just weather, gates how much of that weather a plant can actually use.

A growing degree day accumulates whenever the average temperature is above a crop-specific base temperature (8°C here); a week averaging 20°C contributes 7 × (20−8) = 84 GDD. Crop development — germination, leaf expansion, canopy closure, senescence — tracks cumulative GDD far more reliably than calendar time, which is why agronomists schedule planting, spraying and harvest windows by GDD rather than by date. A logistic curve is used for potential canopy (NDVI) growth because real canopy development is slow at emergence, accelerates through the vegetative stage, then saturates once the canopy fully closes and can absorb no more additional light — an S-shaped, not linear, trajectory that a logistic function captures with a single inflection-point parameter.

Systems such as NASA Harvest, the EU's MARS Crop Yield Forecasting System and commercial platforms like Planet's crop-health products combine real multispectral satellite passes (Sentinel-2, Landsat, MODIS), gridded reanalysis or station weather data, and soil databases, then fuse them with statistical or machine-learning yield models trained on years of historical harvest records per region. This simulation reproduces the same conceptual pipeline — vegetation index, weather-driven stress, light-use-efficiency biomass accumulation, ensemble uncertainty — but with synthetic imagery, hand-set (not fitted) coefficients, and no real historical calibration, so it should be read as a mechanism demonstration rather than a production forecasting tool.

The sliders set the mean of the random weather-generating process for an entire season, not a single week's value, so changing them mid-season would silently rewrite history the model has already "observed" — which is physically incoherent (you cannot retroactively change how much rain already fell). Instead, this simulation treats each slider change as defining a new what-if scenario: click reset (or move a slider and reset) to resample a fresh season, complete with its own weather trajectory, soil-moisture history and ensemble forecast band, from week zero.