How a Crop Turns Sunlight into Yield

Biomass is captured light, priced in radiation-use efficiency

A crop is, energetically, a machine that turns sunlight into dry matter. The FAO-style model behind this simulation follows a chain that traces back to work by de Wit and later Monteith: daily incoming solar radiation is filtered through the canopy, the fraction the leaves actually catch is converted to new biomass at a roughly constant efficiency, and that biomass is then split between roots, stems, leaves and grain according to the plant's growth stage. Nothing here needs weather stations or satellites — four ingredients (radiation, temperature, canopy size and soil water) are enough to get within a useful margin of a real field trial.

The central multiplier is radiation-use efficiency (RUE), typically 1.0 to 1.8 g of dry matter per megajoule of intercepted photosynthetically active radiation (PAR) for C3 cereals like wheat, and noticeably higher for C4 crops such as maize, which fix carbon through a more efficient biochemical pathway. RUE is treated as a crop constant that only drops when the plant is under water or nutrient stress — almost all of the day-to-day variation in growth rate instead comes from how much of the incoming light the canopy manages to intercept.

Beer's law and the leaf area index

How much sunlight a canopy intercepts depends on its leaf area index (LAI) — the total leaf area per unit of ground area, dimensionless, typically climbing from near 0 at emergence to 4 to 6 at full cover. Light attenuation through a stand of leaves follows Beer’s law, borrowed directly from optics:

f_intercepted = 1 − e^(−k · LAI)
PAR_captured  = PAR_incident × f_intercepted
Δbiomass    = PAR_captured × RUE          (g dry matter / m² / day)

The extinction coefficient k (around 0.4 to 0.7 depending on leaf angle) sets how quickly the canopy closes: erect leaves like those of cereals let more light through per unit LAI and need a higher LAI to reach full interception, while flatter, more horizontal leaves shade the ground faster. Past roughly LAI 4 to 5, interception is essentially saturated near 90 to 95%, so further leaf growth buys little extra light capture and the crop’s growth rate flattens even if biomass keeps accumulating.

Thermal time replaces the calendar

Plants do not read a calendar; they respond to accumulated heat. Development is tracked with growing degree days (GDD, also called thermal time), summed daily above a crop-specific base temperature below which growth effectively stops:

GDD_today = max(0, (T_max + T_min)/2 − T_base)
DVS = Σ GDD_today / GDD_to_maturity

The running total defines a development stage (DVS) that moves from 0 at emergence through 1 at flowering to 2 at full maturity, and it is this stage — not the day count — that decides when the plant switches from building leaves and roots to filling grain. It is also why the same variety planted a week apart in a warm spring can flower on almost the same calendar day: both accumulate the same heat sum at different rates.

Water stress throttles the whole system

The FAO-33 approach (Doorenbos & Kassam) treats soil water depletion as a simple bucket: once the readily available water in the root zone is used up, actual evapotranspiration falls below the potential rate, and a water stress coefficient Ks between 0 and 1 multiplies both transpiration and, through it, RUE. A crop at Ks = 0.6 is not merely thirsty for a day — every subsequent day’s biomass increment is scaled down, so a dry spell during the fastest-growing stage costs far more final yield than the same deficit during early establishment or late senescence.

From daily increments to a harvest number

Run the loop — intercept light, add biomass, accumulate heat, deplete and refill soil water — day by day from sowing to maturity, and the outputs are the same numbers agronomists report in the field: total above-ground biomass, final LAI trajectory, and, by applying a harvest index (the grain fraction of total biomass, roughly 0.35 to 0.5 for modern wheat and maize) at maturity, an estimated grain yield in tonnes per hectare. The simplicity is the point: this is essentially the crop-growth logic used inside operational tools like FAO’s AquaCrop and the DSSAT family, minus the soil chemistry.

Frequently asked questions

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Everything above runs in your browser — open Crop Growth and change the parameters while it is running. Nothing is installed, nothing is uploaded, the whole model lives in one tab.