Crop Growth Model: Light, Water and Thermal Time for Wheat, Maize and Soybean

Radiation-use-efficiency crop model with FAO-56 water balance on a Blender field plot: LAI, biomass, grain yield and drought stress.

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The science

What is modelled

One season of a field crop (spring wheat, grain maize or soybean) at a synthetic temperate-continental site at 50 degrees north. Each day the model converts the sunlight the canopy intercepts into biomass, spends water from a soil bucket, advances the crop through its growth stages with thermal time, and splits the new biomass between leaves, stems and grain. The plot, plants, soil and gauges are Blender models; the plants swap between three growth-stage models and change size and colour with the model state.

Equations

  • Sunlight: extraterrestrial radiation Ra = (24·60/π) Gsc dr [ωs sinφ sinδ + cosφ cosδ sinωs] (FAO-56), and Rs = Ra(0.25 + 0.5 n/N) with the sunshine fraction n/N taken from a synthetic cloud series.
  • Canopy light capture (Beer-Lambert): fint = 1 − exp(−k LAI), absorbed PAR APAR = 0.48 Rs fint.
  • Growth (radiation use efficiency): dB = RUE · APAR · fT · Ks, with fT a trapezoid in mean temperature and Ks the water stress factor.
  • Phenology: thermal time TT = max(0, min(Tmean, 30) − Tbase); DVS = ΣTT / TTveg up to anthesis (DVS = 1), then 1 + ΣTT / TTrep up to maturity (DVS = 2).
  • Water (FAO-56): reference evapotranspiration by Hargreaves-Samani ET0 = 0.0023 (T+17.8) √(Tmax−Tmin) Ra/2.45, crop coefficient Kc = Kc,min + (Kc,full − Kc,min) fint, stress Ks = (TAW − Dr)/(TAW − RAW) once the root-zone depletion Dr exceeds RAW = p TAW, actual use ETa = Ks Kc ET0, and Dr' = Dr + ETa − rain − irrigation (excess water drains).
  • Allocation and leaf area: leaf share 0.6 − 0.45 DVS before anthesis, grain share rising to 0.85 between DVS 1.0 and 1.25, the rest to stems; LAI = SLA × leaf biomass; leaves senesce after anthesis and faster under drought.

Checks run in the page

  • Ra against FAO-56 worked example 8 (32.2 MJ/m2/day).
  • Exact water-balance closure over a whole season.
  • The light-limited exponential start against its analytic rate.
  • Phenology days against the thermal-time arithmetic at constant temperature.
  • The shape of Ks and that irrigation never lowers yield.

Honest simplifications

  • The weather is a synthetic, repeatable year (seasonal cycle plus pseudo-random days), not a measured climate; absolute yields are teaching values and the crop parameters (RUE, SLA, thermal-time sums, Kc) are representative round numbers, not calibrated to a cultivar or region.
  • No nutrients, pests, lodging, frost kill, vernalisation, heat damage at flowering or rooting-depth growth; the root zone is one bucket of fixed size and runoff is ignored.
  • No assimilate remobilisation to grain and no root biomass; yields are shoot-based.
  • The plant pictures are three stage models scaled by the state, not a mechanistic 3D plant.

What to try

  • Switch to the dry-year preset and compare rain-fed and irrigated yields.
  • Sow wheat later and see the shorter season and lower yield.
  • Raise the temperature by 3 C: the crop reaches maturity sooner and yields less.
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Shoot biomass and grain yield through the season (t/ha)
Leaf area index and development stage
Soil water fraction, water stress factor and rain

About the Crop Growth Model

This simulation runs a daily FAO-style crop model that grows wheat, maize or soybean from sowing to harvest. Accumulated thermal time above each crop's base temperature drives the development stage (DVS) from 0 to 2, leaf area index builds the canopy, and absorbed photosynthetically active radiation is converted to biomass through radiation use efficiency. A simple soil water balance imposes drought stress on daily growth.

Pick a crop and adjust the sowing day of year, soil water capacity in millimetres, a temperature offset, and rain-fed versus irrigated water supply. Three views chart growth, daily weather, and stress factors. Such radiation-driven, thermal-time models underpin real agronomic decision tools used to forecast yield, schedule irrigation and assess climate impacts on cropping systems.

Frequently Asked Questions

What does this simulation actually compute?

It steps a single crop through up to 250 days from your chosen sowing date, tracking development stage, leaf area index, shoot biomass and grain yield each day. The outputs shown are grain yield and biomass in tonnes per hectare, growing-season length and peak leaf area index.

How does thermal time drive development?

Each day adds growing degree-days equal to mean temperature minus the crop's base temperature (0C wheat, 8C maize, 6C soybean). These accumulate against a vegetative target, then a reproductive target, pushing the development stage from 0 through 1 (anthesis) to 2 (maturity), at which point the run ends.

What is radiation use efficiency and how is biomass formed?

Daily biomass gain equals absorbed PAR multiplied by the crop's radiation use efficiency (RUE) and the water stress factor. Absorbed PAR follows Beer's law, intercepting roughly 48 percent of incoming solar radiation according to leaf area index and an extinction coefficient. RUE ranges from about 1.0 g per MJ for soybean to 1.8 for maize.

What do the sliders and buttons change?

Sowing day shifts the start of the season and so the weather the crop meets. Soil water capacity sets the size of the water store. The temperature offset warms or cools the whole climate by up to 5C, and the irrigation toggle keeps the soil topped up rather than relying on rainfall.

Why does grain only start filling part-way through?

Grain accumulation begins at anthesis, when the development stage reaches 1. After that, a fixed fraction of each day's new biomass (the grain filling ratio, around 0.4 to 0.48 depending on crop) is partitioned into grain rather than leaves and stems.

How is water stress modelled?

A bucket-style soil water balance adds rainfall and any irrigation, then subtracts a radiation-driven evapotranspiration demand each day. When stored water falls below about a quarter of capacity, a stress factor below 1 scales down growth. The Stress view plots soil water, the stress factor and development stage together.

Where does the weather come from?

The model generates a deterministic 365-day temperate climate resembling Ukraine, with temperature following a sinusoid that peaks in summer, cloud-modulated solar radiation, and pseudo-random rainfall events. Because it is deterministic, the same settings always reproduce exactly the same season.

Is this physically accurate?

It captures the correct mechanisms and realistic parameter ranges used in operational crop models, so trends respond sensibly to temperature, water and crop choice. It is a simplified teaching model, though, omitting nitrogen, pests, soil layers and cultivar detail, so absolute yields should be read as indicative rather than field-precise.

Why does leaf area rise and then fall?

During the vegetative phase leaf area index grows with thermal time towards a crop maximum (up to 6 for maize). After anthesis the canopy senesces, so leaf area declines, reducing light interception and shifting the plant's resources from canopy expansion to filling the grain.

What real-world use do models like this have?

Radiation-driven crop models inform yield forecasting, irrigation scheduling, sowing-date and variety selection, and climate-change impact studies. By exploring how warmer temperatures, drier soils or earlier sowing shift the harvest figures here, you can see the same trade-offs agronomists weigh when planning a season.

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