🌱 Greenhouse climate control Live model

Basis — the model behind the numbers

Every relation the simulator uses, with its source. Constants marked as assumptions are illustrative calibrations.

Air temperature follows an energy balance: sun in, heat out through the cover and with ventilation air, heat used to evaporate water, plus the heating.

C·dT/dt = τ·I·(1 − 0.6·0.75·screen) − λ·(E_crop + E_fog) + Q_heat + (U·Ac/Af + ρc_p·Q_v)·(T_out − T) + G_soil·(T_soil − T)[1]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Heat loss through the cover is U × area × temperature difference; a closed screen lowers U, a clear night sky raises it.

U = 6.2 − (6.2 − 4.0)·screen W/m²K (single glass → with thermal blanket); ×(1 + 0.25·clear sky) at night[1]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Ventilation is leakage plus wind-driven flow through the open vents.

Q_v = (N·H/3600 + vent·C_w·max(1, u_wind))·(1 − 0.4·screen), N = 0.75 h⁻¹[1][4]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Saturation vapour pressure rises steeply with temperature; VPD is how far the air is from saturation.

e_s(T) = 0.6108·exp(17.27·T / (T + 237.3)) kPa; VPD = e_s(T) − e_a; RH = e_a / e_s(T)[2]

Water vapour balance: transpiration and fog add moisture, ventilation and condensation on the cold glass remove it.

H·dχ/dt = E_crop + E_fog − Q_v·(χ − χ_out) − k_c·(Ac/Af)·(1 − 0.7·screen)·max(0, e_a − e_s(T_cover)), χ = e·M_w/(R·T)[6][2]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Transpiration has a radiation part and a part driven by dry air (VPD).

E_crop = A·(1 − e^(−k·LAI))·I_in/λ + B·LAI·VPD (A 0.45, k 0.64, LAI 3, B 0.02 kg/m²·h·kPa by day)[3]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Fog cools only as far as it evaporates: about 2.45 MJ per litre, more in dry air than in humid air.

E_fog = fog·0.4 kg/m²·h × min(1, VPD/0.8); each evaporated kg removes λ = 2.45 MJ of sensible heat; the rest wets leaves[1][2]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

CO₂ balance: dosing in, ventilation and crop uptake out.

H·dC/dt = dose − Q_v·(C − C_out) − P_net; dosing ≈ 5.5 g/m²·h holds ≈ 1000 ppm at 1 air change per hour[1]

Photosynthesis responds to light, CO₂, temperature and VPD; the CO₂ response follows a published rule of thumb for greenhouse fruit crops.

P = P_ref·(1 − e^(−I_in/300))·exp(150/400 − 150/C)·f(T: 1 at 17–27 °C)·f(VPD) (from the CO₂ rule dP/P = 1.5 %·(1000/C)² per 100 ppm)[5][7]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Crop stress counters: hours too hot, too cold, or humid enough for grey mould.

heat hours: T > 35 °C · cold hours: T < 10 °C · disease-risk hours: RH ≥ 90 % or wet leaves · GDD = Σ max(0, T − 10)·Δt[1][7][8][10]

Outside weather: daily temperature curve, constant dew point, sunshine reduced by cloud, random cloud and wind fluctuations.

T_out = T̄ + A·cos(2π(h − 15)/24); e_out = e_s(T_dew); I = I_clear·(1 − 0.75·N^3.4); cloud N and wind fluctuate (normal, seeded)[9][2]Assumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Other constants used by the model.

height 4.5 m · cover/floor 1.2 · τ 0.8 · heat capacity 30 kJ/m²K · heating ≤ 180 W/m² · screen blocks 60 % of light (75 % of that as heat) and 40 % of air exchange, and hides 70 % of the cold glass (condensation) · vents 0.016 m³/s·m² per m/s wind · soil 2 W/m²K · fog ≤ 0.4 L/m²·h · CO₂ ≤ 8 g/m²·h · P_ref 4 g CO₂/m²·h · condensation 1.9·10⁻⁸ kg/m²·s·PaAssumption: greenhouse size, heat capacity, vent, screen, fog and crop coefficients are illustrative values for a modern glasshouse; the physics is a single well-mixed air volume. Real sites calibrate each constant.

Randomness: a seeded mulberry32 generator; distributions used — uniform, exponential (inverse CDF), normal (Box–Muller), Poisson (Knuth). The seed is shown and shareable.

Sources

1. ANSI/ASAE EP406.4 JAN2003 (R2008) — Heating, Ventilating and Cooling Greenhouses (eq. 1–4, Table 1 U-values, Table 2 infiltration: new glass or fiberglass 0.50–1.0 h⁻¹, §5.8.5 CO₂ injection, §7.1.3 temperature limits); since withdrawn, available from ASABE as a historical document — American Society of Agricultural and Biological Engineers, 2003
2. R. G. Allen, L. S. Pereira, D. Raes, M. Smith — Crop evapotranspiration, FAO Irrigation and Drainage Paper 56 (eq. 11 saturation vapour pressure, eq. 14 dew point, λ = 2.45 MJ/kg) — FAO, Rome, 1998
3. M. Baille, A. Baille, J. C. Laury — A simplified model for predicting evapotranspiration rate of nine ornamental species vs. climate factors and leaf area — Scientia Horticulturae 59:217–232, 1994
4. T. Boulard, A. Baille — Modelling of air exchange rate in a greenhouse equipped with continuous roof vents — Journal of Agricultural Engineering Research 61(1):37–48, 1995
5. E. M. Nederhoff — Effects of CO₂ concentration on photosynthesis, transpiration and production of greenhouse fruit vegetable crops (PhD thesis; CO₂ rule) — Wageningen Agricultural University, 1994
6. B. H. E. Vanthoor, C. Stanghellini, E. J. van Henten, P. H. B. de Visser — A methodology for model-based greenhouse design: Part 1, a greenhouse climate model for a broad range of designs and climates — Biosystems Engineering 110:363–377, 2011
7. R. R. Shamshiri et al. — Review of optimum temperature, humidity, and vapour pressure deficit for microclimate evaluation and control in greenhouse cultivation of tomato: a review — International Agrophysics 32:287–302, 2018
8. Identifying and Managing Three Major Disease Threats in Greenhouse Tomatoes: Leaf Mold, Gray Mold, and Bacterial Wilt (SPES-820) — Virginia Cooperative Extension
9. F. Kasten, G. Czeplak — Solar and terrestrial radiation dependent on the amount and type of cloud — Solar Energy 24:177–189, 1980
10. G. S. McMaster, W. W. Wilhelm — Growing degree-days: one equation, two interpretations — Agricultural and Forest Meteorology 87:291–300, 1997