PROTECTED CROPPING • VPD MICROCLIMATE • PRECISION FERTIGATION

Greenhouse Irrigation Engineering: VPD Deficit, Solar Radiation, and Nutrient Dosing

Greenhouse environments eliminate natural rainfall from the root zone. We present an autonomous transpiration balance model based on Vapor Pressure Deficit (VPD), shortwave solar radiation, and proportional A+B fertigation implemented on the ESP32-S3 microcontroller.

Greenhouses and polytunnels represent completely controlled environments (Protected Cropping). Applying standard open-field agrometeorological models in this domain leads to critical agronomic failures. External rainfall does not hydrate crops under cover; therefore, hard precipitation interlocks must be deactivated, and water and nutrient dosing must be governed entirely by solar radiation and stomatal transpiration.

No-Rain Interlock Principle:

In the greenhouse profile of the Waveshare 6CH controller, the algorithm zeroes out external precipitation ($ P_{\text{eff}} = 0 $). During an outside downpour, plant transpiration under glass continues unabated, driven by irradiance and air vapor pressure.

1. Vapor Pressure Deficit (VPD) and the Tetens Equation

Relative humidity ($ RH $) alone does not reflect the actual driving force pulling moisture from foliage. The central physiological parameter is VPD (Vapor Pressure Deficit)—the difference between the saturated vapor pressure inside leaf substomatal cavities ($ e_s $) and the ambient vapor pressure of the greenhouse air ($ e_a $):

$$\text{VPD} = e_s - e_a \quad [\text{kPa}]$$

Saturated vapor pressure $ e_s $ at temperature $ T $ [°C] is calculated on the ESP32-S3 using the Tetens formula:

$$e_s = 0.61078 \times \exp\left( \frac{17.27 \times T}{T + 237.3} \right) \quad [\text{kPa}]$$

Actual vapor pressure $ e_a $ derives directly from measured relative humidity $ RH $ [%]:

$$e_a = e_s \times \left( \frac{RH}{100} \right) \quad [\text{kPa}]$$

Agronomic VPD Target Windows:

$ \text{VPD} < 0.4\text{ kPa} $ – Moisture-saturated atmosphere. Transpiration and calcium transport stall; extreme vulnerability to Botrytis (gray mold) and fungal pathogens.
$ 0.8\text{ kPa} \le \text{VPD} \le 1.2\text{ kPa} $ – Photosynthetic optimum. Stomata remain fully open, maximizing CO2 assimilation and nutrient uptake.
$ \text{VPD} > 1.6\text{ kPa} $ – Severe water stress. Atmospheric demand outpaces root absorption capacity; stomata close defensively to avoid desiccation.

2. Solar Radiation ($ R_s $) and Canopy Shading Factors

Transpiration in covered cropping is fundamentally powered by incident solar energy. The algorithm captures global shortwave radiation $ R_s $ [W/m²] and applies the transmittance coefficient of glazing and thermal screens $ S_{\text{coef}} $:

$$R_{\text{eff}} = R_s \times S_{\text{coef}} \quad [\text{W/m}^2]$$

The target daily volumetric irrigation rate per square meter $ D_{\text{m2}} $ [l/m²] is calculated by scaling the crop baseline with radiation ($ M_{\text{rad}} $) and VPD multipliers ($ M_{\text{vpd}} $):

$$D_{\text{m2}} = D_{\text{base}} \times M_{\text{rad}} \times M_{\text{vpd}} \quad [\text{l/m}^2]$$

Total irrigation volume $ V_{\text{water}} $ [liters] required for a greenhouse compartment of area $ A $ [m²] equals:

$$V_{\text{water}} = D_{\text{m2}} \times A \quad [\text{liters}]$$

3. Fertigation Dosing and Waveshare 6CH Relay Actuation

The controller manages both irrigation supply and proportional nutrient injection (A+B stock concentrates). The run time for the primary water solenoid (K1) and the fertilizer injector pump (K2) are calculated directly from hydraulic emitter specifications:

$$t_{\text{K1 (water)}} = \left\lfloor \frac{V_{\text{water}}}{Q_{\text{drip}}} \times 3600 \right\rfloor \quad [\text{seconds}]$$

Concentrate injection volume is dictated by target nutrient dilution $ F_{\text{pct}} $ (typically 0.7% to 1.5% volumetric ratio):

$$t_{\text{K2 (fertilizer)}} = \left\lfloor \frac{V_{\text{water}} \times \left( \frac{F_{\text{pct}}}{100} \right)}{Q_{\text{fert}}} \times 3600 \right\rfloor \quad [\text{seconds}]$$

Crop Profile	Water Baseline ($ D_{\text{base}} $)	Nutrient Ratio ($ F_{\text{pct}} $)	Agronomic Notes
Lettuce (GH_CROP_LETTUCE)	2.2 l/m²	0.7% (Low EC: 1.1–1.4 mS/cm)	Shallow root system; sensitive to root-zone salinity and tipburn.
Gerbera (GH_CROP_GERBERA)	4.5 l/m²	1.2% (Moderate EC: 1.5–2.0 mS/cm)	Cut flowers; high demand for potassium and chelated iron; crown rot sensitive.
Tomato (GH_CROP_TOMATO)	5.5 l/m²	1.5% (High EC: 2.2–2.8 mS/cm)	Intense summer transpiration; high potassium demand during fruit set.

4. Evaporative Cooling and VPD Depressurization (Fogging K3)

During peak summer conditions, mechanical ventilation alone is insufficient, driving ambient VPD above the critical 1.6 kPa threshold. The ESP32-S3 triggers relay K3 (High-Pressure Fogging System) when combined thermal and humidity limits are breached:

$$\text{Trigger K3} \iff \left( T \ge 28.0^\circ\text{C} \quad \wedge \quad \text{VPD} \ge 1.60\text{ kPa} \right)$$

Microscopic fog droplets instantly evaporate in the warm air, absorbing the latent heat of vaporization (~2.45 MJ per kg of water). This lowers canopy temperatures by 3–6°C and increases relative humidity, safely returning VPD to the optimal photosynthetic bracket.

Deployment Architecture: Greenhouse Control on Waveshare 6CH

Implemented within the greenhouse_irrigation.c runtime, the computational engine provides deterministic control directly on the ESP32-S3 microcontroller:

True Edge Autonomy (No-Cloud): Real-time calculations of VPD, dosing rates, and countdown timers execute locally in SRAM in under 2 ms.
Proportional Injection Precision: Synchronous actuation of water relay K1 and injector K2 prevents substrate over-fertilization or salinity burn.
Hardware Fail-Safe Watchdogs: Each output is monitored by an independent 1 Hz hardware interrupt counter, eliminating risk of crop flooding in the event of network disconnection.

Architecture designed and validated for the ProPresta IT ecosystem on the Waveshare ESP32-S3 6CH Relay board.