AGROMETEOROLOGY • SMART AGRICULTURE • EDGE AI

Irrigation Engineering & Water Balance: ESP32-S3 & Waveshare 6CH

Replacing archaic, static timers with autonomous evapotranspiration analytics at the network edge. Leveraging Xtensa LX7 vector instructions, the FAO-56 soil water balance model, and local Open-Meteo telemetry for precision water delivery without cloud mediation.

In legacy irrigation controllers, zones engage based on rigid RTC schedules, completely ignoring the fact that cool weather conserves soil moisture while hot, windy conditions exponentially accelerate plant transpiration. The global standard in agrometeorology is the FAO-56 Penman-Monteith model and its empirical reductions, enabling real-time quantification of moisture depletion within the root zone.

Within the ProPresta IT ecosystem, the algorithm running on the Waveshare 6CH (ESP32-S3) actuator node computes the dimensionless irrigation factor $ K_{\text{irrig}} $, which serves as a dynamic multiplier for the base valve runtimes:

$$K_{\text{irrig}} = \text{clamp}\left( \frac{\text{ET}_c - P_{\text{eff}}}{\text{ET}_{\text{base}}}, \; 0.0, \; 1.5 \right)$$

Physical Interpretation of Balance Parameters:

$ \text{ET}_c $ [mm/day] – Crop evapotranspiration; volume of water depleted from the root zone via direct soil evaporation and plant stomatal transpiration.
$ P_{\text{eff}} $ [mm/day] – Effective precipitation; rainfall volume actually infiltrating the root reservoir, excluding surface runoff and canopy interception.
$ \text{ET}_{\text{base}} $ [mm/day] – Baseline daily water demand (nominally configured at $ 4.0\text{ mm/day} $), corresponding to the operator's baseline valve runtime setting.
$ \text{clamp}(x, 0.0, 1.5) $ – Boundary bounding function preventing singular states; constrains runtime adjustments between zero and a maximum cap of 150%.

1. Decomposition of Physical Components: Evaporation & Effective Rain

A. Actual Crop Evapotranspiration ($ \text{ET}_c $)

Specific crop water demand scales relative to reference grass evapotranspiration using crop coefficient $ K_c $:

$$\text{ET}_c = \text{ET}_0 \times K_c$$

Coefficient $ K_c $ maps the plant phenology and canopy architecture (e.g., residential turf: $ 0.80 $–$ 0.85 $, ornamental shrubs: $ 0.60 $, mature fruiting crops: $ 1.05 $–$ 1.15 $).

On the ESP32-S3 microcontroller, processing temperature $ T $ [°C] and relative humidity $ RH $ [%] inputs from Open-Meteo, reference evapotranspiration $ \text{ET}_0 $ is derived using a reduced Romanenko-Turc approximation:

$$\text{ET}_0 = 0.013 \times \left( \frac{T}{T + 15} \right) \times \left( 23.88 \times R_s + 50 \right) \times C_h$$

The atmospheric humidity correction coefficient $ C_h $ models vapor pressure deficit (VPD). As ambient conditions become hot and arid, soil water depletion increases non-linearly:

$$C_h = \begin{cases} 1.0 & \text{for } RH \ge 50\% \\ 1.0 + \frac{50 - RH}{70} & \text{for } RH < 50\% \end{cases}$$

B. Effective Precipitation Model ($ P_{\text{eff}} $) via USDA SCS

Standard automation erroneously subtracts precipitation 1:1. Minor rain below 1 mm evaporates directly from vegetation leaves without penetrating the root horizon. Conversely, heavy downpours exceed soil infiltration capacity, resulting in surface runoff or gravitational drainage below the roots. We integrate the Soil Conservation Service (USDA) model:

$$P_{\text{eff}} = \begin{cases} 0 & \text{when } P_{\text{tot}} < 1.0\text{ mm} \quad (\text{foliar retention / rapid evaporation}) \\ P_{\text{tot}} \times 0.8 & \text{when } 1.0 \le P_{\text{tot}} \le 15.0\text{ mm} \quad (\text{optimal soil infiltration}) \\ 12.0 + 0.1 \times (P_{\text{tot}} - 15.0) & \text{when } P_{\text{tot}} > 15.0\text{ mm} \quad (\text{soil saturation threshold}) \end{cases}$$

Where cumulative rainfall balance $ P_{\text{tot}} $ integrates past 24-hour recorded precipitation and the upcoming 12-hour forecast:

$$P_{\text{tot}} = P_{\text{hist 24h}} + P_{\text{prog 12h}}$$

2. Vectorized Implementation on ESP32-S3: Taylor Expansion

Solving full iterative non-linear Penman-Monteith systems would consume excessive double-precision FPU cycles, raising operating temperatures on embedded chips.

In the smart_irrigation.c subsystem, we implement a first-order Taylor expansion around the agrometeorological equilibrium point ($ T = 20^\circ\text{C} $, $ RH = 60\% $, $ P = 0\text{ mm} $):

$$K_{\text{irrig}} = 1.0 + 0.03 \cdot (T - 20) + 0.008 \cdot (60 - RH) - 0.20 \cdot P_{\text{eff}}$$

Fail-Safe Soil Interlock (Rain Lockout):

Regardless of polynomial values, hardware interrupts immediately enforce zero runtime during active rain or excessive ground saturation:

$$\left( P_{\text{now}} > 0.5\text{ mm} \quad \text{or} \quad P_{\text{tot}} \ge 5.0\text{ mm} \right) \implies K_{\text{irrig}} = 0.0$$

3. Integration with Waveshare 6CH Hardware Registers

The calculated factor does not drive relays through continuous state polling (which risks locked states upon network dropout). Instead, it modifies the initial values loaded into hardware countdown timers: relay_countdown_timers[zone].

$$t_{\text{exec}} = \left\lfloor t_{\text{base}} \times 60 \times K_{\text{irrig}} \right\rfloor \quad [\text{seconds}]$$

Field Deployment Example:
The operator defines a nominal turf cycle of $ t_{\text{base}} = 10\text{ minutes} $. Under moderate conditions (e.g., 16.7°C, 92% RH, 0.4 mm ongoing drizzle), the heuristic calculates $ K_{\text{irrig}} = 0.47 $. The countdown value written to registers is:

$$t_{\text{exec}} = 10 \times 60 \times 0.47 = 282\text{ seconds (4 minutes 42 seconds)}$$

Water consumption drops by 53% in this single cycle, directly protecting root zones from fungal development and anaerobic saturation.

Parameter	Type & Range	Data Source / Register	Functional Role
$ T $	float [-20.0 .. +50.0 °C]	temperature_2m	Thermal driver of evapotranspiration
$ RH $	int [0 .. 100 %]	relative_humidity_2m	Vapor pressure deficit (VPD) evaluation
$ P_{\text{tot}} $	float [≥ 0.0 mm]	rain + hourly.precipitation	Precipitation offset and storm interlock
$ K_{\text{irrig}} $	float [0.0 .. 1.5]	smart_irrigation_get_factor()	Runtime multiplier for relay coil actuation
Watchdog	uint32_t [seconds]	relay_countdown_timers[6]	Autonomous 1 Hz hardware decrementer

Edge AI Implementation Summary

Deploying vector heuristics on the ESP32-S3 microcontroller eliminates commercial cloud dependencies, providing deterministic microclimate automation directly at the local site:

Autonomous Decision-Making: The $ K_{\text{irrig}} $ factor is computed in local RAM from real-time environmental telemetry. Systems continue cycling even during complete WAN outages based on last-known stable balance states.
FreeRTOS Core Decoupling: Heavy JSON network payloads (allocated in external Octal PSRAM) and floating-point math execute on Core 1, ensuring zero jitter on Core 0 dedicated to encrypted UDP (AES-128-GCM) and GPIO switching.
Power Integrity & Stability: Enforcing constant Wi-Fi modem activity (esp_wifi_set_ps(WIFI_PS_NONE)) alongside a 12V/2A industrial rail completely prevents brownout resets during concurrent relay coil inrushes.
Hardware Watchdog Safety: Independent hardware 1 Hz timer interrupts ensure electrovalves auto-close even in the event of an application software freeze.

Architecture validated on Waveshare 6CH Relay modules within the ProPresta IT platform.