Water Stress

Water Stress gives each field a drought-stress index from 0 to 100, banded low, moderate or high. It computes reference evapotranspiration from the next 24 hours of forecast temperature with the Hargreaves equation and sets that demand against the latest soil moisture reading from a device on the field and the rain forecast for the next three days. Each index carries a confidence of low or moderate. It’s a stress signal, not a soil water balance, so it doesn’t produce an irrigation prescription.

The Science

Evapotranspiration is the water a surface loses to the air. It combines evaporation from soil and transpiration from leaves. Reference evapotranspiration, ETo, is that loss from a defined reference surface. The reference is a hypothetical grass 0.12 m tall, with a fixed surface resistance of 70 s m⁻¹ and an albedo of 0.23, actively growing, fully shading the ground and well watered (Allen et al., 1998). ETo is a property of the weather, not of any crop. FAO Irrigation and Drainage Paper 56 recommends one method for it, the FAO Penman-Monteith equation (equation 6):

ET_o = \frac{0.408\,\Delta\,(R_n - G) + \gamma\,\frac{900}{T + 273}\,u_2\,(e_s - e_a)}{\Delta + \gamma\,(1 + 0.34\,u_2)}

where

R_n

is net radiation and

G

soil heat flux (MJ m⁻² day⁻¹),

T

mean air temperature at 2 m (°C),

u_2

wind speed at 2 m (m s⁻¹),

e_s - e_a

the vapour pressure deficit (kPa, how far the air is from saturation),

\Delta

the slope of the saturation vapour pressure curve and

\gamma

the psychrometric constant (kPa °C⁻¹). It needs radiation, temperature, humidity and wind (Allen et al., 1998). When radiation, humidity or wind are missing, FAO-56 offers the Hargreaves equation (equation 52). It needs only daily maximum and minimum temperature and extraterrestrial radiation

R_a

, the radiation reaching the top of the atmosphere for that latitude and date (Hargreaves and Samani, 1985; Allen et al., 1998):

ET_o = 0.0023\,(T_{mean} + 17.8)\,(T_{max} - T_{min})^{0.5}\,R_a

FAO-56 advises checking the Hargreaves estimate against Penman-Monteith in each new region. Hargreaves tends to under-predict under high wind (above 3 m s⁻¹) and to over-predict under high humidity (Allen et al., 1998). A water balance turns ETo into stress. Crop evapotranspiration is ETo scaled by a crop coefficient. Total available water is the difference between the soil’s water content at field capacity and at wilting point, over the rooting depth:

TAW = 1000\,(\theta_{FC} - \theta_{WP})\,Z_r

(equation 82). Field capacity is the water the soil holds after it has drained. Wilting point is where the crop can draw no more. Readily available water is the fraction

p

of that which a crop can use before it is stressed,

RAW = p \cdot TAW

(equation 83). Root-zone depletion is tracked daily from rain, run-off, irrigation, capillary rise, crop evapotranspiration and deep percolation (equation 85). Once depletion exceeds RAW, the stress coefficient falls:

K_s = (TAW - D_r)/(TAW - RAW)

(equation 84) (Allen et al., 1998). This model doesn’t run that balance. Every term it lacks is listed under limits.

How It’s Applied

Two pure functions run in turn: Hargreaves reference evapotranspiration, then a stress index. Hargreaves needs only what every field has, the forecast temperature and the latitude. Penman-Monteith needs net radiation, wind and humidity at the field. Those aren’t available.

Inputs

Input	Source	If missing
Maximum and minimum air temperature over the next 24 hours	The field’s cached forecast, from a gridded weather model	ETo is taken as zero and the index is computed from the probe alone
Extraterrestrial radiation $R_a$	Computed from the field’s latitude and the date in the published FAO-56 form (Allen et al., 1998), converted to mm per day	Never missing. It’s computed, not fetched
Soil moisture	Metric `220`, the latest reading from a device on the field, for example the AgriHub360 Sensor or a device you bring	A demand-only index from ETo and the rain ahead, at low confidence
Rain over the next 3 days	The field’s cached forecast	Absent with the rest of the forecast: ETo is zero and the index comes from the probe alone
Growth stage	Growth-stage model, through the “stage past the nitrogen window” test shared with Nitrogen Timing	The index is still computed and shown. No advisory is raised

The index is computed whenever a moisture reading or a forecast exists. Only with neither does the model report no_data.

The Rule

ETo        = 0.0023 * (Tmean + 17.8) * sqrt(Tmax - Tmin) * Ra   # Hargreaves, FAO-56 eq. 52
                                                                 # Tmax, Tmin from the next 24 hours of forecast
                                                                 # Ra in mm per day
ETo        = 0                                                   # when there is no forecast
index      = stress(ETo, soil_moisture, rain_ahead)              # 0 to 100
band       = low       if index < 30
             moderate  if 30 <= index < 60
             high      if index >= 60
confidence = moderate  with a probe and a forecast
             low       with a forecast and no probe                # never higher
state      = no_data   only with no probe and no forecast

Parameters

Quantity	Value
Index range	0 to 100
Band edges	30 and 60. Below 30 is low, 30 to 60 is moderate, 60 and above is high
Confidence cap	`moderate`. A temperature-only ETo against a single-point probe never earns more. Without the probe the confidence is `low`
ETo without a forecast	0 mm per day
Soil water-holding capacity, crop coefficient, readily available water	Not in the model

Output and Cadence

The model writes one drought-stress index per field, banded, with a confidence of low or moderate. The state is no_data only when there is neither a moisture reading nor a forecast. Resolution is the field. The job runs every six hours, after the growth-stage job. A sensitive stage is one where water stress still drives yield loss. It is the “stage past the nitrogen window” test shared with nitrogen timing. For a high band while the crop is at a sensitive stage, it writes an advisory row and sends a push and an email, at most once per field every three days. The field-detail card reads the live value on request. The confidence label is the uncertainty the index carries.

Data Flow

The forecast temperature and rain feed the Hargreaves ETo. The ETo and the latest soil-moisture reading make the index and its band. The growth stage gates the advisory only. The scheduled job and the field route share the fetch step and both functions. Only the job writes advisory rows.

The Scheduled Run

The weather ingest job refreshes the forecast every four hours, per grid cell, and writes it to each field in the cell.
The growth-stage job runs at start-up and then daily, and writes a stage row per planting.
Every six hours, and never at start-up, the water stress job lists the fields with an active planting. It reads the latitude, the latest moisture reading, the cached forecast and the stage row for each.
A field with neither a probe nor a forecast is reported as no_data and nothing is written. Otherwise the job computes ETo, zero without a forecast, then the index, band and confidence.
For a high band at a sensitive stage the job writes an advisory row, at most once per field every three days, and sends a push and an email.
The field-detail card asks the field route for the live result, so it never waits for the next run.

Worked Example

The table is an example, not a record. It walks one field at 52.2 °N through four July days.

R_a

is given in its mm per day equivalent so that ETo follows directly from the formula above. The index values are illustrative and the bands follow the edges of 30 and 60.

Day	Tmin, Tmax, $R_a$	ETo, soil moisture, rain ahead	Index and band
19 July	12 °C, 24 °C, 16.09	4.59 mm, 32 per cent, 0 mm	33, moderate
20 July	13 °C, 27 °C, 16.03	5.21 mm, 24 per cent, 0 mm	49, moderate
21 July	14 °C, 28 °C, 15.96	5.33 mm, 15 per cent, 2 mm	62, high
22 July	12 °C, 20 °C, 15.90	3.50 mm, 15 per cent, 18 mm	37, moderate

On 19 July the ETo is

0.0023 \times (18 + 17.8) \times \sqrt{12} \times 16.09 = 4.59

mm per day. The index climbs as the probe dries and the demand rises. It crosses 60 into the high band on 21 July, while the crop is at flag leaf (GS39). It falls back on 22 July when cooler air lowers the demand and 18 mm of rain is forecast, although the probe still reads 15 per cent. The advisory fires once, on 21 July, the day the band turns high.

External Models

This model calls no language model. Its outputs are numbers and states: an ETo, an index, a band and a confidence. Alert text is rendered from templates. The forecast temperature and rain it reads come from a gridded weather model, cached per field and refreshed every four hours. Two language-model features read its output. The Field Health Review folds it into its summary of the field. The Assistant can answer questions about it.

Validation

Validation holds out a whole season, a whole region, or both. The Hargreaves reference evapotranspiration is scored against the FAO Penman-Monteith value computed from full weather records at stations in the held-out region. That is the check FAO-56 asks for in each new region (Allen et al., 1998). The stress index is scored against the FAO-56 stress coefficient

K_s

from a full soil water balance on held-out fields with a soil moisture record. The baseline for the index is a rainfall-only signal: days since the last rain.

Limits

It does not produce an irrigation prescription.
It uses Hargreaves rather than Penman-Monteith. FAO-56 itself sanctions that trade-off when radiation, humidity and wind are missing (Allen et al., 1998).
One moisture probe per field, at one depth, stands for the whole field.
There is no soil water-holding capacity term, so the same index means different things on sand and on clay. In FAO-56 terms there is no $TAW$ , no $RAW$ and no $K_s$ .
There is no crop coefficient and no root-zone depletion model. The index is a stress signal, not a water balance.
Without a probe the index is demand-only and its confidence is low. Without a forecast the demand term is zero. It never estimates a moisture reading.

See the models overview for the rules every model inherits.

References

Allen, R.G., Pereira, L.S., Raes, D. and Smith, M., 1998. Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56. Food and Agriculture Organization of the United Nations, Rome.
Hargreaves, G.H. and Samani, Z.A., 1985. Reference crop evapotranspiration from temperature. Applied Engineering in Agriculture, 1(2), 96–99.

Overview

Crop Development

Field Conditions

Disease & Pest Risk

Language & Vision Models

The Science

How It’s Applied

Inputs

The Rule

Parameters

Output and Cadence

Data Flow

The Scheduled Run

Worked Example

External Models

Validation

Limits

References

​The Science

​How It’s Applied

​Inputs

​The Rule

​Parameters

​Output and Cadence

​Data Flow

​The Scheduled Run

​Worked Example

​External Models

​Validation

​Limits

​References

The Science

How It’s Applied

Inputs

The Rule

Parameters

Output and Cadence

Data Flow

The Scheduled Run

Worked Example

External Models

Validation

Limits

References