The Science Behind Nimbus Earth Agriculture: Remote Sensing & Biophysics

1. Sentinel-2 Radiometric Calibration (DQR nr. 119)

To guarantee reflectance accuracy across different satellite platforms, the platform processes Sentinel-2 multispectral bands according to the latest European Space Agency (ESA) processing guidelines. For the Sentinel-2C satellite platform, a radiometric offset of -50 Digital Numbers (DN) is applied to all reflective bands (B02 to B12) to compensate for baseline sensor differences, converting raw sensor values to surface reflectance (\(\rho\)):

This calibration prevents spectral biases, ensuring indices like NDVI, SAVI, and NDRE remain stable regardless of which satellite passes over your field.

2. Daily Soil Water Balance for Soil Moisture

Each field's topsoil is modelled as a store holding S = 100 mm of water. Each day, rain P and logged irrigation I fill it; evaporation draws it down at the FAO-56 reference rate ET₀ while the store is above 70% full, tapering linearly below that; water above full drains away:

The balance runs over the trailing 92 days of Open-Meteo rain and ET₀ (start-up error under 2 points), and fullness w maps to volumetric soil moisture over a soil-texture range (loam/unknown: 14–41%). Validated against 18 COSMOS-UK farmland stations over two years: r = 0.90, RMSE ≈ 5.5% volumetric moisture content, inside the 6% target; a single probe reading calibrates a field's offset. The Sentinel-1 Water Cloud Model it replaced scored r = 0.43 with a −27-point bias, and radar change detection r = 0.69. Full method: How the App Measures Soil Moisture.

3. Reference Crop Evapotranspiration (FAO-56 Penman-Monteith)

Reference evapotranspiration (\(ET_0\), mm/day) measures the atmospheric water demand from a standardized reference grass crop. The platform implements the internationally recognized **FAO-56 Penman-Monteith** equation:

Where daily weather parameters are integrated from land-anchored meteorological grids:

• \(R_n\): Net radiation at the crop surface (calculated from incoming solar radiation and outgoing net longwave radiation).
• \(G\): Soil heat flux (assumed negligible at a daily scale).
• \(T\): Mean daily air temperature at 2m height.
• \(u_2\): Wind speed at 2m height.
• \(e_s - e_a\): Vapor pressure deficit (VPD) of the atmosphere.
• \(\Delta\): Slope of the saturation vapor pressure-temperature relationship.
• \(\gamma\): Psychrometric constant.

4. Dynamic Crop Water Balance

To schedule irrigation, the platform runs a daily forward-looking root-zone deficit model. The water height that a field can hold before stress occurs—Readily Available Water (RAW, mm)—is calculated from the crop's active root depth (\(z_r\)), depletion fraction (\(p\)), and soil texture field capacity (FC) and wilting point (WP):

Crop water consumption (\(ET_c\)) is computed by multiplying reference evapotranspiration by stage-specific crop coefficients (\(K_c\)):

Daily depletion balances accumulate based on crop transpiration minus effective rainfall (\(P_{\text{eff}}\)), advising farmers precisely how many days remain before the soil moisture dips below the crop's stress threshold.

5. Field Zones (Yield-Stability Management Zoning)

Field zones show where a field consistently performs better or worse than itself. The platform follows the yield-stability approach used for multi-year yield maps, applied to Sentinel-2 greenness. Up to 15 clear, green-season passes are selected from the last three years (at least 90% of the field cloud-free and a field median NDVI of at least 0.3, or 0.25 in arid zones), spread evenly across the period. On each pass \(t\), every 10 m pixel \(i\) is expressed relative to that day's field median, so the crop's seasonal rise and fall cancels out:

Each pixel's zone is set by the median of its ratios across passes, \(\tilde{r}_i\), which ignores one-off outliers such as a cloud edge the mask missed. Its consistency is measured with the robust spread \(s_i = 1.4826 \cdot \text{MAD}_t\, r(i,t)\):

• Low: \(\tilde{r}_i < 0.90\) — consistently more than 10% less green than the field.
• Average: \(0.90 \le \tilde{r}_i \le 1.10\).
• High: \(\tilde{r}_i > 1.10\).
• Variable (drawn fainter): \(s_i \ge 0.10\) — the area moves between zones from year to year.

A 5 × 5 majority filter removes isolated pixels so zones are large enough to manage. Each zone is reported with its share of the field and its typical gap, \(\text{mean}(\tilde{r}) - 1\) (e.g. “28% less green”). Repeatability is a built-in check: the passes are split into two independent halves, each half is classified separately, and the share of pixels that land in the same zone is reported. Fewer than six qualifying passes returns “not enough clear history” rather than a map. Zones describe greenness (NDVI), a strong guide to crop performance but not a direct yield measurement; elevation and slope are reported alongside from the Copernicus DEM (GLO-30, or GLO-90 where unavailable).

6. Selected Scientific References

The algorithms and methods running inside the platform are based on the following published academic research: