Methods · technical note

How the studio computes a field

Light first. From every point on the ground, the share of sky the modules leave open decides the diffuse light that point receives. The figure walks a probe across one row pitch and counts it.

Engine: 13 stages
Time step: 1 h · 8,760 h
Light tier: T0, live
Revised: October 2026

A run couples five models on one weather year: light on the ground from a two-dimensional sky view factor and the projected shadow of every row; energy from an hourly loss chain; crop growth from a radiation-use model driven by the light in each zone; water from the FAO-56 root-zone balance; and land use as the land equivalent ratio. Each output carries its basis and a band, and the engine is re-run against published agrivoltaic trials.

This note gives the governing equations, the assumptions that limit them, and what is not yet modelled.

Photosynthetically active radiation is taken from global horizontal irradiance with a conversion factor that rises from clear to overcast skies, then split into beam and diffuse parts [1].

PAR = k_{PAR} (q) \cdot GHI, q = \frac{DHI}{GHI}, k_{PAR} \in [0.47, 0.50]

(1)

The sky is treated as isotropic. A ground point sees the fraction of it the rows leave open, by the crossed-strings rule summed over every row of the periodic array:

F (x) = 1 - \frac{1}{2} \sum_{k = - K}^{K} (\sin θ_{far, k} - \sin θ_{near, k})

(2)

Each module edge is projected onto the ground along the sun's profile direction; a bin inside that interval, modulo the pitch, is in shadow. Support posts thin both components:

{PAR}_{g} (x) = {PAR}_{d} F (x) (1 - \frac{π}{2} n b H) + {PAR}_{b} s (x) e^{- n b_{⊥} H \cot ε}

(3)

s(x)1 in sun, the module transmittance τ_m in shadow; semi-transparent modules also pass τ_m of the sky they block
n, b, Hpost density per m², post width, post height
εsolar elevation; b_⊥ is the post width seen from the sun's azimuth

Covered designs add the film: its cycle-mean transmittance, aged over one replacement life, with a haze share of the beam scattered into diffuse light.

1.1 The edge of a finite parcel

Equation (2) describes an interior row with identical neighbours on both sides. On a small site the outer rows see more sky. Against a three-dimensional ray trace of a one-hectare parcel:

+0.5%interior rows, 2-D model against 3-D ray trace

+13–20%additional sky at the edge rows

+6–7%parcel mean above the interior

3.6%interior sky removed by the posts

Internal measurement, 23 September 2026.

Figure 1. Ground light across a finite parcel. An illustrative model written for this page, not the studio's engine.

The studio's light map is labelled "edge rows not modelled" where it is read. A finite-parcel tier that ray-casts the real parcel is in build.

Tier	Method	Output	Status
T0	2-D sky view factorInterior row, tiled across the parcel; in the browser	PAR and DLI by zone and month	live
T1	Finite-parcel ray castReal parcel geometry; in a browser worker	Annual PAR at 0.25 m; P50–P90 by zone	in build
T2	Hosted ray-traced solverServer-side	The tier an engineered report would cite	planned

Irradiance is transposed to the plane of the array with the Perez model [2], and incidence-angle losses are applied per component (beam, sky diffuse and ground-reflected) with equivalent angles for the diffuse parts [3]. Cell temperature, DC and AC conversion follow. Where reanalysis diffuse is implausible it is re-split with the Erbs correlation [4], and every weather year is graded A–D before use.

Bifacial rear-side gain is a port of the infinite-sheds model, with ground albedo linked to the crop. It is on for the vertical fence and optional for fixed and tracking arrays.

Solar yield tab: a loss waterfall from horizontal irradiance through transposition, shading, optical, module, electrical and plant losses to net AC energy. — Figure 2. Loss waterfall from horizontal irradiance to net AC energy, grouped by stage family. 1,604 kWp rain-shelter canopy, Stellenbosch. Product screen.

Biomass accumulates with the SIMPLE crop model [5], driven by the radiation each zone receives:

Δ B = Rad \cdot f_{Solar} \cdot RUE \cdot f_{{CO}_{2}} \cdot f_{Temp} \cdot \min (f_{Heat}, f_{Water}), Y = B \cdot HI

(4)

The water-stress term is not estimated separately: f_Water is the FAO-56 stress coefficient K_s of section 4, so crop and water share one root-zone balance. Each zone's diffuse light is carried into a diffuse-light efficiency term, since a shaded canopy uses scattered light better.

3.1 Evidence labels

Every crop carries the weaker of two labels: its shade-response prior and its crop-model parameters. Most parameters are analogues, and the library says so. Tropical sites are capped at low until South-East Asian field data exists. Behind the priors sit 296 trial observations from 54 sources; they are shown beside the result and do not yet move the headline yield.

Figure 3. Evidence labels across the 35-crop library.

Strong: 0
Moderate: 1Soybean
Low: 9Dry bean (common bean), Green bean (snap bean), Groundnut (peanut), Maize, Potato, Rice (aerobic, drip), Sweet corn, Tomato, Wheat
None: 25

When a design shades a crop beyond the range its evidence covers, the yield is flagged as outside the tested range, on the tab and in the points to check.

Crop tab: the crop keeps about 52 % of its covered-reference yield, flagged outside the tested range because the design shades 56 % of the light beyond the 35 % the evidence covers, with an evidence card reading none. — Figure 4. Crop tab, first screen: 56 % shade against evidence that covers 35 %. Strawberry under a rain-shelter canopy. Product screen.

Reference evapotranspiration follows FAO-56 Penman–Monteith with a dual crop coefficient, and root-zone depletion is stepped daily [6]:

D_{r, i} = D_{r, i - 1} - {(P - RO)}_{i} - I_{i} - {CR}_{i} + {ET}_{c, i} + {DP}_{i}

(5)

Runoff uses the daily curve number [7]. Drip irrigation refills the root zone to field capacity once depletion passes the readily available water, and mass is conserved exactly over the season. A covered design sheds the rain, so everything the crop drinks under it is irrigation.

Water tab: the cover sheds the rain; a monthly balance of rain, irrigation and crop evapotranspiration open against under the array; and a season balance where rain reaching the crop falls 88 % and net irrigation rises 13 %. — Figure 5. Monthly and seasonal water balance. Rain reaching the crop falls by 88 % under the canopy and net irrigation rises by 13 %. Product screen.

The land equivalent ratio compares the shared field with the two separate uses it replaces. The parcel, not the cropped area, is the land basis, so land lost to posts and lanes counts against the crop exactly once.

LER = {RY}_{crop} + {RY}_{elec} = \frac{Y_{APV}}{Y_{open}} + \frac{E_{APV}}{E_{PV}}

(6)

E_PV is a reference ground-mount plant on the same parcel and weather, at 1.1 MWp per hectare.

Worked value used to check the implementation of equation (6)

Parcel · cropped	1.0 ha · 0.9 ha
Crop: 0.9 ha × 4.4 t/ha against 5.5 t/ha open	RY_crop = 0.720
Energy: 820 MWh against 1,200 MWh	RY_elec = 0.683
Land equivalent ratio	1.403

No number is printed without its basis. Selecting any figure in the studio opens its record: the exact value, the band around it, the basis it rests on, a note and every source. Bands over weather come from fifteen real years run one by one and are reported as P10, P50 and P90.

Evidence record for annual energy: 1.87 GWh a year, exact value, modelled basis, the P90 to P10 band and a note. — Figure 6. Evidence records for annual energy (modelled) and CAPEX (assumed; a floor, as items are unpriced). Product screens.

Evidence record for CAPEX: 48.7 million rand, assumed basis, flagged as a floor because items are unpriced, with the rate-book band and sources. — Figure 6. Evidence records for annual energy (modelled) and CAPEX (assumed; a floor, as items are unpriced). Product screens.

ModelledOutput of a physical model run on the site's inputs.
DerivedComputed from other results.
LiteratureTaken from a published reference, with the citation.
AssumedNot verified from a primary source, and labelled as such.
InputEntered by the user: a price, a rate, the farmer's own yield.

The engine is re-run on published agrivoltaic trials in Germany, Sweden and Indonesia [8–10], and every modelled value is set against its measurement. The scorecard ships inside the product, failing rows first.

4/ 20engine rows within tolerance

43/ 44steps matching pvlib [11]

26measured targets

3trial sites

Three weather sources are wired, each labelled with whether a commercial project may use it before the run starts.

Source	Data	Commercial use	In the studio
Open-Meteo · ERA5	Hourly reanalysis	free API: no	Default
NASA POWER	Hourly irradiance and weather	allowed	Selectable
PVGIS · SARAH-3	Hourly, satellite-derived	allowed	Selectable

Spitters CJT, Toussaint HAJM, Goudriaan J (1986). Separating the diffuse and direct component of global radiation and its implications for modeling canopy photosynthesis. Part I. Agricultural and Forest Meteorology 38:217–229.
Perez R, Ineichen P, Seals R, Michalsky J, Stewart R (1990). Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44(5):271–289.
Duffie JA, Beckman WA (2013). Solar Engineering of Thermal Processes, 4th ed. Wiley. §5.4, equivalent incidence angles.
Erbs DG, Klein SA, Duffie JA (1982). Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation. Solar Energy 28(4):293–302.
Zhao C, Liu B, Xiao L, Hoogenboom G, Boote KJ, Kassie BT et al. (2019). A SIMPLE crop model. European Journal of Agronomy 104:97–106. doi:10.1016/j.eja.2019.01.009
Allen RG, Pereira LS, Raes D, Smith M (1998). Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper 56. FAO, Rome. Eqs. 82–88.
USDA NRCS. National Engineering Handbook, Part 630 Hydrology, ch. 9: Hydrologic soil-cover complexes.
Weselek A, Bauerle A, Hartung J, Zikeli S, Lewandowski I, Högy P (2021). Agrivoltaic system impacts on microclimate and yield of different crops within an organic crop rotation in a temperate climate. Agronomy for Sustainable Development 41:59. doi:10.1007/s13593-021-00714-y
Campana PE, Stridh B, Hörndahl T et al. (2024). Experimental results, integrated model validation, and economic aspects of agrivoltaic systems at northern latitudes. Journal of Cleaner Production 437:140235. doi:10.1016/j.jclepro.2023.140235
Yoon S, Kim M, Han S, Lee J-Y (2026). Agrivoltaics in the tropics: soybean yield stability and microclimate buffering across wet and dry seasons. Agronomy 16(1):116. doi:10.3390/agronomy16010116
pvlib python, version 0.15.2: the reference implementation for the step check (sun position, incidence, transposition, incidence-angle modifier, cell temperature, DC and AC power) on four reference systems.

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