Lesson 3.1 · Irradiance modelling

Light on the field

Zainali et al. (2025), Modelling, simulation and optimisation of agrivoltaic systems, Applied Energy 386, section 3.1 (pp. 3–10).

Sun lamp on the day's sun pathPins: irradiance on the ground across the rowsShadow strength = beam share of the lightCompass: the dark half of the needle points north, along the rowsThe rows run north–south and, with tracking on, the modules turn from east to west through the day to face the sun. One weather-station number, GHI, is split into beam and diffuse light, moved onto the front and rear faces of the panels, and blocked by the rows before it reaches the crop. Beam light casts the hard shadows; diffuse sky light still reaches the ground between and under the rows, so the pins never fall to zero. Every number on this page comes from the same simple model that draws the shadows and moves the pins.

Single-axis trackingModules turn east to west about the row axis, ±60°, with backtracking.

Time of day10:30 Panel height3.0 m Row spacing6.0 m · GCR 0.33 Module angle

Date21 Dec20 Mar21 Jun

SkyClearHazyOvercast

Ground albedoLey grass 0.19Winter wheat 0.25Snow 0.67

Latitude31.41° N

1 · Decomposition
Sun elevation
GHIglobal horizontal
Clearness index k_t
Diffuse fraction
DNIdirect normal
DHIdiffuse horizontal

2 · Transposition, middle row
Module angle+ faces east, − faces west
True-tracking anglenormal pointed at the sun
Front: beam
Front: sky diffuse
Front: ground-reflected
Front POA total
Rear: beam
Rear total
Rear ÷ front

3–4 · Shading and PAR at the crop
Ground coverage ratio
Mean ground irradiance
Share of GHI reaching crop
Of which diffuse
PAR at crop0.45 × irradiance

How the figure computes its numbers

Sun. Solar time on the chosen date at the chosen latitude, from Eilat (29.56° N) to Kiryat Shmona (33.21° N); the page opens at 31.41° N, the middle of that range, in the northern Negev near Be'er Sheva. Sun elevation and azimuth, the tracker and backtracking angles, the shadows and every readout follow the latitude. The ring is that day's sun path and the lamp sits on it at the chosen time. The time slider covers the hours when the sun is more than about 10° up, where the lamp stays clear of the ring's feet.
Decomposition. Clear-sky GHI from the Haurwitz model, times 1 (clear), 0.7 (hazy) or 0.3 (overcast). The clearness index then sets the diffuse fraction through the Erbs correlation, one simple clearness-index model of the many the review lists. Neither model is named in the article.
Orientation. Rows run north–south, so the modules face east or west. Each module turns about its torque tube, at the panel height.
Tracking on (default). Single-axis tracking about the row axis: the true-tracking angle points the module at the sun in the east–west plane, limited to ±60°. Backtracking turns the modules back toward flat at low sun, so no row shades the next. This uses the standard flat-ground rule (as in pvlib); the article does not describe the algorithm, though it cites a tracking/backtracking study for agrivoltaic plants (Casares de la Torre et al., ref. 34) and notes that view factors are less accurate for single-axis trackers (about 2 %) than for fixed tilt. Modules lie flat at night.
Tracking off. Fixed tilt toward the east, 0° (flat) to 90° (a vertical bifacial fence, the layout the article flags as hardest for transposition models). Mornings light the front, afternoons the rear.
Transposition. Isotropic sky (Liu and Jordan): the sky is an evenly bright dome. Beam on each face is DNI × cos(incidence angle), blocked by the neighbouring rows in the east–west plane.
Shading. A 2-D view-factor model: every row is treated as infinitely long, as the classic method assumes. The model has 31 rows and the bench shows the ones that fit on the bed, so some shadows at the bed's edges come from rows beyond it. Beam light on the ground is either blocked or not; diffuse light is the share of the sky dome each ground point can see between the panels. Posts, beams and light reflected off the panel undersides are ignored. On the drawing the rows are 12 m long, so the shadows also slide along the rows (north–south); the pins and numbers use the 2-D result.
West (rear) face. Beam when the sun is in the west, plus sky diffuse and ground-reflected light: albedo × the irradiance on the patch of ground each rear-facing direction sees (albedo values from the article: ley grass 0.19, winter wheat 0.25, snow 0.67). The view factor method is the one the article reports under-predicting rear irradiance by about 8 % against ray tracing.
PAR. 0.45 × irradiance at crop level, the simple rule in the article. The crop is a flat surface at ground level, which the article notes is how most models treat it.
Readouts are for the middle row and the one pitch of ground beneath it; panels are 2 m wide (one portrait module), height is to the panel centre.

Made by Omer Jerusalem, based on Zainali et al. (2025), Modelling, simulation, and optimisation of agrivoltaic systems: a comprehensive review, Applied Energy 386, 125558. doi:10.1016/j.apenergy.2025.125558