CALC-132
Broadband irradiance of the ASTM G173-03 reference spectra, trapezoid integral over wavelength
What this is
This is the project's own arithmetic, published in full so it can be checked rather than taken on trust. It is not a source. Every input it uses is cited to a record, and the conclusion it reaches only carries as far as those inputs do.
REGISTERED 2026-10-10 (ON-451). Drafted by SBSP-coord (wip/coord-src-nlr-g173-fix 57446c8e), checked FIX by the coord checker (wip/coord-check-nlr-g173 7c20b3e4), FIX applied and confirmed by coord as round 2 PASS; landed by SBSP-coord. verified: VER-2359 CONFIRMED 2026-10-14 (second reader, outputs/review/calc132-vr1-check-2026-10-14.md, FIX applied at landing).
What it computes. The integral over wavelength of each of the three spectral columns in the G173-03 table held as SRC-780, in W/m2, by the trapezoid rule on the table's own uneven wavelength grid.
| Quantity | Value | Source | Stated or assumed |
|---|---|---|---|
| Wavelength grid | 280.0 to 4000.0 nm, 2,002 rows, steps 0.5, 1, 2, 3 and 5 nm | SRC-780 | STATED |
| Etr column (extraterrestrial, AM0) | spectral irradiance in W m-2 nm-1 | SRC-780 | STATED |
| Global tilt column | spectral irradiance in W m-2 nm-1, global on the 37 degree sun-facing tilted surface | SRC-780, SRC-779 (field definitions) | STATED |
| Direct+circumsolar column | spectral irradiance in W m-2 nm-1, direct normal | SRC-780, SRC-779 | STATED |
| Quadrature | trapezoid, sum of (wl[i+1]-wl[i]) * (f[i]+f[i+1]) / 2 | this CALC | ASSUMED (method choice) |
Working. Script integrate_g173.py (python -I, reads the csv, prints its sha256, the row count, the steps and the three integrals). Run 2026-10-10 on the copy of the csv whose sha256 is b48a6635...0954.
| Column | Trapezoid, W/m2 | Left-rectangle cross-check, W/m2 |
|---|---|---|
| Etr (AM0) | 1347.93 | 1348.76 |
| Global tilt | 1000.37 | 1001.03 |
| Direct+circumsolar | 900.14 | 900.72 |
Result. Global tilt 1000.4 W/m2, direct 900.1 W/m2, AM0 1347.9 W/m2 (1 d.p.). These agree with the figures an earlier computation reported (1000.4, 900.1, 1347.9). The integration script here was written without sight of theirs, but the target figures were given to me beforehand, so this is a recomputation, not a blind one. The left-rectangle cross-check differs by under 1 W/m2 (under 0.07 per cent) in each column. At the 1 d.p. quoted the two rules differ, so the 1 d.p. figures are the trapezoid values; the rule does not change them at the precision CLM-1418 uses, "about 1 kW/m2".
Range. The table covers 280 to 4000 nm for all three columns (first and last rows of the held csv). The integrals are therefore of that band only. The AM0 integral of 1347.9 W/m2 is of 280-4000 nm; that this is why it is below the full-spectrum solar constant is a reading the held files do not state: neither held file gives a solar constant or any value outside 280-4000 nm. The shortfall explanation is UNVERIFIED here, and the comparison figure (about 1361 W/m2) is not in the held files either.
Where this fails. The result is only as good as the table. It is not the integral of the standard's own wording, which is not held. A grid with steps up to 5 nm trapezoids smooth parts of the spectrum well but narrow absorption features in the near infrared are sampled coarsely. The left-rectangle cross-check uses the same grid points, so it shows only that the choice of rule moves the result by under 0.1 per cent; it does not test what lies between grid points. The "Global tilt" column is for a plane tilted 37 degrees toward the equator and facing the sun (surface normal pointing at the sun, elevation 41.81 degrees), not a horizontal surface.
Cite this
energyaperture.com/calc/calc-132
CALC-132. The working above, not a source document.