Sky Glow Comparison — Methodology

1. Purpose

Not all lumens make equal sky glow: bluer light scatters more (Rayleigh), and uplight matters more than anything else. This tool compares any two light sources — real measured spectra, or a pasted spectrum — and reports the relative sky glow of the comparison source against a baseline, under a chosen observer position, atmosphere, uplight fraction, and eye weighting. The default baseline is deliberately historical: HPS at 5% uplight, the old "semi-cutoff" street-lighting allowance, so modern fully-shielded warm sources show their real improvement.

2. The model

Sky Glow Index = Σλ [SPD(λ) × SF(λ)] × lumen-output %, where SF is the Kocifaj radiative-transfer scattering function for the selected combination of observer (near/far), atmosphere (clear/moderate/high particulate), uplight fraction, and weighting (photopic or scotopic). The 48 scattering- function tables, 12 example lamp spectra, CIE 1931 colour-matching functions, and V(λ)/V′(λ) curves are taken directly from the PNNL spreadsheet. Results are expressed relative to the baseline — the index is in model units, not cd/m² or mag/arcsec², and only ratios are meaningful.

3. Data

4. Validation

This is the suite's most directly validated tool: every equation was verified line-by-line against the PNNL spreadsheet's worksheet formulas and VBA modules, and against an independent 2022 manual run of the DOE calculator (scotopic weighting, clear/low-particulate, both observer positions). The full equation-for-equation comparison is published alongside the code (VALIDATION.md): chromaticity, SPD normalization, sky-glow summation, and scattering-function selection are identical; normalization constants cancel in the baseline ratio.

5. Known limitations

• Relative, not absolute. The index compares sources; it does not predict a site's sky brightness (the Light Pollution Analyzer and the World Atlas do that).
• The model is per-lumen at the source. Fixture count, mounting, and geography are out of scope — pair with the Lighting Advisor for installation-level judgments.
• Scotopic weighting understates non-visual and ecological effects — melanopic and insect/bird responses weight blue even more heavily, so differences shown here are conservative for those endpoints.
• Example spectra are typical products of their era; a specific product's SPD can differ — paste the data-sheet spectrum for a product-level answer.

6. References

1. Pacific Northwest National Laboratory / U.S. Department of Energy. Sky Glow Comparison Tool (PNNL-SA-138348) — spreadsheet, scattering tables, spectra, and VBA reference implementation.
2. Kocifaj, M. (2007). Light-pollution model for cloudy and cloudless night skies with ground-based light sources. Applied Optics, 46(15), 3013–3022. https://doi.org/10.1364/AO.46.003013
3. Commission Internationale de l'Éclairage. CIE 1931 colour-matching functions; CIE 1951 scotopic luminous efficiency function.
4. Falchi, F., et al. (2016). The new world atlas of artificial night sky brightness. Science Advances, 2(6), e1600377. https://doi.org/10.1126/sciadv.1600377 (context for absolute brightness.)

App: skyglow-calculator/ (private repo darksky_tools). The line-by-line equation audit is in VALIDATION.md beside the code.