Sun Position and Solar Irradiance Calculator

NOAA / Meeus solar geometry follows NOAA’s published solar-calculator equations and source: Gregorian date → Julian day → Julian centuries → solar longitude, anomaly, eccentricity and obliquity → declination and equation of time. Local clock time, east-positive longitude and the entered UTC offset give the hour angle. The north/east/up solar vector yields elevation and compass azimuth using atan2. Standard NOAA refraction is added to geometric elevation; no claim of NREL SPA precision is made.

Clear-sky GHI and DNI use the Ineichen–Perez model without the optional Perez enhancement, as documented in pvlib’s open implementation. Kasten–Young (1989) relative optical air mass is corrected for standard-atmosphere site pressure. Extraterrestrial DNI uses 1366.1 W/m² at 1 AU and the NOAA Earth–Sun distance. DHI closes the horizontal energy balance: $DHI=GHI-DNI\cos z$.

For panel tilt $\beta$, facing azimuth $A_p$, solar azimuth $A_s$ and apparent zenith $z$, $\cos\theta_i=\cos z\cos\beta+\sin z\sin\beta\cos(A_s-A_p)$. Front-side beam is $DNI\max(0,\cos\theta_i)$. Isotropic sky diffuse is $DHI(1+\cos\beta)/2$ and ground diffuse is $\rho GHI(1-\cos\beta)/2$.

A 10-minute grid covers 00:00–24:00 of the local date; trapezoidal integration gives daily incident energy. The same cached sky samples are reused for the 5° tilt sweep, so animation changes only the instantaneous calculation and scene. Sunrise and sunset are roots of geometric centre elevation = −0.833° within the selected local day.

Reference cases compare NOAA geometry against independent NREL SPA values published in pvlib, and the clear-sky function against pvlib’s published scalar regression vector. Sources s2 and s3, attached page 1, contain the quoted expected values.

• Clear sky, a constant user-supplied Linke turbidity throughout the day, and an unobstructed flat horizon. Turbidity 3 and albedo 0.2 are illustrative assumptions, not a weather observation or an automatic local lookup.
• One fixed front-facing panel; isotropic diffuse sky and uniformly reflecting ground with full sky/ground view factors. No circumsolar enhancement, horizon brightening, bifacial collection, obstruction or mutual shading.
• Standard-atmosphere pressure from site elevation; NOAA’s standard refraction is used without a local temperature/pressure adjustment. Solar-centre geometry neglects topocentric parallax.
• True-north bearings; east-positive longitude; the supplied UTC offset remains fixed for the local day. 24:00 is the following midnight.
• The best sampled tilt refers only to this day and this facing direction. If there is no modeled daylight it is reported as unavailable. A missing sunrise or sunset is a valid polar or local-day outcome, not an error.
• The incidence section is rotated for readability; only its beam-to-normal angle is quantitative.

Gregorian dates 1900–2100; latitude −89.9° to +89.9°; elevation −400 to 5000 m; panel tilt 0–90°; Linke turbidity 1–10 and albedo 0–1. These are screening limits, not a universal empirical accuracy guarantee. Below 5° solar elevation, refraction, horizon geometry and attenuation dominate the uncertainty. At exact zenith or nadir azimuth has no physical meaning; an input condition flags this.

NOAA’s method is checked here within 0.03° against the cited SPA position examples, not to SPA’s ±0.0003° precision. Sunrise/sunset use a conventional −0.833° centre elevation, omit observer-height horizon dip and terrain, and are increasingly uncertain at high latitudes. Integration and tilt optimization use finite sampling; narrow grazing daylight intervals may be missed near the polar boundary. No weather forecast, bankable annual yield, PV electrical production, battery sizing or structural mounting design is provided. Installation work belongs to a qualified person.