Solar Positioning

All solar position algorithms available in SolarPosition.jl return solar zenith, elevation, and azimuth angles. Algorithms that include an atmospheric refraction model also return “apparent” (refraction-corrected) values by default. This behavior can be modified by specifying a different refraction algorithm or passing NoRefraction no refraction correction is desired. See the Refraction Correction page for more details on refraction models.

Figure 1: Visualization of solar position angles: azimuth and zenith. Image source: Haputhanthri et al..

The solar azimuth angle is typically measured clockwise from true north. The solar zenith angle is the angle between the sun and the vertical direction directly overhead. The solar elevation angle is the complement of the zenith angle (i.e., elevation = 90°- zenith).

Typically solar position algorithms can take the following set of inputs:

• Observer location: latitude, longitude, and altitude
• Date and time: in UTC or local time with timezone information
• Optional atmospheric parameters: pressure and temperature (for refraction correction)

As an example, we plot the longest day of the year solar path for an observer located at the Van Gogh museum in Amsterdam (52.35888°N, 4.88185°E) on June 21, 2023:

using SolarPosition, Dates, CairoMakie

# define observer location (latitude, longitude, altitude in meters)
obs = Observer(52.35888, 4.88185, 100.0)  # Van Gogh Museum, Amsterdam
times = collect(DateTime(2023, 6, 21, 0):Minute(5):DateTime(2023, 6, 21, 23, 55));
positions = solar_position(obs, times, PSA(), HUGHES());

# plot elevation and azimuth over the day
fig = Figure(backgroundcolor = :transparent, textcolor= "#f5ab35", size = (800, 400))
ax1 = Axis(fig[1, 1], xlabel = "Time (hours)", ylabel = "Elevation (degrees)",
    title = "Solar Elevation on June 21, 2023 - Amsterdam", backgroundcolor = :transparent,
    xticks = 0:3:24)
ax2 = Axis(fig[1, 2], xlabel = "Time (hours)", ylabel = "Azimuth (degrees)",
    title = "Solar Azimuth on June 21, 2023 - Amsterdam", backgroundcolor = :transparent,
    xticks = 0:3:24)
times_hours = [Dates.hour(t) + Dates.minute(t)/60 for t in times]
lines!(ax1, times_hours, positions.elevation, color = "#f5ab35")
lines!(ax2, times_hours, positions.azimuth, color = "#f5ab35")
fig

Available Algorithms

The following solar position algorithms are currently implemented in SolarPosition.jl:

PSA

The PSA (Plataforma Solar de Almería) algorithm is the default high-accuracy solar position algorithm.

The algorithm was originally published by [BALL01] and was later updated by [BMB20] with new coefficients for improved accuracy.

struct PSA <: SolarPosition.Positioning.SolarAlgorithm

NOAA

The NOAA (National Oceanic and Atmospheric Administration) algorithm provides an alternative implementation based on [NOA25].

struct NOAA <: SolarPosition.Positioning.SolarAlgorithm

Walraven

The Walraven algorithm is a solar position algorithm published in 1978 with stated accuracy of ±0.0100°.

The algorithm was originally published by [Wal78] with corrections from the 1979 Erratum [Wal79] and azimuth quadrant correction from [Spe89].

struct Walraven <: SolarPosition.Positioning.SolarAlgorithm

USNO

The USNO (U.S. Naval Observatory) algorithm provides solar position calculations based on formulas from the USNO's Astronomical Applications Department.

The algorithm offers two options for calculating Greenwich mean sidereal time, providing flexibility for different accuracy requirements.

struct USNO <: SolarPosition.Positioning.SolarAlgorithm

SPA

The SPA (Solar Position Algorithm) is the highest-accuracy algorithm available in this package, with uncertainty of ±0.0003° for years between -2000 and 6000.

The algorithm was published by the National Renewable Energy Laboratory (NREL) in [RA04] and implements a complete heliocentric, geocentric, and topocentric solar position calculation with periodic terms for Earth heliocentric longitude and latitude.

struct SPA <: SolarPosition.Positioning.SolarAlgorithm