Fig 1: left — elevation (side view); right — azimuth (top view)
📐 Key parameters
Parameter
Meaning
Range / note
Elevation
Angle between the sun and the horizon (vertical direction) — how high the sun is.
0° at sunrise/sunset, highest at noon; negative = below horizon.
Azimuth
Clockwise angle from North to the sun's horizontal projection.
0°=N, 90°=E, 180°=S, 270°=W. Northern H.: sun is in the south at noon; Southern H.: in the north.
Sunrise / Sunset
Clock times when the sun's upper edge crosses the horizon.
Standard zenith 90.833° (refraction 34′ + solar radius 16′).
Solar noon
When the sun crosses the local meridian (highest point of the day).
Usually not 12:00 — shifted by longitude and equation of time.
Day length
Duration from sunrise to sunset.
Polar day/night shown for polar regions.
Max elevation
Highest elevation the sun reaches at noon that day.
Determined by latitude + season (largest at summer solstice).
Declination
Latitude of the subsolar point in the celestial coordinate system.
≈0° at equinoxes; ≈+23.44° at June solstice; ≈−23.44° at December solstice.
Equation of time
Difference between apparent and mean solar time.
About −14 to +16 minutes; why solar noon ≠ 12:00.
Shadow length / direction
Shadow of an obstacle of given height.
Shadow direction = azimuth + 180°; lower sun → longer shadow.
🗺️ Reading the charts
Map rays: colored rays = sun direction at sunrise / 09:00 / 12:00 / 15:00 / sunset and the selected time (dashed = below horizon).
Polar chart: center = zenith (90°), outer ring = horizon (0°); radius = elevation, angle = azimuth. Dark gray = summer solstice, light gray = winter solstice, orange = selected date (dots = hours), yellow dot = current sun; the dark line from center to South (180°) is the azimuth reference line. For the Southern Hemisphere the solstice dates swap automatically (summer = Dec 21, winter = Jun 21).
3D dome: sky as a hemisphere; the orange arc is the selected day's path.
Why is solar noon not 12:00? Longitude offset from the timezone meridian (China uses 120°E) plus the equation of time (±14 min).
Why is the sun in the southeast at 8 AM? In the Northern Hemisphere the sun's path is south of the zenith; it rises in the SE and sets in the SW.
Negative elevation? The sun is below the horizon (night / polar night).
Southern Hemisphere? Noon sun is in the north; seasons are reversed (December = summer).
Which datum? Use WGS84/CGCS2000 (default) for GPS/maps; use GCJ-02 for coordinates copied from AMap.
📏 Accuracy
NOAA solar position algorithm (Meeus). Error < 0.01° for 1900–2100; max deviation ≈ 0.008° vs pyephem. Sunrise/sunset times iterated for declination, typically < 0.5 min error.
