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Solar Geometry on a Weather Site

Sunrise, sunset, and solar elevation are astronomical calculations. Why radiation and apparent temperature depend on sun angle, not on a thermometer.

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Sunrise, sunset, and solar elevation at a weather site are astronomical calculations. They follow latitude, longitude, date, and time. They are not thermometer readings. A page that draws the sun’s illumination on the Earth is a geometry product. A pyranometer that reports watts per square meter is an observation. Apparent temperature in the sun depends on both: the calculated sun angle and the measured air.

The historical URL /weather-sunearth.php was titled “Sun on Earth Simulation.” The recovered page described a view updated about every 15 minutes, fixed at 33°24′8″ N, 111°52′55″ W over Phoenix, Arizona, using Xearth imagery. That simulation is not rehosted. The coordinates and the refresh note are historical page behavior. They are not a live Earth view and not current weather. This article is the geometry lesson the URL pointed at.

Historical context

Station sites liked a globe with a day–night terminator. It looked like meteorology. It was orbital mechanics plus a map projection. Xearth (Kirk Lauritz Petersen) was one program that drew such a view. This article does not redistribute Xearth and does not restore the 15-minute image loop.

The useful remainder is why a weather publisher calculated the sun at all: to timestamp sunrise and sunset, to interpret solar radiation, and to avoid treating a noon temperature and a sunset temperature as the same radiation environment.

Astronomical calculation versus weather observation

Solar position (elevation and azimuth) is computed from the site’s coordinates and a civil timestamp. NOAA Global Monitoring Laboratory’s solar calculator documents the usual public method: equations from Jean Meeus’s Astronomical Algorithms, with an assumed refraction correction so that “sunrise” is apparent sunrise. NOAA states theoretical sunrise and sunset accuracy within about one minute between ±72° latitude, worse toward the poles, and notes that real atmospheres change the result. The output is a scenario / calculated geometry field, not an observation of the Sun. NOAA also states that the calculator is for research and recreational use and is not certified for litigation.

Solar radiation at the ground is an observation when a pyranometer or similar sensor measures it. Clear-sky irradiance can also be modelled. A model of irradiance is not a measurement. Clouds, haze, smoke, and terrain shade the beam; geometry does not know those until an optical measurement or a cloud field is introduced.

Air temperature is an observation. It does not contain the sun angle. A 95°F reading at 5 p.m. with the Sun low is a different radiation load than 95°F at solar noon.

WMO instrument practice still applies to the radiation sensor: identity, exposure, leveling, and time. A simulated globe does not replace that metadata.

Sunrise, sunset, and solar elevation

Solar elevation is the angle of the Sun above the horizon. Zenith angle is 90° minus elevation. At solar noon the elevation reaches its daily maximum for that date and latitude. In June at Phoenix that maximum is high; in December it is much lower. The seasonal change is astronomy, not a climate essay.

Apparent sunrise and sunset are defined with refraction. NOAA’s sunrise calculation assumes 0.833° of atmospheric refraction. Real refraction varies with pressure, temperature, and humidity, so observed sunrise can differ from the table. Horizon obstacles delay sunrise and advance sunset relative to a mathematical horizon.

Day length is a derived interval from those two calculated times. It is not sunshine duration, which is an observation of how long the beam exceeded a brightness criterion.

Azimuth at sunrise and sunset tells you which wall and which sensor shelter get beam radiation first. A poorly sited temperature screen on an east wall will heat early. That is an exposure problem, not a forecast.

Arizona’s lack of daylight saving time in most of the state is a clock issue. Solar noon is set by longitude and the equation of time. Mixing DST-aware software with Arizona civil time is a common source of “wrong sunrise” on hobby pages.

Why radiation depends on sun angle

Clear-sky beam irradiance at the ground scales with the cosine of the zenith angle: energy is spread over a larger surface when the Sun is low, and the atmospheric path is longer. That is why a pyranometer’s daily curve, on a cloudless day, rises and falls with elevation. A 15-minute globe image that only shows the terminator tells you almost nothing about watts per square meter.

Clouds, aerosol, and precipitable water then modify the flux. Geometry sets the envelope; weather fills it. A station that reports “solar radiation 0 W/m²” at midnight is consistent with elevation below the horizon. The same report at noon is a sensor or a sky story.

Do not infer Starlink performance from this geometry. Solar elevation is not a throughput measurement. Cloud presence is not, by itself, a demonstration that capacity fell.

Apparent temperature and the Sun

NWS heat index is a derived combination of air temperature and relative humidity. NWS states that heat index values were devised for shady, light-wind conditions, and that exposure to full sunshine can increase heat index values by up to 15°F. The heat index chart is therefore not a sun-angle product. Direct beam is an extra load the chart does not fully carry.

Wet Bulb Globe Temperature (WBGT), in NWS heat-tool documentation, is the index built for heat stress in sunlight. It accounts for temperature, humidity, wind, and radiant load, including sun angle and sky cover. WBGT is still a derived index, not a thermometer. It is the right family when the question is outdoor heat stress rather than a shady heat index.

A weather site that prints “feels like” without saying whether the formula assumes shade is mislabeling. Solar elevation tells you whether the shade assumption is even plausible. At elevation 5° the beam is weak; at 75° it is not. The calculation of elevation is cheap. Replacing it with a cartoon Earth does not add physics.

What the simulation image was

A sun-on-Earth still is a derived rendering of calculated geometry: which longitudes are in daylight at a chosen instant, optionally with a pin at Phoenix. A 15-minute refresh is a publishing interval. It is not a satellite observation, not a cloud analysis, and not a radiation measurement. If the image generator stops, the last frame is historical.

For a maintained public calculator, use NOAA’s solar calculator. Treat its output as calculated geometry with the documented refraction assumptions. For official weather forecasts, use weather.gov. For station temperature and radiation, use a labeled observation page such as current conditions—remembering that recovered numbers there are historical if the feed is gone.

Practical checklist

  • Sunrise and sunset on the site cite coordinates, date, timezone, and whether refraction is included.
  • Solar radiation, if shown, is labeled as observed (sensor) or modelled (clear-sky or NWP field).
  • Heat index is labeled as shade-based; WBGT or an explicit sun note is used when beam load matters.
  • A globe or terminator graphic carries a calculation time and is not titled “satellite.”
  • Forecast sky cover is not used as a pyranometer.
  • This URL is not a climate-change article and not a live Earth camera.

Forecast versus observation is the vocabulary for mixing calculated sun fields with NWS sky language. They are different families.

Modern relevance

Geometry of the sky—sun elevation, horizon, beam versus shade—is easy to confuse with weather and with link quality. They are separate questions. TNET’s public review of independent Horizon research on weather and Starlink is what the Horizon research tells us about weather and Starlink. Read that review for atmospheric and performance findings as published. Do not treat solar-elevation tables as Horizon results, and do not treat Horizon findings as a claim that clouds alone set speed.

Official geometry: NOAA GML. Official weather: NWS. Historical station pages: observations hub.

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