ENV201 Environmental Science Lecture 3: The Sun and Solar Geometry Notes

Solar Radiation: Fundamental Terminology and Concepts

• Insolation: This term refers to the incoming solar radiation from the sun, specifically in the form of shortwave radiation.
• Original Material Credits: The course material is authored by Dr. Kaera Coetzer, with acknowledgments to original material by Dr. Barend Van Der Merwe (2023). External figure credits include Eric Snodgrass, Ahrens (2001 Brooks/Cole Publishing), and Jensen (2014) for specific definitions.

Sun-Earth Relationships at the Local Scale

• The relationship between the sun and the Earth reflects both local positions relative to an observer and broader planetary movements.
• Sunrise: Defined as the moment the sun emerging above the horizon.
• Sunset: Defined as the moment the sun drops below the horizon.
• Solar Noon: Occurs when the sun is directly above the local meridian. This represents the sun's highest position in the sky during the day ("midday") and falls midway between sunrise and sunset.
  • Specific Example: In Pretoria on 16 February 2026, solar noon occurred at $12:21\,pm$.
• Navigation and Calibration:
  • Finding Latitude: Latitude can be determined based on the celestial latitude of the sun at a specific date and time.
  • Nautical Almanac: This tool predicts the sun's theoretical position at a specific latitude and date, allowing for the calibration of compass error based on horizon bearing.
  • Twilight Star Sights: These sites provide positions for the Sun, Moon, and planets, as well as data for $57$ Navigational Stars and specific times for sunrise, sunset, and twilight.

Describing the Local Position of the Sun: Geometric Angles

• Zenith: The point in the sky located directly above the observer’s head ($90^\circ$ from the horizon).
  • Note on Location: Solar noon is at the zenith only in the tropics; elsewhere, it occurs slightly North or South of the zenith.
• Zenith Angle ($\theta$): The angle measured between the sun and the vertical (zenith). It is measured from the zenith ($0^\circ$) toward the horizontal/horizon ($90^\circ$).
• Altitude Angle (Elevation Angle): The angular height of the sun in the sky measured from the horizontal plane.
  • The horizon represents $0^\circ$.
  • The zenith represents $90^\circ$.
  • Negative values indicate the sun is below the horizon.
• Azimuth Angle: The compass direction of the sun's position or where the light is originating. It is measured in degrees from $0^\circ$ to $360^\circ$ clockwise from North (standard bearing measurement).
  • $0^\circ$: North
  • $90^\circ$: East
  • $180^\circ$: South
  • $270^\circ$: West
• Angle of Incidence ($\theta$): The angle between the incoming solar ray and the zenith.
  • Convention: According to Jensen (2014), for a horizontal plane, the angle of incidence ($\theta$) and the zenith angle ($\theta_{z}$) are equal.

Interaction Between Solar Radiation and Surface Energy Transfer

• Intensity of Heating: The angle of incidence directly determines the intensity of heating on a flat surface.
  • Small Angle of Incidence/High Altitude Angle: When the sun is high in the sky (closer to the zenith, e.g., altitude angle = $90^\circ$, zenith/incidence angle = $0^\circ$), incoming insolation strikes the surface at right angles. This concentrates energy over a smaller area, resulting in maximum heating and maximum intensity.
  • Large Angle of Incidence/Low Altitude Angle: When the sun is lower in the sky (e.g., altitude angle = $45^\circ$, zenith/incidence angle = $45^\circ$), the same amount of solar energy is spread over a larger ground area. This reduces the radiation intensity and surface heating.
• Atmospheric Attenuation: Solar energy entering at a larger angle of incidence (sun lower in the sky) must travel through a greater portion of the atmosphere.
  • This increases the chance of energy "loss" or attenuation due to interactions with atmospheric molecules and gases.

Planetary Sun-Earth Relationships

• Earth's Axial Tilt: The rotational axis of the Earth is tilted at an angle of $23.5^\circ$ (Aguado and Burt, 2007).
• Orbital Path: The Earth travels around the sun in an elliptical path.
• Determinants of Seasons: The combination of the Earth's position in its orbit and its axial tilt determines the seasonal cycles.
• Insolation and Latitude: Due to the spherical shape of the Earth, the angle of incoming radiation changes depending on latitude.
  • Equator: Solar rays strike more directly, concentrating insolation over a smaller area, making it hotter.
  • Day Length: The length of the day and the times of sunrise and sunset differ based on the latitude and the time of year.

Solstices and Equinoxes (Southern Hemisphere Perspectives)

• Southern Hemisphere (SH) Summer Solstice: Occurs around 21/22 December. Solar radiation is perpendicular to the Tropic of Capricorn (approximately $23.4^\circ\,S$ or $23.5^\circ\,S$). This marks astronomical summer.
• SH Winter Solstice: Occurs around 20/21 June. Solar radiation is perpendicular to the Tropic of Cancer (approximately $23.4^\circ\,N$). This marks astronomical winter.
• SH Autumn Equinox: Occurs around 20/21 March. Solar radiation is perpendicular to the Equator. This marks astronomical autumn.
• SH Spring Equinox: Occurs around 22/23 September. Solar radiation is perpendicular to the Equator. This marks astronomical spring.

Solar Radiation Interaction with the Atmosphere

Radiation passing through the atmosphere (a mixture of gases) is subject to four primary processes:

• Transmission: Incoming radiation passes through the substance without any impact or attenuation.
• Reflection: Incoming radiation "bounces off" a substance in a predictable direction. The incidence angle ($\theta_{1}$) is equal to the reflection angle ($\theta_{2}$).
• Scattering: Incoming radiation "bounces off" in multiple, unpredictable directions.
• Absorption: Incoming radiation is taken up by the substance. This energy is often converted to heat and re-emitted as longer wavelength infrared radiation.
  • Selective Absorption: Different gases only absorb specific wavelengths of the spectrum.
  • Depletion: As radiation passes through the atmosphere, it is "depleted" or attenuated in specific portions of the spectrum corresponding to the gases present.

Albedo and Surface Interactions

• Definition: Albedo is the portion (percentage) of incoming solar radiation reflected by a surface.
• Measurement: Values are expressed as a percentage ($\%$) or a decimal from $0$ to $1$.
  • High Albedo: Surface reflects most radiation (usually lighter-colored surfaces like snow or ice).
  • Low Albedo: Surface absorbs most radiation (usually darker-colored surfaces like asphalt or deep water).
• Global Average: The planetary albedo is approximately $0.30$ ($30\%$).
• Climate Feedback: Changes in surface albedo (e.g., melting sea ice) significantly impact climate. Less white ice means less reflection and more heat absorption by the oceans, accelerating warming.

Questions and Discussion

1. Which line of latitude would have the smallest angle of incidence on the summer solstice?

• Answer: $24^\circ\,S$ (Because it is closest to the Tropic of Capricorn at $23.5^\circ\,S$).

2. The altitude of the sun is $62^\circ$. Which surface will heat up the most?

• Options: Green field crops, Concrete, Dry sand, Deep water.

3. Which of the following surfaces has the highest albedo value?

• Options: Green field crops, Concrete paving, Dirt road, Deep water.

4. Which angle of incidence will result in the most intense surface heating on a horizontal plane? Explain why.

• Answer: $20^\circ$. Smaller angles of incidence (closer to the zenith) mean the sun is higher in the sky, concentrating energy over a smaller surface area and reducing atmospheric attenuation.

5. In which scenario would you expect to have the largest altitude angle?

• Answer: When the angle of incidence is $20^\circ$. (Altitude and Zenith/Incidence angles are complementary; if incidence is $20^\circ$, altitude is $70^\circ$).

6. Which azimuth angle indicates sunlight coming from the East?

• Answer: $90^\circ$.

7. Which position results in the least intense heating?

• Answer: Zenith angle of $75^\circ$, angle of incidence of $75^\circ$, or altitude angle of $15^\circ$ (all describe the same low-sun position).

8. Day Length Comparison (17 February 2026):

• Pretoria: Sunrise $05:54$, Sunset $18:49$. Day length = $12\,hours\,55\,minutes$.
• Umtata: Sunrise $05:45$, Sunset $18:53$. Day length = $13\,hours\,08\,minutes$.
• Result: Umtata has the longer day length.

9. Station Data Analysis (Africa Context):

• Station A: Sunrise $06:05$, Sunset $17:47$, Latitude $-10.6487$.
• Station B: Sunrise $06:19$, Sunset $17:34$, Latitude $-19.5999$.
• Station C: Sunrise $06:34$, Sunset $17:19$, Latitude $-29.5351$.
• Station D: Sunrise $06:42$, Sunset $17:10$, Latitude $-34.0911$.
• Southernmost Station: Station D ($-34.0911$).
• Shortest Day Length: Station D ($10\,hours\,28\,minutes$). Stations further from the equator in this dataset show shorter days, indicating a winter scenario for the Southern Hemisphere.

10. Bonus Question: If the earth was flat, would there still be seasons?

• Discussion Points: Consider the role of axial tilt, the angle of incidence variation across a curved surface, and the necessity of orbital mechanics to create the changing day lengths and solar angles typical of Earth's seasons.