Sun Angle and Seasons

• Solar Radiation Flux to the Outside of the Atmosphere
• Solar luminosity - total energy emitted per second
• Solar energy flux = 6.4 X 10⁷ W/m²
• Sun's surface area = 6.1 X 10¹⁸ m²
• Luminosity = 3.9 X 10²⁶ W (J/s)
• Solar energy output not truly constant
• Variations over time too small to be important for short-term weather
• May be important for longer term climate variability (uncertain)
• Surface area of sphere illuminated increases with square of distance from sun
• Solar energy flux (energy / area / time) decreases with square of distance from sun
• Earth's mean distance from sun is 1.5 X 10¹¹ m
• Area of sphere = 2.8 X 10²³ m²
• Solar constant is flux of solar energy at top of atmosphere
• Flux through area perpendicular to incoming radiation
• Average value = 1367 W/m²
• Actual orbit elliptical, so distance from Sun and solar constant vary through year
• About 1435 W/m² on Jan. 3 (Perhelion)
• About 1345 W/m² on July 3 (Aphelion)

• Sun Angle
• Tilt of Earth's axis of rotation
• Axis of rotation tilted 23.5^o away from perpendicular to plane of Earth's orbit
• Axis points in same direction as Earth orbits the sun
• Creates seasonal variations in which hemisphere is oriented toward sun
• Solstices - summer hemisphere pointed toward incoming solar beam
• Spring and Fall equinoxes - equator pointed toward incoming solar beam
• Solar declination varies seasonally
• Latitude where sun is directly overhead at solar noon
• Ranges from 23.5^oN on June 21 to 23.5^oS on Dec. 21
• Solar zenith angle
• Angle of sun away from vertical
• 90^o - sun angle (angle above horizon)
• Solar noon zenith angle = latitude - solar declination (negative for Southern Hemisphere)
• Highest point in sky sun reaches on a given day
• Santa Barbara latitude is 35^oN
• June 21 solar noon zenith angle = 35 - 23.5 = 11.5^o (sun angle = 78.5^o)
• Dec. 21 solar noon zenith angle = 35 - (-23.5) = 58.5^o (sun angle = 31.5^o)

• Axial Tilt and Solar Radiation at the Surface
• Day length varies with season and latitude
• 12 hour day length every on equinoxes
• 12 hour day length always at equator
• Elsewhere day length longer in summer, shorter in winter
• Magnitude of variation increases at higher latitudes
• Surface area illuminated by incoming solar radiation depends on zenith angle
• Beam spreading reduces energy flux at large zenith angles
• Flux through 1 m² illuminates 1 m² of surface for 0^o zenith angle
• Flux through 1 m² illuminates more than 1 m² of surface for zenith angle > 0^o
• Intensity of solar flux at noon varies with season and latitude
• Depends on cosine of zenith angle
• Always high in tropics
• Always fairly high at summer solstice
• Seasonal variations increase with increasing latitude
• Atmospheric attenuation of incoming solar radiation depends on zenith angle
• Beam attenuation increases at large zenith angles
• Radiation passes through single thickness of atmosphere for 0^o zenith angle
• Radiation passes through greater atmospheric thickness for zenith angle > 0^o

• Seasons
• Seasons caused by radiation variations produced by sun angle and day length
• Equinoxes
• Solar declination = 0 - sun directly overhead at equator
• Day length 12 hours everywhere
• Solar radiation decreases poleward due to increasing zenith angle in both hemispheres
• Northern Hemisphere summer solstice (June 21)
• Solar declination = 23.5 - sun directly overhead at Tropic of Cancer (23.5^oN)
• Day length increases northward
• Poleward decrease in solar radiation due to zenith angle partially offset by increase due to longer days
• Surface flux peaks in mid-latitudes, similar throughout hemisphere
• Northern Hemisphere winter solstice (Dec. 21)
• Solar declination = -23.5 - sun directly overhead at Tropic of Capricorn (23.5^oS)
• Day length decreases northward
• Poleward decrease in solar radiation due to zenith angle reinforces decrease due to shorter days
• Flux decreases rapidly northward throughout Northern Hemisphere