Short-wave Radiation

Emitted from the Sun, it drives the Earth’s climate system.

Short-wave Radiation

Transmission, absorption and scattering (diffuse reflection) of solar radiation in the atmosphere causes a variety of optical effects.

One of our applications in forest and agricultural climatology is the modelling and measurement of short-wave irradiance at the ground after passing through Earth’s atmosphere.

Learning Objectives

• Describe the characteristics of the solar radiation reaching our planet.
• Explain what happens to the solar radiation as it passes through the atmosphere
• Understand the effects of slope on radiation receipt.
• Know the difference between direct and diffuse short-wave radiation.

Planck’s law
 

• Dependence of \(E\) and \(\lambda\) on T

Stefan-Boltzman law

• Integral of Plank’s Law

Wein’s law
 

• Maximum of Plank’s Law

Solar constant \(I_0\)

The radiant flux density (irradiance) at the top of the atmosphere normal to the solar beam an at Earth’s mean distance from Sun.

• Present observations suggest \(I_0 \approx 1361 W m{-2}\)

The Nimbus satellite hosted the first instruments measuring the solar constant(NASA).

The “solar constant represents about the upper limit for solar energy in the Earth-atmosphere system. Imagine astronauts in the space station doing a space walk where they take a a board that is 1 meter by one meter and then measuring how much radiation falls on it when they point it directly at the sun. NOTE: the word “constant” here is a bit misleading. Of courses the distance from the earth varies because of the elliptical orbit of the earth around the sun. The differences are small however.

Average radiation on Earth

The solar constant is a “theoretical maximum”

• True at equator at solar noon

• Actual value is lower everywhere else

Attenuation of solar radiation (iClicker)

On its path from the top of the atmosphere to the ground, solar radiation is reduced. Why?

• A - Reflected back to space by clouds
• B - Scattered by aerosols and droplets
• C - Absorbed by certain gases, droplets and aerosols
• D - All of the above

Reflection

Clouds reflect 40 to 80% of the short-wave radiation incident upon them, the average is 55%.

• We call this the cloud albedo (\(\alpha\)), hence the ratio of the amount of solar (short-wave) radiation reflected by a body to the amount incident upon it.

Reflection from clouds is really important! This is why the earth looks so bright from space. Clouds viewed from the sides or above are also very white (an indicator that they are reflecting all wavelengths of visible light).

Absorption in the atmosphere

The most significant absorbing substances are:

• H₂O (vapor), CO₂, O₂, and O₃
• The atmosphere is quite transparent (\(\tau \approx 1\)) near \(\lambda_{max}\) = 0.48 \(\mu m\)
  • Intensity of solar radiation is greatest here

Absorption Spectra of Gasses in the Atmosphere

What does this Mean?

Optical Effects

Blue light is most easily scattered

At sunset, more blue is scattered away

Smoke scatters lots of light

Figure 1: Scattering of light by the atmosphere

The next images show some of the optical effects of the atmosphere. Some of these are best seen when the sun in low in the sky (sunrise and sunset) and the sun’s rays are passing slantwise through the atmosphere (we call this a long “path-length”)

Scattering

Scattering (diffuse reflection) is when incident light is diffused in all directions by the small molecules.

• Reduces solar radiation reaching the ground
• Diffuse the beam so that it arrives from all parts of the sky hemisphere.

Scattering by particle size

Scattering

• Rayleigh: caused by gas molecules. Tends to scatter in all directions with a preference for shorter wavelengths
• Mie: associated with larger solid or liquid particles. Scatters wavelength equally and mostly in a forward direction.

Scattering by particle size

Transmission

• Typical fractions of the solar getting through to the ground are:
  • “Clean” atmosphere \(\tau\) = 0.65-0.75
  • “Dirty” atmosphere \(\tau\) = 0.45-0.55
  • In Vancouver, a typical value is \(\tau\) = 0.70

Transmission Windows

• Most visible radiation is transmitted

• Second window lets thermal radiation escape

See Video: The “Atmospheric Window” is an important concept. You need to understand it. Simply put, the window part is analogy. It implies that in the 8-11 micrometer longwave (terrestrial) part of the radiation spectrum where there are no gases that absorb outgoing longwave radiation from the earth/atmosphere. Therefore this radiation is free to escape to space through these wavelengths. If this wasn’t the case, then the earth would continue to heat up over time. The role of “greenhouse” gases in the atmosphere is of course part of this story

Transmission (iClicker)

Smokey Skies Reduce Transmission

Cosine law of illumination

Describes how incident radiant flux density (irradiance) of a beam decreases as the beam’s angle varies from overhead.

• The same energy is spread over a larger surface area when a beam is tilted relative to the surface

This is an important concept! Try it yourself at home with a flashlight. You can also shine it on a globe (or ball) to see the impact on Latitude (ie.e why the poles receive less radiation than the tropics.

Cosine law of illumination

Flux density on a surface (\(R_s\)) is proportional to the flux density perpendicular to a beam (\(R_p\)) and the zenith (\(\theta\)).

• For a flat land surface at solar noon

\[ \theta = Latitude - Solar\:Declination \qquad(1)\]

• Solar Declination ranges from:
  • +23.5 (summer solstice)
  • 0 (equinoxes)
  • -23.5 (winter solstice)

\[ R_s = R_p cos(\theta) \qquad(2)\]

Cosine law of illumination

Radiation is distributed according to latitude and solar declination.

Cosine law of illumination (iClicker)

Compare the the flux density of a beam of sunlight at solar noon on the autumnal equinox at the equator and at the Arctic Circle (66 \(^{\circ}\) North latitude).

Note:

• \(R_s = R_p cos(\theta)\)
• At the equator, the sun is directly overhead: \(\theta = 0\)
• At 66 \(^{\circ}\) N latitude: \(\theta = 66\)

Irradiance at 66 \(^{\circ}\) N would be:

• A \(\approx\) 66% that at the equator
• B \(\approx\) 40% that at the equator
• C \(\approx\) 33% that at the equator

Irradiance

Shortwave irradiance (\(SW\downarrow\)) is the integration of all radiative fluxes coming from the upper hemisphere

• Per unit area
• Hence a radiative flux density in W m^-2

Direct vs. Diffuse Irradiance

Two types of solar radiation arrive at the Earth’s surface:

• Direct (s): comes directly in parallel rays from Sun.
• Diffuse (d): after scattering and reflection by the Earth’s atmosphere.

When you look at the horizon on a sunny day you still see BLUE – that is short wavelength visible radiation being scattered toward you (Rayleigh scattering)

Total Irradiance

\[ SW\downarrow = SW\downarrow_S + SW\downarrow_D \qquad(3)\]

Note the differing label convention in this figure. Some sources will use “K” for shortwave radiation. I don’t like that because its too similar to “Kelvin”, so I prefer to use “SW”.

NOTE the symbol K used to describe shortwave radiation and the arrow to indicate whether the radiation is down toward the earth or up and away from the earth.

Direct and diffuse radiation - example

Direct and diffuse radiation - example

Graph interpretation summary

• The diffuse fraction is greater in the early morning and late evening (greater path length).

• The diffuse fraction increases with cloud cover
• Variability with scattered clouds
  • ie. “Partly cloudy”

Pyranometer

Solar irradiance \(SW\downarrow = SW\downarrow_S + SW\downarrow_D\) is measured by a pyranometer.

• Glass domes transmit \(SW\)
  • Prevent conduction / convection
• A thermopile measures the temperature rise of the absorbing black surface

Inside the double glass dome (to prevent convection and conduction) there is a black absorber disk (the sensing element), which is made of a black carbon with a high absorptivity. The temperature rise of the sensing element due to short-wave irradiance is measured relatively to the (more constant) body temperature of the pyranometer. A thermopile (array of thermocouples) measures the temperature difference, which creates a voltage and then is measured by the data logger. The black carbon would be also sensitive to long-wave radiation, but the glass dome filters out the long-wave emission. A double glass dome reduces heating of the inner dome (long-wave emission of the dome).

Measuring Diffuse Radiation

The shade ring follows the solar path and eliminates direct radiation.

• Only D is measured by the pyranometer
• Paired with a non-shaded pyranometer, we can separate S and D

Take home points

• Short-wave radiation = solar radiation.
• What is the meaning of the solar constant I0?
• Solar radiation is reflected, scattered, and absorbed by certain gas molecules, droplets and particles in the atmosphere.
• The magnitude of the short-wave irradiance at the ground is mainly determined by the angle of the beam
  • Cosine law of illumination
• Distinguish between direct and diffuse \(SW\) irradiance.