• Since life on Earth is entirely dependant on the Sun’s energy, it is useful to quantify how much of its energy reaches the top of the atmosphere
  • This is known as the solar constant
• The solar constant is defined as:

The amount of solar radiation across all wavelengths that is incident in one second on one square metre at the mean distance of the Earth from the Sun

• The value of the solar constant varies year-round because:
  • The Earth’s is in an?elliptical orbit?around the Sun, meaning at certain times of year the Earth is closer to the Sun, and other times of year it is further away
  • The?Sun’s output varies?by about 0.1% during its 11-year sunspot cycle
• Calculations of the solar constant assume that:
  • This radiation is incident on a?plane perpendicular?to the Earth's surface
  • The Earth is at its?mean distance?from the Sun

Step 1: List the known quantities

• • Power output of Sun,?P?= 4 × 10²⁶?W
  • Distance between the Earth and Sun,?r?= 1.5 × 10¹¹?m

Step 2: Model the scenario using geometry

• • As light leaves the surface of the Sun, it begins to spread out uniformly through a spherical shell
  • The surface area of a sphere = 4πr²
  • The radius?r?of this sphere is equal to the distance between the Sun and the Earth

Step 3: Write an equation to calculate the solar constant

Albedo

• Albedo,?a, is defined as

The proportion of light that is reflected by a given surface

• It can be calculated using the equation

• More specifically, the albedo of a?planet?is defined as

The ratio between the total scattered, or reflected, radiation and the total incident radiation of that planet

• Earth’s albedo is generally taken to be 0.3, which means 30% of the Sun’s rays that reach the ground are reflected, or scattered, back into the atmosphere
• Earth’s albedo varies daily and depends on:
  • Cloud formations?and?season?– the thicker the cloud cover, the higher the degree of reflection
  • Latitude
  • Terrain?– different materials reflect light to different degrees
• It is useful to know the albedo of common materials:
  • Fresh asphalt = 0.04
  • Bare soil = 0.17
  • Green grass = 0.25
  • Desert sand = 0.40
  • New concrete = 0.55
  • Ocean ice = 0.50 - 0.70
  • Fresh snow = 0.85
• Albedo has no units because it is a?ratio?(or fraction) of power

Emissivity

• Stars are good approximations to a black body, whereas planets are not
  • This can be quantified using the emissivity
• Emissivity,?e, is defined as

The power radiated by a surface divided by the power radiated from a black body of the same surface area and temperature

• It can be calculated using the equation

• Calculations of the emissivity assume that the black body:
  • Is at the same temperature as the object
  • Has the same dimensions as the object

• For a perfect black body, emissivity is equal to 1
• When using the Stefan-Boltzmann law for an object which is not a black body, the equation becomes:

P?= eσAT⁴

• Where:
  • P?= total power emitted by the object (W)
  • e?= emissivity of the object
  • σ = the?Stefan-Boltzmann constant
  • A?= total surface area of the object black body (m²)
  • T?= absolute temperature of the body (K)

• • Albedo = the proportion of radiation that is reflected
  • Therefore, the energy reflected by fresh snow = 0.85

• • If 85% of the radiation is reflected, we can assume that 15% is absorbed
  • Therefore, the energy absorbed by fresh snow = 1 – 0.85 = 0.15