Topic_2_Ch_5_Radiation

Topic 2: Energy and Radiation Balances

Chapter 5: Radiation

• Radiation Fundamentals

  • Speed of light (c) is constant for all forms of radiation:

    • Relationship: c = λ ν (where λ = wavelength and ν = frequency)

  • Shorter wavelengths correlate with more energy, while longer wavelengths correlate with less energy.

  • Energy quantification: Q = h ν or Q = h c/λ

• The Electromagnetic Spectrum

  • All radiation types travel at the speed of light and in a vacuum.

  • All objects emit radiation based on their temperature.

  • Energy transfer occurs via all forms of radiation.

Emission of Radiation

Radiation Laws

• Planck's Law

  • Relates temperature of a substance to its emitted radiation.

• Stefan–Boltzmann Law

  • Emission rate (E) proportional to the fourth power of temperature (T):

    E = ε σ T^4

  • E = flux density (W·m^–2),

  • ε = emissivity (1 for black bodies),

  • σ = Stefan-Boltzmann constant (5.67 × 10^–8 W·m^–2·K^–4).

• Wien's Law

  • Maximum emission wavelength inversely related to temperature.

• Planck's Law (Detailed)

  • Radiation comprises energy bundles called photons.

  • Shorter wavelengths = higher energy per photon.

Shortwave vs Longwave Radiation

• Black body approximation for both Earth and Sun:

  • Sun (T = 5,800 K): emission mainly 0.15 - 3.0 µm (Shortwave)

  • Earth (T = 288 K): emission mainly 3.0 - 100 µm (Longwave)

Radiation Interaction with Surfaces

Absorption, Reflection, and Transmission

• Incident radiation can:

  1. Be absorbed (a)

  2. Be reflected (α)

  3. Be transmitted (t)

• Equation: a + α + t = 1 (or 100%)

Radiation in the Atmosphere

Scattering and Absorption

• Radiation Interaction

  • Absorbed radiation heats the atmosphere.

  • Scattered/reflected radiation can reach Earth's surface as diffuse radiation.

  • Direct radiation reaches the surface without interaction.

• Scattering Types

  1. Rayleigh scattering

  2. Mie scattering

• Absorption Characteristics

  • Longwave radiation absorbs more strongly than shortwave due to selective gases.

  • Key absorbent gases:

    • Oxygen, ozone, water vapor (strong in UV)

    • Water vapor, CO2, methane, nitrous oxide (greenhouse gases for longwave)

The Greenhouse Effect

• Solar radiation transmits well through the atmosphere; Earth's longwave radiation is absorbed by greenhouse gases.

• Without the atmosphere, Earth's temperature would drop by 33 K.

Temperature Structure of the Atmosphere

• Three maximum temperatures occur due to absorption at specific wavelengths:

  1. Upper thermosphere (λ = 0.1–0.2 μm)

  2. Upper stratosphere (λ = 0.2–0.3 μm)

  3. Lowest troposphere (heat from Earth's surface)

Solar Radiation

• Solar Constant: Average solar radiation at top of the atmosphere - approx. 1361 W·m^–2.

• Sphericity Effect: Causes variation in Sun angles based on curvature.

  • Low latitudes: higher Sun angles; High latitudes: lower Sun angles.

Sun Angle Determination

• Illustrated by two definitions:

  1. Altitude angle

  2. Zenith angle

• Influenced by latitude, longitude, time of year, and time of day.

• Lower altitude means lower radiation intensity due to beam spreading and depletion.

Annual Variations by Latitude

Seasons and Solar Energy

• Seasons defined by:

  • Altitude of the Sun above horizon

  • Intensity of Sun energy

  • Duration of day length.

• Earth’s Orbit Details:

  • 23.5° tilt from the perpendicular ecliptic plane.

  • Constant angle and orientation during orbit.

Milankovitch Cycles

• Influential factors impacting climate variability:

  1. Eccentricity: 100,000-year cycle affecting distance from the Sun.

  2. Tilt variation: 40,000-year cycle affecting seasonality.

  3. Direction of tilt: 26,000-year cycle dictating seasonal intensity at perihelion and aphelion.

Conclusion on Seasonal Variations

• Sphericity affects solar intensity across latitudes and leads to varying seasons.

  • Seasonal changes impact duration and intensity of Sun received by Earth, influenced by multiple physical characteristics of Earth and its orbit.