Topic 2_Ch 5_"Radiation"

Topic 2: Energy and Radiation Balances

Chapter 5: Radiation

The Electromagnetic Spectrum

  • Fundamental Equations:

    • Speed of light: ( c = \lambda ,
      u )

    • Energy of radiation: ( Q = h ,
      u ) or ( Q = \frac{h , c}{\lambda} )

  • Characteristics of Radiation:

    • All forms travel at the speed of light.

    • Capable of traveling through a vacuum.

    • Emitted by all entities based on their temperature.

    • Transports energy.

Emission of Radiation

Key Radiation Laws

  • Relationships between temperature and emitted radiation:

    1. Planck’s law

    2. Stefan–Boltzmann law

    3. Wien’s law

Planck’s Curve

  • Represents blackbody radiation.

  • Rate of emission rises sharply with increasing wavelength, peaking at maximum emission wavelength ( \lambda_{max} ), then decreases gradually at longer wavelengths.

The Stefan–Boltzmann Law

  • The emission rate from a black body is proportional to the fourth power of its temperature: [ E = \epsilon , \sigma , T^4 ]

    • E: flux density (W·m⁻²)

    • ( \epsilon ): emissivity (1 for black bodies)

    • ( \sigma ): Stefan–Boltzmann constant (5.67 × 10⁻⁸ W·m⁻²·K⁻⁴)

Wien’s Law

  • Wavelength of maximum emission is inversely proportional to temperature.

    • Shorter wavelength = higher energy per photon (Planck's Law).

    • ( \lambda_{max} \propto \frac{1}{T} )

Shortwave vs Longwave Radiation

  • Approximated black bodies:

    • Sun: Surface temperature ( T = 5800 K ); most emission between 0.15 and 3.0 μm (shortwave).

    • Earth: Surface temperature ( T = 288 K ); most emission between 3.0 and 100 μm (longwave).

Absorption, Reflection, and Transmission of Radiation

  • Interactions with surfaces:

    • Incident radiation can be absorbed, reflected, or transmitted.

    • Energy balance equation: ( a\lambda + \alpha\lambda + t\lambda = 1 ) or 100%.

      • a: absorption

      • α: reflection

      • t: transmission

  • Albedo: Measure of reflectivity.

Radiation in the Atmosphere: Scattering and Absorption

Effects of Radiation

  • Radiation absorbed in the atmosphere results in heating.

  • Radiation that is reflected or scattered can eventually reach the Earth's surface as diffuse radiation.

  • Direct beam of radiation reaches the surface when not absorbed or reflected.

Scattering

  • Scattering redirects radiation in various directions (Rayleigh and Mie scattering).

Absorption

  • Longwave radiation is more strongly absorbed than shortwave radiation.

  • Certain gases selectively absorb radiation:

    • Good absorbers of Sun’s radiation: Oxygen, ozone, water vapor.

    • Good absorbers of Earth’s radiation: Greenhouse gases (water vapor, CO₂, methane, etc.).

The Greenhouse Effect

  • Atmosphere allows solar radiation to pass but absorbs Earth’s longwave radiation.

    • Water vapor and CO₂ are primary absorbers.

    • Earth emits longwave radiation; some is absorbed by the atmosphere and re-emitted downwards.

  • Without the atmosphere, Earth would be 33 K cooler.

The Temperature Structure of the Atmosphere

  • Maximum temperature zones:

    • Upper thermosphere (absorption of 0.1–0.2 μm)

    • Upper stratosphere (absorption of 0.2–0.3 μm)

    • Lowest troposphere (heating at Earth’s surface).

  • Solar Radiation: Solar constant at the top of the atmosphere is 1361 W m⁻².

Sphericity and Sun Angles

Influences of Earth's Shape

  • Curvature effects:

    • Low latitudes: higher Sun angles.

    • High latitudes: lower Sun angles.

    • Seasonal variation in Sun intensity by latitude.

Sun Angle Definitions

  • Types:

    1. Altitude angle

    2. Zenith angle

  • Factors affecting Sun angle: latitude, longitude, time of year, time of day.

Seasonal Variations

Determinants of Seasons

  • Changes in:

    • Sun altitude above the horizon

    • Intensity of Sun's energy

    • Length of day

  • Earth’s Orbit: 23.5° axial tilt affects energy distribution.

Milankovitch Cycles

  1. Eccentricity: 100,000-year cycle affects energy (±17 million km).

  2. Tilt angle: Changes over 40,000 years (±1.2° total variation).

  3. Tilt direction: Changes over 26,000 years affecting seasonality.

Conclusion: Reasons for Seasons

  • Functions of Earth’s physical characteristics and orbit:

    1. Revolution around Sun.

    2. Rotation on axis.

    3. Axial tilt.

    4. Axial parallelism.

    5. Sphericity.

  • Annual march of the seasons.