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.