Greenhouse Effect Study Notes

Greenhouse Effect DPIB Physics: HL Study Notes

Contents

  • Albedo & Emissivity
  • The Solar Constant
  • Greenhouse Gases
  • The Greenhouse Effect
  • Energy Balance Problems

Albedo & Emissivity

Emissivity

  • Definition: Emissivity () is defined as the ratio of the power radiated per unit area by a surface compared to that of a black body at the same temperature.

    • Formula:
      e = \frac{\text{power radiated by an object}}{\text{power emitted by a black body}}

  • Key Characteristics:

    • Stars are good approximations to a black body; planets are not.
    • Calculations assume:
    • The black body is at the same temperature as the object.
    • The black body has the same dimensions as the object.

  • Perfect Black Body: Emissivity is equal to 1.

  • Stefan-Boltzmann Law: For non-black bodies, the equation becomes:

    P = e \sigma A T^4

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

Albedo

  • Definition: Albedo () is defined as the ratio of the total scattered power to the total incident power of radiation reflected by a given surface.
    • Formula:
      a = \frac{\text{total scattered power}}{\text{total incident power}}
  • Planetary Reference: The albedo of a planet is the ratio between total scattered or reflected radiation and total incident radiation.
    • Earth’s Albedo: Approximately 0.3 (30% of the Sun’s rays reflected back into the atmosphere).
  • Albedo Characteristics:
    • An albedo of 1 represents a surface that scatters all incident radiation.
    • Variability factors include:
    • Cloud formations (thicker cloud cover increases reflection).
    • Seasons, latitude, and terrain variations.
  • Common Material Albedo Values:
    • 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
  • Notes: Albedo has no units, as it is a dimensionless ratio.

Worked Example: Albedo Calculation

  1. Average albedo of fresh snow: 0.85
  2. Energy reflected by fresh snow:
    • \text{Energy reflected} = 0.85
  3. Energy absorbed by fresh snow:
    • \text{Energy absorbed} = 1 - 0.85 = 0.15
  4. Ratio:
    • \frac{\text{Energy absorbed}}{\text{Energy reflected}} = \frac{0.15}{0.85} = 0.1764 \approx 0.18

The Solar Constant

  • Definition: The solar constant (S) is the intensity of the Sun's radiation arriving perpendicularly to the Earth's atmosphere when the Earth is at mean distance from the Sun.
  • Average Value: 1.36 × 10^3 W/m².
  • Seasonal Variation: Varies year-round due to:
    • Earth's elliptical orbit around the Sun.
    • Variations in the Sun’s output during its 11-year sunspot cycle.
  • Assumptions for Calculations:
    • Radiation incident on a plane perpendicular to the Earth's surface.
    • Earth is at mean distance from the Sun.
  • Planetary Intensity Variation: Different planets have varying intensity of solar radiation based on their distance to the Sun.
    • Example: Venus receives more solar radiation than Earth due to its proximity.

Incoming Radiative Power

  • Surface Area of a Planet: For radius r, surface area = 4πr².
  • Radiative Intensity: Covers a cross-sectional area of πr.
  • Mean Radiative Power:
    • S = \frac{S \cdot \left( \frac{\pi r^2}{4 \pi r^2} \right)}{S}

Worked Example: Calculating the Solar Constant

  1. Given Values:
    • Sun’s power output, P = 4 × 10²⁶ W
    • Distance (mean) from Earth to Sun, r = 1.5 × 10¹¹ m
  2. Model: Light spreads uniformly through a spherical shell:
    • Surface area = 4πr².
  3. Solar Constant Equation:
    • \text{S} = \frac{P}{4 \pi r^2}
  4. Calculation:
    • \text{S} = \frac{4 \times 10^{26}}{4 \pi (1.5 \times 10^{11})^2} = 1415 \text{ W/m}^2
    • Solar constant = 1.4 kW/m² (2 significant figures).

Important Note

  • The solar constant is defined above the Earth’s atmosphere, not at the surface.

Greenhouse Gases

Main Greenhouse Gases

  • Major greenhouse gases have both natural and human-generated origins, ranked by contribution:
    1. Water vapour (H₂O) - from evaporation.
    2. Carbon dioxide (CO₂) - from volcanic eruptions, wildfires, respiration.
    3. Methane (CH₄) - emitted from oceans, soils, and as a byproduct of decomposition.
    4. Nitrous oxide (N₂O) - from soils and oceans.
  • Function: Greenhouse gases absorb long-wave radiation re-radiated by the Earth, preventing loss to space, akin to glass in a greenhouse.
  • Significant Impact Gases:
    • Mainly CO₂ and H₂O have the most significant impact on the greenhouse effect.
  • Other Gases with Lesser Effects:
    • Ozone (O₃), Methane (CH₄), Nitrous oxides (N₂O).
  • Examiner Note: Ozone depletion ("hole in the ozone layer") is irrelevant to the greenhouse effect and should not be confused.

Greenhouse Gases & Infrared Radiation

  • Absorption Characteristics:
    • Approximately 25% of solar radiation (mostly short wavelength) is absorbed by the atmosphere while about 80% of the long-wave radiation from Earth is absorbed by greenhouse gases.
    • Incoming UV radiation absorbed by ozone; re-emitted infrared radiation absorbed by greenhouse gases.
  • Climate Impact: Imbalance can lead to fluctuations in Earth's mean surface temperature.
  • Relevance of Concentration: The significance of a greenhouse gas depends on its atmospheric concentration and its absorption capability for specific wavelengths.
  • General Understanding: Each greenhouse gas has both natural and man-made sources.

Absorption Characteristics of Specific Gases

  • Ozone (O₃):
    • Absorbs nearly 100% of incoming UV radiation, significantly absorbs outgoing infrared radiation (9 μm - 10 μm).
    • Not a major contributor to the greenhouse effect due to lower concentrations in the atmosphere.
  • Carbon Dioxide (CO₂):
    • Effective absorber of infrared radiation in the ranges of 1.5 - 30 μm, particularly strong absorption at 15 μm.
    • Increased atmospheric concentration signifies its vital role in the greenhouse effect.
  • Water Vapour (H₂O):
    • Best absorber of infrared radiation (0.8 - 35 μm).
    • Concentration increases as air warms.
  • Total Atmosphere Composition:
    • Most ultraviolet, infrared, and microwave radiation is absorbed by the atmosphere, yet it is mostly transparent to visible radiation.

The Greenhouse Effect

General Mechanism

  • Around 25% of primarily short wavelength solar radiation is absorbed by the atmosphere, while about 80% of long wavelength re-emitted radiation is absorbed back into the atmosphere.
    • UV radiation absorbed by ozone; re-emitted infrared radiation absorbed by greenhouse gases.
  • Habitable Temperature Maintenance: Absorbed radiation helps maintain a habitable temperature on Earth.
  • Chemical Composition Imbalance: Can cause fluctuations in Earth's mean surface temperature.

Resonance Model of Global Warming

  • Radiation Profile:
    • Incoming solar radiation consists mainly of UV and visible light; visible light isn’t absorbed by the atmosphere but by Earth's surface.
    • At night, Earth re-radiates absorbed radiation as infrared.
  • Role of Greenhouse Gases: These gases absorb some infrared radiation and reflect it back towards Earth. The higher the concentration, the more heat is trapped in the Earth-atmosphere system.
    • Results in the greenhouse effect and an increase in average temperatures.

Molecular Energy Level Model

  • Mechanics of Absorption:
    • High-frequency UV light can break molecular bonds; infrared light increases molecular vibration.
    • Greenhouse gases resonate and heat up upon absorbing infrared light, which they re-emit towards Earth's surface.

Radiation Characteristics

  • Solar radiation is primarily short-wave; Earth re-emits as long-wave radiation.

The Enhanced Greenhouse Effect

Human Impact

  • Increased greenhouse gas levels due to human activity:
    • CO₂ concentration increased to over 420 ppm in 2020.
    • An enhanced greenhouse effect is observed due to these increased levels leading to:
    • Reduced escape of long-wave radiation (heat).
  • Temperature Increase: Average global temperatures have risen over 1°C since pre-industrial times.

Sources of Greenhouse Gases from Human Activity

Carbon Dioxide (CO₂)
  • Sources:
    • Burning of fossil fuels (power stations, vehicles).
    • Burning wood.
    • Deforestation (less CO₂ absorbed).
Methane (CH₄)
  • Sources:
    • Decay of organic matter (manure, landfill waste, crops).
Nitrous Oxide (N₂O)
  • Sources:
    • From artificial fertilizers and fossil fuel burning.

Summary of the Greenhouse Effect

  • The greenhouse effect arises from natural phenomena, but human activities exacerbate the enhanced greenhouse effect.

Worked Example: Effects of the Enhanced Greenhouse Effect

  • Question: Which of the following is the result of the enhanced greenhouse effect?
    • A. Increasing global average temperature due to natural causes
    • B. Decreasing global average temperature due to human activity
    • C. Increasing global average temperature due to human activity
    • D. Decreasing global average temperature due to natural causes
  • Answer: C. The enhanced greenhouse effect leads to increasing average global temperatures and is caused by human activity.

Energy Balance Problems

Earth’s Energy Balance

  • Understanding Earth's energy balance is crucial to determining how much incoming energy from the Sun is used and how much is returned to space.
  • If incoming and outgoing energy are balanced, Earth's temperature remains constant.
  • Models can predict temperature fluctuations based on current and increased concentrations of greenhouse gases.

Worked Example: Energy Balance Climate Model

Given Data
  • Current mean temperature of Earth’s atmosphere: 242 K
  • Current mean temperature of Earth’s surface: 288 K
  • Solar intensity per unit area at the top of the atmosphere: 344 W/m²
  • Emissivity of the atmosphere: 0.720
  • New temperature increase in atmosphere: 6 K
Steps for Calculation

  1. List Known Quantities:

    • Solar intensity: I = 344 W/m²
    • Stefan-Boltzmann constant: σ = 5.67 × 10⁻⁸ W/m²K⁴
    • Albedo of the atmosphere: a = 0.280.

  2. Calculate Intensity Absorbed at Earth's Surface:

    • Is = e \cdot Ia
    • I_s = 0.720 \cdot 344 W/m^2 = 247.68 W/m^2 \approx 248 W/m^2

  3. Power per Unit Area Emitted by a Body:

    • I = e \sigma T^4

  4. New Intensity Radiated by the Atmosphere:

    • I = 0.720 \cdot (5.67 \times 10^{-8}) \cdot (248^4) = 154.43 W/m^2 \approx 154 W/m^2

  5. New Intensity Absorbed by Earth’s Surface:

    • I_s = 248 + 154 = 402 W/m^2

  6. Calculate New Temperature of Earth’s Surface:

    • Is = \sigma Ts^4
    • Assuming black body emissivity, Is = 1540 (after unit conversion) = (5.67 \times 10^{-8}) \cdot Ts^4
    • Solve for T_s :
    • T_s = ((402) / (5.67 \times 10^{-8}))^{1/4} = 290 K

  7. Temperature Increase:

    • \Delta T = 290 - 288 = 2 K

Simplified Climate Models

  • Generally assume Earth’s surface and the atmosphere:
    • Act as black bodies (emissivity of the surface equals 1).
    • Stay at a constant temperature.