Earth's Temperature: Energy Balance and the Greenhouse Effect
Earth's Temperature: Concepts and Models
Earth's Observed Temperature and Fundamental Questions
The Earth's temperature has increased by approximately .
Fundamental questions arise:
Why has the temperature gone up, not down or stayed the same?
Why is the Earth's average temperature and not or ?
The Black Box Model: A Conceptual Starting Point
To understand Earth's temperature, scientists use conceptual models.
A physical black box model (not a numerical computer model) is used to illustrate how objects that act like black bodies absorb and emit radiant energy.
Perfect Black Body Characteristics:
Absorbs all incoming energy it receives.
Emits an equivalent amount of energy as it receives.
Achieves an equilibrium temperature (or energy quantity) inside when incoming and outgoing energy are equal.
Application to Earth: Earth's temperature is conceptually dictated by the balance between incoming and outgoing energy.
This implies the Earth receives a quantity of energy roughly balanced by the energy it radiates back to space.
The Stefan-Boltzmann Law
Developed by Stefan Boltzmann, this law describes how black bodies emit energy as a function of their temperature.
Equation: e temperature in Kelvin.
Implication: As a body's temperature rises, its energy output increases exponentially (). Higher temperature means much more energy emitted.
Application to Sun and Earth
Sun's Output: Plugging the Sun's measured temperature into the equation yields an output of approximately .
The Sun predominantly emits energy in the visible spectrum, but also significantly in the infrared and ultraviolet.
Earth's Output: Using Earth's average temperature ( or ) results in an output of approximately .
Most of Earth's emitted energy is in the infrared wavelength.
Initial Discrepancy: The vast difference between the Sun's total output () and Earth's output () highlights that the simple black box model needs refinement for Earth.
Earth's Energy Reception: Accounting for Geometry
Solar Constant: The energy from the Sun reaching Earth. It's considered nearly constant, with minor variations.
Surface Area for Absorption: Only one side of Earth faces the Sun at any given time.
The effective area for absorbing sunlight is the area of a circle, (where is Earth's radius).
To account for absorption over the entire spherical surface, the Solar Constant is effectively divided by .
Earth's Received Energy: This calculation shows Earth receives approximately over its surface, which is much closer to its emitted energy () than the Sun's total output.
Energy Balance Goal: The ultimate goal is to determine if the incoming energy to Earth equals the outgoing energy, and thus explain the temperature.
This requires solving for temperature () by considering the solar constant, area of energy reception, Earth's albedo (reflectivity), surface area for energy emission, emissivity, and the Stefan-Boltzmann constant.
Complications to the Simple Black Box Model
The Earth is not a perfect black box; it's a dynamic system with several complexities:
Shape and Rotation: Earth is a rotating sphere, not a stationary box.
Different surfaces (land, water) have varying capacities to absorb solar radiation.
Water: High capacity to absorb energy.
Land: Lower capacity to absorb energy.
Ice-covered land: Highly reflective, low absorption (high albedo).
The Moon: A large object collided with Earth ~ billion years ago, forming the Moon. This satellite interacts with Earth, influencing its dynamics (though not immediately addressed in this simplified model).
Axial Tilt: Earth's axis is tilted at relative to its orbital plane. This tilt causes seasons:
Half the year, the Northern Hemisphere tilts toward the Sun, receiving more radiation.
The other half, the Southern Hemisphere receives more. This complicates energy distribution.
Elliptical Orbit: Earth's orbit around the Sun is elliptical (not a perfect circle), meaning the distance to the Sun and thus incoming energy varies throughout the year.
Albedo and Surface Characteristics: Different parts of Earth reflect varying amounts of sunlight.
Areas with ice (e.g., polar regions) reflect a lot of energy.
Oceans absorb most energy.
Deserts (e.g., Sahara) and highly cloudy regions (e.g., monsoon regions, equatorial Pacific) also have high reflectivity.
Initial Predicted Temperature Without an Atmosphere
When all known values (solar input, Earth's physical characteristics, but excluding the atmosphere) are plugged into the energy balance equation, the predicted equilibrium temperature of Earth is .
This is a significant discrepancy of approximately from the observed average temperature of , indicating a missing fundamental component in the simple model.
The Crucial Role of the Atmosphere
The Missing Piece: The Earth's atmosphere is responsible for the difference.
Atmosphere as a Black Body: The atmosphere itself acts as a large black body, interacting with both incoming solar radiation and outgoing terrestrial radiation.
Atmospheric Properties: It possesses:
Albedo (reflectivity).
Capacity to absorb energy.
Capacity to transmit energy (allowing it to pass through).
Refined Model: When realistic values for atmospheric properties are incorporated into the energy balance calculation, the predicted equilibrium temperature becomes approximately – closely matching the observed value.
Significance: The atmosphere is essential for making Earth habitable at . Without it, Earth would be a frozen planet.
Energy Absorption: The atmosphere has a significant capacity to absorb radiation emitted from the Earth's surface. It also re-emits this energy both upwards to space and downwards back to the Earth's surface, thus playing a major role in regulating surface temperature.
Heat, Temperature, and Energy Transfer
Heat vs. Temperature: It's vital to distinguish between heat and temperature.
Temperature: A measure of the average kinetic energy of the particles in a substance.
Heat: The transfer of energy within a system due to a temperature gradient.
Temperature Gradients: Differences in radiational heating or cooling create temperature gradients.
According to the Second Law of Thermodynamics, energy (heat) always flows from a region of higher temperature to a region of lower temperature.
Examples:
Energy flows from Earth's warmer surface to the cooler atmosphere.
A temperature gradient exists between the equator (low latitudes, more solar energy) and the poles (high latitudes, less solar energy), driving energy transport across the globe.
Forms of Heat Transfer:
Sensible Heat: Energy transferred that changes the temperature of a substance without changing its phase (e.g., warming water).
Latent Heat: Energy transferred that changes the phase of a substance without necessarily changing its temperature (e.g., solid to liquid, liquid to gas).
Evaporation Example: When solar radiation hits the Equatorial Pacific, some energy warms the water (sensible heat). As the water reaches a certain temperature, it evaporates, converting liquid water to water vapor. The energy required for this phase change is transferred as latent heat to the atmosphere, where the water vapor carries that energy.
Water has a specific sensible heat of evaporation, requiring a considerable amount of energy to change its state. This energy is transferred to the atmosphere, raising its energy content.
Earth's Energy Budget and the Greenhouse Effect
Quantified Energy Flows: Scientists quantify different forms of energy flow:
Solar energy (shortwave radiation).
Infrared radiation (longwave).
Latent heat.
Sensible heat.
Overall Budget: Summing all incoming and outgoing energy flows reveals that, currently, more energy is coming into the Earth system than is leaving.
Reason for Excess Energy Storage: This imbalance is primarily due to Greenhouse Gases (GHGs) in the atmosphere, which trap outgoing infrared radiation.
Most Abundant Greenhouse Gas: Water vapor is by far the most abundant GHG, contributing 49-71 hinspace ext{%} of the total greenhouse effect.
Without water vapor, Earth's temperature would be much colder, closer to .
Carbon Dioxide (CO): Accounts for approximately 22-29 hinspace ext{%} of the greenhouse effect.
Other GHGs include methane and ozone.
Radiation Pathway Summary:
Incoming shortwave solar radiation (UV, visible, microwave) largely passes through the atmosphere unimpeded.
This radiation is absorbed by the Earth's surface and converted into heat.
The Earth, at its average temperature of (), emits this energy back towards space as infrared radiation.
However, this outgoing infrared radiation must pass through the atmosphere, which is highly absorbent of infrared radiation, primarily due to water vapor.
The Atmospheric Window: A Critical Concept
Incoming Radiation and Protection: The atmosphere selectively blocks certain wavelengths of incoming solar radiation.
For example, it protects Earth by blocking and absorbing much of the incoming shortwave ultraviolet (UV) radiation, which helps limit heating and protects life from damage.
Outgoing Radiation and the Window: This is the most crucial takeaway for Earth's energy balance.
While Earth emits a broad spectrum of infrared radiation, there is a specific, narrow band of infrared wavelengths known as the atmospheric window through which Earth's energy can escape into space.
All other infrared regions are efficiently absorbed by atmospheric gases and cannot escape.
The atmospheric window is located within the infrared spectrum.
The Greenhouse Effect Explained: This critical window is