Question

Treating Figure \(9.9\) somewhat literally, in which one out of every four infrared photons escapes without being absorbed by a greenhouse gas molecule, what would the effective upward radiation be if \(400 \mathrm{~W} / \mathrm{m}^{2}\) left the ground, and re-radiation of the absorbed fraction was split equally between upward radiation and radiation returning to the ground? \(^{83}\)

Short answer

Answer: To find the effective upward radiation, we follow these steps: Step 1: Calculate the absorbed radiation: Absorbed radiation = 0.75 * 400 W/m² = 300 W/m². Step 2: Calculate the re-radiated upward portion: Re-radiated upward portion = 0.5 * 300 W/m² = 150 W/m². Step 3: Calculate the effective upward radiation: Effective upward radiation = 150 W/m² (re-radiated upward portion) + 100 W/m² (escaped radiation) = 250 W/m². So, the effective upward radiation is 250 W/m².

Step-by-step solution

Calculate the absorbed radiation

Given that one out of every four infrared photons escapes without being absorbed, so the absorption rate is 75%, meaning that 75% of the radiation is absorbed by the greenhouse gases. To find the absorbed radiation, we can find 75% of 400 W/m²: Absorbed radiation = (75% of 400 W/m²) = 0.75 * 400 W/m².

Calculate the re-radiated upward portion

Now that we have the absorbed radiation, we can find the re-radiated portion that goes upward. The absorbed radiation is split equally between upward radiation and radiation returning to the ground, so half of the absorbed radiation is radiated upward: Re-radiated upward portion = (50% of absorbed radiation) = 0.5 * absorbed radiation.

Calculate the effective upward radiation

To find the effective upward radiation, we can add the re-radiated upward portion (from Step 2) to the escaped radiation (25% of 400 W/m²). So: Effective upward radiation = Re-radiated upward portion + Escaped radiation. Now substituting the values from Steps 1 and 2 to find the effective upward radiation.

Key concepts

Infrared Radiation

Infrared radiation is a type of electromagnetic radiation. It is invisible to the human eye, but it can be detected as heat. When you feel warmth from the sun, you're experiencing infrared radiation. This radiation is emitted by all objects based on their temperature. Warmer objects emit more radiation.

• Infrared radiation has longer wavelengths than visible light.
• It plays a significant role in energy balance on Earth.
• It is key in processes like the greenhouse effect.

Greenhouse gases in the atmosphere absorb infrared radiation emitted from the Earth’s surface. They then re-emit the radiation in all directions. This process warms the planet and is what we refer to as the greenhouse effect. Without this, Earth would be too cold to support life as we know it.

Energy Transfer

Energy transfer describes the movement of energy from one place or system to another. In the context of the Earth’s climate, significant energy transfer occurs via radiation. This is the primary way heat moves from the Earth's surface into the atmosphere.

• Radiative energy transfer involves the emission and absorption of infrared radiation.
• Greenhouse gases play a crucial role by absorbing and re-emitting energy.
• This process heats up the atmosphere and is fundamental to climate systems.

In the exercise, energy transfer involves infrared photons leaving the Earth's surface. Not all of this energy escapes to space directly. Much of it is absorbed by greenhouse gases, which then re-radiate it, thereby trapping heat. This process balances Earth's temperature.

Radiative Forcing

Radiative forcing is a measure of the influence a factor has on the energy balance of the Earth's atmosphere. It is expressed in terms of the change in energy in the atmosphere due to a specific factor.

• It can be positive (warming effect) or negative (cooling effect).
• Greenhouse gases typically have a positive radiative forcing.
• This impacts global temperatures.

For instance, when greenhouse gases absorb and re-emit infrared radiation, they cause a positive radiative forcing. This leads to more energy being trapped in the Earth's atmosphere, influencing climate change. Understanding radiative forcing is crucial in predicting future climate change scenarios.