The Energy Out Sector

Figure 1. A very simple STELLA model of Earth’s climate system. The three colored sectors show the parts of the model that keep track of the energy coming in to the Earth from the Sun, the energy leaving the Earth through emitted heat, and the average surface temperature of the Earth.

Click for a text description of Figure 1.

This STELLA diagram visually represents the planetary climate model by categorizing key climate-related variables into three main groups: Energy In (yellow area), Temperature (red area), and Energy Out (blue area).

• Energy In (Yellow Area):
  • Factors affecting incoming solar energy: Solar Constant, Albedo, Surf Area.
  • These variables influence Insolation, which directs energy to Earth Heat.
• Temperature (Red Area):
  • Includes Ocean Depth, Water Density, and Heat Capacity, which influence Temperature.
  • Temperature interacts with Earth Heat and contributes to heat exchange processes.
• Energy Out (Blue Area):
  • Outgoing energy factors include Heat Emitted, LW Int, and LW Slope.
  • Earth Heat emits energy, balancing the system.

Arrows show the flow of energy and interactions between these factors. The diagram helps illustrate the components regulating planetary climate.

David Bice @ Penn State is licensed under CC-BY-NC-4.0

The Energy Out sector (blue above) of the model controls the amount of energy emitted by the Earth in the form of infrared (thermal) radiation, which is a form of electromagnetic radiation with a wavelength longer than visible light, but shorter than microwaves. You saw earlier that this is often described using the Stefan-Boltzmann Law which says that the energy emitted is equal to the surface area times the emissivity times the Stefan-Boltzmann constant times the temperature raised to the fourth power:

A is the whole surface area of the Earth (units are m²), ε is the emissivity (a number between 0 and 1 with no units), σ is the Stefan-Boltzmann constant (units are W/m² per °K4), and T is the temperature of the Earth (in °K). The problem with this approach is that it ignores the greenhouse effect, which is a very important part of our climate system. We could represent the greenhouse effect by choosing the right value for the emissivity in the Stefan-Boltzman law, but here, we will use a different approach, one in which Eout is based on actual observations. With a satellite above the atmosphere, we can measure the amount of energy emitted in different places on Earth and figure out how it relates to the surface temperature. As it turns out, this is a pretty simple relationship, described by a line:

$${\mathrm{E}}_{\text{out}}= ( ⟦ \mathrm{LW} {⟧}_{\mathrm{int}}+ ⟦ \mathrm{LW} {⟧}_s\times T ) \times A$$

The part inside the parentheses is just the equation for a line, with an intercept (LW_int with units of W/m²) and a slope (LWs with units of W/m² per °C). This new way of describing Eout is shown as the red line in the figure below:

Figure 2. Three different schemes for representing the long-wavelength energy (heat) emitted by Earth. The blue curve is the simple Stefan-Boltzman Law, which suggests that at the average temperature of the Earth (15°C), our planet would emit way more energy than we get from the Sun, and so we would cool down until the temperature reached -18°C at which point the Ein = Eout and we have a steady state. The green curve shows the Stefan-Boltzman Law modified by including a new term called emissivity (0.6147), which brings us into an energy balance (steady state) at a temperature of 15°C. The red curve instead represents this relationship based on actual measurements from satellites — notice that it too puts us at a steady state when the temperature is 15°C. The red curve is what we will use in this model.

Click for a text description of Figure 2.

This graph plots Long-wave Energy Emitted (W/m²) on the y-axis against Temperature (°C) on the x-axis to illustrate how Earth's natural greenhouse effect raises the planet’s temperature.

• The blue curve represents E_out = σT⁴, showing energy emitted without an atmospheric greenhouse effect.
• The green line represents E_out = 0.6147σT⁴, depicting energy emission with Earth's greenhouse effect.
• The red line represents E_out = 210 + 2T, another approximation of outgoing energy.
• A horizontal dashed line at 240 W/m² represents energy absorbed from the Sun (343(1 - albedo)).
• The intersection of the green line with the 240 W/m² level indicates Earth's actual average surface temperature of 15°C.
• Without the greenhouse effect, the temperature would be -18°C, marked on the graph.
• A label notes that Earth’s greenhouse raises the temperature by 33°C.

David Bice @ Penn State is licensed under CC-BY-NC-4.0

The key thing here is that the hotter something is, the more energy it gives off, which tends to cool it, and it will continue to cool until the energy it gives off is equal to the energy it receives — this represents a negative feedback mechanism that tends to lead to a steady temperature, where ${\mathrm{E} }_{\text{in }}= {\mathrm{E} }_{\text{out }}$.