# Understanding a diagram of Earth's radiation balance

Trying to understand this image. Can someone tell me if I have the right reasoning here:

• Sun has 100% SW shooting to earth

• 30% of that 100% is reflected by clouds

• 70% remains
• Of that 70%, 45% of that SW is absorbed by Earth's surface.
• That leaves 25%, where does that go/factored into?

The entire right half of this diagram confuses me, what is happening there? Why is there a red line connecting 70%SW and 70%LW? What does "??%LW" mean?

Thank you

• sw is short wave radiation and lw is longwave radiation(infrared or heat radiation) Mar 14, 2018 at 18:53
• @trondhansen Thanks. I understood that part. And I know that Earth emits long-wave radiation (for some unknown reason) and the Sun emits short-wave radiation (for some unknown reason). So with the two we have to work out how the energy that Earth naturally emits and the energy that comes into Earth is balanced out. So everything SW is by the Sun, and everything LW is from Earth? What does 70%SW and 70%LW and ??%LW and the red line connecting the two mean?
– yre
Mar 14, 2018 at 18:57
• What happens to that 25-35% that doesn't make it to the surface?
– yre
Mar 14, 2018 at 19:01
• it gets reflected back to space before it reaches the planet. Mar 14, 2018 at 19:03
• Can't say I've ever dug into the details fully... but know sun emits primarily shortwave and the Earth longwave because $f_{max} \propto T$ as shown in Wien's Law (looks like Wikipedia has some quick explanation of how he made the proof of that)... which then also results out from the larger Planck's Law (once again the Wikipedia article discusses it's derivation). If looking for more simple conceptual understanding, it might be a good separate question! Mar 14, 2018 at 20:00

SW = Shortwave radiation (i.e. Visible + Ultraviolet light)

For the left part of the diagram, it shows that the 30% of the total incoming energy (mostly delivered as shortwave radiation) gets reflected by clouds and the Earth's surface. Therefore, 70% is the total absorbed by the planet (45% of it is absorbed by the Surface and 25% by the atmosphere).

The red line refers to the fact that given that Earth energy budget is assumed to be in balance, meaning that the same amount of energy that goes IN the system (as shortwave radiation) must go OUT the system, in the form of longwave radiation, that is the main kind of radiation the Earth emits given its temperature (see Wien's law). This energy balance assumption is a good one, because even if you think that more energy gets IN than OUT, that would lead Earth's temperature to increase, increasing then the amount of emitted energy (according to Stefan–Boltzmann law), until it reaches a point where the outgoing radiation released equals the amount received energy from the Sun. Therefore, establishing the energy balance.

Due to this balance, the right part of the diagram shows that the same 70% of the energy must be emitted back to space as longwave radiation (the same amount that was absorbed), and for that to be true, it is asking you what would be the required amount of energy that the atmosphere must emit towards Earth as LW radiation to keep the system in balance. Or at least that's my interpretation of the question marks in the absence of further information.

• This is a really good explanation. Especially mentioning Wien's law and Stefan-Bolzmanns law. Reading it, I see that Wien explains where the peak radiation occurs in the EMS, so for the sun it's 0.5um and for Earth it is 10um. And then Stefan-Boltzmann tells us how much energy is being emitted by the blackbody. Still a little unsure how to connect the dots and their relationship here and with climate-change/greenhouse effect.
– yre
Mar 15, 2018 at 3:10