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Very difficult sentence structure. The bold part is very confusing.

Although these molecules allow radiation wavelength, where most of the energy of sunlight is concentrated, to pass through, they absorb some of the longer wavelength, infrared emissions radiated from Earth's surface, radiation that would otherwise be transmitted back into space.

The bold part is very awkward. My friend told me "radiation that would otherwise be transmitted..." is the appositive clause to "infrared emissions radiated.....". I don't trust her. So what is the interpretation of the bolded part?

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    You're right: it's very awkward and clumsy and comma splice-ridden. Your friend is also right, that is meant to be an appositive to infrared emissions. – Janus Bahs Jacquet Jul 1 '15 at 20:24
  • The sentence is poorly constructed. – Hot Licks Jul 1 '15 at 21:14
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    The problems start with 'Although these molecules allow radiation wavelength,' which doesn't make sense. I'd suggest 'Although these molecules allow radiation in the visible wavelengths (where most of the energy of sunlight is concentrated) to pass through, they absorb some of the longer wavelengths: infrared emissions, the range predominately radiated from the Earth's surface, which would otherwise be subsequently transmitted back into space.' – Edwin Ashworth Jul 1 '15 at 22:16
  • What does to pass through refer to? What is passing through what, and if this is light passing through air or water, what's a purpose infinitive doing here? Is this Creationist physics? – John Lawler Jul 1 '15 at 23:47
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    TBH, I think the bold is the least awkward part of that sentence. – Kevin Jul 2 '15 at 2:05
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I believe your friend is correct.

The easiest way I've found to interpret it is to break it into the two thoughts that it's trying to express.

Infrared emissions radiated from Earth's surface.

This radiation would otherwise be transmitted back into space.

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