Honestly, that unit reads like bullshit to me, when stated out of context- I did used to work in energy and emission forecasting, but never that deeply into the academics so feel free to disregard my comments on that basis - we relied on scientific advisors for that stuff.
Personally I'd hope that all the papers quoting such a thing should have a simpler literal maybe step by step explaination of what the fuck they're trying to measure . But i really did hate academia generally for its introverted tendencies, I don't think they write those papers to inform oiks like me.
If the unit is supposed to be a scale for the long term average net flow of greenhouse gases from the planet's surface into the atmosphere, then that is a complex thing; I think it deserves a load of words to explain the what is being described - more than a few of letters and numbers.
Here's my attempt at what I think the abbreviation is trying to say:
"Average mass of greenhouse gas emissions with equivalent potential to warm the planet as a gigatonne of carbon dioxide, less any amounts absorbed back into the earth, per year over the last 100 years (GtCO2e)"
I dont feel the "y-1" adds anything since the unit is dimensionally a number of tonnes - unless I've misinterpreted -which seems likely.
One shouldn't just use an abbreviation if one want's to communicate to non-specialists.
I'd always advise to spell it out in real words and sentences. If complex, try to break it down into simple parts.
Then after a full explanation, you can later reply on the abbreviation - for example in a graph label.
If the measurement or estimate is important, then the audience deserves enough words to explain it.
If the measurement or estimate does not come with enough words to explain it then in my opinion the author doesn't care enough to try to explain it so it can't be that important. It may be just a rhetorical grph or it just looks good - no real meaning.
The only exception for me is the "standard units", metre, kilogramme etc. as we can rely on S.I. for those standard measures overing the main material dimensions.
Look it proably really is all just me being an asshole, but I get very sick of hearing vague, imprecise bullshit like "Carbon" being used as a term for "greenhouse gas emissions". I did have a job where the difference between C and CO2 caused a factor of 0.278 discrepancy in some arguably important figures. High school fucking chemistry. Those people should have known better and resolved their unit of measure ahead of time.
I get that some people had a hard time in school, but I think it should be about trying to help them understand more and learn , not dumbing stuff down to imprecise terms because we're so scared of confusing someone . If a person doesn't know the basics, say the difference between an element, an atom and a molecule; we should help them learn that before going on at them about complex atmospheric concentrations and global warming equivalent potentials.