Here are my workings, if you spot any glaring errors, please leave a comment. It's all round figures, I'm not going to bicker about anything more accurate than the first significan figure.
How many trees would we need to clear the backlog?
CO2 in atmosphere = 3,000 billion tonnes (3 x 10^12)
One-third of that is the increase since 1850 = 1,000 billion tonnes, this is apparently the Bad and Planet Warming portion. 1850 level is accepted as beneficial.
World population = 8 billion
Bad CO2 per person = 125 tonnes.
Trees consist of mainly CO2 by mass, plus a bit of H.
An 80 foot tall hardwood tree = 9 tonnes
Let's say an average medium sized tree = 5 tonnes.
(A four foot long section of tree trunk with diameter 2 foot = 1 tonne, so if the main trunk is 16 feet high (two storeys of a house) plus 25% for boughs and branches, that's 5 tonnes)
So we'd need to grow another 25 trees per person to catch up. Sure, those trees will take decades to grow, but you have to start somewhere.
Ongoing emissions
At present, total CO2 in atmosphere is going up by 1% a year. (See comments - might be only 0.5%).
1% x 3,000 billion tonnes = 30 billion tonnes.
30 billion ÷ 8 billion people = 4 tonnes per person.
Let's say each tree soaks up 0.1 tonnes of CO2 per year while it's growing (from above - 5 tonnes divided by 50 years)
That's 40 trees per person i.e. each person plants that many to offset the element of their lifetime emissions which aren't being soaked up naturally. This sort of overlaps with the 25 from above for older people, but hey.
The maths gets super tricky after that. People are born and they die. Dead trees can be buried underground in such a way so as not to just release all the CO2 as well if they burn or rot, arguable either way. So I won't bother looking that far ahead.
Land area needed
25 to clear the backlog, plus 40 for ongoing = 65 per person.
Number of trees in the world = about 400 per person
So broadly speaking, an increase in tree cover of one-sixth
Forests (and presumably other wooded areas) = 31% of global land area
So that would have to go up to 36%, which seems do-able.
Applied to the UK
Decent sized trees per acre = 200. (In the dense wood at the top of my road, there are fairly big trees whose trunks were about 5 or 6 yards apart, so each tree has its own circle = 24 sq yards. 4,840 sq yards ÷ 24 sq yards = 200)
So the UK would need to 65 trees per person/200 trees per acre x 70 million people = 23 million acres, or 40% of the UK land area.
There's not that much suitable land (Scottish grouse moors, marginal farmland and such like) in the UK, but maybe we could get half-way there?
Countries like the UK that don't have enough land area per person and especially city-states like Monaco or Hong Kong will have to buy up some land in Canada or Siberia, where the land costs pennies, and let their trees grow there.
Alternative calculations welcome!
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