To be ecologically truly sustainable, no live trees should be cut. That will most closely mimic a natural ecosystem instead of turning them into managed tree plantations (which ain't properly forests).


## "Only take dead wood"

Now forests naturally create also a lot of biomass in the form of dead coarse wood, dead fine wood and dead leaves. That would slowly release its carbon as CO<sub>2</sub> through natural decay, so we might as well collect and burn that. We can extract (let's say) half of that, while leaving the other half as habitat for animals etc.:

> Dead wood, whether standing (snags) or down, plays an important role in forest ecology, acting as habitat for animals such as cavity-nesting birds, plants and microbial lives. (source: [Carbon sequestration via wood burial (2008)][1])

Also let's say we only would take the coarse wood (typically understood as having 10 cm stem diameter and up), as that is easiest to handle. In that case, a rough estimation can be based on this:

> For example, a 1 km × 1 km area (100 hectares) would accumulate about 100 tonne of carbon per year for a typical coarse wood production rate of 0.1 kgC m<sup>-2</sup> y<sup>-1</sup> […]. 500 tonnes of carbon [are equivalent to] […] about 1000 tonne dry wood mass […]. (source: [Carbon sequestration via wood burial (2008)][1])

So 100 t y<sup>-1</sup> km<sup>-2</sup> of carbon yield from coarse deadwood in a mature forest, based on the naturally occurring tree deaths. Which is equivalent to about 200 t y<sup>-1</sup> km<sup>-2</sup> of dry wood mass.

Finally, taking out only half of that wood results in a production of 100 t y<sup>-1</sup> km<sup>-2</sup> of dry wood mass.


## Comparing results

For comparability with the [answer by m.w.jacobsen][2]: my number of 100 t y<sup>-1</sup> km<sup>-2</sup> is equivalent to 1 t y<sup>-1</sup> ha<sup>-1</sup>, while m.w.jacobsen had 5.4 t y<sup>-1</sup> ha<sup>-1</sup>, both of dry wood mass.

The differences are that **(1)** I only include half the coarse deadwood (otherwise it's 2 t y<sup>-1</sup> ha<sup>-1</sup> when including all coarse deadwood, or roughly 4 t y<sup>-1</sup> ha<sup>-1</sup> when also including fine deadwood), **(2)** I don't include any clearcutting or cutting of live trees – but it is [not too clear][3] what impact that has on forest productivity, if any and **(3)** the numbers from the study I quote are quite rough. They are derived from global average forest productivity instead of that for only the temperate or tropic climate zone. Boreal forests have a lower productivity ([see][4]), lowering the average.


  [1]: https://doi.org/10.1186/1750-0680-3-1
  [2]: https://sustainability.stackexchange.com/a/2753
  [3]: https://sustainability.stackexchange.com/q/6967
  [4]: https://cbmjournal.biomedcentral.com/articles/10.1186/1750-0680-3-1#Fig4