Polar Ice caps are melting? Questions on enviromental impact
I think you misinterpret the article you cited. In the article it is stated that:


  The melting of the polar ice-caps has
  an effect "the equivalent of about 20 years of additional CO$_2$ being
  added by man"


This is due to the energy in sunlight which is no longer reflected by the white ice and snow of the polar caps. This energy will be partly absorbed by the darker surface of the ocean or land which will be underneath the ice-caps. This absorption of energy (instead of reflection) has an effect which is equal to "the equivalent of about 20 years if additional CO$_2$ being added by mankind".

There probably are models that can tell how much CO$_2$ can be absorbed by trees. However, an ecosystem which is in balance (e.g. a full grown forest) doesn't absorb that much CO$_2$ anymore. This is because the growth of new trees is equal to the dying and decomposition of old trees (in balance). Only a little part might be stored in the soil.

An increase of CO$_2$ might increase the growth rate of trees due to in increase of effectiveness of photosynthesis. (Stomata will have to be open less longer to require the same amount of CO$_2$ and therefore trees will lose less water for example).

Our ocean does absorb CO$_2$ as well. Algea, phytoplankton, and chemical process all make this happen. What you mean with recycle -- as well I'm not sure.