There may be some negative feedback for a while but in the long run this is likely to be overwhelmed by the effects of rising temperature and droughts on natural sinks that remove carbon dioxide from the atmosphere. 

It is correct that increasing carbon dioxide levels over the next few decades may boost the growth of some land plants but only under certain conditions. However in the longer term, warming and changes in precipitation, and the direct effects of changes in atmospheric composition and of deforestation are likely to lead to a decline in the ability of land sinks to remove carbon dioxide and a large increase in the release of soil and biomass carbon to the atmosphere.

Amazonia accounts for more than half the world’s rainforest and has been highly important in the past in removing an estimated 2 billion tonnes of carbon dioxide from the atmosphere each year. However recent droughts, particularly the harsh ones of 2005 and 2010, have killed many trees and drastically reduced the forest’s ability to take up carbon dioxide. Furthermore, drought has increased the rate at which carbon is lost from Amazonian soil to the atmosphere. These droughts turned the Amazon forest from being a net remover (‘sink’) of carbon dioxide to a net producer. The 2005 and 2010 droughts are thought, respectively, to have added an estimated 5 billion and 7 billion tonnes of carbon dioxide to the atmosphere.

In addition, higher atmospheric carbon dioxide levels are making the oceans more acidic. Although acidification is likely to seriously affect the ability of many marine animals and planktonic plants to form calcium carbonate shells the possible future impact of acidification on marine carbon dioxide sinks is uncertain. However the impact may be serious as marine acidification in the geological past has been linked to mass extinctions of species.

The effects of drought and other mechanisms on tropical rainforests provide positive (amplifying) feedback mechanisms and are likely to accelerate climate change. Other possible positive feedbacks include the reduced ability of warmer sea water to dissolve and hence store carbon dioxide and the increased warming of the Arctic Ocean resulting from the decreased reflection of heat into space, as the ice melts, known as the albedo effect. Most seriously, melting of the permafrost on land and warming of the oceans could lead to accelerated release of huge quantities of methane, an even more powerful greenhouse gas than carbon dioxide, from wetlands and sediments.