This website explains with excellent infographics what the short and long term carbon cycles are in relation to increasing atmospheric carbon.
Composite from National Research Council and UNEP:
It is the carbon cycle that determines the fact that global warming, climate change, and ocean acidification cannot ever stabilize without civilization stopping constantly adding carbon to the cycle.
The essential fact to know is that there are two carbon cycles.
That is a short term and an ultra long term cycle.
Short term carbon cycle
This cycle operates over one to a few hundreds of years.
What are often called carbon sinks like tropical forests only store carbon temporarily. The only real carbon sinks operate by the long term cycle.
This is what ‘the carbon cycle’ is understood to be, but it cannot help us to mitigate global warming and climate change because it does not remove CO2 from the atmosphere in time frame for humanity. It recycles carbon between the atmosphere land and ocean.
It depends on life, food chain on land and in oceans.
For both the land and oceans this cycle works by photosynthesis of green plants, the largest contribution comes from ocean surface phytoplankton – the tiniest of green plants.
Photosynthesis uses captures energy from sunlight via chloroplast cellls which energizes the growth and metabolism of the plant. But when the plant decays and dies that CO2 is returned to the atmosphere.
On land the dead life sinks through the ground and is thereby pressurized. This forms coal oil and natural gas.
In the oceans the carbon sinks to the ocean floor by means of what is called the ocean biological carbon pump by which atmospheric carbon is incorporated into sea shells as calcium carbonate.
Before industrialization through the long period of global climate stability the short term carbon cycle had been in balance.
Long term carbon cycle
It is only this extremely long term carbon cycle that sinks carbon in terms of removing carbon (CO2) from the carbon cycle in relevant to humanity and most life.
It operates over thousands to hundreds of thousands of years through the land and oceans. In both cases the organic carbon from dead life forms is pressurized over ages to time to form solid carbon.
On land this is fossil carbon- coal, oil and gas. The coal we burn up in no time took about 300 million years to form.
The ocean process forms rock- limestone and dolomite. This starts with the minute ocean surface plants called phytoplankton. This is how most of the carbon dioxide gets absorbed. Through the ocean food chain the carbon gets converted by shell forming organisms to calcium carbonite. Through ages of time and pressure in the ocean floor sediment calcium based rock is formed – limestone and dolomite.
We are rapidly returning this carbon to the atmosphere by burning it. Land fossil carbon we burn to produce heat energy as fossil fuels. Limestone we burn to make cement.