How Can Global Warming Accelerate if Effect of CO2 is Logarithmic?

      If scientists agree that the greenhouse effect is approximately logarithmic — which means that as we add more CO₂ to the atmosphere, the effect of extra CO₂ decreases, why does the IPCC projects that if we don't take steps to reduce our emissions, global warming won't just get worse, it will speed up?

      The answer can be found in a 28 March 28, 2018 post by DPiepgrass at 
https://skepticalscience.com/why-global-warming-can-accelerate.html

      Although CO₂ has less effect at higher CO₂ concentrations, this "logarithmic effect" is overpowered by these 4 factors:

1. Exponential growth of energy use
2. Past CO2 emissions that nature has not yet absorbed
3. Carbon sink saturation
4. Committed warming

Exponential growth of CO₂ emissions

      Historical carbon dioxide emissions can be approximated using exponential function, i.e. one that grows by a constant factor every year. That means continually increasing growth rate. In Figure 4 an exponential function growing at a rate of 2.8% yearly was superimposed on the graph of historical CO₂ emissions.

Growth of carbon dioxide emissions from burning fossil fuels during the period 1751-2012 (black line); source: CDIAC. Blue line represents exponential function growing at a rate of 2.8% per year (i.e. doubling every 25 years).

CO₂ emissions are doubling every 25 years. After 50 its 4x, after 75 its 8x, and after 100 its 16x larger. 

Carbon Sink Saturation

       The main natural carbon sinks are plants, the ocean and soil. Plants grab carbon dioxide from the atmosphere to use in photosynthesis; some of this carbon is transferred to soil as plants die and decompose. The oceans are a major carbon storage system for carbon dioxide. Marine animals also take up the gas for photosynthesis, while some carbon dioxide simply dissolves in the seawater.

      Combined, the Earth’s land and ocean sinks absorb about half of all carbon dioxide emissions from human activities. (Paul Fraser of the Commonwealth Scientific and Industrial Research Organization)

      The sink strength shows high interannual variability and there is evidence that the sink cannot be sustained indefinitely. It is conceivable that by the end of this century or earlier the terrestrial sink may significantly decrease or disappear.

https://www.globalcarbonproject.org/global/pdf/Canadell.2007.SinkSaturation.Springer.pdf  

Committed warming

      Committed warming refers to future warming effects that would still happen even if CO₂ levels stop increasing. A large source of delayed warming worldwide is the oceans, which  have not kept up with the warming of the land:

 

      Earth's climate system has feedback loops that magnify the warming effect of CO₂. For example, as the arctic ice melts, it exposes ocean. The ocean is much darker than the ice, so more sunlight is absorbed instead of being reflected back to space. This enhances the arctic warming effect. This effect is time-delayed, since it takes many years for the arctic ocean to warm up (which in turn causes the ice to melt more quickly in the future, which in

turn helps the ocean to heat up even more.