CO2 acceleration vs rate of change of SST

It is recognised that rate of change of CO2 is well correlated to SST. Here each dataset is again differentiated to remove the slope in CO2.

It is notable that there is no obvious ‘trend’ in 2nd derivative of CO2 showing that a quadratic is a reasonable approximation to the long term variation. Mathematically a quadratic rise is stronger than an exponential and some literature has referred to this as a “super-exponential” rise in CO2.

With the exception of a brief period post 2000 the two series show strong correlation and no visibly obvious divergence.

CO2 mean = 0.0282617; SD = 0.797774
ICOADS mean = 0.00628281; SD = 0.10201

mean of d/dt(SST) = 0.63 K/century from 1950 onwards.
mean CO2 accel = 2.8 ppm/year/century 1958 onwards.

Currently CO2 is increasing at about 2ppm/year

Scaling the two according to with a ratio of approx 8 gives mean CO2 / mean SST of 57%. Short term variability is about twice as strong as long term.

The two largest excursions in both datasets are centred on 1973 and 1998.