The ocean soaks up about 90 percent of the heat of climate change, because of ocean heating. When using the formula of Svante Arrhenius to calculate forcing due to atmospheric $CO_2$

$\Delta F=\alpha\ln(\frac{C}{C_0})\quad[W/m^2]$

and the formula

$\Delta T_s = \lambda \Delta F\quad[K]$

the steady-state surface temperature become higher than the measured temperature of global warming. I would like to find out how to correct Arrhenius formula because of the cooling effect from the oceans.

Is it possible to do that based on the estimate that 90 % of the heat is accumulated in the 70 % of the surface that is water?

$\alpha=5.35,\,\lambda=0.8,\,C=410,\,C_0=280$ gives
$\Delta T=0.8\times5,35\times \ln(\frac{410}{280})\approx 1.6^oK$ For the period 1850-2019.

Arrhenius formula gives temperature raise $1.6$ K and measured temperature raise is about $1.1$ K which gives a factor of correction $\approx 0.7$.


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