Cooling effect from the oceans in global warming

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 $$\approx 0.7$$.