Moving on...
Using the simplified IPCC ΔF = 5.35*ln(C/C0) formula and knowing that 1 Joule is equivalent to 1 Watt*second let's now figure out how accurate it is.
ΔF = 5.35*ln(380/280) = 1.633792 W/m²
That is 1.633792 extra Joules per second per square meter that are being added since the CO2 concentration was 280 ppm back around 1750.
Given:
-
Earth's surface area is about 510,072,000 km² = 5.1 x 10^14 m²
- Using 365.25 days per year (standardized for leap years), there are 31557600 seconds per year
Joules added each year = 1.633792 * 5.1 x 10^14 * 31557600 = 26294862753792000000000 J = 2.629486x10^22 J
In other words, there is 2.629x10^22 Joules per year of extra energy being trapped by CO2 if the formula is correct.
Now, how much energy is needed to increase the atmosphere by 1 °C?
Given:
-
Total atmospheric mass is 5.1480×10^18 kg
-
Specific heat capacity of air (cp) is 1.0035 kJ/kg*K = 1003.5 J/kg*K
Therefore, heat required to raise temperature of atmosphere 1 °C = 5.137 x 10^18 x 1003.5 = 5.1549795 x 10^21 J.
Dividing J added each year by the J needed to raise the temperature of atmosphere 1 °C we get the number of degrees for the Joules of excess energy per year:
2.629486x10^22 / 5.1549795 x 10^21 = 5.1 °C
Our temperature is not rising that much each year. It is not even rising 0.5 °C each decade. If the natural log relationship is correct, then that means their 5.35 constant is off by more than a factor of 100.
