Temperature Increase Equation for Global Warming

Alternative Form of Temperature Increase Equation

Select the Global Warming Temperature Increase Calculator

Example
How much warming does carbon dioxide itself contribute to the current surface temperature of the Earth?
We can calculate the CO_{2} flux density (F) at concentration C in the current atmosphere using the fundamental equation: F = 5.35 ln C. CO_{2} concentration reached 400 ppm on 11^{th} May 2013 and therefore, ΔF = F = 32.05 W/m^{2}. The surface temperature, T_{s} = 288.15^{o}K (15^{o}C) and from the equation above we have ΔT = 0.31 ΔF and
therefore, ΔT = 0.31 X 32.05 = 10^{o}C
Water vapour adds a further 75 W/m^{2} giving total ΔF = 107.05 W/m2. Surface temperature increase ΔT = 0.31 X 107.05 = 33^{o}C. That is, CO_{2} and water vapour increase the surface temperature of the Earth by 33^{o}C. Greenhouse gases, including CO_{2} and water vapour, keep the surface temperature about 33^{o}C warmer than it would otherwise be.

Dangerous warming
The Earth is absorbing 0.5 Watts/m^{2}, more than it is radiating to space. As we add more CO_{2} to the atmosphere this absorption increases. If we multiply this rate by the surface area of the Earth (5.100656 X 10^{14} m^{2}) we find that the Earth is accumulating heat at a rate of 2.6 x 10^{14} Watts (or Joules per sec). Given the Hiroshima atomic bomb yielded an explosive energy of 6.3 x 10^{13} Joules, this is equivalent to four Hiroshima bombs of heat per second.
Our climate in 2013 absorbed 126,227,704 such bombs in accumulated energy. Humans added a further 36 billion tons of CO_{2} in 2013 so the rate of heating increases each and every day.


Equation for Global Warming
Derivation and Application
Amazing carbon dioxide View
Why a small increase in carbon dioxide (CO_{2}) content in the atmosphere makes a critical difference to the actual global surface temperature of the Earth.
Derivation of IPCC equation: ΔF = 5.35 ln (C/C_{0})
View
Equation gives the increase in heat flux density, ΔF (in Watts/m^{2}) when CO_{2} concentration increases from C_{0} to C ppm.
Two distinctly different derivations are given:
2.1 Derivation One  uses an equation derived from the Heat Transfer Equation.
2.2 Derivation Two  mostly uses first principles and includes:
 Derivation of the basic equation: F = 5.35 ln C
 Setting of initial conditions giving: ΔF = 5.35 ln (C/C_{0})
 Calculation of CO_{2} flux density and comparison with the other noncondensing
greenhouse gases that maintain a temperature structure for the atmosphere.
Derivation of temperature increase equation: ΔT = 1.66 ln (C/C_{0})
View
Equation gives the temperature increase, ΔT (in ^{o}C) when CO_{2} concentration increases from C_{0} to C ppm.
Calculation of temperature increase for doubling CO_{2} content
View
Calculation of the temperature increase for instant doubling the atmospheric CO_{2} content when there is:
 feedback from a change in water vapour opacity due to a change in
temperature.
Evaluation of the temperature increase for instant doubling the atmospheric CO_{2} content when all feedbacks are included.
Global warming and storms View
Why the strongest storms driven by latent heat will become more powerful as a result of Global Warming.
Global warming and extreme weather View
Why a small increase in global surface temperature can mean a large increase in extreme weather.
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List of the most intense tropical cyclones, hurricanes and typhoons
Google+ Conversation with Al Gore about combating climate change
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Fundament Equation for Global Warming

Alternative Form of Fundamental Equation for Global Warming

Example
Let us calculate the temperature increase for instant doubling the atmospheric CO_{2} content when there is no feedback.
The average global surface temperature, T_{s} = 288.15^{o}K (15^{o}C). We calculate ΔT by setting C = 2 C_{0} in Temperature Increase Equation:
ΔT = 1.66 ln (C/C_{0}) = 1.66 X 0.693 = 1.2^{o}C
The increased surface temperature from the instant doubling of CO_{2} content allows an increased water vapour content by maintaining a constant relative humidity. The extra water vapour increases the overall absorption by water vapour itself raising the surface temperature further by about another 1.2^{o}C. The total increase is about 3^{o}C when all feedbacks are included. (More details in full PDF document)

