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 CO2 flux density (F) at concentration C in the current atmosphere using the fundamental equation:
F = 5.35 ln C.
CO2 concentration reached 400 ppm on 11th May 2013 and therefore,
ΔF = F = 32.05 W/m2. The surface temperature, Ts = 288.15oK (15oC) and from the equation above we have
ΔT = 0.31 ΔF and therefore,
ΔT = 0.31 X 32.05 = 10oC

Water vapour adds a further 75 W/m2 giving total ΔF = 107.05 W/m2. Surface temperature increase ΔT = 0.31 X 107.05 = 33oC. That is, CO2 and water vapour increase the surface temperature of the Earth by 33oC. Greenhouse gases, including CO2 and water vapour, keep the surface temperature about 33oC warmer than it would otherwise be.

Dangerous warming

The Earth is absorbing 0.5 Watts/m2, more than it is radiating to space. As we add more CO2 to the atmosphere this absorption increases. If we multiply this rate by the surface area of the Earth (5.100656 X 1014 m2) we find that the Earth is accumulating heat at a rate of 2.6 x 1014 Watts (or Joules per sec). Given the Hiroshima atomic bomb yielded an explosive energy of 6.3 x 1013 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 CO2 in 2013 so the rate of heating increases each and every day.

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Equation for Global Warming

Derivation and Application

Amazing carbon dioxide View

Why a small increase in carbon dioxide (CO2) 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/C0) View

Equation gives the increase in heat flux density, ΔF (in Watts/m2) when CO2
concentration increases from C0 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/C0)

  • Calculation of CO2 flux density and comparison with the other non-condensing greenhouse gases that maintain a temperature structure for the atmosphere.

Derivation of temperature increase equation: ΔT = 1.66 ln (C/C0) View

Equation gives the temperature increase, ΔT (in oC) when CO2 concentration increases from C0 to C ppm.

Calculation of temperature increase for doubling CO2 content View

Calculation of the temperature increase for instant doubling the atmospheric
CO2 content when there is:

  • no feedback; and

  • feedback from a change in water vapour opacity due to a change in
    temperature.

Evaluation of the temperature increase for instant doubling the atmospheric
CO2 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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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 CO2 content when there is no feedback.

The average global surface temperature, Ts = 288.15oK (15oC). We calculate ΔT by setting C = 2 C0 in Temperature Increase Equation: ΔT = 1.66 ln (C/C0) = 1.66 X 0.693 = 1.2oC

The increased surface temperature from the instant doubling of CO2 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 1.2oC. The total increase is about 3oC when all feedbacks are included. (More details in full PDF document)

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