Global Warming Theory

[dtotire]

Arrhenius developed a theory to explain the ice ages, and first speculated that changes in the levels of carbon dioxide in the atmosphere could substantially alter the surface temperature through the greenhouse effect.<3> He was influenced by the work of others, including Joseph Fourier. Arrhenius used the infrared observations of the moon by Frank Washington Very and Samuel Pierpont Langley at the Allegheny Observatory in Pittsburgh to calculate the absorption of CO2 and water vapour. Using 'Stefan's law' (better known as the Stefan Boltzmann law), he formulated his greenhouse law. In its original form, Arrhenius' greenhouse law reads as follows:

if the quantity of carbonic acid increases in geometric progression, the augmentation of the temperature will increase nearly in arithmetic progression.

This simplified expression is still used today:

ΔF = α ln(C/C0)
Arrhenius estimated that halving of CO2 would decrease temperatures by 4 - 5 °C (Celsius) and a doubling of CO2 would cause a temperature rise of 5 - 6 °C<4>. In his 1906 publication, Arrhenius adjusted the value downwards to 1.6 °C (including water vapour feedback: 2.1 °C). Recent (2007) estimates from IPCC say this value (the Climate sensitivity) is likely to be between 2 and 4.5 °C. Arrhenius expected CO2 levels to rise at a rate given by emissions in his time. Since then, industrial carbon dioxide levels have risen at a much faster rate: Arrhenius expected CO2 doubling to take about 3000 years; it is now estimated in most scenarios to take about a century



From the values given, can anyone come up with a approximate value for the constant alpha? The CO2 level at the time was 280 ppm. The temperature should also be the absolute temperature, i.e. F+460, or C+259. It would be an interesting exercise for a math or physics major. The approximate world temperature at the time was around 10 deg. C. (or 50 deg. F.)

[kestrel91316]

1. I suffered through ONE physics class back in 1978, and NOBODY is gonna

make me study that shit again. Ever. It takes the hardest parts of math and chemistry and throws them together.

Get. It. Away.

:rofl:

[joshcryer]

2. Link to easy to understand lectures about atmospheric (greenhouse) modelling:

http://understandingtheforecast.org/lectures.html

[timeforpeace]

3. The British govt announced a three year review of all climate data, checking the math as it were.

http://www.timesonline.co.uk/tol/news/environment/article6945445.ece

[muriel_volestrangler]

4. No need for an absolute temperature; but what is 'F'?

If 'F' is a temperature, then you're working out a change in it (the delta symbol), so you don't need to consider absolute temperatures. However, temperature is normally represented by 'T' in equations; so 'F' may be something else - eg Forcing; see this Wikipedia article http://en.wikipedia.org/wiki/Radiative_forcing , which includes

ΔT = λ ΔF

Since that's a linear relationship, we can also say

ΔT = λα ln(C/C0)

and then say:

λα = ΔT / ln(C/C0)

and for the case of doubling CO2,

λα = ΔT / ln(2)
So for Arrhenius' estimate of 2.1°C,

λα = 2.1 / ln(2) = 3°C

and the lower and upper limits for the IPCC's 2007 values

λα = 2 / ln(2) = 2.9°C

λα = 4.5 / ln(2) = 6.5°C

[dtotire]

5. Interesting. Bookmarked it. Tnx. n/t

[izquierdista]

6. Free Energy

It's an equilibrium equation relating the change in free energy to the logarithm of the concentrations (or activities).