'Just-in-Case': How to Think About Uncertainty and Global Warming

TCS Daily ^ | 14 Feb 2007 | Arnold Kling

[spunkets]

JUst using numbers from memory. The Earth's avg temp is 18^oC. You gave a value of 1.2W/m² for the additional absorption due to doubling the CO₂, instead of the 3.7W/m² for a dry atmosphere. I assume the 1.2W/m² is due to absorption outside the band overlap? Then the temp rises 0.22^oC from CO₂. That would result in a 1.01% increase in avg water vapor concentration, and 0.062^oC of cooling, resulting in a net increase of 0.16^oC. What temp increase would the 1.01% increase in water, plus the overlap increase in CO₂ give?

[ancient_geezer]

The eq I = A ln(C/C_o) Represents an increase in absorbance over some fixed concentration C_o. The factor A, must be evaluated at some fixed P_o and C_o. If either of those change, the relation no longer holds.

Ahem, interesting that for logarithmic relationships, my spread sheet and slide rule demonstrates otherwise.

The change is a fixed amount for a given percentage change in concentration no matter what initial C_o one may select, the constant is a never mind where change in forcing is concerned, necessary only for when one needs to express the total cumulative change from 0 concentration, which is not what the functions convey, nor can they, as 0 concentration is undefined in a logarithmic relation as well as when chosen as a denominator in a fraction.

On a logarithmic curve, it doesn't matter what I choose as my C_o as long as it is not 0 and the log relationship holds in the range I wish to evaluate. The increment in the result remains fixed for a percentage change in C. That is an inherent characteristic of the log function and why it is the basis of the slide rule.

The change from any C_o remains constant for a doubling or indeed for any percentage one chooses to evaluate. It doesn't matter what your initial C_o is as long as the selected value of Co is such that it is within the empirical range of values for which the logarithmic relation holds.

[ancient_geezer]

JUst using numbers from memory. The Earth's avg temp is 18^oC.

Actually, the estimates are closer to 288K-273. i.e 15^oC give or take half a degree for global average surface temperature circa 1990. But I digress.

You gave a value of 1.2W/m² for the additional absorption due to doubling the CO₂, instead of the 3.7W/m² for a dry atmosphere. I assume the 1.2W/m² is due to absorption outside the band overlap? Then the temp rises 0.22^oC from CO₂.

Correct.

That would result in a 1.01% increase in avg water vapor concentration, and 0.062^oC of cooling, resulting in a net increase of 0.16^oC.

Possibly, assuming clear sky and that clouds and precipitation do not change in response to the change in atmospheric conditions.( The other and greatest uncertainty when attempting to model climate change in response to anything.)

What temp increase would the 1.01% increase in water, plus the overlap increase in CO₂ give?

Assuming that increase, the approximate increase in absorption due to a 1.01% increase in water vapor in the atmosphere would be in the ball park of 0.25 w/m² if you use 1 w/m² absorbed per 1 mm increase in total column water vapor [http://www1.cira.colostate.edu/Climate/wvre/wvre.HTM], given that total column water vapor (aka precipitatble water vapor) is about 24.5 mm at present http://isccp.giss.nasa.gov/products/browseatmos.html.

 

Looks like about an additional 0.05^oC give or take a bunch for a 1.01% increase in water vapor content of the atmosphere.

[ancient_geezer]

P.S. to answer your question, the net with water vapor absorption, using your figure for cooling, the net works out to be +0.207K change in temperature at the surface give or take the accuracy of the CIRA & ISCCP empirical atmospheric water vapor studies.

[cogitator]

This further suggests that it is temperature that is driving CO2 concentrations instead of CO2 concentrations driving temperature. If it were CO2 concentrations driving temperatures, there should not be an oscillation of the CO2 concentrations in such a cyclical fashion.

The oscillations are due to seasonal uptake of CO2 by northern deciduous forests.

[cogitator]

Through the use of very precise laboratory instruments taking millions of readings over many years and analyzing them with statistics scientists can barely detect that human CO2 generation exists.

That's incorrect. The use of very precise instruments and observations of the change in both the 14C/12C ratio and the 13C/12C ratio (in seawater and tree rings and carbonate sediments and ice cores) indicate that the increase in atmospheric CO2 concentrations since the mid-1800s is due primarily to fossil fuel combustion for energy production.