Estimating the impact of CO2 on global mean temperature

chriscolose

I think the Hansen et al number of 0.85 W m^-2 was based on the year 2005 relative to some pre-industrial baseline, not a long-term value.

skypunter

Pardon me if this is a stupid question.
Does this formula take into account the logarithmic reduction in the effect of additional CO2 in the atmosphere?
For example, it takes a doubling to increase temperature a certain amount, but it takes another doubling of the new base to increase temperature the same amount as the first doubling. That is logarithmic, correct?
This simple formula does not appear to have a logaritmic component, and that makes me skeptical.

skypunter

Here is another stupid question.
Why are CO2 emissions referred to as "carbon" emissions, when the chemical contains more oxygen atoms than carbon. Shouldn't CO2 emissions be referred to as "Oxygen" emissions?

sylas

Three replies in one here; to chris and skypunter.

The value was based on a model; and even in the 2005 paper it is apparent that the model value is greater than what is obtained from ocean data. A later lecture by Hansen uses smaller values for model based estimate, and clearly distinguishes the ocean data based estimates. The estimates in the 2005 paper were based on the decade 1993-2003. Here is the content of a chart in a lecture he gave earlier this year.

Chart 14:

Modeled Imbalance: +0.75 +/- 0.25 W/m²
Ocean Data Suggest: +0.5 +/- 0.25 W/m²

Now, the ultimate question: can we stabilize climate? We would need to restore the planet’s energy balance. The underlying imbalance (averaging over short-term fluctuations) is probably close to 0.5 W/m².

—Air Pollutant Climate Forcings within the Big Climate Picture, Talk given by J. Hansen at the Climate Change Congress, “Global Risks, Challenges & Decisions”, Copenhagen, Denmark, March 11, 2009

This is not an "anomaly" in the sense that it is measured with respect to a baseline of any kind. It is an absolute value for a total energy flux. The flux will vary from year to year, so you can certainly look for averages over a time span. The very long term average is effectively zero, because there's no significant source of energy in the ocean; it is almost all ultimate a redistribution of energy from the Sun.

I discuss this in more detail in msg #31 of thread "Ocean Heat Storage". In my opinion, this is a quantity where we are likely to get better estimates in time. I've stuck my neck out in that post to suggest that something a bit less than 0.5 is probable; but that's just my guess. 0.5 works for back of the envelope approximations.

The answer to this is yes and no. You are quite right that it is not consistent with the logarithmic relation in the sense that you couldn't use this number over a very wide range of concentrations. For example, if you calculate this value again in a condition of substantially greater concentrations, you'd get a smaller value, for precisely the reason you identify.

However it is consistent in the sense that the underlying mathematical models used to calculate the number do indeed have this logarithmic relationship, and the number given works for estimating impacts in the present. Current CO2 values are approaching 400ppm. This number is a guide for the effects emissions on temperature in this case. There are substantial uncertainties in the number (the range is 1.0 to 2.1 at the 5th and 95th percentiles) and the consequences of the logarithmic relation are not particularly significant in this range.

Here is figure 2 from Allen et al (2009). What we are looking at here is temperature on the vertical axis, being the peak in warming over a pre-industrial average; and total carbon emissions on the horizontal axis. Currently we are at a bit over 0.4 trillion tons. The white crosses are best fit values, where each cross is a difference scenario. The grey shading represents a likelihood distribution.

You can see the logarithmic relation pretty clearly in how the white crosses lie. If you go over to 3 or 4 trillion tons, then the effect is clearly dropping off, as you should expect from the logarithmic relation of atmospheric carbon to temperature. But for total emissions of up to 1 trillion tons (basically emit in the future a bit more than what we've emitted since the start of the industrial revolution), the value proposed works well. It's not bad over higher values up to 1.5 or (yeesh) 2 trillion.

Note that this is only looking at carbon dioxide effects. This is one of the largest factors, but there are many other significant anthropogenic factors involved with industrial emissions as well. This is also noted in the papers cited.

That's a point well worth emphasizing when looking at numbers. Numbers that get thrown around are sometimes for carbon, sometimes for CO₂, sometimes for mass and sometimes for volume. The conversions are not hard, but I've tripped up before this by mixing up the actual quantities being used in some report.

We don't refer to oxygen emissions because the oxygen involved comes from the atmosphere anyway. Burning of carbon based fuels takes oxygen out of the air, and carbon out of the fuel, and returns CO2 to the air.

It's useful to focus on the carbon, because what matters is the carbon content of the various fuels we use. Also, the Earth's carbon cycle involves various chemical reactions where carbon moves in and out of different compounds. The one common factor is the carbon; and so we speak of the carbon cycle and the carbon content of various reservoirs, without worrying about whether the carbon is there as CO₂, or (C₆H₁₀O₅)_n (cellulose, in wood), or H₂CO₃ (carbonic acid, in the ocean), or any number of other forms.

Cheers -- sylas

skypunter

Such as the press.