vanesch said:
This is food for thinking. How does this then apply to something like DESERTEC ?
Clearly, the CSP plants will have a much darker color than the original desert ?
Yes, changes and landcover and changes in vegetation have a substantial effect, by altering albedo.
However, there seems something to be missing in the whole balance.
The Earth receives about 176 PW from the sun, and the potential unwanted greenhouse effect comes from a drive of the order of a few watts per square meter of Earth surface, which corresponds to about 1% of the average solar influx if I'm not mistaking.
Sounds about right. I tend to think in terms of values per square meter. The total solar input is about 340 W/m
2. 30% or so is reflected, and so Earth absorbs roughly 240 W/m
2. Some of that is absorbed by cloud and the atmosphere; we get roughly 184 W/m
2 at the surface; of which some more is reflected to give approx 160 W/m
2 absorbed at the surface, on average.
(Numbers from Trenberth and Keihl, cited and illustrated in [thread=307685]msg #1[/thread] of "Estimating the impact of CO2 on global mean temperature".)
Doubling of CO2 would give an additional 3.7 W/m
2; this works out to about 2% of the solar flux seen at the surface where it could be reflected by surface cover. Actual CO2 increases from human activity are less than a doubling, so far. Your estimate seems a good guide to me.
Now, humanity as a whole consumes about 16 TW of technical energy (mainly fossil fuels), which is less than 1/10000 of the solar power, while the potentially problematic greenhouse effect is rather of the order of 1 % so 100 times more. In other words, the extra "heating power" due to the greenhouse effect that we think will give us trouble, is of the order of 1.7 PW or something (1% of the total solar power we receive) - we're talking orders of magnitude.
Yes indeed. The impact of actual direct energy production is a drop in the bucket. However, reducing your energy consumption has a much stronger impact on the Earth's energy balance indirectly. Most of our energy for power is from fossil fuels; and so when you consume less energy, you reduce the greenhouse impact. That is how energy use makes an impact, if you feel so inclined.
There's another reason why heat from consumed energy is not so important. That gives you a certain energy per unit CO2. But once the CO2 is in the atmosphere, it gives a certain power per unit CO2 of continuous additional heating.
I said I would try my own numbers. And, by the way, Chu appears to have been referring to an upcoming publication by other scientists; not his own calculations directly. The paper is not yet available. When it is, we can compare our own estimates with their methods.
Here are my numbers:
Heating effect of one ton of carbon dioxide
The atmosphere weighs about 10 tons per square meter. (This is air pressure)
The atomic weight of air averages out at about 29, carbon dioxide averages out at about 44. There's about 385 ppm(v) of carbon dioxide. Carbon dioxide therefore weighs in at about 10 * 44 / 29 * 385 * 10
-6 = 5.84 kilograms, per square meter.
Surface area of the Earth is about 5.15 * 10
14 square meters.
The extra energy feeding to the surface from additional carbon dioxide is a logarithmic relation; you get 3.7 W/m
2 per doubling. The rate at which this increases from increasing CO2 levels is given by a derivative. Let S be the surface area, and C be the total tonnage of carbon dioxide in the atmosphere. Let P be the difference in energy by adding an additional tonnage D. The derivative dP/dD, at D=0 for the present, gives the rate at which available power increases with additional CO2. We have
\begin{align*}<br />
P & = 3.7 S \log_2 \left( \frac{C+D}{C} \right) \\<br />
\frac{dP}{dD} & = \frac{3.7 S}{\log_e(2) (C+D)} \\<br />
C & = 5.84 \times 10^{-3} \times S \\<br />
\frac{dP}{dD}_{[D=0]} & = \frac{3.7}{0.693 \times 5.84 \times 10^{-3}} \approx 914 W<br />
\end{align*}
That is; one ton of CO2 in the air is about an additional 914 W of heating; almost a kiloWatt.
To compare with how much energy you actually get to use from burning fuels; numbers vary depending on the fuel and application. For example, using coal for power generation, you get a bit less than 1 kilogram of CO2 for about 1 kWhr of generated power.
Hence, 1 ton of CO2 is emitted to get enough energy to power a 914 W heater about 1000 hours, or around 42 days.
There's another wrinkle here. Not all emissions remain in the atmosphere. About half gets flushed into other reservoirs, especially the ocean. The trend of increase in atmospheric CO2 is roughly half the rate of emissions.
The effect of painting a roof
Moving a roof from an albedo of 0.2 to 0.7 seems entirely feasible. We have about 184 W/m
2 available to be reflected. Reflect half of that from a 100 m
2 roof, and you are saving power at a rate of 9200 W. That should offset about 10 tons of CO2.
These numbers are annual global averages. You would of course reflect nothing at night, and much more in the day. But the global annual average works out as calculated.
Now looking at the reference given by Ivan Seeking back in [post=2292644]msg #19[/post], I see that the study by Akbari et al, apparently quoted by Professor Chu, speaks of retrofitting a roof to give at least 0.4 extra albedo, with 100m
2 of roof off-setting about 10 tons of CO2. The calculations will, I suppose, be available when the paper comes out soon.
But in the meantime, their estimate fits well with the technique I have used... except that I used CO2 actually in the atmosphere, rather than CO2 emitted. 10 tons in the atmosphere results from about 20 tons emitted.
We'd need to reflect back about 100 times more energy than we are consuming. We'd need to paint an area white that is about 100 times bigger than the solar farm that would power humanity.
I don't think we really care very much about the energy being consumed itself. It doesn't make much difference to Earth's energy balance. What makes more difference is the changes in the impact of the Sun's energy as the composition of the atmosphere changes.
Note that in Professor Chu's comparison, he compares a certain area of reflective surface with cars being used for a certain period of time. That is; a reflective surface gives you a certain wattage of reflected power, continuously. Consuming fuel gives you a certain fixed amount of energy. The emitted CO2 gives you a certain wattage of absorbed heat, which continues to have its impact year upon year long after you've finished with the energy it produced.
Cheers -- sylas