Örjan Hallberg
Hallberg Independent Research
oerjan.hallberg@swipnet.se
Updated 2001-06-06. Comments are appreciated, Örjan
Hallberg
I have added a link to the response to questions regarding the climate change
from the political parties in Sweden. (Summary in Swedish).The global temperature
has been projected for three differnt scenaria of fossil fuel consumption. In
2100 the excess temperature will range from +3,5 to
+6,5 oC based on the min, avg and max scenaria. It may well be even
more, the logarithmic model does not feel very convincing to me. Look at Figure
5b.
Are we doing enough to save this planet?
If you can read Swedish you may want to
read what the political parties
The extraction of oil and other fossil products ends up in carbon dioxide, CO2 that accumulates in the air. Since 1800 around 320 Giga ton of equivalent oil has been used and eventually burned (1). We can also see that the CO2 level has increased over the same time. Figure 1 gives the accumulation of both products over time. As can be seen the shape is almost identical that indicates that there might be a connection.
Figure 1. The accumulated production of fossil fuels and the increase of CO2 ppm-level since 1800.
In a longer perspective we can study the variation of temperature and CO2 ppm level over the last ice-age. Figure 2 shows that the temperature exceeded the reference level (0 deg C) for about 20,000 years. It also shows that the CO2 level increased by about 70 ppm in 10,000 years. This is shown at the ends of the two last ice periods. However, note that the explosive increase of the CO2 level during the last century gives the same increase in only 100 years, i.e. 100 times faster than when a natural warm period starts. The CO2 level is also already much higher than ever has been present for millions of years.
Figure 2. Temperature and CO2 in ppm since the end of the second last ice period including the next 100 years.
Looking back only 1000 years gives a clear picture of the fast increase in CO2 level that we see right now. See Figure 3.
Figure 3. The development of CO2 level in the atmosphere and temperature anomalies over the last 1000 years. The expected CO2 level during the next 100 years is also shown assuming 'business as usual'.
From Figure 1 it is clear that for the last 200 years there has been a simple linear relationship between the accumulation of fossil energy extraction and the CO2 level. The relation can be written as follows:
CO2 = 285 + 1/3,2*[AccOil] ........(1)
Here CO2 is measured in ppm and AccOil is measured in Gton equivalent Coal. This is used to predict the future CO2-level as shown in Figure 4. In reality it might become worse due to nonlinear effects caused by the ocean warming and reduced uptake (possible release) of CO2 by the oceans. Using eq (1) the CO2 level will follow the accumulation of fossile fuels in GtC as predicted by IPCC [2].
Figure 4. The expected CO2-level in the atmosphere as a function of future fossile fuel production. The scattered plot is the global temperature change measured in mC. See also Figures 2 and 3.
Note that in order to stop the increase we need to completely seal the oil towers and stop using coal or natural gas supplies. According to the Swedish Environmental Ministry there is a goal to stay below 550 ppm CO2. Figure 4 indicates then that we have maximum 50 years to completely replace fossil fuels by e.g. solar energy.
I was told that the most likely relationship between temperature increase and CO2 contents in the air would be a logarithmic one. A preliminar modelling against known data arrived at the following expression:
DT = 10,9*log(ppm/280)-0,22 ... (2)
Figure 5 shows the result, that is within the span estimated by IPCC (1,5-6 C). The CO2 level is calculated from eqn (1) based on the min, max and median fossil fuel consumption scenaria by IPCC. However, equation (2) does not convince for high CO2-levels. Even if the atmosphere was 90 At of CO2 as at Venus today, equation (2) would only predict 60C of temperature increase. The temperature at Venus is around 500C and this would be the temperature here as well. A completely different calculation was done to find the best fitting function to respond between increase in CO2 and temperature. This is shown in Figure 5b, unfortunately a bit more pessimistic than what the (unrealistic?) equation (2) predicts in Figure 5 and 6.
Figure 5. Measured and calculated increase in CO2 and the predicted global temperature based on the median estimated fossil fuel consumption.
Figure 5b. A best fit analysis of the relationship between CO2-increase and temperature increase. An increase by 5C is predicted already in 2070 by this model.
Figure 6 gives the projected temperature anomalies based on the three CO2 scenaria shown in Figure 5. The temperatures are calculated according to eqn (2). In year 2100 the global temperature anomaly is estimated to range from 3,5 to 6,5 oC.
Figure 6. Three global temperature forecasts based on the three IPCC scenaria for fossil fuel consumption.
Temperature and consumed carbon
By combining eqns (1) and (2) a simple expression for the temperature increase vs. accumulated fossil fuel consumption is found:
DT = 10,9*log(1+1,116*TtC) - 0,22 ..... (3)
where DT = global temperature increase since 1800
and TtC is the accumulated fossil fuel consumption expressed in Tera-ton of
carbon.
This expression is shown in Figure 7. Since the sea water will increase in area as well as temperature the moisture content in the air will also increase. It has been pointed out (6) that the major factor behind the temperature increase is the increased moist contents in the atmosphere. Without moist the temperature would have been 25C lower than today (7). The effect of today's CO2 is only 3 C (7).
So, if 380 ppm CO2 gives 3 C increase one might expect that 900 ppm would increase the temperature by another 4C increase. The max moisture partial pressure in today's average air temperature of 14C is 12 mm Hg. According to ref (7) the average air temperature at 0 mm Hg would be 14-25 = -11C. An increase in the average air temperature by 4C due to CO2 outlet would increase the max moisture pressure to 16 mm Hg. But this gives a temperature increase of 8C if linearly extrapolated. So, if the moisture content is initially elevated due to the CO2 increase, but then causes a temperature increase due to the new moisture level, we would end up in a thermal run-away.
Figure 7. The expected global temperature increase vs. accumulated fossil fuel consumption accordning to equation (2). This prediction is probably too optimistic. If 0,3 TtC gives 1C of temperature increase then it is not likely that 7TtC only gives 10C, rather 23 C or more.
Look at figure 2. At first glance one might think that the temperature very soon will increase by 50-60 C. The oceans would then release more CO2 and we would end up in a thermal run-away like at Venus. However, the main driving force for the temperature changes during the ice periods is not variations in CO2 levels but small (+/- 1,5 o) tilting of the polar axis of the Earth with respect to a line perpendicular to its orbit [3]. A temperature change of 8 C due to this tilting results in changes in forests and other CO2 sinks that normally change the CO2 level around 80 ppm. The same pattern has been repeated during several ice-periods, see Figure 8.
Figure 8. The variation in CO2 level during the 4 last ice-periods (4). The triangles to the right are the expected level during the next 100 years based on IPCC-data.
IPCC have estimated that the total temperature increase the next 100 years will stay between 1-6C (but be much higher in the arctic regions). Thus, at present, an immediate threat from a thermal run-away may not be realistic. But C Sagan (5) says in his famouse book Cosmos (p 102) that we might end up like Venus (500C, 90 atm CO2) if we do not act carefully. He says that "even a one- or two-degree rise in the global temperature can have catastrophic consequences".
IPCC now talks about 4 or even 6 degrees of temperature rise within 100 years. None of the experts that I have approached could show that a run-away situation is impossible..
It is interesting that both Venus and Mars several billion years ago (around 3) have had atmospheric conditions quite similar to those of the Earth at present, see ref [3]. Those who like to speculate about ancient history might want to take a look at these obviously machine-made spheres found in a 2,8 billion old geological layer in South Africa.
Sweden has assigned an environmental tax of 0:37 SEK per kg CO2 (0.037 USD). In Sweden the CO2-tax is not being funded to cover future environmental costs.
If the energy consumption is not cut down the planet will be badly damaged within 50 years. Estimate the total value of this damage to 50 times the GDP which is in the order of 20 TUSD per year. In total this gives 1000 TUSD. The total energy consumption is equivalent to 8 GT oil equivalents per year or for 50 years 400 GToe. If we distribute the cost for this damage over these oil equivalents we end up in 2.5 USD/kg oe.
1. Japan Energy Handbook, 1999
2. www.ipcc.ch
3. 4. Beatty et al., The New Solar System, ISBN 0-521-64587
4. E Källén, MISU
5. C Sagan, "COSMOS", ISBN 0-394-50294-96.
6. J Nilson, MISU, private communication
7. H Sundqvist, DN, 2000-12-2, A4