The Sixth 3-km Layer

The following graph shows the absorption of long-wave radiation by the sixth 3-km layer of the Earth's atmosphere, from altitude 15 km to 18 km. This line is the same as the 15-km line in our Earth's Atmosphere post. The absorption is typical of a clear day in April, at latitude 30° North. Water vapor content is only 1 ppm, which is one tenth thousandth the concentration in the surface layer. But CO2 concentration is 330 ppm, which is the same as in the surface layer. Air pressure is 220 mbar, which is 22% of the pressure in the surface layer. What is striking about the sixth layer is that the temperature is 220 K, or −53°C, which is the same as in the fifth layer.



In the sixth layer, absorption by water vapor is nowhere more than 5%. But absorption by CO2 remains strong. As before, we say our 3-km layer is opaque at a particular wavelength when it absorbs more than 63% of that wavelength, and is transparent otherwise. The sixth 3-km layer is opaque from 14.3 to 15.7 μm and transparent otherwise. The fifth layer, immediately below, is opaque to 14.2 to 15.8 μm. It radiates in these wavelengths also. The sixth layer absorbs 90% of the heat radiated upwards by the fifth layer, but the remaining 10% will pass out into space.

The fifth and sixth layers are at the same temperature. We did not make up the temperatures, pressures, and concentrations we use in our 3-km atmospheric layers. We obtained them from actual measurements of the Earth's atmosphere.

We have talked at length about the tropopause that exists at the top of the convection cycle in an atmospheric greenhouse. In our simple examples, the tropopause marks the top of the convection cycle, and occurs when the atmosphere above becomes so thin as to allow heat to radiate directly into space. The Earth's atmosphere is not so simple as in our examples. Above 12 km, the Earth's atmosphere is transparent to most long-wave radiation, but remains opaque in the narrow band that is absorbed by CO2. At a high enough altitude, this CO2 will become thin enough that it becomes transparent. But the tropopause of the Earth's atmosphere appears to occur at a lower altitude. It occurs when the atmosphere is transparent to over 90% of long-wave radiation.

In later posts, we will see how absorption by ozone in the stratosphere effects our greenhouse convection cycle. In the meantime, we will accept that there is very little change in temperature from altitude 12 km to 18 km, and therefore these altitudes mark the top of the Earth's greenhouse convection cycle.

First Differences

Over at Climate Audit, Hu McCulloch as a guest post The First Differences Method that describes a simple way to calculate the global surface trend from station data. This method turns out to be same as the Integrated Derivative Method we describe in our Climate Analysis essay. I said as much in the comments of Hu's post, and pointed to our Continuous Stations plot, which we generated with our Integrated Derivative Method.

The Fifth 3-km Layer

The following graph shows the absorption of long-wave radiation by the fifth 3-km layer of the Earth's atmosphere, from altitude 12 km to 15 km. This line is the same as the 12-km line in our Earth's Atmosphere post. The absorption is typical of a clear day in April, at latitude 30° North. Water vapor content is 10 ppm, which is one tenth the concentration present in the fourth 3-km layer, just below. Air pressure is 300 mbar (that's 30% of the pressure at sea level), temperature is 220 K (that's −53°C), and CO2 concentration is still 330 ppm.



As before, we say our 3-km layer is transparent at a particular wavelength when it absorbs less than 63% of that wavelength, and opaque otherwise. The fifth 3-km layer is transparent from 5.0 to 14.2 μm and from 15.8 to 30 μm.

Between the fourth and fifth layer of the Earth's atmosphere, water vapor concentration drops from 100 ppm to 10 ppm. Absorption by water vapor almost disappears. So far as our transparent-opaque simplification is concerned, the absorption by water vapor does indeed disappear. The atmosphere becomes transparent to all long-wave radiation except for 14.2 to 15.8 μm. These wavelengths are absorbed by CO2. Unlike water vapor concentration, CO2 concentration remains constant as we ascend from 0 km to 12 km.

The concentration of C02 may be constant, but the amount of CO2 in each cubic meter of air is still decreasing. The density of the air decreases as we ascend. Thus the absorption by CO2 in the fifth layer is less intense than in the fourth layer. The CO2 in the fourth 3-km layer absorbs radiation from 14.1 to 15.9 μm. By radiative symmetry, these are the same wavelengths that the fourth layer itself radiates up to the fifth 3-km layer. Of this radiation, only the narrow ranges 14.1 to 14.2 μm and 15.8 to 15.9 μm will pass through the fifth layer and out into space. The remaining 90% will be absorbed by CO2 in the fifth layer.

The Fourth 3-km Layer

The following graph shows the absorption of long-wave radiation by the fourth 3-km layer of the Earth's atmosphere, from altitude 9 km to 12 km. This line is the same as the 9-km line in our Earth's Atmosphere post. The absorption is typical of a clear day in April, at latitude 30° North. Water vapor content is only 100 ppm (that's 0.01%), which is one tenth the concentration present in the third 3-km layer, just below. Air pressure is 410 mbar and temperature is 230 K (that's −43°C). We have CO2 present in 330 ppm, just as in the earlier layers.



As before, we simplify our analysis of the absorption spectrum by saying that our 3-km layer is transparent when it absorbs less than 63% of a wavelength and opaque otherwise. The fourth 3-km layer is transparent from 5.0 to 14.1 μm, with the exception of a couple of narrow bands around 6 μm which we will ignore for the sake of simplicity. The fourth layer is again transparent from 15.9 to roughly 28 μm.

The biggest change between the third and fourth layers is the new transparency from 5.4 to 7.3 μm. In the third 3-km layer, water vapor was still absorbing at these wavelengths, but now the water vapor is so sparse that it becomes transparent. Radiation by water vapor in the third 3-km layer at these wavelengths will pass through the fourth and higher layers, and so out into space. We also see an end to the absorption by water vapor for the range 23 to 28 μm.

Another thing that is striking about the fourth 3-km layer is how clearly the absorption by CO2 stands out and remains strong. Let us apply our opaque-transparent simplification to the absorption of the third and fourth layers to estimate how CO2 affects radiation into space by the third 3-km layer. In the third layer, CO2 was opaque from 13.8 to 16.2 μm. In this layer it is opaque from 14.1 to 15.9 μm.

To the first approximation (we split the atmosphere into layers and we assume the atmosphere is either opaque or transparent but never half-way between), 80% of the upward-going radiation emitted by the CO2 in the third layer will be absorbed by the CO2 in the fourth layer, and 100% of the downward-going radiation emitted by the CO2 in the fourth layer will be absorbed by the CO2 in the third layer.

This Time It's Different

In The Right and the Climate, an opinion piece for the New York Times, Ross Douthat discusses the abandonment of cap-and-trade legislation by the US senate. He argues that Democrats must share the blame for the failure of cap-and-trade because they have exhausted the population's patience for doomsday stories. "The Seventies were a great decade for apocalyptic enthusiasms, and none was more potent than the fear that human population growth had outstripped the earth’s carrying capacity," he says. "The catastrophes never materialized, and global living standards soared." But the global warming doomsday story is different, Douthat says, because, "History, however, rarely repeats itself exactly — and conservatives who treat global warming as just another scare story are almost certainly mistaken."

People like Paul Ehrlich, who predicted global famine, and Rachel Carson, who claimed that DDT was killing humans, both believed in what they were saying. It turns out that they were wrong in their most famous claims, but they were doing their best to understand the dangers presented by lower infant mortality and widespread use of new chemicals. They believed in their cause and they believed in what they told us.

When Douthat says, "the evidence that carbon emissions are altering the planet’s ecology is too convincing to ignore," he seems to think that the evidence for global famine and chemical poisoning were unconvincing at the time that Ehrlich and Carson made their claims. But that's not the case. The evidence was convincing. A lot of people were convinced, including the US government under John Kennedy. But "convincing" is not the same as "correct". It turns out that their arguments were convincing but not correct.

Douthat is an example of the many well-educated people who have chosen to believe in anthropogenic global warming despite the history of environmental scare-mongering. The internet bubble was caused by people saying "this time it's different: revenue counts, not profit." The housing bubble was caused by people saying, "this time it's different: prices will never go down." The anthropomorphic global warming bubble has been caused by people saying, "this time it's different: the evidence is too compelling."

Here's my prediction: this time it's not different.

The Third 3-km Layer

The following graph shows the absorption of long-wave radiation by the third 3-km layer of the Earth's atmosphere, from altitude 6 km to 9 km. The graph is typical of a clear day in April, at latitude 30° North. Water vapor content is 1,000 ppm (that's 0.1%), CO2 is 330 ppm, air pressure is 550 mbar, and air temperature is 250 K (that's −23°C). This line is the same as the 6-km line in our Earth's Atmosphere post.



As before, we say our 3-km layer is transparent at a particular wavelength when it absorbs less than 63% of that wavelength. The third 3-km layer is transparent from 5.0 to 5.4 μm, 7.3 to 13.8 μm, and 16.3 to 23.1 μm.

The transparency in the range 16.3 to 23.1 μm is due to the drop in water vapor concentration and pressure that occurs as we ascend through the atmosphere. Absorption in this band is due mostly to water vapor dimers instead of bonds within the water molecule. Absorption by dimers is proportional to the square of the pressure. Continued absorption in 5.4 to 7.3 μm is due to bonds within water vapor molecules, and does not drop with pressure as quickly as absorption by dimers. Continued absorption in the range 13.8 to 16.3 μm range is mostly due to CO2.