May 31 2007
Basic Climate Science Refresher - II
The Earth emits radiation according to the Stefan-Boltzmann law (same as the sun). This says that the power (or energy per area) radiated is proportional to the temperature to the fourth power - σT4. So the total energy emitted is the energy per area times the area. But in this case, we need to use the surface area of the entire Earth - 4πR2. Thus the total energy emitted is 4σT4πR2.
When we set these two values equal, we get S0(1-A)πR2=4σT4πR2. Cancelling out the πR2 on both sides gives us S0(1-A)=4σT4. Since we know S0 and σ and A (about 0.3 for the Earth), we can solve for T. We end up with a value of 254.8 Kelvin (-18.3 C / -1 F). The measured average temperature of the earth is around 15 degrees Celsius. What did we do wrong? We didn’t account for the effect of greenhouse gases.
Greenhouse gases are radiatively inactive in the visible spectrum, and radiatively active in the infrared. The majority of incoming solar radiation is in the visible spectrum. Most of this shortwave radiation passes through the atmosphere and is absorbed by the surface. The earth, like every other object with a temperature greater than absolute zero, radiates. The amount and at what frequency is determined by its temperature. The higher the temperature, the more an object radiates, and at higher frequencies. The earth is a lot cooler than the sun, thus the earth emits its radiation at a lower frequency - in the infrared.
As I said before, greenhouse gases are active in the infrared, which means that the radiation that the earth emits will be absorbed by these gases. Then, because the gases have a temperature above absolute zero, they emit radiation. But, this emited radation is radiated isotropically - meaning in all directions. Thus, for each photon that is absorbed by a greenhouse gas, half of the energy will be sent back towards the surface. So the surface of the earth is heated by the sun and the atmosphere and its temperature is greater than if it was heated by the sun alone.
[Added June 5, 2007]
The striked sentance above makes it sound like the atmosphere re-radiates energy it absorbs. This is incorrect. The atmosphere radiates because it has a temperature above absolute zero.
CO2 vs. Water Vapor
It’s these greenhouse gases which account for less than 1% of the atmosphere that warm it by about 33 C. The most important greenhouse gas is water vapor. But water vaper is not directly controlled by human involvement. The amount of water vapor in the atmosphere is determined by the temperature. The higher the temperature, the more water vapor there will be in the atmosphere. However, if there is more water vapor in the atmosphere, the surface of the Earth will warm due to the greenhouse effect, which will cause there to be even more water vapor in the atmosphere. This is what is called a positive feedback.
On the other hand, CO2 is what is called a forcing. Humans are extracting carbonaceous material from the Earth and burning it for energy. One of the byproducts of combustion is CO2. The CO2 enters the atmosphere, where it stays anywhere from a couple days to hundreds of years.
RealClimate: Water vapour: feedback or forcing? goes into more detail.
Temperature Leads CO2 in Ice Cores
Paraphrasing from What does the lag of CO2 behind temperature in ice cores tell us about global warming?
Studies have shown that at the start of glacial terminations, temperatures start rising about 800 years before CO2 rises. These previous glacial and inter-glacial periods were likely caused by the various wiggles and wobbles in the Earths rotation around the Sun, called the Milankovitch cycle. This leads to ice ages which occur about every 100000 years. However, the fact that temperatures lead CO2 does not mean that CO2 does not cause global warming. Previous warming, from glacial to inter-glacial periods, took around 5000 years. As stated above, the lag between temperature and CO2 is only about 800 years. All this shows is that the CO2 did not cause the first 800 years of warming. Because of the correlation with the Milankovitch cycle, it is likely that the initial change in temperature was caused by changes in Earths orbit. But that does not mean that the remaining 4200 years of warming were not caused by increases in CO2 concentration.
The probable sequence of events at the termination of an ice age may follow something like this. Some currently unknown process causes Antarctica and the surrounding ocean to warm. This causes CO2 concentrations to start rising about 800 years later. This CO2 further warms the whole planet, see the section on greenhouse gases above for details. This leads to even further CO2 release, and further warming. The initial change toward higher temperatures has lead through a series of events which causes the temperature to increase even more. This is what is known as a positive feedback.
Sunspot Reconstruction vs. Observations / Solar Variability
I’ve previously posted on my blog about the Foukal (2002) paper. A Correlation between Neptune Brightness, Earth Temperature and Total Solar Irradiance?
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The panel of interest is (C). We see a reconstructed TSI dating from 1920. Remember the model attempts to reconstruct TSI based upon dark sunspots and bright magnetic plage elements. So as long as these measurements were made, no problem. The problem comes when we look at how the model compares to direct observations, which started in the early 1980s. Below is an image of a TSI composite from Greg Kopp.
From Greg’s TSI Page
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We see that the actual TSI from 1980 onward has oscillated dramatically, but in general has stayed about the same; some may even say it has decreased. Since this (newest) paper was published in 2007, they had access to the latest TSI data, which shows a decrease from 2000-2007. I should point out that the non-smoothed model data does show an increase from 1920-2000, but since there has been no observed increase from 1980-2000 as shown in the direct measurements, there is probably something wrong with the model.
To recap, total solar irradiance has not increased in the last 30 years. If anything, it has decreased. There is a strong 22-year cycle, as evidenced in the TSI and the sunspot number, but this is not correlated with the increase in temperature. At the moment, we are in a weak period of the solar cycle. If solar variations were the cause of climate change on the Earth, we should currently be experiencing a cooling trend.
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4 Responses to “Basic Climate Science Refresher - II”
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“Thus, for each photon that is absorbed by a greenhouse gas, half of the energy will be sent back towards the surface. So the surface of the earth is heated by the sun and the atmosphere and its temperature is greater than if it was heated by the sun alone.”
This statement is not logically correct. The energy emitted by a greenhouse gas is dependent on its emissivity and temperature, not on the amount of energy absorbed. The global energy budget shows that the atmosphere emits more IR radiation than it absorbs. Also, the earth’s surface emits more IR radiation than the back radiation it absorbs. The total radiant energy absorbed at the surface is less than the radiant energy from the sun alone.
Overall, solar radiation tends to heat the earth’s surface and IR radiation tends to cool the atmosphere. Energy is exchanged between the surface and the atmospheric boundary layer by way of conduction and evaporation, the former heating the boundary layer.
The energy accumulating in the atmospheric boundary layer is prevented from mixing through the atmosphere because the total energy per unit mass (enthalpy plus potential energy) increases with altitude. Mixing will bring energy from high altitude to lower altitude.
This conundrum of warming boundary layer and cooling atmosphere was solved by Herbert Riehl and Joanne Malkus in 1958 (Riehl, H and J. Malhus, 1958. The heat balance of the equatorial trough zone. Geophysica). In moist convection latent energy and enthalpy are converted to potential energy in the updrafts while potential energy is converted to enthalpy in the compensating unsaturated surrounding subsidence.
Once the atmospheric lapse rate exceeds the moist adiabatic lapse rate then buoyant moist convection occurs and boundary layer energy is mixed through the troposphere by way of protected deep tropical convection towers.
The global energy balance is achieved when the greenhouse gases in the atmosphere radiate IR to space at about 253-255 W/m2. Averaged over all greenhouse gases this emission layer is at about 5 km (IPCC TAR). That is, the surface temperature must be about 33C warmer than the temperature of the emission layer, or about 15C.
It is the elevation of the emission layer above the earth’s surface and the need for convection and a near moist adiabatic lapse rate in the troposphere that causes the surface temperature to be about 33C warmer than the equilibrium radiation temperature of -18C.
“However, if there is more water vapor in the atmosphere, the surface of the Earth will warm due to the greenhouse effect, which will cause there to be even more water vapor in the atmosphere. This is what is called a positive feedback.”
You omit to mention that energy is necessary to get water vapour into the atmosphere.
The positive forcing of the back IR radiation from CO2 and water vapour must be offset by increased IR emission and increased latent energy exchange with evaporation. Each of the latter requires a rise in surface temperature.
We can accurately calculate the rate of increase in surface IR with temperature. It is about 5 W/m2 per degree C.
Evaporation from water bodies (earth is 70 percent water surface) is often represented by bulk aerodynamic formula of the form C*U*(qs - q),
where C is a drag coefficient, U is mean wind speed, qs is saturated specific humidity at the surface temperature and q is the specific humidity above the surface.
Relative humidity is expected to remain constant with global warming (IPCC) therefore to first order global mean evaporation is related to saturated vapour pressure at the temperature of the earth’s surface. The rate of change of latent energy exchange (evaporation) can be estimated from the clausius clapeyron relationship using data from the global energy budget. At 15C the rate of change of latent energy exchange with temperature is about 5 W/m2.
The radiative forcing (increased back IR radiation) from a doubling of CO2 without water vapour feedback is about 3 W/m2. From the combined effects of increased IR emission and latent energy exchange this direct forcing can be offset by a surface temperature rise of only 0.3C. Although the additional water vapour in the atmosphere at 0.3C increase in temperature will amplify the back IR radiation there will continue to be the powerful damping effect of IR emission and evaporation to constrain the surface temperature rise.
“The probable sequence of events at the termination of an ice age may follow something like this. Some currently unknown process causes Antarctica and the surrounding ocean to warm. This causes CO2 concentrations to start rising about 800 years later. This CO2 further warms the whole planet, see the section on greenhouse gases above for details. This leads to even further CO2 release, and further warming. The initial change toward higher temperatures has lead through a series of events which causes the temperature to increase even more. This is what is known as a positive feedback.”
Don’t be taken in by such wooly conjecture! Ask yourself why did each of the interglacial warming episodes cease at about the same global average temperature?
As the earth warms then evaporation, which increases nearly exponentially with temperature, exerts a stronger damping effect on further temperature rise.
The fact is that there are many unknowns concerning the glacial-interglacial cycles and it is self-delusion and misleading to others to put forward simplistic and probably incorrect explanations.
Regarding the first two comments, this was attempted to be written at a level a 15 year old could understand.
“The energy emitted by a greenhouse gas is dependent on its emissivity and temperature, not on the amount of energy absorbed.” Are you saying that when a gas (greenhouse or otherwise) absorbs radiation that its kinetic energy does not increase?
For the third comment, I already said I wasn’t a paleoclimate expert. I borrowed that sequence of events from RealClimate, as I’m sure they know much more about it than me.