Many people have requested an analysis of Miskolczi’s theories.
I start with his more recent paper: The Stable Stationary Value of the Earth’s Global Average Atmospheric Planck-Weighted Greenhouse-Gas Optical Thickness, Energy & Environment (2010).
It’s an interesting paper and clearly Miskolczi has put a lot of time and effort into it. I recommend people read the paper for themselves, and the link above provides free access.
The essence of the claim is that the optical thickness of the earth’s atmosphere is a constant – at least over the last 60 years – where water vapor cancels out any change from CO2. So if more CO2 increases the optical thickness, then the optical thickness from water vapor will reduce.
In his paper he make this statement:
Unfortunately no computational results of E_{U}, S_{T}, A, T_{A} and τ_{A} can be found in the literature, and therefore our main purpose is to give realistic estimates of their global mean values, and investigate their dependence on the atmospheric CO2 concentration.
Among the terms noted in this quote, τ_{A} is the optical thickness of the atmosphere.
As we delve into the paper, hopefully the reasons why this value isn’t calculated in any papers will become clear. In fact, the first question people should be asking themselves is this:
If the result is of significant importance why has no one else calculated this parameter before?
There are thousands of papers about radiative transfer, CO2 and water vapor.
Why has no one (apparently) published their calculations of the globally averaged optical thickness of the atmosphere and how it has changed over time?
There is a reason..
What is Optical Thickness?
You can find a more complete explanation of optical thickness in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations, which I definitely recommend reading even though it has many equations. (Actually, because it has many equations..)
Because optical thickness isn’t an obvious parameter, let’s start with a simpler property called transmittance.
Transmittance is the proportion of radiation which is transmitted through a body (in this case, the atmosphere). We will use the letter “t” to refer to it.
t has a value between 0 and 1. Slightly more formally, we can write 0 ≤ t≤ 1.
For t = 1, the body is totally transparent to incident radiation.
For t = 0, the body is totally opaque and absorbs all incident radiation.
For non-scattering atmospheres (note 1), absorptance, a = 1- t, which means that whatever is not absorbed gets transmitted. This is simple enough, and everyone would expect this from the First Law of Thermodynamics.
Now for optical thickness. We will use τ for this parameter. τ is the Greek letter “tau”.
The Beer-Lambert law says that the transmittance of a beam of radiation:
t = exp(-τ)
The “exp” is a mathematical convention for “e to the power of”. So this can alternatively be written as:
t = e^{-τ}
Which means that when τ = 1, t = 0.36; when τ = 2, t = 0.14; and when τ = 10, t = 0.000045.
Optical thickness is tedious to calculate because the properties of each gas vary strongly with wavelength.
In brief, for each molecule at each wavelength, the total optical thickness is equal to the total number of molecules in the path x the absorption coefficient (which is a function of wavelength).
So optical thickness is a very handy parameter. Calculating it does take some work and a pre-requisite is a database of all the spectroscopic values for each molecule – as well as knowing the total amount of each gas in the path we want to calculate.
Absorption and Emission
The atmosphere absorbs and also emits.
Absorption, as we have just seen, is a function of the total amount of each gas (in a path) as well as the properties of each gas.
And, in case it is not obvious, the total radiation absorbed is also a function of the intensity of radiation travelling through the body that we want to calculate. This is because absorption = incident radiation x absorptance.
What about emission?
Emission of radiation is a function of the temperature of the atmosphere, as well as its emissivity, ε. This parameter emissivity is equal to the absorptivity or absorptance, of a body at any given wavelength – or across a range of wavelengths. This is known as Kirchhoff’s law.
Emission = ε . σT^{4} in W/m², where T is the temperature of the atmosphere at that point.
If we want to calculate the radiative transfer through the atmosphere we need both terms.
Here is a simple example of why. Readers who followed the series Understanding Atmospheric Radiation and the “Greenhouse” Effect will remember that I introduced a simple atmosphere with two molecules, pCO2 and pH2O. These had a passing resemblance to the real molecules, but had properties that were much simpler, for the purposes of demonstrating some important aspects of how radiation interacts with the atmosphere.
This following example has three scenarios. Each scenario has the same total amount of water vapor through the atmosphere, but a different profile vs height. These are shown in the graph:
Figure 1
The bottom graph shows the top of atmosphere (TOA) flux from each of the three scenarios.
If we calculated the total transmittance through the atmosphere it would be the same in each scenario (update: correction – see Ken Gregory’s point below). Because the optical thickness is the same. The optical thickness is the same because the total number of pH2O molecules in the path is the same.
Yet the TOA flux is very different.
This is because where the atmosphere emits from is very important in calculations of flux. For example, in the case of the 3rd scenario, the TOA flux is lower because more of the water vapor is at colder temperatures, and less is at hotter temperatures.
From Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations:
dI_{λ}/dτ = I_{λ} – B_{λ}(T) [12]
which is also known as Schwarzschild’s Equation – and is the fundamental description of changes in radiation as it passes through an absorbing (and non-scattering) atmosphere. B_{λ}(T) = the Planck function, which is a function of temperature. And the subscript λ in each term identifies the wavelength dependence of this equation.
For the mathematically minded, it will be clear reviewing the above equation that total optical thickness tells you less than you need. As the location of optical thickness varies, if temperature varies (which it does in the atmosphere) then you can get different results for the same optical thickness.
That is, the simulations above demonstrate what is clear, and easily provable, from the form of the fundamental equation.
This is why papers on total optical thickness of the atmosphere over time are hard to come by. It is of curiosity value only.
What About Methane, Nitrous Oxide and Halocarbons?
The total optical thickness of the atmosphere is not just determined by water vapor and CO2. If the atmosphere has an invariant optical thickness then surely all molecules should be included?
According to WM Collins and his co-authors (2006):
The increased concentrations of CO2, CH4, and N2O between 1750 and 1998 have produced forcings of +1.48, +0.48, and +0.15 W m, respectively [IPCC, 2001]. The introduction of halocarbons in the mid-20th century has contributed an additional +0.34 Wm for a total forcing by WMGHGs of +2.45Wm with a 15% margin of uncertainty.
I’m sure someone with enough determination can find some results for the changes in the radiative forcing from CH4 and N2O between 1950 and 2010. But this at least demonstrates that there is some significant absorption characteristics for other molecules. After all, halocarbons have added a quarter of the longer term CO2 increase in radiative forcing from CO2 (from 1750 to the present day) in just half a century.
So if total optical thickness from CO2 and water vapor has stayed constant over 60 years then surely total optical thickness must have increased?
This is not mentioned in the paper and seems to be a major blow to the not-particularly-useful result calculated.
Update, 31st May: Ken Gregory, a Miskolczi supporter armed with the spreadsheet of calculations, says that minor gases were kept constant. So Part Six demonstrates my basic calculations of optical thickness changes due to CO2 and some minor gases.
Cloudy Thinking
Miskolczi says:
In all calculations of A, T_{A}, t_{A}, and of the radiative flux components, the presence or absence of clouds was ignored; the calculations refer only to the greenhouse gas components of the atmosphere registered in the radiosonde data; we call this the quasi-all-sky protocol. It is assumed, however, that the atmospheric vertical thermal and water vapor structures are implicitly affected by the actual cloud cover, and that the atmosphere is at a stable steady state of cloud cover.
Assumed but not demonstrated.
Clouds have a huge impact on the radiative (and convective) heat transfers in the atmosphere. From Clouds and Water Vapor – Part One:
Clouds reflect solar radiation by 48 W/m² but reduce the outgoing longwave radiation (OLR) by 30 W/m², therefore the average net effect of clouds – over this period at least – is to cool the climate by 18 W/m².
Are they constant?
Here is a snapshot from Vardavas & Taylor (2007):
From Vardavas & Taylor (2007)
Figure 2
Another important point – given the non-linearity of the equations of radiative transfer, even if the cloud cover stayed at a constant global percentage but the geographical distribution changed, the optical thickness of the atmosphere cannot be assumed constant.
Here are some values of cloud emissivity from Hartmann (1994):
From Hartmann (1994)
Figure 3
Just for some perspective, as emissivity reaches 0.8, τ = 1.6; with emissivity = 0.9, τ = 2.3. And Miskolczi calculates the global average optical thickness of the atmosphere – without clouds – at 1.87.
At the end of his paper, Miskolczi concludes:
Apparently, the global average cloud cover must not have a dramatic effect on the global average clear-sky optical thickness..
I can’t understand, from the paper, where this confidence comes from.
Conclusion
There is more in the paper, including some very suspect assumptions about radiative exchange. However, six out of the 19 references in the paper are to Miskolczi himself and the fundamental equations brought up for energy balance (where radiative exchange is referenced) rely on his more lengthy 2007 paper, Greenhouse effect in semi-transparent planetary atmospheres.
I will try to read this paper before commenting on these energy balance equations.
However, the key points are:
- optical thickness of the total atmosphere is not a very useful number
- the useful headline number has to be changes in TOA flux, or radiative forcing, or some value which expresses the overall radiative balance of the climate system (update: see this comment for the correct measure)
- optical thickness calculated as constant over 60 years for CO2 and water vapor appears to prove that total optical thickness is not constant due to increases in other well-mixed “greenhouse” gases
- clouds are not included in the calculation, but surely overwhelm the optical thickness calculations and cannot be assumed to be constant
Other Articles in the Series:
Part Two – Kirchhoff – why Kirchhoff’s law is wrongly invoked, as the author himself later acknowledged, from his 2007 paper
Part Three – Kinetic Energy – why kinetic energy cannot be equated with flux (radiation in W/m²), and how equation 7 is invented out of thin air (with interesting author comment)
Part Four – a minor digression into another error that seems to have crept into the Aa=Ed relationship
Part Five – Equation Soufflé – explaining why the “theory” in the 2007 paper is a complete dog’s breakfast
Part Six – Minor GHG’s – a less important aspect, but demonstrating the change in optical thickness due to the neglected gases N2O, CH4, CFC11 and CFC12.
Further Reading:
New Theory Proves AGW Wrong! – a guide to the steady stream of new “disproofs” of the “greenhouse” effect or of AGW. And why you can usually only be a fan of – at most – one of these theories.
References
The Stable Stationary Value of the Earth’s Global Average Atmospheric Planck-Weighted Greenhouse-Gas Optical Thickness, Miskolczi, Energy & Environment (2010)
Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), Collins et al, JGR (2006)
Radiation and Climate, Vardavas & Taylor, Oxford University Press (2007)
Global Physical Climatology, Hartmann, Academic Press (1994) – reviewed here
Notes
Note 1 – For longwave radiation (>4 μm), scattering is negligible in the atmosphere.
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The Mystery of Tau – Miskolczi
Posted in Atmospheric Physics, Commentary on April 22, 2011| 60 Comments »
Many people have requested an analysis of Miskolczi’s theories.
I start with his more recent paper: The Stable Stationary Value of the Earth’s Global Average Atmospheric Planck-Weighted Greenhouse-Gas Optical Thickness, Energy & Environment (2010).
It’s an interesting paper and clearly Miskolczi has put a lot of time and effort into it. I recommend people read the paper for themselves, and the link above provides free access.
The essence of the claim is that the optical thickness of the earth’s atmosphere is a constant – at least over the last 60 years – where water vapor cancels out any change from CO2. So if more CO2 increases the optical thickness, then the optical thickness from water vapor will reduce.
In his paper he make this statement:
Among the terms noted in this quote, τ_{A} is the optical thickness of the atmosphere.
As we delve into the paper, hopefully the reasons why this value isn’t calculated in any papers will become clear. In fact, the first question people should be asking themselves is this:
There are thousands of papers about radiative transfer, CO2 and water vapor.
Why has no one (apparently) published their calculations of the globally averaged optical thickness of the atmosphere and how it has changed over time?
There is a reason..
What is Optical Thickness?
You can find a more complete explanation of optical thickness in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations, which I definitely recommend reading even though it has many equations. (Actually, because it has many equations..)
Because optical thickness isn’t an obvious parameter, let’s start with a simpler property called transmittance.
Transmittance is the proportion of radiation which is transmitted through a body (in this case, the atmosphere). We will use the letter “t” to refer to it.
t has a value between 0 and 1. Slightly more formally, we can write 0 ≤ t≤ 1.
For t = 1, the body is totally transparent to incident radiation.
For t = 0, the body is totally opaque and absorbs all incident radiation.
For non-scattering atmospheres (note 1), absorptance, a = 1- t, which means that whatever is not absorbed gets transmitted. This is simple enough, and everyone would expect this from the First Law of Thermodynamics.
Now for optical thickness. We will use τ for this parameter. τ is the Greek letter “tau”.
The Beer-Lambert law says that the transmittance of a beam of radiation:
t = exp(-τ)
The “exp” is a mathematical convention for “e to the power of”. So this can alternatively be written as:
t = e^{-τ}
Which means that when τ = 1, t = 0.36; when τ = 2, t = 0.14; and when τ = 10, t = 0.000045.
Optical thickness is tedious to calculate because the properties of each gas vary strongly with wavelength.
So optical thickness is a very handy parameter. Calculating it does take some work and a pre-requisite is a database of all the spectroscopic values for each molecule – as well as knowing the total amount of each gas in the path we want to calculate.
Absorption and Emission
The atmosphere absorbs and also emits.
Absorption, as we have just seen, is a function of the total amount of each gas (in a path) as well as the properties of each gas.
And, in case it is not obvious, the total radiation absorbed is also a function of the intensity of radiation travelling through the body that we want to calculate. This is because absorption = incident radiation x absorptance.
What about emission?
Emission of radiation is a function of the temperature of the atmosphere, as well as its emissivity, ε. This parameter emissivity is equal to the absorptivity or absorptance, of a body at any given wavelength – or across a range of wavelengths. This is known as Kirchhoff’s law.
Emission = ε . σT^{4} in W/m², where T is the temperature of the atmosphere at that point.
If we want to calculate the radiative transfer through the atmosphere we need both terms.
Here is a simple example of why. Readers who followed the series Understanding Atmospheric Radiation and the “Greenhouse” Effect will remember that I introduced a simple atmosphere with two molecules, pCO2 and pH2O. These had a passing resemblance to the real molecules, but had properties that were much simpler, for the purposes of demonstrating some important aspects of how radiation interacts with the atmosphere.
This following example has three scenarios. Each scenario has the same total amount of water vapor through the atmosphere, but a different profile vs height. These are shown in the graph:
Figure 1
The bottom graph shows the top of atmosphere (TOA) flux from each of the three scenarios.
If we calculated the total transmittance through the atmosphere it would be the same in each scenario (update: correction – see Ken Gregory’s point below). Because the optical thickness is the same. The optical thickness is the same because the total number of pH2O molecules in the path is the same.
Yet the TOA flux is very different.
This is because where the atmosphere emits from is very important in calculations of flux. For example, in the case of the 3rd scenario, the TOA flux is lower because more of the water vapor is at colder temperatures, and less is at hotter temperatures.
From Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations:
dI_{λ}/dτ = I_{λ} – B_{λ}(T) [12]
which is also known as Schwarzschild’s Equation – and is the fundamental description of changes in radiation as it passes through an absorbing (and non-scattering) atmosphere. B_{λ}(T) = the Planck function, which is a function of temperature. And the subscript λ in each term identifies the wavelength dependence of this equation.
For the mathematically minded, it will be clear reviewing the above equation that total optical thickness tells you less than you need. As the location of optical thickness varies, if temperature varies (which it does in the atmosphere) then you can get different results for the same optical thickness.
That is, the simulations above demonstrate what is clear, and easily provable, from the form of the fundamental equation.
This is why papers on total optical thickness of the atmosphere over time are hard to come by. It is of curiosity value only.
What About Methane, Nitrous Oxide and Halocarbons?
The total optical thickness of the atmosphere is not just determined by water vapor and CO2. If the atmosphere has an invariant optical thickness then surely all molecules should be included?
According to WM Collins and his co-authors (2006):
I’m sure someone with enough determination can find some results for the changes in the radiative forcing from CH4 and N2O between 1950 and 2010. But this at least demonstrates that there is some significant absorption characteristics for other molecules. After all, halocarbons have added a quarter of the longer term CO2 increase in radiative forcing from CO2 (from 1750 to the present day) in just half a century.
So if total optical thickness from CO2 and water vapor has stayed constant over 60 years then surely total optical thickness must have increased?
This is not mentioned in the paper and seems to be a major blow to the not-particularly-useful result calculated.
Update, 31st May: Ken Gregory, a Miskolczi supporter armed with the spreadsheet of calculations, says that minor gases were kept constant. So Part Six demonstrates my basic calculations of optical thickness changes due to CO2 and some minor gases.
Cloudy Thinking
Miskolczi says:
Assumed but not demonstrated.
Clouds have a huge impact on the radiative (and convective) heat transfers in the atmosphere. From Clouds and Water Vapor – Part One:
Are they constant?
Here is a snapshot from Vardavas & Taylor (2007):
From Vardavas & Taylor (2007)
Figure 2
Another important point – given the non-linearity of the equations of radiative transfer, even if the cloud cover stayed at a constant global percentage but the geographical distribution changed, the optical thickness of the atmosphere cannot be assumed constant.
Here are some values of cloud emissivity from Hartmann (1994):
From Hartmann (1994)
Figure 3
Just for some perspective, as emissivity reaches 0.8, τ = 1.6; with emissivity = 0.9, τ = 2.3. And Miskolczi calculates the global average optical thickness of the atmosphere – without clouds – at 1.87.
At the end of his paper, Miskolczi concludes:
I can’t understand, from the paper, where this confidence comes from.
Conclusion
There is more in the paper, including some very suspect assumptions about radiative exchange. However, six out of the 19 references in the paper are to Miskolczi himself and the fundamental equations brought up for energy balance (where radiative exchange is referenced) rely on his more lengthy 2007 paper, Greenhouse effect in semi-transparent planetary atmospheres.
I will try to read this paper before commenting on these energy balance equations.
However, the key points are:
Other Articles in the Series:
Part Two – Kirchhoff – why Kirchhoff’s law is wrongly invoked, as the author himself later acknowledged, from his 2007 paper
Part Three – Kinetic Energy – why kinetic energy cannot be equated with flux (radiation in W/m²), and how equation 7 is invented out of thin air (with interesting author comment)
Part Four – a minor digression into another error that seems to have crept into the Aa=Ed relationship
Part Five – Equation Soufflé – explaining why the “theory” in the 2007 paper is a complete dog’s breakfast
Part Six – Minor GHG’s – a less important aspect, but demonstrating the change in optical thickness due to the neglected gases N2O, CH4, CFC11 and CFC12.
Further Reading:
New Theory Proves AGW Wrong! – a guide to the steady stream of new “disproofs” of the “greenhouse” effect or of AGW. And why you can usually only be a fan of – at most – one of these theories.
References
The Stable Stationary Value of the Earth’s Global Average Atmospheric Planck-Weighted Greenhouse-Gas Optical Thickness, Miskolczi, Energy & Environment (2010)
Radiative forcing by well-mixed greenhouse gases: Estimates from climate models in the Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report (AR4), Collins et al, JGR (2006)
Radiation and Climate, Vardavas & Taylor, Oxford University Press (2007)
Global Physical Climatology, Hartmann, Academic Press (1994) – reviewed here
Notes
Note 1 – For longwave radiation (>4 μm), scattering is negligible in the atmosphere.
Read Full Post »