A long time ago I started writing this article. I haven’t yet finished it.
I realized that trying to write it was difficult because the audience criticism was so diverse. Come to me you huddled masses.. This paper, so simple in concept, has become somehow the draw card for “everyone against AGW”. The reasons why are not clear, since the paper is nothing to do with that.
As I review the “critiques” around the blogosphere, I don’t find any consistent objection. That makes it very hard to write about.
So, the reason for posting a half-finished article is for readers to say what they don’t agree with and maybe – if there is a consistent message/question – I will finish the article, or maybe answer the questions here. If readers think that the ideas in the paper somehow violate the first or second law of thermodynamics, please see note 1 and comment in those referenced articles. Not here.
==== part written article ===
In 1997, J. T. Kiehl and Kevin Trenberth’s paper was published, Earth’s Annual Global Mean Energy Budget. (Referred to as KT97 for the rest of this article).
For some reason it has become a very unpopular paper, widely criticized, and apparently viewed as “the AGW paper”.
This is strange as it is a paper which says nothing about AGW, or even possible pre-feedback temperature changes from increases in the inappropriately-named “greenhouse” gases.
KT97 is a paper which attempts to quantify the global average numbers for energy fluxes at the surface and the top of atmosphere. And to quantify the uncertainty in these values.
Of course, many people criticizing the paper believe the values violates the first or second law of thermodynamics. I won’t comment in the main article on the basic thermodynamics laws – for this, check out the links in note 1.
In this article I will try and explain the paper a little. There are many updates from various researchers to the data in KT97, including Trenberth & Kiehl themselves (Trenberth, Fasullo and Kiehl 2009), with later and more accurate figures.
We are looking at this earlier paper because it has somehow become such a focus of attention.
Most people have seen the energy budget diagram as it appears in the IPCC TAR report (2001), but here it is reproduced for reference:
From Kiehl & Trenberth (1997)
History and Utility
Many people have suggested that the KT97 energy budget is some “new invention of climate science”. And at the other end of the spectrum at least one commenter I read was angered by the fact that KT97 had somehow claimed this idea for themselves when many earlier attempts had been made long before KT97.
The paper states:
There is a long history of attempts to construct a global annual mean surface–atmosphere energy budget for the earth. The first such budget was provided by Dines (1917).
Compared with “imagining stuff”, reading a paper is occasionally helpful. KT97 is simply updating the field with the latest data and more analysis.
What is an energy budget?
It is an attempt to identify the relative and absolute values of all of the heat transfer components in the system under consideration. In the case of the earth’s energy budget, the main areas of interest are the surface and the “top of atmosphere”.
Why is this useful?
Well, it won’t tell you the likely temperature in Phoenix next month, whether it will rain more next year, or whether the sea level will change in 100 years.. but it helps us understand the relative importance of the different heat transfer mechanisms in the climate, and the areas and magnitude of uncertainty.
For example, the % of reflected solar radiation is now known to be quite close to 30%. That equates to around 103 W/m² of solar radiation (see note 2) that is not absorbed by the climate system. Compared with the emission of radiation from the earth’s climate system into space – 239 W/m² – this is significant. So we might ask – how much does this reflected % change? How much has it changed in the past? See The Earth’s Energy Budget – Part Four – Albedo.
In a similar way, the measurements of absorbed solar radiation and emitted thermal radiation into space are of great interest – do they balance? Is the climate system warming or cooling? How much uncertainty do we have about these measurements.
The subject of the earth’s energy budget tries to address these kind of questions and therefore it is a very useful analysis.
However, it is just one tiny piece of the jigsaw puzzle called climate.
Uncertainty
It might surprise many people that KT97 also say:
Despite these important improvements in our understanding, a number of key terms in the energy budget remain uncertain, in particular, the net absorbed shortwave and longwave surface fluxes.
And in their conclusion:
The purpose of this paper is not so much to present definitive values, but to discuss how they were obtained and give some sense of the uncertainties and issues in determining the numbers.
It’s true. There are uncertainties and measurement difficulties. Amazing that they would actually say that. Probably didn’t think people would read the paper..
AGW – “Nil points”
What does this paper say about AGW?
Nothing.
What does it say about feedback from water vapor, ice melting and other mechanisms?
Nothing.
What does it say about the changes in surface temperature from doubling of CO2 prior to feedback?
Nothing.
Top of Atmosphere
Since satellites started measuring:
- incoming solar (shortware) radiation
- reflected solar radiation
- outgoing terrestrial (longwave) radiation
– it has become much easier to understand – and put boundaries around – the top of atmosphere (TOA) energy budget.
The main challenge is the instrument uncertainty. So KT97 consider the satellite measurements. The most accurate results available (at that time) were from five years of ERBE data (1985-1989).
From those results, the outgoing longwave radiation (OLR) from ERBE averaged 235 W/m² while the absorbed solar radiation averaged 238 W/m². Some dull discussion of error estimates from earlier various papers follows. The main result being that the error estimates are in the order of 5W/m², so it isn’t possible to pin down the satellite results any closer than that.
KT97 concludes:
Based on these error estimates, we assume that the bulk of the bias in the ERBE imbalance is in the shortwave absorbed flux at the top of the atmosphere, since the retrieval of shortwave flux is more sensitive than the retrieval of longwave flux to the sampling and modeling of the diurnal cycle, surface and cloud inhomogeneities.
Therefore, we use the ERBE outgoing longwave flux of 235 W/m² to define the absorbed solar flux.
What are they saying? That – based on the measurements and error estimates – a useful working assumption is that the earth (over this time period) is in energy balance and so “pick the best number” to represent that. Reflected solar radiation is the hardest to measure accurately (because it can be reflected in any direction) so we assume that the OLR is the best value to work from.
If the absorbed solar radiation and the OLR had been, say, 25 W/m² apart then the error estimates couldn’t have bridged this gap. And the choices would have been:
- the first law of thermodynamics was wrong (150 years of work proven wrong)
- the earth was cooling (warming) – depending on the sign of the imbalance
- a mystery source of heating/cooling hadn’t been detected
- one or both of the satellites was plain wrong (or the error estimates had major mistakes)
So all the paper is explaining about the TOA results is that the measurement results don’t justify concluding that the earth is out of energy balance and therefore they pick the best number to represent the TOA fluxes. That’s it. This shouldn’t be very controversial.
And also note that during this time period the ocean heat content (OHC) didn’t record any significant increase, so an assumption of energy balance during this period is reasonable.
And, as with any review paper, KT97 also include the results from previous studies, explaining where they agree and where they differ and possible/probable reasons for the differences.
In their later update of their paper (2009) they use the results of a climate model for the TOA imbalance. This comes to 0.9 W/m². In the context of the uncertainties they discuss this is not so significant. It is simply a matter of whether the TOA fluxes balance or not. This is something that is fundamentally unknown over a given 5-year or decadal time period.
As an exercise for the interested student, if you review KT97 with the working assumption that the TOA fluxes are out of balance by 1W/m², what changes of note take place to the various values in the 1997 paper?
Surface Fluxes
This is the more challenging energy balance. At TOA we have satellites measuring the radiation quite comprehensively – and we have only radiation as the heat transfer mechanism for incoming and outgoing energy.
At the surface the measurement systems are less complete. Why is that?
Firstly, we have movement of heat from the surface via latent heat and sensible heat – as well as radiation.
Secondly, satellites can only measure only a small fraction of the upward emitted surface radiation and none of the downward radiation at the surface.
Surface Fluxes – Radiation
To calculate the surface radiation, upward and downward, we need to rely on theory, on models.
You mean made up stuff that no one has checked?
Well, that’s what you might think if you read a lot of blogs that have KT97 on their hit list. It’s easy to make claims.
In fact, if we want to know on a global annual average basis what the upward and downward longwave fluxes are, and if we want to know the solar (shortwave) fluxes that reach the surface (vs absorbed in the atmosphere), we need to rely on models. This is simply because we don’t have 1,000’s of high quality radiation-measuring stations.
Instead we do have a small network of high-quality monitoring stations for measuring downward radiation – the BSRN (baseline surface radiation network) was established by the World Climate Research Programme (WCRP) in the early 1990’s. See The Amazing Case of “Back Radiation”.
The important point is that, for the surface values of downward solar and downward longwave radiation we can check the results of theory against measurements in the places where measurements are available. This tells us whether models are accurate or not.
To calculate the values of surface fluxes with the resolution to calculate the global annual average we need to rely on models. For many people, their instinctive response is that obviously this is not accurate. Instinctive responses are not science, though.
Digression – Many Types of Models
There are many different types of models. For example, if we want to know the value of the DLR (downward longwave radiation) at the surface on Nov 1st, 2210 we need to be sure that some important parameters are well-known for this date. We would need to know the temperature of the atmosphere as a function of height through the atmosphere – and also the concentration of CO2, water vapor, methane – and so on. We would need to predict all of these values successfully for Nov 1st, 2210.
The burden of proof is quite high for this “prediction”.
However, if we want to know the average value of DLR for 2009 we need to have a record of these parameters at lots of locations and times and we can do a proven calculation for DLR at these locations and times.
An Analogy – It isn’t much different from calculating how long the water will take to boil on the stove – we need to know how much water, the initial temperature of the water, the atmospheric temperature and what level you turned the heat to. If we want to predict this value for the future we will need to know what these values will be in the future. But to calculate the past is easy – if we already have a record of these parameters.
See Theory and Experiment – Atmospheric Radiation for examples of verifying theory against experiment.
End of Digression
And if we want to know the upward fluxes we need to know the reflected portion.
Related Articles
Kiehl & Trenberth and the Atmospheric Window
The Earth’s Energy Budget – Part One – a few climate basics.
The Earth’s Energy Budget – Part Two – the important concept of energy balance at top of atmosphere.
References
Earth’s Annual Global Mean Energy Budget, Kiehl & Trenberth, Bulletin of the American Meteorological Society (1997) – free paper
Earth’s Global Energy Budget, Trenberth, Fasullo & Kiehl, Bulletin of the American Meteorological Society (2009) – free paper
Notes
Note 1 – The First Law of Thermodynamics is about the conservation of energy. Many people believe that because the temperature is higher at the surface than the top of atmosphere this somehow violates this first law. Check out Do Trenberth and Kiehl understand the First Law of Thermodynamics? as well as the follow-on articles.
The Second Law of Thermodynamics is about entropy increasing, due to heat flowing from hotter to colder. Many have created an imaginary law which apparently stops energy from radiation from a colder body being absorbed by a hotter body. Check out these articles:
Amazing Things we Find in Textbooks – The Real Second Law of Thermodynamics
Absorption of Radiation from Different Temperature Sources
The Amazing Case of “Back Radiation” – Part Three and Part One and Part Two
Note 2 – When comparing solar radiation with radiation emitted by the climate system there is a “comparison issue” that has to be taken into account. Solar radiation is “captured” by an area of πr² (the area of a disc) because the solar radiation comes from a point source a long way away. But terrestrial radiation is emitted over the whole surface of the earth, an area of 4πr². So if we are talking about W/m² either we need to multiply terrestrial radiation by a factor of 4 to equate the two, or divide solar radiation by a factor of 4 to equate the two. The latter is conventionally chosen.
More about this in The Earth’s Energy Budget – Part One
The Science of Doom 
Thank you for this article. You touch on a question I’ve had. The 2009 paper cites a 0.9 w/m^2 energy imbalance. Do I understand correctly that most of the 0.9 w/m^2 is energy being absorbed by the increased greenhouse effect and it has yet to reveal its effect in the climate system? For example, it’s being absorbed by the oceans or icesheets? Also, how does energy absorbed in photosynthesis fit into the energy budget? Is this energy measured in units of tenths or hundredths w/m^2?
thanks,
jg
It’s fun to look at all the energy balance diagrams in various meteorological texts.
Like fingerprints, no two are the same.
>>> “What does this paper say about AGW? — Nothing.”
No.
KT97 indicates thermal equilibrium to the nearest W/m^2 over the period of measurement.
The paper does say something about AGW – that the measurements are not precise (or accurate) enough to make a conclusion.
KT09 does say that there is thermal imbalance of 0.9W/m^2. This is a rather remarkable claim given the uncertainty inherent in KT97. Do we really know the input and output ten times better ( to the nearest tenth of W/m^2 ) than we did in 97?
I don’t think so.
The key components are solar irradiance, which is actually bounded fairly well ( but still with a W/m^2 or so effective uncertainty after applying geometry and albedo):
Then, as you have referenced, albedo:
Was KT97 INaccurate for alebdo? Is albedo still falling (as referenced by sod)?
Why does Hansen’s model use such a highly erroneous albedo?
Do the other GCMs use such erroneous data?
Finally, the outgoing longwave:
KT and others deserve credit for trying to nail down the energy budget.
But I think the same thing of KT09 as KT97 – the measurements are not known precisely (or accurately ) enough to make a conclusion about energy imbalance, in spite of the 0.9 number published.
While I’ve not read your links, I concur.
Best regards, Ray Dart.
jg,
That 0.9 W/m² imbalance is a model calculation. If it were real, it would be showing up in the ocean heat content data. (There’s that h word again.) If the ARGO measurements are correct, the OHC has been flat, i.e. no significant imbalance, since 2003. Estimates of photosynthetic energy conversion range from ~1% to 0.05% of total insolation (~2.4-0.12 W/m²). The high end would have to be gross primary production. If it were net, the atmospheric CO2 level would be going down, not up. Gross production is going to be nearly balanced by decay back to CO2 and thermal energy. Another 1% or so goes into wind and water circulation. But that’s a dissipative process which ends up as an increase in thermal energy too.
“That 0.9 W/m² imbalance is a model calculation.”
The problem with ‘model calculation’ is that we aren’t sure that we include all of the ‘degrees of freedom’ within the ‘model’ used.
“If it were real, it would be showing up in the ocean heat content data. (There’s that h word again.) If the ARGO measurements are correct, the OHC has been flat, i.e. no significant imbalance, since 2003.”
Again, ‘lack of definition’. We’re looking at a digital ‘multi-meter’ at less than half full scale deflection (if the model is correct)! There’s a better model.
Atmospheric reconfiguration is more likely to advance understanding here.
“Estimates of photosynthetic energy conversion range from ~1% to 0.05% of total insolation (~2.4-0.12 W/m²). The high end would have to be gross primary production. If it were net, the atmospheric CO2 level would be going down, not up. Gross production is going to be nearly balanced by decay back to CO2 and thermal energy.”
To a point, I concur. Insolation is a wide waveband that’s absorbed in different ways by different Earth systems atractors. Photosynthetic atractors tend to absorb the red range of ‘vis’ insolation, thus, the blue and yellow insolation wavelengths of the ‘vis’ spectra tend to be reflected by vegetation biomass as an ‘amalgam’ of ‘green vis’ spectral reflection. Thus, ‘Leaves are Green’!
I intended to finish this response, but it’s late, I’m knackered and I’m off to bed.
Best regards, Ray Dart.
SoD – apologies for putting a question up without having a proper read of the post and references in detail, but I remember a while ago looking at this and concluding that the Kiehl et al 1994 paper was a necessary building block – “The simulated earth radiation budget of the National Center for Atmospheric Research community climate model CCM2 and comparisons with the Earth Radiation Budget Experiment (ERBE).”
I wasn’t able to find one on open access and I haven’t tried since – if you have any thoughts I’d be interested to hear them. From what you say above it sounds as if you may have been refering to this work with your comment re: “Some dull discussion of error estimates from earlier various papers follows.”? Thanks in advance for any insights.
Well, from my perspective, SOD is an elitist site, slightly different from the disgusting RC site in that it doesn’t censor much; but it simply IGNORES adverse comments. BUT, the “bottom line” is the same: VERY BIASED MISINFORMATION.
I’m not a cheerleader, but this is one of the best sites because sod is writing it out of personal curiosity and uses data, ‘maths’, and textbook scans to further understanding. Opinion can creep in for everyone when, as with this subject, there is uncertainty in the measurements, but overall ++ for sod.
I disagree. This site is fine. I am a fan and barring the insults from DeWitt will be for a long time. I fully enjoy the site. I disagree with some of the conclusions, but so what we are free in American to do that. If you cannot hold your own then pity you but don’t blame SOD.
Ask an intelligent question.
jae
Your allegations are baseless as far as I can see. I have been reading SOD articles since last summer, and after months of reading them, I still didn’t know if SOD agreed with the mainstream or was a skeptic or was agnostic. This seems like the least biased climate science site I have been at.
curious:
I don’t think that paper is a necessary building block. It’s used as a reference for ERBE TOA flux values. However, the paper is mainly about the flux values from the model CCM2 – and comparing model results with the measured data from the satellite. But many other papers also contain the globally averaged ERBE data and could also have been used.
Error estimates for the satellite TOA data were referenced via these papers:
Measurement error estimates is a necessary but dull subject.
jg:
The important point with this value is that if we set it to zero instead then what is the impact on the values that are of interest in this paper?
In the 1997 paper they used 0. 12 years later they used 0.9.
It has no impact on anything of significance in the paper.
ClimateWatcher:
The whole point about KT97 or 09 is they don’t make a claim that this IS known. The paper is about measurements and estimates. One method of “closing” the TOA budget would be to set it to zero, one would be to use the actual instrument values in spite of the error in their known absolute accuracy, another would be to use a model.
If the real value is zero, we now have a 1W/m2 error in a paper where they address much larger errors that cannot be further refined.
If the major query about the paper is whether the TOA net flux should be 0 or 1 then that’s a good result.
SoD thanks – follow up appreciated.
I’ve always liked KT energy budget. When one subtracts 324 DLR from 390 upward LWR, one learns that radiation NET LWR isn’t the most important mechanism for cooling the surface of the earth. Furthermore, 40 of the 66 W/m2 of net upward LWR escapes directly to space. Our atmosphere already has so much GHG that LWR emitted by the lower troposphere has little chance of reaching space. Convection (including latent heat) dominates radiation in cooling the surface of the earth.
Note that convection is the net energy flux produced by upward and downward flows, just as net LWR is the net flux of upward and downward radiation. Do K&T discuss the relative importance of these cooling mechanisms?
You write : “In their later update of their paper (2009) they use the results of a climate model for the TOA imbalance. This comes to 0.9 W/m². In the context of the uncertainties they discuss this is not so significant. ”
So what you are confirming is that there really is no firm evidence that the net energy balance is not in equilibrium on timescales of one year. Therefore the presumption that the oceans are absorbing net energy now, thereby delaying warming by decades could be untrue. Simple energy balance arguments show that in this case deltaT = 1.6Ln((CO2/C0) leading to warming by 2100 of just 0.7-1.0C, even assuming CO2 levels were to reach 6-700 ppm by then. The observed temperature rises since 1750 follow better 2.5ln(C02/C0). If we assume that all observed warming is due to AGH and none to natural effects, this implies that 2/3 of warming is simple CO2 increases and the rest probably due to other increases in greenhouse gasses, leaving little room for positive feedbacks.
Clive Best:
The paper is actually about something else.
And the satellite observing systems cannot provide absolute accuracies necessary to determine whether the planet has a net radiative imbalance or not.
You can see a little about the last 50 years of ocean heat changes in The Real Measure of Global Warming and the followup Part Two – the Sad Case of the Expendable Bathythermographs.
I don’t really follow your calculations and that reminded me.. on another note I tried to add a comment to your blog but there’s some glitch that forwards me to another blog when I try to enter a comment. You say:
You haven’t understood what radiative forcing is.
And if I quote my own conclusion for the article you reference:
That should alert you that radiative forcing is not calculated from temperature change. No assumptions about temperature change are necessary or used or involved.
Radiative forcing is calculated from the net change in TOA flux if the radiatively-active gases (“greenhouse” gases) change in composition. It is a pre-feedback calculation, with “all other things being equal”.
Grasping these concepts is important.
Sorry for the delay in replying. My basic argument is very simple and can be found here http://clivebest.com/blog/?p=2241. Please feel free to pick holes in it ! Yes I do know what radiative forcing means. If we ignore possible feedbacks, this leads to a simple logarithmic dependence of temperature increase on CO2 concentrations. Some of the enhanced temperature increases in the 1990s may well be due to a decadel oscillation in global temperatures which is now declining. Evidence for this is that supported by the observation that temperatures have not increased since 2000.
Once again I would like to praise Science of Doom for the headline articles and the way in which the commentary is moderated. It is wonderful to find a site where a full and frank, even robust, discussion can take place without abusive, distractive and unedifying mud slinging.
I have long been interested in K&T. I read it as a globally averaged budget over a number of years.
As I understand it, our measurements are not sufficiently precise to determine if there is an energy imbalance at the planetary boundary (which is much higher than “TOA”.) The only reasonable assumption is that there is, on average, no imbalance.
I have a few quibbles. The Surface Radiation is 390W/m^2, which appears to be calculated from the Stephan-Boltzmann equation, using 15DegC as the surface temperature. I think that may be mathematically incorrect – if the average temperature is 15DegC, the average radiation will be higher than 390W/m^2 due to the T^4 term.
I also think the label “thermals” is wrong. This is the direct CONDUCTION from the surface to the air, not the convected heat. It depends solely on the temperature difference between the surface and the air directly in contact with it.
But whether the figures are exactly precise or not, the main energy flows are identified and ball-park quantified. We can see:
1. The main energy transfer from the Surface to the atmosphere is evaporated water (three fifths), with conduction and radiation amounting to about one fifth each.
2. If the surface temperature rises, the radiation from the surface rises as also does the evaporation. We must assume that the conduction remains the same (same temperature difference between surface and air in contact with it) so for balance to be maintained either:
2A. Incoming sunlight has to increase, or
2B. Back Radiation has to increase by more than the outgoing surface radiation.
The implication is that the surface sensitivity is bounded by the rate of change of evaporation with temperature. My calculation is that the surface sensitivity is between 0.095 and 0.15DegC/W/m^2.
“The Surface Radiation is 390W/m^2, which appears to be calculated from the Stephan-Boltzmann equation, using 15DegC as the surface temperature. I think that may be mathematically incorrect – if the average temperature is 15DegC, the average radiation will be higher than 390W/m^2 due to the T^4 term.”
From a theoretical standpoint, I completely agree. The ‘surface temperature’ is a ‘hygrometric’ ‘wet-bulb’ temperature where a Stephan-Boltzmann calculation will show only radiated energy from a ‘sensible heat’ temperature and can’t capture any ‘latency’ component.
“I also think the label “thermals” is wrong. This is the direct CONDUCTION from the surface to the air, not the convected heat. It depends solely on the temperature difference between the surface and the air directly in contact with it.”
I also think the ‘label’ is wrong, but for other reasons. Ignoring latency for the time being, the ‘boundary layer’ between the ‘atmosphere proper’ and the ‘surface’ is quite deep. If Earth’s atmosphere didn’t include any ‘Greenhouse Gasses’ (GHGs), then you’d be correct. However, the GHGs are there, and do absorb surface ‘Outgoing Long-wave Radiation’ (OLR). Thus, the OLR component of “thermals” isn’t solely a product of “direct CONDUCTION”, it also contains a limited radiative component that can be observed. This ‘radiative component’ is also detrimental to “thermals” at higher altitudes, as it tends to average all energy fluxes and remove ‘hot spots’ that generate thermal convection.
I’ll now bring latency back into this scenario and explain why I think “the label “thermals” is wrong”.
‘Water vapour’ (WV) can’t exist as a unique and unmixed gas at a ‘standard temperature and pressure’ (STP) due to its ‘triple point’, but if it could it would display a density of ~3/5 the density of Earth’s mixture of other atmospheric components. This implies that where WV is produced, vertical convection must follow. Thus, WV, being the sole major ‘lighter than air’ candidate of Earth’s gasses, must also be the major ‘gas component’ for convection. However, it doesn’t alter the temperature because of its ‘latency’.
“1. The main energy transfer from the Surface to the atmosphere is evaporated water (three fifths), with conduction and radiation amounting to about one fifth each.”
“(Three fifths)”? That’s both odd and interesting when the density of WV is ~3/5 the density of Earth’s other atmospheric components!
“2. If the surface temperature rises, the radiation from the surface rises as also does the evaporation. We must assume that the conduction remains the same (same temperature difference between surface and air in contact with it) so for balance to be maintained either:
2A. Incoming sunlight has to increase, or
2B. Back Radiation has to increase by more than the outgoing surface radiation.
The implication is that the surface sensitivity is bounded by the rate of change of evaporation with temperature. My calculation is that the surface sensitivity is between 0.095 and 0.15DegC/W/m^2.”
I like your analysis Mr Davidson! The major area of Earth’s surface is ocean. This places an averaged Earth response to ‘warming’ within the realm of the Clausius-Clapyron relationship that is ‘invisible’ to a ‘sensible heat’ computation!
Best regards, Ray Dart.
I have a question about “Radiative Forcing”.
This is defined as the energy imbalance at the Tropopause assuming a step change in GHG concentration but that resultant stratospheric changes have occured. (IPCC AR4(2007) WG1 Chapter 2 Section 2.2)
Many authors equate Tropopause with TOA. But the Tropopause is a very highly variable beastie – in the Tropics it’s around 17km, in Temperate latitudes around 11km, and in polar latitudes around 6-9km.
1. Is the IPCC definition of “Radiative Forcing” accurate?
2. When people talk about TOA, what do they intend to convey? Is it the Radiative “top”, is it the 95% of gases level?
3. The 3.7W/m^2 “Radiative Forcing” for a doubling of CO2 is obviously an average figure. How is it estimated – after all the amount of atmosphere above the Tropopause at the equator is only 7ish%, but above the poles it’s 30ish%?
The tropopause can be loosely defined as where convection stops. Whether or not a gas molecule emits a photon is not related to whether convection is occurring or not.
The mean altitude of emission to space is around 5-6 km.
I don’t know what everyone thinks of with respect to TOA, but the definition that makes the most sense to me is the altitude at which the likelihood of a photon emitted upward being absorbed before it reaches space drops to some level below which you don’t care anymore. There is no abrupt end to the atmosphere; so, where this altitude is can be somewhat arbitrarily decided. However, it makes little sense to use the tropopause as the TOA.
Colin Davidson:
Thanks for your kind comments.
You are correct.
In their 2009 update they say (extract from the section Spatial and Temporal Sampling):
You said:
The process that takes place is conduction across the surface-air boundary, followed by convection.
For convection to take place, conduction across the boundary is a pre-requisite. But the conductivity of air is so low that the average 24 W/m2 moving up into the troposphere from the surface cannot take place due to conduction through the air. It can and does occur through a very thin laminar boundary layer a few millimeters deep.
How did you do this calculation?
SoD says “it helps us understand the relative importance of the different heat transfer mechanisms in the climate, and the areas and magnitude of uncertainty.”
As long as its understood that the diagram doesn’t represent anywhere on the earth. It represents averages (averaging seasonally, diurnally and latitudinally) and the actual values are quite different from moment to moment and place to place.
Colin Davidson:
They are good questions and I would like to revisit my notes and do some more homework and possibly write an article on it. The last time I had a good look at this was well over a year ago.
Some brief points.
The tropopause doesn’t have only one definition. The important thing is knowing the definition chosen.
If I define the center of Manhattan as The Empire State Building then it might be X miles from New Haven, CT to “the center of Manhattan”, and if I define the center of Manhattan as City Hall it will be X+3 miles. Neither definition might be the “right” definition, but so long as you know which was chosen for the distance to the center of Manhattan, you can make use of the calculation.
It is just a definition so various researchers can compare apples with apples. If you have a scan through some of the many papers over 20 or more years on this subject you see that there are different values cited but based on different definitions. So the purpose is to pick the most useful definition and then have everyone (who is interested) provide their number against that definition.
Depends on the person, usually it is “above” the atmosphere. But then the question becomes is this 99% of the atmosphere, or 99.999%?
There are some papers on this that I would like to delve back into and summarize the info in an article. A brief comment is that after repeatable results in calculating the radiative forcing for 2xCO2 on a “standard atmosphere”, the question then arose of what is the average radiative forcing on area-weighted actual atmospheres? And various people had a go at producing the numbers.
Science of Doom asked how I estimated the sensitivity of the surface to changes in energy balance.
Using the K&T diagram, the energy exported from the surface equals the incoming sunlight (Surface Energy Balance):
Absorbed_Sunlight = (Radiation_from_the_Surface – Back-Radiation) + Conduction (“Thermals”) + Evaporation
Rewriting,
Absorbed_Sunlight + Back-Radiation = Radiation_from_the_Surface + Conduction (“Thermals”) + Evaporation
Let us call the LHS “Surface Forcing”. The quantities on the RHS are the responses to that forcing.
What happens if an increased in forcing drives a temperature increase in the surface? Let us assume that that has happened, and that the temperature increase is 1DegC.
We first look at the RHS. We believe that the atmosphere will also increase in temperature by roughly the same amount, so there will be no change in the conductive term. The increase in the Radiative term is roughly 5.5W/m^2. The increase in the evaporative term is much more difficult, but is believed to be in the range 2-7%/DegC. So the increase in the evaporative term is 1.5 to 5.5W/m^2, for a total change on the RHS of 7 to 11 W/m^2.
Since balance is an assumption, the LHS changed by the same amount. The surface sensitivity is therefore 0.095 to 0.15 DegC/W/m^2. Note that this is the sensitivity to changes in Surface Forcing, whatever the source. It is NOT the response to Radiative Forcing – there is no response of the surface to Radiative Forcing, it can only respond to Sunlight and Back-Radiation.
Furthermore, if insolation and albedo are fixed, then any increase in surface temperature implies an increase in evaporation and a corresponding DECREASE in net radiation from the surface (back radiation increases to cover both the increase in surface radiation and the increase in evaporation).
Science of Doom wrote “The tropopause doesn’t have only one definition.”
Does anyone know what definition is used in IPCC AR4(2007) WG1?
TOA looks to me to be a vague and ill-defined term – it can mean different things to different people. In particular many use TOA when talking about “Radiative Forcing” – but this vague term has nothing to do with the IPCC definition, which specifically identifies the Tropopause as the boundary.
From a radiative point of view, the definition of the top of the atmosphere is relatively easy. It’s the altitude where downward thermal atmospheric radiation becomes indistinguishable from the background. For the Earth, it’s below 100 km. MODTRAN calculates that at 70 km looking up for the Tropical atmosphere, the flux is 0.05 W/m2 from 100-1500 cm-1. Ignoring the tails, that would be an effective temperature of 30 K compared to the cosmic microwave background of 2.7 K.
I have several issues with KT97:
The first is the absorbing 67 W/m^2 of the post albedo by the atmosphere and bringing it to the surface as part of the 324 W/m^2 return path all lumped in as ‘back radiation’. Counting this twice is a violation of Conservation of Energy and highly misleading.
The second is there is no return path for latent heat and thermals in the form of precipitation, weather, etc. It’s also all lumped in as part of the 324 W/m^2 designated as ‘back radiation’.
The third is the atmospheric ‘window’ of 40 W/m^2 from the surface to space and 30 W/m^2 from the cloud tops to space for a total ‘window’ of 70 W/m^2. There is no reference to this figure in the paper and it appears just be a rough estimate or guess. It also requires greater than half of what is absorbed by the atmosphere to be emitted to space and less than half emitted back to the surface (specifically 165 up and 155 down). This is inaccurate – it should be a 50/50 split.
I’d like to add one other important criticism:
The 324 W/m^2 of downward emitted LW all designated as ‘back radiation’ is very misleading. It makes it look like of the 390 W/m^2 emitted at the surface, 324 W/m^2 is coming back when in reality COE dictates than only 155 W/m^2 is coming back from the atmosphere.
They should have separate return paths or at least refer to the 324 W/m^2 path as ‘downward radiation’ instead of ‘back radiation’.
RW… there is 342 W m^2 incoming, 107 is reflected as short wave, and the remaining 235 W m^2 is radiated out as long wave… there is no energy creation or destruction… The “back radiation”, is the result of energy in transit through the system… it cant just disappear(which would be energy destruction). And it is quite easy to check back radiation… with a thermometer … Saying 324 W m^2 BR is the same as saying the average T at the surface of earth is 15C… This is what you are really disputing with your first point. This has been gone intpo depth a few times here at this blog, with some excellent articles dealing with it.
Second point, is kinda the same as the first, the T profile is a result of convection(latent heat transport is part o convection…to me) and radiation, but back radiation is just temperature. So you are disputing the average T at the surface?
They are able to observe the atmospheric window, by looking down with a satellite at the upcoming LW, and seeing what brightness T it has originated from… But im not going to go chase it up, but you would be able to check approximations yourself with modtran if you like. Or check satellite observations if the model thing dosnt sit well with you.
RW
You don’t understand conservation of energy, that’s why you have issues with reality – as presented in KT97.
If body 1 absorbs energy then radiates/conducts/convects some of this energy to body 2 and body 2 then radiates/conducts/convects some of this energy to body 3, you need to include the amount in each body’s energy calculation.
But previously I have explained some points about conservation of energy and you didn’t understand them, so not much point going through the basics again.
Take a look at a heat transfer textbook and follow some worked examples. Try problem 1.1 on p37 of Lienhard’s online heat transfer textbook.
I have a feeling that very much of the incorrect criticism and confusion comes from the use of the terrible-awful-dreadful term “back-radiation”. I’m sure the person who came up with it at first meant well, but he/she should really issue an public apology for the unnecessary confusion it has caused. From what I’ve understood, the 324 W value is mostly just the amount of radiation a gaseos body, such as our atmosphere emits towards the center. “Mostly” is used because I’m guessing the part reflected from the clouds is factored into this value(?). If we removed the part of surface radiation, that is reflected, from the equation and then took away all the surface radiation somehow (paint it white or something) while leaving other paramters the same (temperatures and things like that) this value wouldn’t really change that much. Which is why I find the use of the term “back-radiation” is rather idiotic for this value.
But in the end this is just a lousy choice of words, nothing more.
I don’t have a problem with “Back-Radiation”, but I agree that the K&T numbers for “through the window” surface emissions to space, and “Back-Radiation” include reflection from clouds. There may or may not be a little too much of this in these numbers. [See SOD’s posts on Radiation from CO2. He has the atmosphere as 44% opaque at 280ppm, 50% opaque at 560ppm. Shall we say 48% opaque at 380ppm? Cloud cover is 60%. So emission through the window should be about 0.4x.52×390 = 80W/m^2. I think the K&T numbers are all open to discussion, but that it is the changes in these numbers that is important.]
Another point is that gases are not black bodies – not even close. They emit at preferred frequencies (“lines”), not in a continuous spectrum. It therefore doesn’t make much sense to talk of the “characteristic BB temperature” of an emitting low temperature, low pressure gas.
All that said, it seems true that:
1. The surface and the atmosphere are nearly in radiative balance, ie the NET transfer of radiated energy from the Surface into the atmopsphere is small.
2. If the system heats up, the atmosphere will radiate more strongly. I have previously assumed that this would be at the Stephan-Boltzmann Law rate, but am now not sure that is the case. If it doesn’t increase emissions at the SB rate, then heating the system will increase the radiative imbalance between the Surface and the atmosphere, tending to cool the Surface.
KT97 has total ‘window’ of 70 W/m^2 (40 W/m^2 through the clear sky and 30 W/m^2 through the cloudy sky). I agree 80 W/m^2 is more likely. An 80 W/m^2 ‘window’ with these numbers gives exactly half up/half down, specifically 155 W/m^2 up to space and 155 W/m^2 down to the surface (390 – 80 = 310 W/m^2, 310/2 = 155; 155 + 80 = 235, which is the exact amount leaving; 155 + 235 = 390, which is the exact amount emitted from the surface).
I would argue it’s more like 240 W/m^2 entering and leaving with a 90 W/m^2 ‘window’ and 150 W/m^2 going to space and 150 W/m^2 going to the surface.
I’m not sure if this “characteristic BB temperature” part was directed at my comments, but I’ll point out just in case, that I never mentioned Black Bodies and even “characteristic” might not be an entirely appropriate description in that context. I pretty much said that our atmopsphere emits as much radiation as it emits (which is correct by definition). The point was rather that it would do so regardless of the existance of other emitting bodies in the vicinity, as long as other parameters remain the same.
science of doom says:
“If body 1 absorbs energy then radiates/conducts/convects some of this energy to body 2 and body 2 then radiates/conducts/convects some of this energy to body 3, you need to include the amount in each body’s energy calculation.”
The point is the 67 W/m^2 has to get to the surface if energy is to be conserved. It cannot stay in the atmosphere or be emitted to space. So technically counting it twice is not a violation of COE, but it’s confusing in this way because there is not a separate path showing the 67 W/m^2 getting to the surface. It’s lumped in the ‘back radiation’ return path – only it’s not ‘back radiation’ but downward emitted LW ‘forward radiation’ that last originated from the Sun yet to reach the surface (key distinction).
Instead of referring to the 324 W/m^2 as ‘back radiation’ they should just call it ‘downward emitted’ LW radiation. That would alleviate some of the confusion.
In response to my statement:
“I also think the label “thermals” is wrong. This is the direct CONDUCTION from the surface to the air, not the convected heat. It depends solely on the temperature difference between the surface and the air directly in contact with it.”
Science_Of_Doom wrote:
“The process that takes place is conduction across the surface-air boundary, followed by convection.
For convection to take place, conduction across the boundary is a pre-requisite. But the conductivity of air is so low that the average 24 W/m2 moving up into the troposphere from the surface cannot take place due to conduction through the air. It can and does occur through a very thin laminar boundary layer a few millimeters deep.”
I generally agree, except that the implication is that it is only the conducted energy being convected. It would be more accurate to label the flow as conduction, and to omit the wiggly line altogether, or put it somewhere else. All energy into the atmosphere heats the air. And heated air rises by convection. But this process is not depicted on the K&T diagram, nor should it be – it is internal to the atmosphere, not a boundary phenomenon. It is similar to the not-shown conduction and convection within the Surface.
Suricat also responded:
“I also think the ‘label’ is wrong, but for other reasons. Ignoring latency for the time being, the ‘boundary layer’ between the ‘atmosphere proper’ and the ‘surface’ is quite deep. If Earth’s atmosphere didn’t include any ‘Greenhouse Gasses’ (GHGs), then you’d be correct. However, the GHGs are there, and do absorb surface ‘Outgoing Long-wave Radiation’ (OLR). Thus, the OLR component of “thermals” isn’t solely a product of “direct CONDUCTION”, it also contains a limited radiative component that can be observed. This ‘radiative component’ is also detrimental to “thermals” at higher altitudes, as it tends to average all energy fluxes and remove ‘hot spots’ that generate thermal convection.”
I don’t agree that this term contains the net absorption of IR by the atmosphere (although because these numbers atre almost the same – 24W/m^2 for thermals and 26W/m^2 for net absorption of surface radiation by the atmopsphere, I have in the past wondered…). Nor is it dependant on the width of the boundary layer. I think I have it correct – it is the energy transferred from the surface to the air directly in contact with it.
Colin Davidson says:
“Another point is that gases are not black bodies – not even close. They emit at preferred frequencies (“lines”), not in a continuous spectrum. It therefore doesn’t make much sense to talk of the “characteristic BB temperature” of an emitting low temperature, low pressure gas.”
The heated gases of the atmosphere do indeed emit a Planck spectrum of BB radiation. The emitted spectrum is then subject to further absorption and so on and so forth through the whole atmosphere. Obviously the further up in the atmosphere, the absorption gaps widen as there is less and less water vapor and other GHGs to absorb the emitted energy.
Any heated object emits a Planck spectrum of energy, even if it’s not a perfect black body and even if it’s only a heated gas. Its emitted spectrum is considerably less because of its low emissivity, but it still emits a broad band Planck spectrum of energy.
Think about it, how could a heated gas ever cool if it didn’t emit black body radiation like any other object does?
“Think about it, how could a heated gas ever cool if it didn’t emit black body radiation like any other object does?”
That’s easy RW. Water vapour contains ‘latent heat’ invisibly within its thermal makeup until the molecule ‘distils’ at cooler altitudes.
Best regards, Ray Dart.
RW:
A gas does not radiate as a black body. A black body has an emissivity of 1. A gas like CO2 does not have an emissivity of 1.
You are writing a mish mash of technical words that you obviously don’t understand.
A heated gas cools because it emits radiation.
Have a read of Planck, Stefan-Boltzmann, Kirchhoff and LTE.
I know a gas does not radiate as black body. Technically nothing radiates as a black body because nothing is perfect black body, even the surface of the Earth. The point is the heated gases of the atmosphere emit a broad band Planck spectrum of energy according to their temperature just like any other heated object.
Not always RW. There are occasions where ‘latency’ rears its ghostly head and proves that all energy may not be accounted for where a ‘phase change’ is encountered.
Best regards, Ray Dart.
I disagree with RW.
O2, N2, Ne, Ar in the atmosphere don’t radiate IR (more accurately they radiate very little IR). These species do not have the capability to generate photons at the IR frequencies, nor to accept them. That’s why they are not IR gases. They are simply teetotallers at a bacchanalian orgy.
CO2, H2O, O3 etc are IR active, but have different preferred frequencies (=energy levels). These preferred frequencies show up as emission lines/absorption holes.
This behaviour is quite unlike the continuous frequency spectrum emitted by a solid, liquid or a very high temperature gas(eg the sun), which is described as plank radiation.
Emission lines for the various species can be found here (Thanks for this link, DeWitt Payne) http://spectralcalc.com/spectral_browser/db_intensity.php
A good explanation of radiation and absorption is John Nicol’s paper at http://www.middlebury.net/nicol-08.doc
But be careful with the final parts – it is definitely wrong in equations 26,27 and 28 – the problem with 26 is that he has omitted conduction and evaporation, and neglected that surface radiation is NET not gross.
suricat,
The surface temperature is dry bulb, not wet bulb. It does not capture the latent heat content of the air. You need both the dry and the wet bulb temperature to do that, or the dry bulb temperature and relative humidity. It’s unlikely, though, that we’ll ever convince meteorologists, much less the general public, to accept joules/m3 or /kg rather than temperature and relative humidity.
“The surface temperature is dry bulb, not wet bulb.”
What part of the oceans, mid latitudes and polar regions did you miss? OK I’ll give you ‘heat islands’. 🙂
I wouldn’t expect a ‘wet bulb’ temperature in an arid region, but these regions are in the minority on a global scale. I also think you may be ignoring ‘evapotranspiration’.
BTW, in case I caused confusion. I’m implying ‘surface temperatures’, not ‘near surface atmospheric temperatures’ (though the two aren’t ‘dissimilar’).
“It does not capture the latent heat content of the air.”
??? I’m not sure what you imply, however.
Ground water evaporates and cools the surface, thus, evolves water vapour that mixes with the atmosphere giving the atmosphere its ‘latent heat’ quality from the energy at the surface. This effect is more pronounced over ocean surface.
Have you ever contemplated the reasons why a ‘bare earth’ patch in your lawn is hotter than the grass covered areas following a short ‘dry spell’? That’ll mostly be ‘Evapotranspiration’. 🙂
There may be confusing coms between us, so I’ll leave it there for now.
Best regards, Ray Dart.
Colin Davidson,
You should have stopped at your first sentence. Oxygen has a magnetic dipole moment so it does radiate and absorb in the IR and microwave region. The oxygen IR lines are more important for absorption of incoming solar radiation, though, than emission in the thermal band as they are near 8,000 cm-1. All diatomic molecules also undergo collision induced absorption, so O2 and N2 have a very weak continuum spectrum in the thermal IR. For spectral purposes, it’s only important when the water vapor content is very low like a path that only goes through the upper atmosphere.
I’ve been round and round with RW on the K&T energy balance on another thread. It’s hopeless.
I would like to thank DeWitt Payne for this clarification.
KingOchaos
… there is no energy creation or destruction… The “back radiation”, is the result of energy in transit through the system…
Energy in transit is “heat”/thermal energy.
So do a heat transfer equation showing the ground and this back radiation.
DeWitt Payne stated:
“All diatomic molecules also undergo collision induced absorption, so O2 and N2 have a very weak continuum spectrum in the thermal IR.”
I wonder if he could provide a reference, as I was not aware of this phenomenon until now. [And if this is the case why not also emission?][Apologies to SOD, as this question is OT]
so you want me to write a line by line radiative/convective/conductive heat transfer equation for the atmosphere… to prove the existence o back radiation?
It isnt going to happen 😉 One, i dont think you would be willing to pay enough… to motivate me to go to ALL that trouble..
Two, its “*questionable” that i personally would be capable o doing this on a piece o A4 🙂
And thirdly, im not trying to over turn established thermodynamics theory’s … if you believe “heat” is intelligent… Prove it. If you believe the average T o the atmosphere is -18C… prove it. If you believe the optical depth of the atmosphere has been misrepresented prove it.. ans so on.
* questionable, as in no way in hell, something simple like heating a body o water, or combustion engine, can do… fluid dynamics… not so much my thing.
OH this was directed at MKelly sorry.
Also Mkelly, at this site, and indeed all over the net you can find neat little graphs of the measured spectrum o radiation looking up, from this, you can see at what altitude, the radiation has originated from… im sure youve seen them.
Nope. No line by line only one heat transfer equation in which you input back radiation.
You said back radiation was “The “back radiation”, is the result of energy in transit through the system…” well energy in transit is thermal energy/heat.
So write one equation that uses what you stated as an input. It can be a radiative heat transfer equation, conduction, convection I personally do not care but just one with “back radiation” as an input.
King Ochaos says:
“The “back radiation”, is the result of energy in transit through the system… it cant just disappear(which would be energy destruction). And it is quite easy to check back radiation… with a thermometer … Saying 324 W m^2 BR is the same as saying the average T at the surface of earth is 15C… This is what you are really disputing with your first point. This has been gone intpo depth a few times here at this blog, with some excellent articles dealing with it.
Second point, is kinda the same as the first, the T profile is a result of convection(latent heat transport is part o convection…to me) and radiation, but back radiation is just temperature. So you are disputing the average T at the surface?”
As I said, not all of the downward emitted LW is ‘back radiation’. It is also virtually impossible to get a global average for downward emitted LW unless you have measuring instruments all over the globe looking up. Also, ‘back radiaton’ implies downward emitted LW that last originated from surface emitted, or the amount coming back to the surface from the 390 W/m^2 emitted at the surface.
My key objection to the diagram is it does not show the most crucial aspect of the entire greenhouse effect, which is how much of the 390 W/m^2 emitted at the surface is coming back from the atmosphere. This is what ultimately determines the surface temperature. To the extent there are multiple forms of energy transport from the surface to the atmosphere, from the atmosphere to other parts of the atmosphere, and from the atmosphere back to the surface is less important. The bottom line is the net energy flux at the surface is 390 W/m^2. If 235 W/m^2 are from the Sun, then 155 W/m^2 have to be coming back from the atmosphere (235 + 155 = 390). The diagram does not show this, and in fact – I would argue, obfuscates. Of course, not all of the 155 watts have to be coming back as LW radiation. Some could come back in the form of latent heat via precipitation, for example, but this just offsets energy that would otherwise be radiated back to the surface. The same is true of the 235 W/m^2 from the Sun. No doubt it also gets to the surface in multitude of ways – some directly via SW, some indirectly via LW and some via kinetic energy (latent heat and thermals). Again, this just offsets energy that would otherwise go straight to the surface as SW infrared.
Ode to Al “Hothouse” Gore:
In response to RW, I guess it is what you think is important that matters.
The only real force is Sunlight. So I reckon:
Absorbed_Sunlight = (Radiation_from_the_Surface – Back-Radiation) + Conduction (“Thermals”) + Evaporation
is the best (most descriptive) form of the Surface Energy Balance.
Colin Davidson,
Search ‘collision induced absorption’ . You’ll find lots of scholarly articles and books. That’s the term of use in academia. Of course there’s emission too as required by Kirchhoff’s Law. Basically a collision between two molecules distorts their electric field and induces a temporary dipole moment allowing absorption and emission of radiation. It’s continuum, not line.
Thank you DeWitt Payne.
Well we are talking about an equilibrium situation, so E in = E out
So how is back radiation equated with T(seriously?) 15c… 288k E=εσT4 with an emissivity of .83,(first figure i found with a google), it will give us 323.796 W/m2… round it up, 324 W/m2 the surface has an emissivity of around .98 (this is an averaged figure, it varies between .99-.8 from equator to pole… you get 390 with an emissivity o 1) which gives us an upward flux o 382W/m2 so T1^4-T2^4 =58W/m2 radiated moved through radiation from the surface.(ignoring clouds, radiation coming back down through this window)
Close to the surface, the opacity o the atmosphere, is such, that the majority of the back radiation, is from the immediate vicinity… it is not shining down from a magical ghg shell… so the bulk movement of energy from these layers will be through convection/latent heat transport, but as the path length decreases as the pressure drops with altitude, radiation will move more and more of this energy… which is what drives the T differential which drives convection… it is variable for wave length vrs altitude,,, there is not a simple way to calculate it.(you cant do a purely conductive/or convective, or radiative equation form a semi transparent fluid)
So E in=E out, at the surface(assumed T 288k) E in = 168w/m2- (E=εσT1^4- E=εσT2^4)= 58w/m2 moved via radiation, leaving 110W/m^2 moved from the surface via conduction/ convection/latent heat transport(.. and radiated away at a higher altitude when the path length shortens…. but the E=εσT1^4- E=εσT2^4 is going to apply as you rise through the atmosphere…. ill repeat, there is not a simple way to calculate it.(im ignoring whats absorbed in the atmosphere here obviously)
Think of a body of water being heated via SW, it only radiates from the surface… its not that its not radiating below the surface, its that it will be in LTE, with the path length so long that what a molecule radiates, it receives from its immediate neighbors, so it can be ignored, with energy loss from the surface, driving the differential that causes convection within the body.
So you admit that “back radiation” is not correct and only temperature difference is to be used. Very good.
At least we can agree that back radiation is nonsense.
The atmosphere is semi transparent(unlike water), so energy is still moved out via radiation from the surface, so its still necessary to know the back radiation to know how much is moved up via surface radiation.
The path length at altitude though is really more important as far as a change in the energy budget… but if you raise the average height of emission a little bit, it should lead to an increase in T’s below, to maintain the T profile, to get the higher altitude warm enough that its radiating out the incoming… all things staying the same?
I think back radiation can be used quite misleadingly, but not really in the literature on the subject, more on peoples interpretations of it.
The Surface Balance equation derived from the K&T diagram is:
Absorbed_Sunlight = (Radiation_from_the_Surface – Back-Radiation) + Conduction (“Thermals”) + Evaporation
If we change the surface temperature, say by 3 degrees (the IPCC most likely value for a doubling of CO2), and allow the system to rebalance (NB. I’m not talking instantaneous change, but drawing a new K&T diagram in 2100):
1. The Conduction (“Thermals”) term does not change. The temperature relationship between the atmosphere and the surface is usually assumed not to change (for example, the equilibrium lapse rate should be the same, as there is very little change in the amount of energy going into the atmosphere from the surface), there is no a priori reason to do so.
2. The Evaporation term increases. It’s pretty fundamental – if it gets hotter, more water gets evaporated. There is huge disagreement among scientists about how much, but the consensus seems to be between 2 and 7% per DegC. So this term increases between 4W/m^2 and 16.5W/m^2.
3. Therefore the Net Radiation term (Radiation_from_the_Surface – Back-Radiation) DECREASES. But we know that Radiation_from_the_Surface increases by around 16W/m^2. So to maintain the increased temperature of the surface (ie to maintain energy balance, a fundamental requirement in the K&T diagram) there needs to be an increase of between 20 and 32.5W/m^2 in the Back-Radiation.
I look forward to a detailed explanation of this increase. At present I cannot see it, and consider the IPCC predictions to be rubbish. The IPCC concentration on the thin, tenuous and insubstantial tropopause, instead of the surface (which after all is driving the atmosphere – the lapse rate is tied to surface temperature, not to the tropopause, and the quantity we are interested in – boundary layer temperature – is closely tied to surface temperature, but not to tropopause temperature) is in my view an unfortunate irrelevancy. The surface rules.
So let’s see the K&T budget for a 3 degree higher surface temperature, and in particular a detailed breakdown of the huge Back- Radiation increase, which overwhelmingly swamps the paltry 3.7W/m^2 “Radiative Forcing” at the Tropopause.
Colin, you’re like a breath of fresh air. 🙂
“The Surface Balance equation derived from the K&T diagram is:
Absorbed_Sunlight = (Radiation_from_the_Surface – Back-Radiation) + Conduction (“Thermals”) + Evaporation”
The ‘+ Evaporation’ is what often causes confusion here, because it also represents a ‘- to temperature’ at the surface. Energy into ‘Evaporation’ remains as ‘latent energy’ until it is released into a higher atmospheric altitude when WV condenses. This makes no difference to a TOA budget, but it wreaks havoc when trying to make logical sense of tropospheric atractors!
“If we change the surface temperature, say by 3 degrees (the IPCC most likely value for a doubling of CO2), and allow the system to rebalance (NB. I’m not talking instantaneous change, but drawing a new K&T diagram in 2100):”
OK, I’ll go along with this thought experiment.
“1. The Conduction (“Thermals”) term does not change. The temperature relationship between the atmosphere and the surface is usually assumed not to change (for example, the equilibrium lapse rate should be the same, as there is very little change in the amount of energy going into the atmosphere from the surface), there is no a priori reason to do so.”
This is a confusing scenario. ‘Evaporation’ also generates “Thermals”! However, I concur that a corresponding ‘dry’ atmosphere would exhibit negligible change to ‘thermal convection’ following a 3°C temperature increase.
“2. The Evaporation term increases. It’s pretty fundamental – if it gets hotter, more water gets evaporated. There is huge disagreement among scientists about how much, but the consensus seems to be between 2 and 7% per DegC. So this term increases between 4W/m^2 and 16.5W/m^2.”
This ‘is fundamental’ and its root lays in the ‘Clausius-Clapyron Relationship’ that proves RH is dependant on temperature. The only ‘scientific argument’ on this is the availability of liquid water to evaporate within the focus of observation, thus, surface water available and atmospheric water available are in dispute for varying regions. The ‘thrust’ of the argument is that a ‘low RH’ generally exhibits a higher ‘sensible heat’ that would eventually provide water with more energy to generate WV, thus, gives a ‘desert’ or ‘dry’ ‘label’ to the region within the focus of observation when RH is low.
Much of this ‘argument’ depends upon the antics of the hydrospheric cycle’s aberration caused by temperature change.
“3. Therefore the Net Radiation term (Radiation_from_the_Surface – Back-Radiation) DECREASES. But we know that Radiation_from_the_Surface increases by around 16W/m^2. So to maintain the increased temperature of the surface (ie to maintain energy balance, a fundamental requirement in the K&T diagram) there needs to be an increase of between 20 and 32.5W/m^2 in the Back-Radiation.”
This is the ‘problematic’ scenario that I described in ‘point 1’.
The release of heat energy by WV at altitude can only increase ‘back-radiation’ towards Earth’s surface whilst at the same time providing a more ‘open’ ‘window’ for OLR radiation to TOA.
The ‘Cartoon’ depicts TOA balance, not the machinations below this (TOA).
It’s a mess, isn’t it. 🙂
Best regards, Ray Dart.
Colin Davidson on June 29, 2011 at 10:55 am:
You make a very interesting point.
This has been covered by the great Ramanathan in his 1981 paper that is well worth a good read (it’s not a quick read).
The role of ocean-atmosphere interactions in the CO2 climate problem, V Ramanathan, Journal of Atmospheric Sciences, 1981.
Possibly others have since covered the subject more thoroughly. In any case it is a simplified model. Ramanathan comments on the 1981 explanation in Trace-gas greenhouse effect and global warming, V Ramanathan, Ambio, 1998:
On probably more than one occasion I have said that I will do an article on this subject and I hope readers can remind me of this if many more months go by with no article.
Colin Davidson says:
“In response to RW, I guess it is what you think is important that matters.
The only real force is Sunlight. So I reckon:
Absorbed_Sunlight = (Radiation_from_the_Surface – Back-Radiation) + Conduction (“Thermals”) + Evaporation
is the best (most descriptive) form of the Surface Energy Balance.”
From a certain point of view, yes. But it still obfuscates what’s really going on from a gross energy balance perspective, which is by far the most critical component of the entire system. The bottom line is it takes about 390 W/m^2 emitted at the surface to allow 235 W/m^2 to leave the system, offsetting the 235 W/m^2 entering the system from the Sun. Or more specifically, it takes about 1.6 W/m^2 of surface emission to allow 1 W/m^2 to leave the system (390/235 = 1.6). This figure already accounts for the lion’s share of the feedbacks in the system from decades, centuries and even millenia of solar forcing. How could it not?
This the fatal flaw in the 3 C rise theory that few seem to be recognizing. None of the energy in the system is trapped or hidden – its exit is just delayed. It takes 16.6 W/m^2 of additional power at the surface for a 3 C rise in temperature for a total net flux of 406.6 W/m^2. Conservation of Energy dictates this +16.6 W/m^2 flux has to be coming from somewhere. The atmosphere only provides about +6 W/m^2 at the surface (3.7 x 1.6 = 6 W/m^2) , leaving a deficit of 10.6 W/m^2. Where is the 10.6 W/m^2 coming from? The claim is it comes from the positive ‘feedbacks’, but why doesn’t feedback cause this much change on solar forcing? In other words, why doesn’t it take 1055 W/m^2 at the surface to offset the 235 W/m^2 from the Sun (16.6/3.7 = 4.5; 1055/235 = 4.5)???
This is the 64 million dollar question that no one seems to be able to answer: Why GHG forcing will be so enormously amplified when solar forcing is not.
What’s so special about the next 3.7 W/m^2 that the system will respond to it 3 times more powerfully than the original 98+% (235 W/m^2) from the Sun?
And this is even assuming all of the 3.7 W/m^2 is incident on the surface. In reality only about half of it does (less than half using Trenberth’s numbers) – making a response over 5.5 times more powerful than solar forcing needed for a 3 C rise.
My main point here is people seem to be getting lost in a lot of the micro details and not seeing the forest through the trees, largely I believe because of this Trenberth diagram. A 3 C rise from a +3.7 W/m^2 perturbation is way outside the system’s measured bounds. While this does not make it an absolute impossibility, it does – I think, make it an extraordinary claim requiring extraordinary proof.
Many people don’t understand the purpose of an energy budget. Many people haven’t read the article either.
What do Trenberth and Kiehl say in this paper about the response of the climate to a doubling of CO2?
Other papers explain that subject but this paper does not. It does not attempt to, and does not claim to.
If someone has a criticism of the values or the approach in Trenberth & Kiehl’s paper, please state them.
Are the values wrong?
Is a globally annually averaged energy balance diagram invalid?
If the criticism is that they should have written a completely different paper on a different subject..
“If someone has a criticism of the values or the approach in Trenberth & Kiehl’s paper, please state them.”
I have many, which I have already stated. Another is where is the return path for latent heat of water in the form of precipitation? The water is not leaving at the TOA – it has to be coming back to the surface, but this is not shown in the diagram.
Also, I agree that the paper does not say or imply anything about the response of the climate to a doubling of CO2, but it’s none the less highly misleading and obfuscatory in a multitude of ways. I also believe the diagram is one of the main reasons why so many people are confused about how the atmosphere actually contributes to the energy balance of the system and ultimately the surface temperature. Essentially, all the atmosphere does is act as ‘filter’ between the surface and space, where each pass through the ‘filter’ about 60% of what’s emitted at the surface escapes to space and about 40% is returned to the surface. The 40% returned is the greenhouse effect.
You’re all neglecting the point that a step change in forcing from ghg’s results in a reduction of outgoing radiation at the tropopause, not an increase of incoming radiation at the surface. Also, an increase in ghg concentration plus an increase in surface temperature at constant RH means that after equilibration atmospheric thermal radiation downward at the surface increases faster than outgoing radiation from the surface. And that’s not counting the increased forcing from the thermal expansion of the atmosphere causing the tropopause to move higher and increase the temperature differential between the tropopause and the surface. That same expansion will cause increased circulation and heat transfer from low to high latitudes. That’s where most of the temperature increase should occur.
RW,
In the case of latent heat transfer, the diagram only shows the net transfer of energy. The surface loses energy both by the evaporation of water and by warming the cooled water droplets that rain back down. It’s a heat engine cycle resulting in a net transfer of energy from the surface to the atmosphere with water and water vapor as the working fluid. The same thing applies to sensible heat transfer because the rising air has to come back down again too.
To be consistent, I also do not agree that the temperature rises by 1DegC in the “no-feedbacks” case. [The 1DegC figure is agreed by virtually all scientists, and is calculated as the average the radiating-to-space surfaces would have to rise if they were black bodies.]
In a doubled CO2 scenario, DeWitt Payne has stated that the incoming sunlight is further attenuated by about 1W/m^2 due to increased absorption. Because the back-radiation from CO2 is from lower in the atmosphere, I think that there is an increase of around 0.5W/m^2 in this due to a doubling of CO2. So the net effect at the surface is a cooling of 0.5W/m^2 (1W/m^2 less of absorbed sunlight, partly offset by increased back-radiation.)
At the same time there is increased absorption of surface radiation by the atmosphere [on SOD’s previous calculations, this amounts to about 6W/m^2:
390W/m^2 x (50%-46% change in opacity) x 40% no cloud cover.]
So the lower atmosphere gets warming by about 6W/m^2, less the 1W/m^2 less exported surface energy, less the 0.5W/m^2 increased back radiation. The upper atmosphere gets 1W/m^2 more due to increased absorption.
These will change the lapse rate, allowing a hotter upper atmosphere. I should think the net result is a slightly warmer upper troposphere and very little surface temperature effect. Certainly not 1DegC. More like 0.1DegC.
I don’t agree with either of you. What is happening is this:
When there is a radiative imbalance, i.e. from additional CO2 added to the atmosphere which redirects more outgoing surface radiation back to the surface, there is reduction in the amount of LW radiation leaving at the top of the atmosphere (more radiation is arriving from the Sun than is leaving at the top of the atmosphere). To achieve equilibrium, the system warms up until it again radiates the same amount of energy as is arriving from the Sun.
To give a numerical example, there is about 240 W/m^2 arriving post albedo from the Sun and 240 W/m^2 leaving at the top of the atmosphere. This represents the system in equilibrium (energy in = energy out). If there was a radiative imbalance (or ‘radiative forcing’) of say 3.7 W/m^2 from a doubling of CO2, the energy leaving at the top of the atmosphere would reduce by 3.7 W/m^2 to 236.3 W/m^2. Currently, there is about 390 W/m^2 emitted by the surface. In this example, an additional 3.7 W/m^2 is received by the surface for a total of 393.7 W/m^2. If the +3.7 W/m^2 is treated the same as the 240 arriving from the Sun, it will be amplified by a factor of about 1.6 (390/240 = 1.6), as this is a measurement of the surface response to forcing of any kind. 3.7 W/m^2 x 1.6 = +6 W/m^2 to allow an additional 3.7 W/m^2 to leave the system to restore equilibrium (240 W/m^2 in and out). The new surface emitted radiation would be 396 W/m^2 (390 W/m^2 + 6 W/m^2), which corresponds to a 1.1 C rise in temperature.
What is misleading about the often quoted 1.1 C of ‘intrinsic’ or ‘no feedback’ warming is that 3.7 W/m^2 only provides about 0.7 C of direct warming. The additional 0.4 C comes from adding on net transmittance to space of about 0.6 (3.7 x 0.6 = 2.3 W/m^2, which equals 0.4 C and 0.4 C + 0.7 C = 1.1 C). Why this is misleading, as I mentioned before, is the net transmittance to space of 0.6 already accounts for the lion’s share of the feedbacks in the system from decades, centuries of solar forcing.
Colin Davidson on June 30, 2011 at 4:40 am:
As two side-notes:
1. No blackbody assumption is used in the calculation.
2. Using the calculation above the correct result will turn out less. The transmittance calculation I did was averaged only across 500-850 cm-1, not across the complete spectrum of surface radiation. And to get the complete effect it should be “Planck weighted” across 4-50μm.
Your calculation is fundamentally flawed.
In this calculation, at the end, the whole climate system is still out of balance. You have attempted to calculate the instantaneous surface result from a top of atmosphere imbalance.
Ok. So you have done the calculation but the radiative imbalance still exists. (Or if you think not, you need to explain why this surface change has restored the TOA energy balance). What happens when more energy is absorbed by the climate system than leaves the climate system? It continues to absorb energy – even with your new surface balance.
Where is the energy absorbed? It doesn’t actually matter for the purposes of the “broad brush” analysis.
Until such time as the climate system emits the same approximate value of flux as it absorbs it will continue to absorb energy. And the surface temperature will keep increasing.
This is why, even though none of us live at the TOA, it is important for calculating the surface result.
And, another side note, the changing lapse rate is part of the feedback. The “no feedback” result is without a lapse rate change. The predicted increasing lapse rate is a negative feedback – as more energy will be radiated to space with a hotter upper troposphere.
I would like to thank SOD for his response, and particularly for clarifying that the transmittance calculations are for a restricted part of the spectrum. If I may scribble further on the envelope:
1. The surface radiation absorbed by CO2 at present is about 16% of the power in the spectrum [a crude approximation is total opacity between 13.5 and 17um]
2. I think the transmittance numbers imply that the percentage would increase, to about 18%.
There is no question that the atmosphere will heat up – and from the bottom up if SOD’s numbers are correct. I just don’t see a huge effect at the surface.
If we take the IPCC numbers for “Radiative Forcing” and “Surface Forcing” (IPCC AR4 (2007) WG1 Chapter 2, Figure 2.23 http://www.ipcc.ch/publications_and_data/ar4/wg1/en/figure-2-23.html ), we see a claimed change of 2W/m^2 “Radiative Forcing” due to LLGHGs from 1850, but only 0.4W/m^2 change in “Surface Forcing” due to the same cause. ie the RF is translated to the surface but only as a fraction of the original. So the effect on the surface of high tropospheric temperature change is minimal.
I want to consider SOD’s post further, [and then question the statement that back-radiation increases faster than surface radiation.]
Colin: The differences between calculating radiative forcing at the surface and at the tropopause is mostly due to saturation. In a comment to one of SOD’s posts on his models of the greenhouse effect, I calculated that the maximum radiative forcing for 2X CO2 occurs at wavelengths that absorb and transmit 50% of the outgoing radiation. Doubling CO2 increases absorption to 75% and reduces energy flux by 25%. In contrast, wavelengths where 5% is transmitted, doubling CO2 reduces the transmittance to 0.25%; a 4.75% decrease in energy flux. At wavelengths where 5% is absorbed, doubling CO2 increases absorption to 9.75%; a 4.75% decrease.
CO2’s absorption partially overlaps with water vapor. Due to the high humidity near the surface, many wavelengths that are nearly opaque near the surface (and therefore can’t produce much radiative forcing) are partially transparent at the tropopause (and can produce significant forcing). This appears to be the major reason why forcing at the surface is less than at the tropopause.
The difficulty with using the radiative forcing calculated near the surface is that surface temperature is controlled by the lapse rate and not by radiative equilibrium near the surface. The IPCC calculates radiative forcing at the tropopause, calculated the no-feedbacks temperature change anticipated at the tropopause from this radiative forcing, postulates that the lapse rate from tropopause to the surface won’t change and therefore that the surface temperature will rise as much as the tropopause. Climate models, but not fundamental physics, are used to suggest that this analysis is correct. Unfortunately, climate models don’t have the resolution to properly model convection. Other than climate models, I’m not aware of any fundamental reason why a 1 degK temperature rise at the tropopause can’t be associated with an 0.5 or 0.1 degK rise in surface temperature and an increase in the rate at which energy is convected upwards. The unpublished draft of a paper mentioned at PielkeSr’s blog SPECULATES about how this might occur. http://pielkeclimatesci.wordpress.com/2011/05/01/guest-post-by-marcel-severijnen-in-memory-of-noor-van-andel/
Colin Davidson:
You can see the same idea in a simple model in Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Four – take a look at figure 7 and the explanation. It is easy to create a scenario with a TOA imbalance yet zero change to the surface balance.
Does this scenario mean zero change to surface temperature?
It does today and tomorrow. But not over decades.
Or at least, this is true in the “no feedback” case. Important to consider the “no feedback” case because it is simpler and therefore there is less room for us to reach different conclusions.
SoD asks “Is a globally annually averaged energy balance diagram invalid?”
I dont think its a case of being “invalid” so much (although others will argue about the values used) rather its a case of how useful it is.
So for example where the earth is thought to be warming the most in the North of the Northern hemisphere, the values for “Reflected by Surface” are quite “wrong” due to the much larger albedo there. So thinking about how CO2 effects and is effected by the values from KT97 is going to be misleading.
I guess what I’m really saying here is that changes in the KT values are going to have non-linear and non-obvious effects on the other values. So a reduction in cloud cover would alter the KT97 values quite differently depending on where and when it happened.
I’m not convinced these kinds of arguments are appreciated by everyone who looks at that diagram.
RW wrote: “Currently, there is about 390 W/m^2 emitted by the surface. In this example, an additional 3.7 W/m^2 is received by the surface for a total of 393.7 W/m^2.”
A 3.7 W/m2 reduction in outgoing OLR at the tropopause does not have to produce a 3.7 W/m2 increase in flux at the surface or any particular change at the surface. Since upward energy flux by convection can change in response to changes in radiative forcing, energy that can’t escape to space by radiation can reach the tropopause by convection.
The IPCC assumes all the 3.7 W/m^2 will be incident on the surface. This is how they are getting a 1.1 C rise from 2xCO2.
BTW, the 3.7 W/m^2 is not really the reduction in OLR at the tropopause, it is the reduction in the net surface transmittance to space. It is the additional amount absorbed by the atmosphere that previous passes straight through the atmosphere as if the atmosphere wasn’t even there.
SOD: KT97 doesn’t seem to be available online, so I have what appears to be a simple (possibly dumb) question: How is energy transfered vertically by thermals? Upward convection in one location must be associated by downward convection in another location. Why does the NET process transfer energy upwards?
The situation might be analyzed in terms of a cyclic flow of a packet of air from the surface to the tropopause and back again. At a given altitude, an air packet has a certain amount of potential energy (mgh) and thermal energy (RT). One is converted to the other. There is also PV work done during expansion and contraction, but that may net out to zero in a cycle. If there is an average total energy (mgh + RT) for an altitude, unusually hot air at the surface with more than average total energy might rise and then radiatively cool until it becomes average.
Frank,
If all atmospheric motions were adiabatic (no heat transferred) then the movement of air from the surface up into the atmosphere and back down to the surface would result in net heat transfer = 0.
The fast motions of the atmosphere establishes the temperature profile quite close to the adiabatic lapse rate, but not all air movement is adiabatic.
In any case, the sensible heat transfer from the surface into the atmosphere is difficult to ascertain. In the 1997 paper the authors say:
Hopefully this is clear. Their approach is to find sensible heat (SH) as the balancing item.
The alternative is to use a “bulk aerodynamic formula”, which has the form:
SH = cpρCDUr(Ts-Ta(zr)
CD = an empirically determined value, of the order of 10-3
Ur = the wind speed at reference height zr
Ts = the surface temperature
Ta(zr) = the atmospheric temperature at the reference height.
cp = specific heat capacity
ρ = density
Then of course you need a comprehensive dataset (like from a reanalysis project like ERA40 or NCEP/NCAR) to be able to make an estimate of this value.
Free link to paper: Earth’s annual global mean energy budget
Thanks, SOD. I not surprised to learn that KT was using sensible heat as a “fudge factor” to bring everything into balance. It’s nice to read that this factor agrees with pre-AGW estimates of sensible heat transfer over the ocean.
If I think about heat transfer from my car engine to the radiator, it’s fairly easy to derive a formula for sensible heat transfer involving the temperature difference between the working fluid coming and going, the flow rate of the fluid, and the heat capacity of the fluid. I can imagine the Hadley circulation as being somewhat analogous (except that we now need to include the potential energy of the working fluid in the calculation and PV work done by the fluid). (I assumed that KT’s thermals represented bulk flow if sensible heat like the Hadley circulation.) The analogy becomes more confusing when I ask how heat enters and leaves the working fluid. In the engine and the radiator, this happens by conduction. By what mechanism can the surface of the earth warm the Hadley circulation when it is near the surface of the earth (the trade winds)?
The Hadley circulation presumably can lose heat at the top of the troposphere by radiation (like any air at this altitude). If it is warmer than most air at this altitude due to its sensible heat content, it could radiate more heat than typical for this altitude. Therefore the “working fluid” appears to have a mechanism for losing heat.
In the case of the Hadley circulation, the temperature difference between the ascending and descending branches (at a specified altitude) doesn’t directly tell us about sensible heat transfer because the ascending branch is dramatically warmed by latent heat. (This provides a great mechanism for getting heat into the “working fluid”, but it doesn’t happen at the surface.) Unfortunately, the descending branch reaches the surface above some of the hottest deserts in the world, so it not obvious the descending branch is cooler than the ascending branch. The descending branch is also slower and wider than the ascending branch so it has more time to equilibrate by radiative mechanisms.
The formula you cite for bulk aerodynamic flow certainly doesn’t describe a process like the Hadley circulation. I assume this formula applies to some other form of convection or turbulent mixing. The formula looks a little strange because the distance over which energy is transfered is not explicitly input into the formula – though it certainly enters indirectly through the temperature difference.
Is sensible heat transfer by large scale circulation (like the Hadley circulation) is trivial compared with bulk heat transfer?
Frank:
Sorry, I didn’t give a very complete response. The formula cited is the first step in the process – the transfer of heat from the surface to the ocean. (And the latent heat formula is similar in form).
You have described the mechanisms of heat transfer within the total atmospheric circulation.
Is it necessary to do this calculation – GCM-like?
Probably not (unless you want to get a better understanding of the processes of how this sensible heat moves through the climate system), because if you know the atmospheric temperature at 10m and the surface temperature, plus the wind speed at 10m then you can make a reasonable stab at the net transfer from the surface -> atmosphere.
The references in KT97 are mostly to books. There is a reference to the uncertainties in making these calculations due to the paucity of data. Uncertainties in global ocean surface heat flux climatologies derived from ship observations, Gleckler & Weare (1995).
In Trenberth, Fasullo & Kiehl (2009) – the updated paper – they describe the data as available from reanalyses:
And a reanalysis would compute the heat transfer in and out of every grid cell at every time step. So it would be possible, at least within the constraints of the accuracy of a reanalysis project, to track how and where the heat is transferred up from the surface and lost into the general atmosphere + out to space.
RW said:
This is incorrect. I note this for readers other than RW who are interested in finding things out and being accurate.
OK, then how do they get a +1.1 C surface temperature from the 3.7 W/m^2?
You do understand that if the surface temperature increases by 1.1 C it must also radiate an additional 6 W/m^2, and this +6 W/m^2 flux at the surface has to be coming from somewhere, right?
RW,
You have exhausted my patience. So far (e.g. here) you have demonstrated that you are not interested in learning anything. Only in telling everyone what you already know. Much of which is wrong.
To help other readers, who might mistake your huge confidence for accuracy, I will point out some mistakes from time to time.
Anyone can easily just declare someone as being wrong. If you’re not willing to back up the claim or just don’t want to engage in discussion to support it, that’s fine with me. Ultimately, the readers can decide for themselves.
Personally, I thought the questions I asked were perfectly reasonable.
That being said, I would like to applaud you for this site. Unlike other sites that heavily filter and moderate the content to suit their particular point of view, you do not and essentially let everyone make up their own mind. That says a lot about you’re own personal and scientific integrity.
I meant to say ‘your own personal and scientific integrity’. Feel free to fix if you like.
It would be wonderful to see a K&T diagram for an 18DegC Surface Temperature, which is the median of what we are assured will happen if CO2 is doubled.
I have been trying to get at the numbers:
1. The LW radiation from the surface will be 406W/m^2.
2. The Evaporation from the surface will be somewhere in the range 84-94W/m^2.
3. The Conduction from the Surface will be 24W/m^2.
4. DeWitt Payne has stated that the sunlight hitting the Surface will be reduced by 1W/m^2 due to the increased absorption by the thicker CO2.
5. There will be a balancing increase in Back-Radiation, which must therefore lie between 347 and 357W/m^2.
6. There will be increased absorption of photons by the higher concentration of CO2. I am unsure by how much.
[7. There will be a change in the Lapse Rate due to the increased energy absorbed by the lower atmosphere (6 above minus the 1W/m^2 at 4 above). This will increase the temperature throughout the lower atmosphere.
8. There will also be increased energy to be radiated to space from the upper atmosphere due to the increased CO2. This will be partly supplied by 4 above.]
The big unknown for me is paragraph 5. It would be nice to see a detailed budget for this quantity:
A. How much is due to increased atmospheric temperature?
B. How much is due to increased CO2, lowering the effective height from which radiation is occurring, thus increasing the temperature of the emitting molecules, thus increasing the intensity at CO2 frequencies?
C. Is there any change in cloud cover due to the increased evaporation rate? If so does it also impact on 4 above?
D. How much is due to increased Water Vapour along the lines of B above?
Of great interest is the uncertainties in the numbers. 2 above has a very large plausible range, and I suspect C and D above are also highly uncertain.
Scdience of Doom wrote:
“And, another side note, the changing lapse rate is part of the feedback. ”
My thesis was that increased CO2 meant increased absorption of surface radiation by the atmosphere (the “window” closes a little). That increase in energy entering the atmosphere immediately means a change in the Lapse Rate.
In my view this is not a feedback.
Colin Davidson,
Where did you get the 406 W/m^2 value from? Is it based on some sort of models?
From the Stefan Boltzmann equation. E=5.67×10-8T4.
The emissivity of the surface is close to 1. At least, emissivity=1 is a good working assumption for the purposes of this exercise.
The 406 W/m^2 (+16 W/m^2) comes from the Stefan-Boltzman Law. At a temperature of 291K (+3 C), the surface will emit 406 W/m^2.
Colin Davidson,
I think you’re missing the bigger picture. When CO2 is doubled, the ‘window’ closes by 3.7 W/m^2. Using Trenberth’s 70 W/m^2 “window’, this will reduce to 66.3 W/m^2 and the atmosphere will absorb an additional 3.7 W/m^2 that previously passed straight through as if the atmosphere wasn’t even there. I know SoD says otherwise, but the IPCC claims the 3.7 W/m^2 is the equivalent of 3.7 W/m^2 of solar forcing – all of which goes to the surface to affect its temperature. How could it affect the surface temperature if it doesn’t go the surface?
Even if you don’t think the full post albedo reaches the surface, if watts of GHG ‘forcing’ are equivalent to watts of solar forcing as the IPCC claims, this doesn’t really matter. 235 W/m^2 from the Sun ‘forces’ the climate system and this forcing results in a surface emitted energy of 390 W/m^2. If 3.7 W/m^2 additional watts of ‘forcing’ from 2xCO2 is to become 406.6 W/m^2 (+16.6 W/m^2) required for a 3 C rise, you might ask K&T why it doesn’t take 1054 W/m^2 at the surface to offset the 235 W/m^2 from the Sun (16.6/3.7)*235 = 1054. You might also ask K&T where the +12.9 W/m^2 flux at the surface is coming from (16.6 – 3.7 = 12.9)
SoD,
I don’t think you can derive W/m^2 value from average temperature (which Colin used as basis I understood) simply with the Stefan-Boltzman thingy due to the power of 4 relationship between E and T?
But I suppose Kiehl and Trenbeth made the same simplification for their picture.
Have a look at the comment above.
Calculating the flux at every point and every time gives a similar answer although slightly larger. And to calculate the change in surface radiation from a surface temperature change we have no reason to consider the min/max profile changing.
Sorry about missing that, but I wouldn’t call 6-7 W/m^2 “slightly” to be honest. At least not in the context of the topic. Emissivity probably isn’t 1 either though, so for illustrative purposes I suppose it’s ok to cheat a bit on that.
I think we can say that for the purposes of Colin’s argument, an increase in 3’C will lead to an increase of 16 W/m2 in surface emitted radiation, unless significant changes take place in diurnal, seasonal or geographical distribution of temperature.
Colin
Higher SST does not necessarily mean more evaporation http://www.aoml.noaa.gov/phod/docs/wang_etal-99b.pdf
“Physically, in responseto a decrease (increase) in SST, the surface wind speed is strengthened (weakened). The strengthening (weakening) of the surface wind speed increases (decreases) the latent heat flux, which, in turn, results in more (less) SST cooling.”
RW
1 W/m2 at TOA from CO2 does not equal 1 W/m2 from solar because much of the solar is reflected at the surface.
It equals 1 W/m^2 of post albedo solar.
RW,
Normally I wouldn’t bother to reply, but I believe this point might actually be of interest.
That is simply not true as can be easily demonstrated by doing the RTE calculation at MODTRAN ( http://geoflop.uchicago.edu/forecast/docs/Projects/modtran.orig.html ). I ran the calculation for both the US standard atmosphere and the tropical atmosphere. The atmospheric transmittance is available in the text file (scroll all the way to the bottom ) that can be obtained by clicking on the ‘View the whole output file’ link at the bottom of the lower graph.
In MODTRAN as implemented on the web power is calculated for frequencies from 100-1500 cm-1. Transmittance below 100 and above 1500 cm-1 is zero. All calculations are for clear sky as transmittance from the surface through clouds is zero for any CO2 concentration.
US standard atmosphere:
0 km looking down: 360.472 W/m²
280 ppmv CO2 transmittance 0.2551 or 91.96 W/m²
560 ppmv CO2 transmittance 0.2491 or 89.94 W/m²
difference 2.02 W/m²
12 km looking down (lower tropopause)
280 ppmv CO2 267.62 W/m²
560 ppmv CO2 264.20 W/m²
difference 3.4 W/m²
Tropical atmosphere
0 km looking down 417.306 W/m²
280 ppmv CO2 transmittance 0.1465 or 61.14 W/m²
560 ppmv CO2 transmittance 0.1440 or 60.09 W/m²
difference 1.05 W/m²
17 km looking down (tropopause)
280 ppmv CO2 290.921 W/m²
560 ppmv CO2 286.431 W/m²
difference 3.49 W/m²
The forcing is the difference in upward radiation at the tropopause and not the difference in directly transmitted radiation from the surface.
You have to be “looking down” from the same height – preferably from the TOA if you want the total transmittance ‘window’ through the atmosphere.
I think you’re forgetting that there are three possible sources of emitted energy that passes through the ‘window’ to space. There is surface emitted, cloud top emitted and also the heated gases of the atmosphere also emit – some of which too passes through the ‘window’ directly to space.
Let me ask you this: if the 3.7 W/m^2 from 2xCO2 is not a decrease in the ‘window’ transmittance to space, how could it warm the surface? If it’s just absorbing energy that is already being absorbed by the atmosphere, there would no effect. Or are you saying only part of it represents a reduction in the ‘window’?
What I mean is the net radiative ‘forcing’ from 2xCO2 can’t be more than the reduction in ‘window’ transmittance since by definition anything that isn’t passing through the ‘window’ prior to CO2 being doubled is already being absorbed by the atmosphere.
RW,
Duh! Teach your grandmother to suck eggs.
See first reply. All that stuff is built into MODTRAN. As for cloud tops, you did read where I said that I used only clear sky conditions.
Umm. Less energy is being emitted so the atmosphere is absorbing more energy than was previously absorbed. When more energy is absorbed than emitted, warming happens. When that warming has happened, the surface will see more radiation from the warmer atmosphere than it did before. But the IPCC calculates forcing before the atmosphere below the tropopause and the surface can equilibrate.
My patience was exhausted by you long before SoD. You have officially been added to my mental killfile (mental because the killfile script doesn’t work here) so any further comments from will probably be ignored. Back in the USENET days this was indicated by the following sound effect: *plonk*.
Trenberth numbers seems to be wrong in the most important part for AGW models.
Where the solar heat is absorbed. Average of 168 w/m2 is far to high when 250 w/m2 are for clear sky conditions.
Trenberth over estimate earth surface absorbation which suit CO2 AGW models. In reality are atmospheric absorbation about the same number as surface absorbation.
The temperature on the surface are very much depending on where the average atmospheric absorbation are in altitude due to the gas law.
If this altitude increase will earth be warmer.
“http://earthobservatory.nasa.gov/Features/BlanketClouds/”
Do you have some evidence for your claim about atmospheric absorption being approximately equal to surface absorption of solar radiation?
The globally averaged values of surface and atmospheric absorption of solar radiation are calculated, but they are also constrained by measurements from a high quality network called BSRN (baseline surface radiation network).
[You can see more about the BSRN in The Amazing Case of “Back-Radiation”.]
Kiehl and Trenberth note an important uncertainty in their 1997 paper:
This is because:
a) the calculation of absorption of solar radiation in a cloudy atmosphere is more difficult than in a clear atmosphere and both are more difficult than calculating longwave absorption
b) limited high quality measurements at ground stations
In the 2009 update to the paper, the authors note (re their comment cited above):
And they write more about this subject, so I recommend reading the 2009 paper.
I am thinking that if there is a change in TOA imbalance of 0.9 it would show up in the 40w clear window as a slight reduction if CO2 and water closed the window slightly. Is this correct as understood today by Trenbarth.
Looking at the diagram further and thinking harder I would change the TOA imbalance to show up in the emitted to atmosphere part 165 W according to Trenbarth. Is this correct?
What the imbalance would mean, is that the top of the tropospheres path length would increase around 15micron, raising the altitude at which this energy being radiated in this band can effectively escape our atmosphere… so the bottom of the tropopause would raise slightly, and then need to warm enough that it is radiating this energy out… which would mean that the lower levels would also need to warm to move the energy up to this altitude…
Put very simply, but as you increase T’s you are also going to increase loses through other wavelengths at various altitudes. This blog is a good place to start hunting for conceptual understanding, the series CO2 – An Insignificant Trace Gas? is a good place to start. Im still working on my understanding of it too 😉
[…] a discussion a little while ago on What’s the Palaver? – Kiehl and Trenberth 1997, one of our commenters asked about the surface forcing and how it could possibly lead to anything […]
Thanks for posting the above. The energy tally seems like an useful tool for verifying models,etc. In a very simple model I have (semigrey) when there is no convection the ground temp and the bottom air layer temp differ quite a bit. In order to bring these two temps to be the same a large amount of heat must transfer from the ground to the atmosphere. So far I get in the order of 1/2 of the incoming radiation. Trenbert etc has about (78+24)/342 ~ 30%
I was also surprised to see that the percentage of the energy absorbed by the atmosphere of the energy that actually reaches the ground is so high (67/168 ~40%) which means that the general assumption of a tranparent atmosphere to visible (shortwave) radiation is not a very goof one (and it is one more thing one must add to a model)
Because of your post I went looking and I found this newer version of his info:
Trenberth paper 2009
SoD,
This is a good write up, but most importantly still, Trenberth’s depiction does not show net energy flux in any discernable way, and he incorrectly mixes non-radiative and radiative energy fluxes in a way that doesn’t account for the non-radiative energy returned to the surface as the temperature component of precipitation, wind, weather, etc.
I saw an entertainingly bad article on tallbloke’s blog about ocean emissivity and wrote some comments on it.
For example, here:
I followed with a few other caustic comments including on the spreadsheet presented for earth’s energy balance with a low value of emissivity. This seemed to be just “invent a number” and divide it by another number and get an invented emissivity – that matched the number “found” on the MODIS plot.
This started a fascinating approach to science by the blog owner.
Well, being as my final summary got deleted for reasons that will be obvious – and because they relate to the subject of this article I thought they were worth repeating:
tallbloke wrote:
So I asked what were glaring errors and the merry-go-round started. It’s not very interesting but can be seen by working through the blog comments.
It finished with a summary by me of:
————————————
[Tallbloke Reply] You are editorialising innacurately. Stick to discussing the science, including the incorrect ‘window’ figure.
—————————————
So I replied in a comment that was deleted:
And reduced to this:
My adieu was also deleted:
—————————————
Which pretty much confirms the substance of this article in the first place – e.g. I wrote “As I review the “critiques” around the blogosphere, I don’t find any consistent objection. That makes it very hard to write about.“.
Usually each person stays with one objection though..
[…] What’s the Palaver? – Kiehl and Trenberth 1997 Do Trenberth and Kiehl understand the First Law of Thermodynamics? Understanding Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations […]
A “consistent objection” is the missing source for the atmospheric radiation,
as N2, O2, and Argon are not able to radiate at all in the troposphaere and CO2 does not want under the pressure of other gases.
But K&T says more than 500W/m2 ???
The collisions with N2, O2 and Ar are what keep a constant fraction of the ghg molecules like CO2 and H20 in an excited state. That fraction is determined by the kinetic temperature of the gas, the excitation energy and the degeneracy of the excited state. The rate of emission is then determined, to a first approximation, by the product of the number density of excited molecules and the respective Einstein A21 coefficients at each wavelength. If CO2 and H2O don’t emit radiation, then what are the IR Spectrophotometers like the AERI instrument, measuring? The answer, of course, is that they do emit. I’m assuming that the 500 W/m² you quote is the sum of the upward radiation to space and the downward radiation to the surface by the atmosphere.
If that radiation didn’t exist, it would be a whole lot colder. And please don’t try to tell me that there is no such thing as downward radiation because it would violate the Second Law. That issue is addressed elsewhere in this blog.
w.paul,
You say:
Can you explain what you mean by “CO2 does not want under the pressure of other gases” ?
Then at least we can determine what your objection is.
Please also take a look at:
The Amazing Case of “Back Radiation” -Part One – all about DLR or “back radiation” and the measurements from ground stations around the world.
The Amazing Case of “Back Radiation” – Part Two – the spectra of DLR – demonstrating that DLR is emitted from the trace gases in the atmopshere.
Theory and Experiment – Atmospheric Radiation – real values of total flux and spectra compared with the theory.
These three articles might help – as they provide measurements of upward and downward atmospheric radiation, and how these results are consistent with the well-established theory of radiative transfer – for the maths and fundamental physics behind radiative transfer please take a look at Atmospheric Radiation and the “Greenhouse” Effect – Part Six – The Equations.
If you still have an idea that somehow the measurements and/or theory are wrong, it will be wonderful to hear.
What is usually lacking in any “critique” of KT97 is any alternative values. This is one of the most entertaining sides of hearing how KT97 is so flawed.
It will be the work of moments for me to point out the flaws in any alternative values that entertain substantial changes from KT97/TFK2009 – I expect that the alternative values will:
1. Require a new theory of the measurement of radiation – which will overturn the last 140 years of measurements and require all physics textbooks which include the theory of thermal radiation to be rewritten.
2. Require a new theory of radiative transfer in the atmosphere – which will overturn the last 60 years at least since Subrahmanyan Chandrasekhar’s work in this field.
3. Require a new theory of the emission and absorption of radiation by “radiatively-active molecules” – undermining the last half a century at least of spectroscopy.
Turgid volumes like Journal of Quantitative Spectroscopy & Radiative Transfer will probably need to close up shop as they have been party to the crazy ideas of atmospheric radiation, in papers like The HITRAN 2008 molecular spectroscopic database, LS Rothman et al, 2009.
Of course, we all know that LS Rothman et al 2009 is a compilation of work by others, so there is merely the task of refuting 389 papers in the field of spectroscopy.
Please delight the readers of this blog with the unusual approach of providing:
a) alternative values
b) where the previous 100+ years of textbook physics and spectroscopy basics went wrong.
@ w.paul & SoD …
one of the main problems with w. paul (his name here, Dr. Paul @ the EIKE climate blog in german) is, that he believes eg. DLR does not exist, instruments like Pyrgeometers do only messure temperature and at all, this instruments and the so called greenhouseffekt are part of the “great global climate conspiracy”
First, all his statements had some funny part, now, some years later the statements did not change one mm, but became more frequent and today Paul visits foreign blogs, because in his “homeblog” nobody, not the biggest sceptics at all, find any usefull argument and the “admins” are not realy able to stop the tousands of times repeated nonsens. It´s just boring and a shame.
Anyway, good work here, very professional page and best informations on how climate works.
Greetings from Austria,
Gunnar
Anay
Gunnar,
Jetzt, alles ist klar.
Thanks for finally writing about >Whats the Palaver?
– Kiehl and Trenberth 1997 | The Science of Doom <Loved it!