I don’t think this is a simple topic.
The essence of the problem is this:
Can we measure the top of atmosphere (TOA) radiative changes and the surface temperature changes and derive the “climate sensivity” from the relationship between the two parameters?
First, what do we mean by “climate sensitivity”?
In simple terms this parameter should tell us how much more radiation (“flux”) escapes to space for each 1°C increase in surface temperature.
Climate Sensitivity Is All About Feedback
Climate sensitivity is all about trying to discover whether the climate system has positive or negative feedback.
If the average surface temperature of the earth increased by 1°C and the radiation to space consequently increased by 3.3 W/m², this would be approximately “zero feedback”.
Why is this zero feedback?
If somehow the average temperature of the surface of the planet increased by 1°C – say due to increased solar radiation – then as a result we would expect a higher flux into space. A hotter planet should radiate more. If the increase in flux = 3.3 W/m² it would indicate that there was no negative or positive feedback from this solar forcing (note 1).
Suppose the flux increased by 0. That is, the planet heated up but there was no increase in energy radiated to space. That would be positive feedback within the climate system – because there would be nothing to “rein in” the increase in temperature.
Suppose the flux increased by 5 W/m². In this case it would indicate negative feedback within the climate system.
The key value is the “benchmark” no feedback value of 3.3 W/m². If the value is above this, it’s negative feedback. If the value is below this, it’s positive feedback.
Essentially, the higher the radiation to space as a result of a temperature increase the more the planet is able to “damp out” temperature changes that are forced via solar radiation, or due to increases in inappropriately-named “greenhouse” gases.
Consider the extreme case where as the planet warms up it actually radiates less energy to space – clearly this will lead to runaway temperature increases (less energy radiated means more energy absorbed, which increased temperatures, which leads to even less energy radiated..).
As a result we measure sensitivity as W/m².K which we read as Watts per meter squared per Kelvin” – and 1K change is the same as 1°C change.
Theory and Measurement
In many subjects, researchers’ algebra converges on conventional usage, but in the realm of climate sensitivity everyone has apparently adopted their own. As a note for non-mathematicians, there is nothing inherently wrong with this, but it just makes each paper confusing especially for newcomers and probably for everyone.
I mostly adopt the Spencer & Braswell 2008 terminology in this article (see reference and free link below). I do change their α (climate sensitivity) into λ (which everyone else uses for this value) mainly because I had already produced a number of graphs with λ before starting to write the article..
The model is a very simple 1-dimensional model of temperature deviation into the ocean mixed layer, from the first law of thermodynamics:
C.∂T/∂t = F + S ….[1]
where C = heat capacity of the ocean, T = temperature anomaly, t = time, F = total top of atmosphere (TOA) radiative flux anomaly, S = heat flux anomaly into the deeper ocean
What does this equation say?
Heat capacity times change in temperature equals the net change in energy
- this is a simple statement of energy conservation, the first law of thermodynamics.
The TOA radiative flux anomaly, F, is a value we can measure using satellites. T is average surface temperature, which is measured around the planet on a frequent basis. But S is something we can’t measure.
What is F made up of?
Let’s define:
F = N + f - λT ….[1a]
where N = random fluctuations in radiative flux, f = “forcings”, and λT is the all important climate response or feedback.
The forcing f is, for the purposes of this exercise, defined as something added into the system which we believe we can understand and estimate or measure. This could be solar increases/decreases, it could be the long term increase in the “greenhouse” effect due to CO2, methane and other gases. For the purposes of this exercise it is not feedback. Feedback includes clouds and water vapor and other climate responses like changing lapse rates (atmospheric temperature profiles), all of which combine to produce a change in radiative output at TOA.
And an important point is that for the purposes of this theoretical exercise, we can remove f from the measurements because we believe we know what it is at any given time.
N is an important element. Effectively it describes the variations in TOA radiative flux due to the random climatic variations over many different timescales.
The climate sensitivity is the value λT, where λ is the value we want to find.
Noting the earlier comment about our assumed knowledge of ‘f’ (note 2), we can rewrite eqn 1:
C.∂T/∂t = - λT + N + S ….[2]
remembering that - λT + N = F is the radiative value we measure at TOA
Regression
If we plot F (measured TOA flux) vs T we can estimate λ from the slope of the least squares regression.
However, there is a problem with the estimate:
λ (est) = Cov[F,T] / Var[T] ….[3]
= Cov[- λT + N, T] / Var[T]
where Cov[a,b] = covariance of a with b, and Var[a]= variance of a
Forster & Gregory 2006
This oft-cited paper (reference and free link below) calculates the climate sensitivity from 1985-1996 using measured ERBE data at 2.3 ± 1.3 W/m².K.
Their result indicates positive feedback, or at least, a range of values which sit mainly in the positive feedback space.
On the method of calculation they say:
This equation includes a term that allows F to vary independently of surface temperature.. If we regress (- λT+ N) against T, we should be able to obtain a value for λ. The N terms are likely to contaminate the result for short datasets, but provided the N terms are uncorrelated to T, the regression should give the correct value for λ, if the dataset is long enough..
[Terms changed to SB2008 for easier comparison, and emphasis added].
Simulations
Like Spencer & Braswell, I created a simple model to demonstrate why measured results might deviate from the actual climate sensitivity.
The model is extremely simple:
- a “slab” model of the ocean of a certain depth
- daily radiative noise (normally distributed with mean=0, and standard deviation σN)
- daily ocean flux noise (normally distributed with mean=0, and standard deviation σS)
- radiative feedback calculated from the temperature and the actual climate sensitivity
- daily temperature change calculated from the daily energy imbalance
- regression of the whole time series to calculate the “apparent” climate sensitivity
In this model, the climate sensitivity, λ = 3.0 W/m².K.
In some cases the regression is done with the daily values, and in other cases the regression is done with averaged values of temperature and TOA radiation across time periods of 7, 30 & 90 days. I also put a 30-day low pass filter on the daily radiative noise in one case (before “injecting” into the model).
Some results are based on 10,000 days (about 30 years), with 100,000 days (300 years) as a separate comparison.
In each case the estimated value of λ is calculated from the mean of 100 simulation results. The 2nd graph shows the standard deviation σλ, of these simulation results which is a useful guide to the likely spread of measured results of λ (if the massive oversimplifications within the model were true). The vertical axis (for the estimate of λ) is the same in each graph for easier comparison, while the vertical axis for the standard deviation changes according to the results due to the large changes in this value.
First, the variation as the number of time steps changes and as the averaging period changes from 1 (no averaging) through to 90-days. Remember that the “real” value of λ = 3.0 :
Figure 1
Second, the estimate as the standard deviation of the radiative flux is increased, and the ocean depth ranges from 20-200m. The daily temperature and radiative flux is calculated as a monthly average before the regression calculation is carried out:
Figure 2
As figure 2, but for 100,000 time steps (instead of 10,000):
Figure 3
Third, the estimate as the standard deviation of the radiative flux is increased, and the ocean depth ranges from 20-200m. The regression calculation is carried out on the daily values:
Figure 4
As figure 4, but with 100,000 time steps:
Figure 5
Now against averaging period and also against low pass filtering of the “radiative flux noise”:
Figure 6
As figure 6 but with 100,000 time steps:
Figure 7
Now with the radiative “noise” as an AR(1) process (see Statistics and Climate – Part Three – Autocorrelation), vs the autoregressive parameter φ and vs the number of averaging periods: 1 (no averaging), 7, 30, 90 with 10,000 time steps (30 years):
Figure 8
And the same comparison but with 100,000 timesteps:
Figure 9
Discussion of Results
If we consider first the changes in the standard deviation of the estimated value of climate sensitivity we can see that the spread in the results is much higher in each case when we consider 30 years of data vs 300 years of data. This is to be expected. However, given that in the 30-year cases σλ is similar in magnitude to λ we can see that doing one estimate and relying on the result is problematic. This of course is what is actually done with measurements from satellites where we have 30 years of history.
Second, we can see that mostly the estimates of λ tend to be lower than the actual value of 3.0 W/m².K. The reason is quite simple and is explained mathematically in the next section which non-mathematically inclined readers can skip.
In essence, it is related to the idea in the quote from Forster & Gregory. If the radiative flux noise is uncorrelated to temperature then the estimates of λ will be unbiased. By the way, remember that by “noise” we don’t mean instrument noise, although that will certainly be present. We mean the random fluctuations due to the chaotic nature of weather and climate.
If we refer back to Figure 1 we can see that when the averaging period = 1, the estimates of climate sensitivity are equal to 3.0. In this case, the noise is uncorrelated to the temperature because of the model construction. Slightly oversimplifying, today’s temperature is calculated from yesterday’s noise. Today’s noise is a random number unrelated to yesterday’s noise. Therefore, no correlation between today’s temperature and today’s noise.
As soon as we average the daily data into monthly results which we use to calculate the regression then we have introduced the fact that monthly temperature is correlated to monthly radiative flux noise (note 3).
This is also why Figures 8 & 9 show a low bias for λ even with no averaging of daily results. These figures are calculated with autocorrelation for radiative flux noise. This means that past values of flux are correlated to current vales – and so once again, daily temperature will be correlated with daily flux noise. This is also the case where low pass filtering is used to create the radiative noise data (as in Figures 6 & 7).
Maths
x = slope of the line from the linear regression
x = Cov[- λT + N, T] / Var[T] ….[3]
It’s not easy to read equations with complex terms numerator and denominator on the same line, so breaking it up:
Cov[- λT + N, T] = E[ (λT + N)T ] – E[- λT + N]E[T] ….[4], where E[a] = expected value of a
= E[-λT²] + E[NT] + λ.E[T].E[T] – E[N].E[T]
= -λ { E[T²] – (E[T])² } + E[NT] – E[N].E[T] …. [4]
And
Var[T] = E[T²] – (E[T])² …. [5]
So
x = -λ + { E[NT] – E[N].E[T] } / { E[T²] – (E[T])² } …. [6]
And we see that the regression of the line is always biased if N is correlated with T. If the expected value of N = 0 the last term in the top part of the equation drops out, but E[NT] ≠ 0 unless N is uncorrelated with T.
Note of course that we will use the negative of the slope of the line to estimate λ, and so estimates of λ will be biased low.
As a note for the interested student, why is it that some of the results show λ > 3.0?
Murphy & Forster 2010
Murphy & Forster picked up the challenge from Spencer & Braswell 2008 (reference below but no free link unfortunately). The essence of their paper is that using more realistic values for radiative noise and mixed ocean depth the error in calculation of λ is very small:
From Murphy & Forster (2010)
Figure 10
The value ba on the vertical axis is a normalized error term (rather than the estimate of λ).
Evaluating their arguments requires more work on my part, especially analyzing some CERES data, so I hope to pick that up in a later article. [Update, Spencer has a response to this paper on his blog, thanks to Ken Gregory for highlighting it]
Linear Feedback Relationship?
One of the biggest problems with the idea of climate sensitivity, λ, is the idea that it exists as a constant value.
From Stephens (2005), reference and free link below:
The relationship between global-mean radiative forcing and global-mean climate response (temperature) is of intrinsic interest in its own right. A number of recent studies, for example, discuss some of the broad limitations of (1) and describe procedures for using it to estimate Q from GCM experiments (Hansen et al. 1997; Joshi et al. 2003; Gregory et al. 2004) and even procedures for estimating from observations (Gregory et al. 2002).
While we cannot necessarily dismiss the value of (1) and related interpretation out of hand, the global response, as will become apparent in section 9, is the accumulated result of complex regional responses that appear to be controlled by more local-scale processes that vary in space and time.
If we are to assume gross time–space averages to represent the effects of these processes, then the assumptions inherent to (1) certainly require a much more careful level of justification than has been given. At this time it is unclear as to the specific value of a global-mean sensitivity as a measure of feedback other than providing a compact and convenient measure of model-to-model differences to a fixed climate forcing (e.g., Fig. 1).
[Emphasis added and where the reference to "(1)" is to the linear relationship between global temperature and global radiation].
If, for example, λ is actually a function of location, season & phase of ENSO.. then clearly measuring overall climate response is a more difficult challenge.
Conclusion
Measuring the relationship between top of atmosphere radiation and temperature is clearly very important if we want to assess the all-important climate sensitivity.
Spencer & Braswell have produced a very useful paper which demonstrates some obvious problems with deriving the value of climate sensitivity from measurements. Although I haven’t attempted to reproduce their actual results, I have done many other model simulations to demonstrate the same problem.
Murphy & Forster have produced a paper which claims that the actual magnitude of the problem demonstrated by Spencer & Braswell is quite small in comparison to the real value being measured (as yet I can’t tell whether their claim is correct).
The value called climate sensitivity might be a variable (i.e., not a constant value) and it might turn out to be much harder to measure than it really seems (and already it doesn’t seem easy).
References
The Climate Sensitivity and Its Components Diagnosed from Earth Radiation Budget Data, Forster & Gregory, Journal of Climate (2006)
Potential Biases in Feedback Diagnosis from Observational Data: A Simple Model Demonstration, Spencer & Braswell, Journal of Climate (2008)
On the accuracy of deriving climate feedback parameters from correlations between surface temperature and outgoing radiation, Murphy & Forster, Journal of Climate (2010)
Cloud Feedbacks in the Climate System: A Critical Review, Stephens, Journal of Climate (2005)
Notes
Note 1 – The reason why the “no feedback climate response” = 3.3 W/m².K is a little involved but is mostly due to the fact that the overall climate is radiating around 240 W/m² at TOA.
Note 2 - This is effectively the same as saying f=0. If that seems alarming I note in advance that the exercise we are going through is a theoretical exercise to demonstrate that even if f=0, the regression calculation of climate sensitivity includes some error due to random fluctuations.
Note 3 - If the model had one random number for last month’s noise which was used to calculate this month’s temperature then the monthly results would also be free of correlation between the temperature and radiative noise.
For pure greenhouse effect is the overall change in the TOA radiation is equal to 0, because emitted power = absorbed power. What changing by the greenhouse effect is the wavelength distribution of emitted radiation. In the wavelength range of atmospheric window increases the emission, in the wavelength range of stratospheric emission decreases the emission.
In equilibrium is an increased back-radiation. As long as no balance, there’s the overall change in the TOA radiation unequal 0. At the TOA due to the fluctuations of the temperature variations can compute a sensitivity to fluctuations in surface temperature – but no sensitivity to changes in CO2 concentration.
To equilibrium is also the flow into the ocean depths, does not change so quickly. Strictly speaking, this sensitivity is measured by just how quickly the heat spreads into the ocean depths, because as a change in the TOA has only one difference between the slow change of the heat flow in the depth with respect to rapid changes in the emission in the universe.
SOD, I think climate sensitivity must be a variable because isn’t that a measure of how effectively the atmosphere blocks outgoing terrestrial radiation (positive feedback) or reflects incoming solar radiation (negative feedback)?
In this case, it is a function of cloud formation, evaporation and condensation of water, outgassing of CO2 from oceans, and melting of icesheets in response to 1C increase in temp. Aren’t these thing chaotic and unpredictable in principle? Even if we can determine their exact historical relationships, history will not repeat itself.
The denominator in this equation is just Var[T], and E[N] = 0 of by construction, so equation:
x = -λ + { E[NT] – E[N].E[T] } / { E[T²] – (E[T])² }
x = -λ + E[NT]/Var[T]
However, E[NT]/Var[T] can have either sign, so this represents an error term (and one that likely depends on the measurement period, see my prior comments on the effect of measurement periods on variance for red/pink noise). So I really don’t see how this conclusion follows:
The math makes sense to me but the interpretation seems to have problems.
I was wondering about the same thing at Barry’s
http://bbickmore.wordpress.com/2011/02/25/roy-spencers-great-blunder-part-1/#comment-3064
It does seem pretty obvious that E[NT] must have either sign.
The other thing to note is that E[NT] may change sign in a very smooth fashion as you change your window length…that’s a pretty common feature when the “noise” is dominated by coupled internal oscillations like the Earth’s atmosphere.
It’s also likely that E[NT]/Var[T] → 0 for a large enough observation time. Something worth testing I suppose.
It’s also interesting to me how many blogs float ad homs when they don’t like the conclusions of a particular author. (Referencing the title of that blog post.)
Carrick,
Since you made your point I can’t find a fault in it.
Yet Murphy & Forster 2010 do a calculation for an infinite time series and conclude:
[Note that is the "error" in λ]
Which is based on the Appendix:
Click for a larger image
With both sides of this particular argument believing the same I didn’t think about it enough.
So I need to think about why the results almost always show a lower estimated λ than the actual. It’s probably “obvious”..
Carrick,
On your other point:
I don’t think this is the case. This is the assertion in Forster & Gregory 2006 assuming as they do that N is uncorrelated with T. If N is uncorrelated with T, then this is true, as short time series won’t have zero E[NT].
I have run some of the simulations for 1,000,000 time steps (days) and there is no tendency to zero error. In fact, the mean of estimated λ stays the same while the standard deviation of the results reduces dramatically, as would be expected – and as can be seen from the comparisons between 10,000 and 100,000 time steps in the article.
Hi Sod,
Thanks for the comments.
Regarding the first point, if T is assumed to be related linearly to N, then we will can have E[NT] > 0, but that seems like a consequence of an assumption, not a real consequence of the equation, or of the underlying physics for that matter.
Regarding the second point, I was being a bit too thin on details I think. I was considering the spectral characteristics of the “realistic” temperature fluctuations, and assuming “N” follows these too, in making that statement.
In that case, as you increase your time window, E[NT] should get smaller relative to Var[T]. (Var T grows without bounds, while E[NT] being band limited is bounded.) This is the sort of thing one would need to do a proper Monte Carlo to separate out.
If you are using something akin to a realistic spectral distribution for T and N, then of course I concede the point.
Gaussian white noise is a completely horrible assumption for climate fluctuations of course. I haven’t read Murphy and Foster in any detail, but it does appear this is what they are doing.
Carrick
Editorial comment here: I think all of the models posed by the various published authors are way over simplified. You don’t have to go (I think anyway) to 5-d hyperdimensional space to get it right, but I think you do need to start with assumptions that more carefully reflect the underlying physical behavior of the system.
I think another problem is the short duration of the CERES dataset. I’m not sure that can be fixed by anything but more observation time.
(insert “reduced to:” between the equations. I managed to delete it.)
This is settled science – right?
SoD
Free pdf of Spencer & Braswell (2008) here:
http://www.drroyspencer.com/Spencer-and-Braswell-08.pdf
SoD,
“Note 1 – The reason why the “no feedback climate response” = 3.3 W/m².K is a little involved but is mostly due to the fact that the overall climate is radiating around 240 W/m² at TOA.”
The ‘no feedback’ response is actually derived from the surface response to solar forcing, which is about a 1.6 to 1 power to power ratio (390/240 = 1.625) – meaning it takes about 1.6 W/m^2 of radiative surface flux to allow 1 W/m^2 to leave the system, or it takes about +5.4 W/m^2 at the surface to allow 3.3 W/m^2 to leave at the TOA (3.3 x 1.625 = 5.4). +5.4 W/m^2 at the surface = +1C rise in temperature.
This is the origin of the so-called ‘Planck response’ or ‘no-feedback’ response of about 1.1 C from 2xCO2 (3.7/3.3 = 1.1). The problem is this is not a ‘no feedback’ or ‘pre-feedback’ response, but an upper limit on sensitivity because net negative feedback is required for basic stability. The 1.6 to 1 power densities ratio already includes the lion’s share of feedback in the system from decades, centuries, millenia, millions of years of solar forcing from which the feedbacks in the system have already manifested themselves.
SoD (or anyone else),
If you really think that net positive feedback of 300% or more from 2xCO2 is possible for a 3 C rise (+16.6 W/m^2), you should explain why it does not take 1077 W/m^2 of surface power to offset the 240 W/m^2 of incident post albedo solar power. (16.6/3.7)*240 = 1077.
If watts are watts, how can watts of GHG ‘forcing’ have a greater ability to warm the surface than watts from the Sun? The 3.7 W/m^2 of ‘forcing’ from 2xCO2 is supposed to be the equivalent of +3.7 W/m^2 of post albedo solar power, is it not?
Attempts to determine climate sensitivity by looking at the correlation between surface temperature (anomaly) and TOA flux (anomaly) seem to be based on hopelessly simplistic models. Only about 15% of OLR is emitted from the surface of the earth. The remaining OLR is emitted from higher in the atmosphere. If atmospheric temperature at various locations in the troposphere moved in parallel with surface temperature, then we might observe a reasonable correlation between surface temperature and TOA flux. Unfortunately, surface temperature anomalies could require a significant amount of time to rise to higher altitudes, so most of the TOA response could lag surface temperature anomalies. Spencer and others have shown there is a modestly stronger (but still weak) correlation between TOA flux and surface temperature 2-3 months earlier. However, the rise of surface temperature anomalies through the troposphere could also be inhomogeneous, with some parts moving more slowly than others. The TOA response to a surface temperature anomaly today might be spread out over the next six months. That would partially explain why correlation coefficients between TOA flux and Ts are so poor at all time lags.
How long should it take for a temperature anomaly to rise through the atmosphere and escape to space? This would depend on the mechanism of energy transfer. It apparently takes months for radiative equilibrium to be established between the tropopause and the stratosphere, so radiation is slow. The residence time of water vapor in the atmosphere is only 9 days (after the time required for the evaporative response to a temperature anomaly). At the UAH website (http://discover.itsc.uah.edu/amsutemps/execute.csh?amsutemps), the warmest sea surface temperatures occur during March (ca +0.3 degK above mean), but the warmest temperatures at 4.5 km (and 7.5 km) occur during July (+1.0 degK above mean). This data suggests that it could take four months for the annual SST anomaly to rise into the upper troposphere, but isn’t proof of mechanism. However, it certainly shows that that sea surface temperature and upper troposphere temperature don’t move in parallel.
This is my 2 pence worth….
It is a matter of definition as to whether you define Stefan Boltzman radiation as energy balance or negative feedback. The effective temperature of the Earth as measured by radiation to space (240 w/m2) results in a value of Teff=255K . Differentating Stefan Boltzman equation we get DS/DT = 4*sigma*T^3. Therefore a 1 degree rise in the “effective” temeperature would be balanced by an increase in rediation of 3.7 w/m2 – or a negative feedback.
Earth’s average surface temperature is T=288K because of the greenhouse effect. The normalised greenhouse effect works out at ~0.3 — i.e. resulting in Tsurf^4*(1-0.3) = Teff^4
Therefore assuming zero other feedbacks if the surface temperature rises by 1 degree Teff will rise by 0.9 degrees. This then works out at 3.3 watts/m2 K-1 !
Science of Doom: Thank you for providing this excellent resource on the fundamentals of climate science.
I’m still a learner in most things to do with climate, but from my reading so far I’m inclined to agree with Frank, that “Attempts to determine climate sensitivity by looking at the correlation between surface temperature (anomaly) and TOA flux (anomaly)…” seem at best optimistic, and possibly doomed to failure. There are just too many ‘forcings’ (an ugly and ill-defined term in my view, but there it is) and too many feedbacks. Yes, there is a well-established and generally agreed figure for the no-feedbacks change in average surface temperature resulting from a given change in atmospheric CO2 content. But there are feedbacks, and we seem to be little nearer evaluating those than we were 20 or more years ago. See for instance Mitchell et al, 1989: ‘CO2 and climate: a missing feedback’ (Nature, vol 341, 132-4). I’m tempted to ask, what is the point of all this? Apart that is from keeping climate modellers, journal editors and the remainder of the climate change industry legitimately occupied? Are we actually learning anything? But maybe I should drop such questions and try to make a more constructive suggestion.
The feedbacks, both known and unknown (or ‘missing’), seem to be imponderable. It’s fun (and profitable) studying them, but if what we are ultimately interested in is the net effect of small changes in the earth’s energy budget on changes in the earth’s surface air temperature, why don’t we look for a method that takes into account the existing feedbacks, known and unknown, (as well as the forcings)?
A number of scientists have come up with something like this, but only a small number seem to have made it into the print journal literature, and I can find no reference to this type of approach in those IPCC reports I have searched (WG1 of TAR 2001 and AR4 2007).
The following example is from an article by Hug and Barrett, which can be found at http://www.john-daly.com/forcing/hug-barrett.htm
“The Stefan-Boltzmann equation linking the energy of emission of a cavity radiator to its temperature:
E = (sigma) T4
may be differentiated with respect to temperature:
dE/dT = 4(sigma)T3
and inversion gives a value for the sensitivity:
dT/dE = 1/4(sigma)T3
If a value of 288°K (a mean value for the troposphere at sea-level) is inserted into the equation the value for the sensitivity is 0.18 K(W m-2)-1.”
That would as I understand it translate to about 0.7K per doubling of atmospheric CO2.
The example is a simple one, perhaps over-simplistic, but is it any less valid than the no-feedbacks approach with added feedbacks? Or is it just nonsense?
Coldish:
The important point to understand here is that climate science is attempting to measure the actual climate sensitivity.
So no assumptions about negative or positive feedback are necessary or involved in this method.
In fact, that is what the measurements are attempting to ascertain.
The challenge is if climate sensitivity is a variable, e.g. a function of location, surface temperature, season, and phase of ENSO. In that case, the current measurement attempts will not work.
Another challenge, explained in the article in more detail, is where the “radiative noise” (random fluctuations in flux) prevents accurate measurement of climate sensitivity.
In respect of the link you provided the writers clearly have so little understanding of what climate science accepts and understands as the basics that I wouldn’t know where to start. Anyone who has read a few textbooks on atmospheric physics will be able to pick apart the confusion.
Otherwise it might sound convincing.
Section 2 – Applicability of Kirchhoff’s Law is a nice example of a mishmash of true, false and strawman ideas all stirred together into a pot of confusion. And in so few sentences.
Let’s pick one sentence and challenge you to demonstrate its truth:
Where does the IPCC claim to believe the atmosphere is in thermodynamic equilibrium?
This would be absurd. The only published paper I have found such a confused notion is in Miskolczi’s paper, which is not exactly mainstream as it claims to overturn anything close to consensus.
Over to you to find the relevant IPCC reference.
I expect the writers of this article have no idea what Kirchhoff’s law is or why emissivity = absorptivity is true (for equal wavelengths) even under conditions of non-thermodynamic equilibrium.
Have a read of Planck, Stefan-Boltzmann, Kirchhoff and LTE.
Science of doom: Thank you for your reply. I will indeed read the post you refer to. However I wasn’t asking you to comment on the remainder of Hug and Barrett’s article, merely on the validity/meaning of the particular passage I quoted.
I have by the way no problem with your statement that
”The important point to understand here is that climate science is attempting to measure the actual climate sensitivity. So no assumptions about negative or positive feedback are necessary or involved in this method. In fact, that is what the measurements are attempting to ascertain. The challenge is if climate sensitivity is a variable, e.g. a function of location, surface temperature, season, and phase of ENSO. In that case, the current measurement attempts will not work.”
Everybody active in this field is presumably trying to measure or estimate a quantity which as you point out may well be a variable function of a number of variable factors. In what direction would you like to see the research going?
Coldish wrote: “The Stefan-Boltzmann equation linking the energy of emission of a cavity radiator to its temperature:
E = (sigma) T4
may be differentiated with respect to temperature:
dE/dT = 4(sigma)T3
and inversion gives a value for the sensitivity:
dT/dE = 1/4(sigma)T3
If a value of 288°K (a mean value for the troposphere at sea-level) is inserted into the equation the value for the sensitivity is 0.18 K(W m-2)-1.”
Until you inserted 288 degK as the temperature, everything appears to be right (and agree with SOD’s earlier posts). These equations derive the relationship between temperature and radiation – but only when temperature is controlled only by radiation. The surface of the earth is cooled by convection of latent and simple heat as well as by radiation (and warmed by incoming solar and LWR radiation from the atmosphere). So the answer you get from using 288 degK doesn’t tell us anything useful about the surface (IMO).
Above the altitudes where convection occurs, temperature is controlled by radiative equilibrium and it makes sense to apply your equations. If you use 237 degK as the temperature, you get SOD’s value of 0.33 K(W m-2)-1 for the NO-FEEDBACKS climate sensitivity.
Calculations show that 2XCO2 will reduce outgoing radiation by about 3.7 W/m2 at the tropopause (where it is probably a little colder). This is your dE term. This gives a no-feedbacks climate sensitivity for doubling CO2 of about 1 degK; 1.2 degK using SOD’s numbers.
This part of climate science might be termed “settled”. The controversies begin when we attempt to predict how 1 degK of warming at the tropopause effect surface temperature and how feedbacks may amplify warming. In this post, SOD is discussing observational evidence relating outgoing radiation to surface temperature as a way of predicting how radiative forcing at the tropopause will change temperature at the surface (rather than the tropopause). Unfortunately, the relationship is very noisy, possibly for the reasons I proposed above. (I’m hoping someone will tell me why I’m wrong.)
Frank,
“Calculations show that 2XCO2 will reduce outgoing radiation by about 3.7 W/m2 at the tropopause (where it is probably a little colder). This is your dE term. This gives a no-feedbacks climate sensitivity for doubling CO2 of about 1 degK; 1.2 degK using SOD’s numbers.
This part of climate science might be termed “settled”. The controversies begin when we attempt to predict how 1 degK of warming at the tropopause effect surface temperature and how feedbacks may amplify warming. In this post, SOD is discussing observational evidence relating outgoing radiation to surface temperature as a way of predicting how radiative forcing at the tropopause will change temperature at the surface (rather than the tropopause). Unfortunately, the relationship is very noisy, possibly for the reasons I proposed above. (I’m hoping someone will tell me why I’m wrong.)”
The calculated reduction of 3.7 W/m^2 at the tropopause is assumed to cause net increase in energy flux into the surface of 3.7 W/m^2, which then the surface has to warm up an additional 2.3 W/m^2 (62% more) to re-emit the 3.7 W/m^2 back out at the TOA to restore equilibrium. This arises because about 38% of what emitted from the surface is ‘blocked’ by the atmosphere and returned or re-circulated back to the surface.
The ‘no-feedback’ sensitivity of 1.1-1.2 C is derived from the 1.625 W/m^2 to 1 W/m^2 ratio of radiative power emitted from the surface to power emitted at the TOA (390/240 = 1.625). This includes all the non-radiative 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. All of these fluxes are in between the surface and the TOA. At the TOA, it’s all photons entering and leaving.
RW: The definition of radiative forcing used by the IPCC (TAR) cited by Wikipedia is:
“The radiative forcing of the surface-troposphere system due to the perturbation in or the introduction of an agent (say, a change in greenhouse gas concentrations) is the change in net (down minus up) irradiance (solar plus long-wave; in Wm-2) at the tropopause …
… AFTER allowing for stratospheric temperatures to readjust to radiative equilibrium, …
… but with surface and tropospheric temperatures and state held fixed at the unperturbed values.”
Upward and downward LWR fluxes are calculated for various layers in the atmosphere using: pressure, mixing ratio of GHG’s, temperature (emission is temperature dependent) and absorption/emission data for all GHGs at relevant wavelengths. Changes in TOA flux (often calculated at the tropopause) and changes in surface DLR are NOT directly linked: the radiative forcing for 2XCO2 is 3.7 W/m2 at the tropopause and a little less than 1 W/m2 at the surface. For a demonstration, see SOD’s post on this subject. http://scienceofdoom.com/2011/02/06/understanding-atmospheric-radiation-and-the-“greenhouse”-effect-–-part-five/ Although these calculations appear to contradict the law of conservation of energy, radiative convective models automatically get conservation of energy correct by assuming that convection increases or decreases enough to balance incoming and outgoing radiative fluxes in the troposphere. At the tropopause, there is not convection. Using dW = 4oT3.dT and knowing dW = 3.7 W/m2, we can calculate the temperature rise at the tropopause needed to restore the balance between incoming and outgoing radiation.
Hopefully, this will explain the rational for the calculations in my comment. I don’t understand the basis for your calculations, possibly because you are using a different meaning for 3.7 W/m2 than the radiative forcing for 2XCO2.
Frank,
The problem is the ambiguity of the definition. What matters ultimately is the net change in energy flux into the surface as a result of the perturbation from 2xCO2. The IPCC is suspiciously vague on exactly what the 3.7 W/m^2 means. My interpretation is they are assuming it is equal to an increase in post albedo solar power of 3.7 W/m^2. I do not agree with this interpretation or assumption, and as best I can derive the 3.7 W/m^2 is the reduction in ‘window’ transmittance (the amount of surface radiative flux that passes straight through the atmosphere to space as if the atmosphere wasn’t even there) or is the incremental atmospheric absorption.
For example, using Trenberth’s ‘window’ transmittance of 70 W/m^2 (40 W/m^2 through the clear sky and 30 W/m^2 through the cloudy sky), a doubling of CO2 reduces this value to 66.3 W/m^2 and the atmosphere absorbs and additional 3.7 W/m^2 that previously went straight from the surface to space.
I suggest you ask SoD specifically where the watts are coming from to cause the +6 W/m^2 flux into the surface that causes the claimed 1.1 C ‘zero-feedback’ temperature increase from 2xCO2, as when asked no one ever seems to know. He won’t talk to me anymore.
They have just assumed it causes a +3.7 W/m^2 flux into the surface, which then the surface has to warm up an additional 2.3 W/m^2 (62% more) in order to re-emit the -3.7 W/m^2 at the TOA (or tropopause) back out to space to restore equilibrium. This arises because about 38% of the radiative flux from the surface is ‘blocked’ by the atmosphere and returned or recirculated back to the surface – only 62% of what’s emitted is allowed to leave at the TOA, i.e. the planet’s emissivity of about 0.62 (240/390 = 0.62; 390-240 = 150; 150/390 = 0.38).
Since I can’t directly post a reply to your October 1, 2011 at 2:11 am comment found below, I’ll place one at the bottom.
Even though I don’t really know what the graphs are saying it did immediately stand out to me that results were generally less than 3 rather than greater. Have you had any insights yet why this is so? Do you think this is a quirk of your methodology or a wider problem?
SOD,
Excellent post. A few comments/questions:
1) MF10 essentially does what the new Dessler11 paper does (in one part), which is to determine the value of S (F_Ocean) based on the mixed-layer heat capacity times the temperature fluctuations (C * dT/dt) and then subtracting from that the TOA flux. The problem is that using (C * dT/dt) substantially overestimates the energy flux of those top 100 meters compared to actual Argo measurements, as you can see in Dr. Spencer’s post or here. The reasons for that might be that even though the mixed layer is near uniform in temperature, small transfers of energy from the sea surface to lower parts of the mixed layer will result in a supposed energy loss from the whole mixed layer when nothing of the sort is actually happening. Furthermore, one is then aliasing all errors from calculations of C * dT/dt and TOA flux, which may be substantial relative to the fluctuations, in with the S term. Thus even white noise will cause a bias in the ratio of S/N.
2) To the point that Frank raised above relative to the atmospheric temperature lag, I went over this a bit here. If there is a two-month lag between sea surface and TLT in the real world, and we can see that, at least for the Planck response, 80% of the OLR is coming from the atmospheric temperature changes that occur 2 months AFTER sea surface temperatures, how can we properly diagnose the climate feedback from TOA fluxes occurring in sync with the surface temperatures? Both the Spencer and Forster camp seem to agree that feedbacks occur simultaneously with surface temperatures, which I cannot understand given the atmospheric temperature lag time. Seems to be a fundamental problem with the model. Any thoughts?
These are good questions. I don’t know the answers but I’m thinking about them.
I have to experiment more with models and play around with equations and see what comes to light.
You have some good articles, I’ll add your site to the “Climate Website” list aka blogroll.
Troy wrote: “Both the Spencer and Forster camp seem to agree that feedbacks occur simultaneously with surface temperatures, which I cannot understand given the atmospheric temperature lag time.” Can the data be analyzed with a model that says that X% of TOA flux anomaly varies with current surface temp, Y% lags by M months, Z% lags by N months, etc? There is controversy about what observations of dW/dTs mean in terms “climate sensitivity” expected for future forcings. However, useful “climate sensitivity” is more likely to be the change in TOA flux integrated over some period of time with surface temperature rather than the instantaneous response at any particular time. Is such a statistical analysis impossible when monthly Ts anomalies are undoubtably correlated? Could principle components help?
Some bright person needs to figure out how to “tag” energy from a known source so it can be tracked as it circulates in the system. Yeah, sounds crackpot, but right now it’s too fungible to know what is really happening.
Thanks for the post. I read in detail.
RW: In your comment dated October 1, 2011 at 2:11 am, you complain about the ambiguity of the definition of radiative forcing. The IPCC’s definition is not ambiguous, it is quite precise; you simply appear to prefer a non-conventional meaning. When people use different definitions for different concepts, rational discussion is impractical. I’m not surprised that our host has lost patience.
To calculate radiative flux through the atmosphere, one needs to break the atmosphere up into layers with a defined pressure, temperature and composition for each layer. With this information and the appropriate spectral data for all components of the atmosphere, scientists can calculate the upward and downward radiative fluxes between the layers, ground and space. (SOD has done a wonderful job of illustrating how this is done in his long series of posts on Understanding the Greenhouse Effect.) Then one can increase the concentration of a GHG and find out how those fluxes change. For regions of the atmosphere where temperature is controlled solely by radiation, one can iterate to find the new equilibrium temperature once it has responded to the new radiative flux. One can’t do that in convective regions, because the temperature in those regions is not controlled solely by radiation. (Convection reduces surface temperature about 60 degK below what it would be if it were controlled by radiative equilibrium alone.)
This provides the rational for all three sections of the IPCC’s definition of radiative forcing (see above), how they calculate 3.7 W/m2 of radiative imbalance and a temperature rise of about 1 degK AT THE TROPOPAUSE.
You wrote: “I suggest you ask SoD specifically where the watts are coming from to cause the +6 W/m^2 flux into the surface that causes the claimed 1.1 C ‘zero-feedback’ temperature increase from 2xCO2, as when asked no one ever seems to know.”
You are certainly correct when you calculate that a surface temperature rise of 288 to 289.1 degK will increase upward radiate flux from 390 to 396 W/m2 (before correcting for emissivity being slightly less than 1). The KT energy balance diagram also shows 333 W/m2 of DLR, which would come from an atmosphere with an average temperature of 276.8 degK – if its emissivity were 1. Assuming the lapse rate from the surface to this altitude remained constant, the temperature there would also rise 1.1 degK, to 277.9 degK, increasing DLR by 5.3 W/m2. However, because the atmosphere would be optically thicker from 2X CO2, the average photon arriving at the surface would have been emitted from a lower, warmer altitude. So, it is trivial to see where the additional 6 W/m2 (or more) might come from, but it is difficult to calculate properly. (The assumption that the emissivity of the atmosphere is 1 is incorrect. It varies somewhat with CO2 concentration.)
However, we are NOT required to balance upward and downward radiative fluxes – the total downward flux is about 100 W/m2 greater than the upward at the surface! The difference, of course, is convection. Our theories about atmospheric stability suggest that convection AUTOMATICALLY increases or decreases to correct for any imbalance associated with too steep a lapse rate (radiative-convective equilibrium). Any shortage (or surplus) in your needed 6 W/m2 that doesn’t come from radiation can always be provided by reduced (or increased) convection! Short of GCMs, we don’t know how to calculate the energy flux provided by convection from first principles; we only know what the maximum lapse rate should be after an unspecified and variable amount of energy has been convected upwards. The IPCC avoids the problem of convection by incorporating the lowest altitude where convection is no longer important – the tropopause – into its definition of radiative forcing.
Frank,
If the definition isn’t ambiguous, then what is the reduction in ‘window’ transmittance or the incremental absorption from 2xCO2? Is it 3.7 W/m^2 or some other amount? If it is some other amount then what’s the amount?
I assume you’re aware that not all the surface emitted LW absorbed by the atmosphere is emitted back down the surface, right?
The figure of 3.7 W/m² is a reduction of emission, mostly. The transmittance can also be calculated. Using MODTRAN and the 1976 standard atmosphere with clear sky, the transmittance from 100-1500cm-1 at 280 ppmv CO2 is 0.2551. At 560 ppmv, it’s 0.2492. At a surface temperature of 288.2 K and an emissivity of 0.98 the radiative flux at the surface upward is 360.472 W/m². So the reduction in transmission at 100 km altitude for clear sky is 2.13 W/m² . But that’s clear sky. Clouds cover ~60% of the Earth’s surface and are totally opaque to IR from the surface. It’s much trickier to calculate the reduction in emission from cloud tops.
Frank,
Before I reply in more detail, how much does Trenberth’s ‘window’ transmittance of 70 W/m^2 reduce when CO2 is doubled?
Trenberth “window” may not be 70 W/m2. They claim that only 40 W/m2 is emitted from the surface and escapes directly to space (mostly through the 8-12 um window). This is the value I always cite for the “window”, but I don’t clearly understand how they arrive at this number. (Miskolczi believes 23 W/m2 may be more accurate.) K&T also claim that 165 W/m2 is emitted by the atmosphere in general and to this they add 30 W/m2 of “long wavelength cloud forcing” which is equal to the difference in TOA LW emission between clear and cloudy sky (but reduce incoming SWR by 50 W/m2). I presume this means that clouds are better LW emitters than the atmosphere (because they have higher emissivity? or are warmer?). If you look carefully at the Figure, the 165 W/m2 originate from both clear and cloud sky, the 30 W/m2 originates only from clouds, and the 40 W/m2 has its own special channel through the atmosphere. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.168.831&rep=rep1&type=pdf
I presume that the window transmittance doesn’t change after doubled CO2, because CO2 doesn’t have significant absorptions in the window. However, you need to remember that CO2 is both and absorber and an emitter. 2X CO2 emits twice as much radiation as 1X CO2. The radiative forcing from 2X CO2 occurs because the average photon escaping to space is emitted from a higher/colder altitude than when 1X CO2 is present. Oversimplified ideas about trapping or blocking radiation spread by the CAGW crowd are misleading.
Thank you for this post – It is a really good summary of the key issue of the climate debate. If net feedbacks turn out to be zero or negative then a maximum temperature rise of ~1C can be expected from a doubling of CO2 levels which will have a relatively minor impact. If however IPCC models are correct with an average net positive feedback of ~2.0 W/m2K-1 then we can expect a 2-5 degree rises for a doubling of CO2 with well known consequences. However, I cannot believe that feedbacks (mainly due to water) can possibly be a constant linear response.
Such assumed feedbacks in IPCC models are incompatible long trem with the Earth’s early history because of the fact that we know that the planet has been continuously covered in liquid water. I find it very difficult to accept that the net effect of water on climate can be a positive feedback. While it is true that water vapor greenhouse effects depend on surface temperatures though the Claussius-Claperyon equation, high and low level cloud change to the Earth’s albedo seemingly must be more important. The evidence is that global surface temperatures have changed little over the Earth’s history. This is incompatible with a simple linear net positive long term feedback from water vapor and clouds. During the early lifetime of the Earth total feedback from water must have been negative to avoid run away surface heating as the sun brightened.
SOD,
I agree with your idea that climate sensitivity may be variable. The problem is how do you prove this? If true, the present preoccupation of climate scientists in trying to determine climate sensitivity from historical data is futile. The future climate sensitivity will be different from the past. They cannot contruct a model with predictive power.
It seems to me the more productive line of research is trying to prove that climate sensitivity is indeed variable. This may entail combining chaos theory with atmospheric physics. It may be beyond the expertise of climate scientists. They may have to collaborate with mathematicians or mathematical physicists on this research.
Roy and SOD: For large changes in Ts, climate sensitivity is obvious not constant. At a high enough temperature, water vapor feedback is anticipated to produce a runaway greenhouse effect. At low enough temperature, the ocean will freeze. The issue is whether or not climate sensitivity is roughly constant over +/-3 degK around our current temperature.
If one focuses on the surface energy balance (rather than TOA), the change in upward and downward LWR with temperature is very likely to be linear over this temperature range. The 4oT3.dT terms are linear and the rate at which the altitude/temperature from which the average DLR photon reaches the surface of the earth probably decreases roughly linearly. On the other hand, convection appear less likely to change linearly with Ts, since convection often begins when a critical threshold is crossed. Feedback may also play a role: convection increases surface winds, surface windows which increase evaporation, evaporation increases convective potential and diminished SWR due to clouds.
Roy,
From the many papers I have read there is a very diverse field of expertise within what is today known as the discipline of climate science. And there doesn’t appear to be a shortage of other opinions within published papers.
Many papers point this out, for example:
This is from a climate skeptic known as James Hansen, Climate Response Times: Dependence on Climate Sensitivity and Ocean Mixing (1985).
SoD,
It’s good that Hansen and others recognize the variability of climate sensitivity. If climate is unpredictable in principle, how can IPCC make a forecast with 90% confidence level? If the system is truly chaotic, this is not possible.
Correct me if I’m wrong but a Monte Carlo simulation will only work in a random system but not in a chaotic system. I think the probability distribution of a chaotic system is not a bell curve but a box. There is no most probable value. Each value within the range of possible values is equally probable. This is my guess. Mathematicians may use chaos theory to prove it.
There’s a little bit about this, an intro at least, in Models, On – and Off – the Catwalk – Part Three.
ScienceofDoom,
You have defined sensitivity: “In simple terms this parameter should tell us how much more radiation (“flux”) escapes to space for each 1°C increase in surface temperature”.
When the average temperature on Earth is very slow changing, and when storage (to the ocean) is small enough, the radiation out has to closely match (on average) the absorbed solar radiation in. The surface temperature can slowly change even under this condition by the simple process of the location of the effective altitude of the outgoing radiation becoming higher. In fact, once the surface temperature has risen then leveled off to a new level of surface temperature, the outgoing radiation will be back to the level before the rise, but the ground can be much warmer. The only difference would be the greater altitude of outgoing radiation. The definition you give is flawed.
The lapse rate is the cause of the increase in ground average temperature if it occurs. If other gases (CH4, etc.) filled the window of direct radiation to space from the ground, and the amount of all radiation blocking gases slowly increased, back radiation to the ground would increase, as would the ground level temperature, but the increase in both upward and back radiation would be the result, not cause of the increased ground temperature. The only radiation average heat transfer is up (there can be local reversal, but not average), and is due to the difference of up less down radiation. However, evaporation and water condensation, and air convection adjust to maintain the lapse rate at the value only dependent on composition of the gases and condensation effects.
The presence of blocking clouds raises the ground temperature for some cases, due to blocking the direct radiation window. This and change in the albedo may affect the sensitivity (say due to feedback from change in CO2 increase), but the issue here is definition of sensitivity.
I didn’t explicitly state the equation that defines climate sensitivity, λ :
λ = ΔF / ΔT
Is this definition flawed?
Well, unconventional. It’s usually expressed as ΔT / ΔF
Which reflects the causality people have in mind.
I’ll also cast a vote for sensitivity as change in temperature caused by a certain change in radiative forcing, rather than change in radiative output caused by a change in temperature.
The IPCC (AR4 WGI 8.6.2) sez:
“…the global annual mean surface air temperature change experienced by the climate system after it has attained a new equilibrium in response to a doubling of atmospheric CO2 concentration is referred to as the ‘equilibrium climate sensitivity’ (unit is °C), and is often simply termed the ‘climate sensitivity’.”
Which also points to the difference between “transient” and “equilibrium” sensitivity, which is another can o’ worms (as in, which of these is effectively measured by a given calculation?).
Dan Hughes found this excellent review article on feedback usages in the Earth sciences. It says SoD’s fraction is the feedback factor; the inverse is the sensitivity.
Nick Stokes,
I checked back through a bunch of papers and you are correct about the standard terminology.
Climate sensitivity = ΔT / ΔF
And climate feedback = ΔF / ΔT
However, as one is the inverse of the other if we can correctly calculate one we have the other in an instant.
My question was really for Leonard Weinstein who said:
So I thought the first thing to establish was whether we agreed that “climate feedback” = 1/”climate sensitivity” = ΔF / ΔT, and then we could move from there.
SOD,
Delta F from TOA to space is zero when the increase in temperature has leveled out to a new level. If the surface T is constantly increasing rather than leveled out, the delta F at TOA depends on the rate of heating (due to storage terms). You need another choice of sensitivity definition. If it is the impulse response, this may do, but here storage (mainly sea water) complicates the issue.
SOD,
If you are claiming it is the direct radiation through the atmosphere window to space that is the delta F you are referring to, that is a better choice for CO2, but even more wrong for gases that close the window (CH4, etc.).
SOD,
It occurred to me that when you talk about delta F, you may be referring to change in equivalent solar flux intensity that would change the ground temperature by that amount if there were no greenhouse gas. I do not dispute that definition.
SOD,
Even if the solar equivalent change is used in the definition, I do not see how that can be a measured factor for fixed solar intensity but increase in a greenhouse gas.
The top of atmosphere forcing from double CO2 must be determined using a line-by-line radiation code that computes directional transmittance by integrating over the hemisphere, and which includes the actual measured water vapour profiles. The HARTCODE program with the NOAA water vapour profile was used to calculate the effects of changing surface temperature (Ts), water vapour and CO2 content on the outgoing longwave radiation (OLR). The OLR is broken into two components, the radiation from the surface St and the radiation from the atmosphere Eu.
The results are shown here:
http://members.shaw.ca/sch25/Ken/rr_s.xlsx
Line 5 of the spreadsheet shows the unperturbed values.
The red lines (lines 6 – 17) show the effects of changing the surface temperature.
The blue lines (lines 18 – 29) show the effects of changing the water vapour content.
The black lines (lines 20 – 41) show the effects of changing the CO2 content.
SoD writes a 1 Celsius increase in Ts would cause a no-feedback OLR increase of 3.3 W/^2.
Row 15 shows a 1 Celsius increase in Ts causes the OLR to increases by 3.79 W/m2. This includes 1.39 from the surface (St) and 2.40 W/m^2 from the atmoshere (Eu). The no-feedback climate sensitivity = 1/3.79 = 0.264 K/(W/m^2). The IPCC adopts the value 0.30 K/(W/m^2), which is 13.6% more than estimated by HARTCODE.
Row 41 shows that doubling CO2 causes the OLR to decrease by 2.52 W/m^2. This includes 1.45 from St and 1.05 W/m^2 from Eu. Note that this is only 68% of the 3.71 W/m^2 estimate using the IPCC adopted formula 5.35Ln(2).
Using the proper water vapour content is critical. This graph
http://members.shaw.ca/sch25/Ken/USst76-NOAA_CO2.jpg
shows the huge difference in optical depth change with doubled CO2 between assuming the USST 76 versus the actual NOAA water vapour profile. Using the USST 76 water vapour profile overestimates the optical depth change of double CO2 by 94%!
IPCC forcing is not calculated at the TOA but at the tropopause after allowing the stratosphere to adjust to the change in CO2 concentration by cooling. Above the tropopause, an instantaneous change in CO2 causes a decrease in forcing with altitude because the stratosphere warms with altitude and increasing CO2 increases radiation which has a cooling effect.
If you use the global average specific humidity and the global average temperature, you get greater than 100% RH at the surface. The presence of cloud cover explains much of the difference between the total column precipitable water of the clear sky US 1976 standard atmosphere and global average column precipitable water. You can’t simply pretend that clouds aren’t there and assume that all water in the atmosphere is in the form of vapor.
Thanks for your reply. I am aware that the IPCC uses the tropopause for the IPCC forcing definition. I don’t know how to estimate the tropopause forcing from the OLR change. We need to know this because the satellites measures the TOA OLR, not at the tropopause. If the change in OLR is 2.51 W/m^2m due to double CO2 holding surface temperature constant, how do I calculate the change in OLR at the tropopause and exactly how do I adjust this to somehow allow for stratospheric cooling? Is there a formula?
The NOAA data for 2010 shows the global average specific humidity is 10.633 g/kg at 1000 kPa. The corresponding 2010 global average temperature is 15.522 C. The NOAA relative humidity is 78.235%. I don’t get a RH greater than 100% at the surface.
I don’t see how cloud cover can explain the difference between US 1976 std atmosphere and the NOAA water vapor profile. The NOAA specific humidity in g/kg is the mass of water vapour per kg of air. Are you suggesting the NOAA specific humidity includes the amount of liquid water in clouds? I don’t think so!
I am not pretending that clouds aren’t there. I am assuming that the cloud cover fraction does not change when CO2 is doubled, which may not be accurate.
SoD refers to a paper by Murphy & Forster 2010 which claims that the error in the forcing parameter is small, refuting the Spencer & Braswell 2008 claim that the error is large. Unfortunately SoD did not link to or discuss Dr. Spencer’s response to the M&F2010 claim.
Dr. Spencer’s response is here:
http://www.drroyspencer.com/2010/07/can-climate-feedbacks-be-diagnosed-from-satellite-data-comments-on-the-murphy-forster-2010-critique-of-spencer-braswell-2008/
Dr. Spencer comments that the diagnosed feedback of the FGOALS model of 0.77 W/m^2/K is much less than the known feedback of 2 W/m^2/K of the model.
M&F used the HadSM3 climate model to show that an accurate feedback could be diagnosed from the model output. But the model experiment used an instantaneous quadrupling (!) of the CO2 content, then held constant, so the feedback signal was huge compared to any radiative forcing noise. In the real world, the radiative forcing noise is large compared to the feedback signal when CO2 increases by only 2 ppm/year.
M&F changed the averaging time of the model output, which Spencer agrees with. But M&F changed the depth of the mixed ocean layer from 50 m to 100 m. For diagnosing feedbacks from satellite data, the time scales of variability affecting the data are 1 to only a few years. On those short time scales, the equivalent mixing depths are pretty shallow. Spencer thinks 50 m may be too deep.
The Figure 2 above shows that changing the mixed layer from 50 m to 100 m would have an insignificant effect on the feedback parameter. So why does Figure 3 of M&F 2010 show a large change to 110 m of mixed ocean layer?
Thanks for the link, I have updated the article.
SoD you say:
“Climate sensitivity = ΔT / ΔF
And climate feedback = ΔF / ΔT
However, as one is the inverse of the other if we can correctly calculate one we have the other in an instant.”
But, isn’t that not correct because it ignores the blurring between feedbacks and forcings as a product of time; see Andrews and Forster [2008]:
http://content.imamu.edu.sa/Scholars/it/net/andrewsforster08.pdf
“However, disadvantageously, including non-instantaneous processes clearly blurs the distinction between forcing and feedback as there is no longer a clear timescale to separate the two; further including these processes in the forcing incorporates more uncertain aspects of a climate models response [Forster et al., 2007].”
cohenite:
Let’s say that if such a thing as climate sensitivity exists and can be measured then climate feedback = 1/(climate sensitivity) by definition.
Does such a thing as a climate sensitivity constant exist?
And if it exists can it be measured?
I haven’t claimed an answer to either of these questions.
I usually find I can understand only a little piece of the puzzle at a time, unlike many of my readers, and I’m glad that so many people continue with the very slow progress of this blog.
“Let’s say that if such a thing as climate sensitivity exists and can be measured then climate feedback = 1/(climate sensitivity) by definition.”
I suppose one can define things as one wishes but this is a large departure from the classical (Bode 1945) definition and is I think the source of much confusion. If we have a system with a feed-forward transfer function A (which the IPCC refers to as the no-feedback sensitivity k taken as a constant independent of frequency) and feedback B(s) as depicted here, the classical definition of system sensitivity is the gain from input to output which is given by the feedback equation A/(1 – A * B(s)). In “normal” formulations, the feedback is not 1/sensitivity but rather B(s). Equally confusing (perhaps more so) is the re-definition of what constitute positive feedback. Whereas in the classical formulation, the sign of feedback = sign of B(s), climatologists instead define positive feedback as any B(s) s.t. A/(1 – A * B(s)) > A, i.e. |A * B(s)| <1. This is a particularly poor formulation, as it obscures the fact that the sign of B(s) can change if it contains two or more poles because it is a complex function of frequency (s= i*w) and each pole contributes 90degs of phase shift.
Frank wrote this:
“Troy wrote: “Both the Spencer and Forster camp seem to agree that feedbacks occur simultaneously with surface temperatures, which I cannot understand given the atmospheric temperature lag time.”
I’m having trouble with that given Figure 3 from Spencer and Braswell 2011
Note that the SB2011 paper says:
“While there is a substantial time lag between forcing and the temperature response due to the heat capacity of the ocean, the radiative feedback response to temperature is _nearly simultaneous_ with the temperature
change.”
Figure 3 does not dispute this point, but instead notes that at zero lag the unknown radiative forcing (N) will make it difficult to isolate the feedback among the measured TOA flux. So, according to SB11, it’s still expected to be there at zero lag, but the signal is confounded most at that point (LC11 try to go out to further lags to retrieve the signal).
Thank you troyca; you may be interested in David Stockwell’s take on lags here:
http://vixra.org/pdf/1108.0020v1.pdf
My take on what David is saying is that if TSI is above the TSI mean for a period then temperature will rise; if TSI is below temperature will fall; the rates of temperature response will depend on the direction of the TSI movement; for instance if TSI is above the mean but decreasing towards the mean then temperature will still be increasing but at a slower rate. When TSI crosses the mean the temperature response also changes direction, without lag.
[...] Murphy and Forster 2010 used a similar method in their response to Spencer and Braswell 2008. Science of Doom has been looking into this as well, and gives some background on the origins of why this is [...]
Many thanks for researching and writing a detailed post on this important issue. You don’t mention Lindzen and Choi’s recent research, which involves regressions at varying lags. It is very relevant to the issues that you discuss, I think.
I was going to point out that you had terminologically confused climate sensitivity with the climate feedback factor (or, as I prefer, to avoid confusion with usage of the term ‘feedbacks’, climate response factor). But I see that Nick Stokes has already pointed this out.
As I commented earlier:
SoD,
Is it fair to ask you if you believe in the positive feedback 3C warming hypothesis put forth by the IPCC?
If the answer is yes, can you give a summary as to why? Can you also provide a falsification test for the hypothesis?
Since you apparently aren’t willing to answer any of my questions is why I’m asking (in good faith, BTW).
RW –
I would venture that your question is NOT fair. SoD has said that he/she is taking this one piece at a time, and has done a very meticulous job of investigating each piece. A summary of the whole “big issue” in one comment will inevitably be unsatisfactory, and will not include specific, detailed analysis that this site has become known for. As Steve says at CA, OT discussions regarding the “big issue” turn every thread into the same thing.
I agree he’s done a good job investigating the many separate pieces, but I think it’s very easy to lose sight of perspective going into as much micro detail as he has – most of which is ‘noise’ in regards to the fundamental question. In the end, it boils down the combined net feedback of water vapor and clouds, and this should be the primary focus, IMO.
I certainly don’t dispute that the physics and data supports a likelihood of some effect or that humans can and have influenced climate to some degree, but I firmly believe the magnitude of 3 C or more being predicted cannot be supported by any real science or data – just what amounts to guessing, which is not real science, let alone something any kind of public policy should be based upon.
And I’ve yet to see any pro-AGW proponent provide a falsification test, which is why I’m asking. Maybe SoD doesn’t really believe in the 3C rise or is not convinced by the purported evidence. Maybe it’s not fair to ask for a summary. Anyway, I thought I’d ask. It’s up to him if wants to answer.
In About this Blog, I state:
SoD,
Might I ask how it’s possible that watts of GHG ‘forcing’ can have a 3x greater ability to warm the surface than watts from the Sun, especially since each incident watt in the system causes proportionally less and less warming?
That’s because they don’t. GHG forcing is expressed as W/m² precisely so it can be compared to other forcings such as an increase in TSI. When you calculate the change in TSI, you need to correct for the surface area of the sphere and albedo. A change of solar forcing of 3.7 W/m² would be the same as a change in the solar constant of 1368*3.7/239 = 21 W/m² or 1.55%.
I thought watts of GHG ‘forcing’ were supposed to be equivalent to watts of post albedo solar power, or that the 3.7 W/m^2 of ‘forcing’ from 2xCO2 is supposed to be the same as if the post albedo solar power were to increase from about 240 W/m^2 to 243.7 W/m^2. Is this not correct?
RW:
You can read the definition of radiative forcing in CO2 – An Insignificant Trace Gas? Part Seven – The Boring Numbers.
Radiative forcing of 3.7 W/m2 is comparable to an increase in solar radiation of 3.7 x 4 / (1-0.3) = 21 W/m2.
The explanation of how to compare solar and terrestrial or atmospheric radiation is given in The Earth’s Energy Budget – Part One.
The solar incident flux at top of atmosphere = 1367 W/m2.
The solar absorbed flux at top of atmosphere = 1367 * (1-0.3) = 957 W/m2.
The solar absorbed flux per unit surface area of the earth = 1367 * (1-0.3) /4 = 239 W/m2.
SoD,
I’m not sure I understand what you’re doing there. Are you saying that a doubling of CO2 is not equivalent to an increase in post albedo solar power of 3.7 W/m^2 but instead an increase in post albedo of 21 W/m^2 (or and increase from about 240 W/m^2 to 261 W/m^2)???
Black body radiation from the Earth’s surface is the primary negative feedback on any temperature rise DT. The differential of Stefan Boltzman’s law gives the effective feedback parameter:
DS/DT = 4sigmaT^3 (= 3.75W/m2K-1 for T=288K)
Hence a temperature rise of about 1C for a doubling of CO2. The feedback estimates used by IPCC models concern water vapour and clouds. The total feedbacks used range from +1.6 to 2.5 i.e. an average total positive feedback of ~ 2.0 W/m2K-1. Only with these feedbacks does a doubling of CO2 lead to large temperature increases of between 2 to 5 deg.C. If however it turns out that total feedbacks are actually negative or zero then global temperatures would rise only 0.3 to 1.1 degrees C. So feedback is the make or break issue for significant AGW.
The sun has brightened 30% over the last 4 billion years and current average solar radiation is 342 watts/m2. Assuming a slow linear increase of solar radiation with time gives a net forcing of 0.02 watts/m2 every 1 million years. Taking a simple IPCC linear feedback factor 2.0 W/m2K-1 to calculate past temperatures using DT( 4sigmaT^3 -F) = DS then gives non physical results, because the temperature eventually falls so that F= 4sigmaT^3.
Therefore this simple model must be wrong. Another possible model is that a balance between cloud albedo and H2O greenhouse effects enables the earth to self regulate its temperature. When solar radiation is below some optimum H2O greenhouse effects dominate while above it cloud albedo effects dominate.
The increase would be 240 + 3.7 W/m² = 243.7 W/m². If you agree that this is correct, why do you think that “watts of GHG ‘forcing’ can have a 3x greater ability to warm the surface than watts from the Sun”? Any increase in TOA or tropopause forcing from any source will increase the surface temperature by much more than the increase in temperature at the tropopause. Or to put it another way, the increase in radiative flux at the surface must increase faster than the increase of flux at the tropopause. Any feedback, such as increased water vapor at higher temperature depends only on the surface temperature, not the reason why the surface temperature increased.
Mind you I fully understand that the solar constant of 1367 W/m^2 has to be divided by 4 to get the global average because the Earth is a sphere (or very close to a sphere). 1367/4*(1-0.3) = 239 W/m^2 globally averaged post albedo.
It’s my understanding that the net change of 3.7 W/m^2 at the tropopause is for the global average or that the outgoing LW flux of about 239 W/m^2 (or whatever the flux is there) reduces by 3.7 W/m^2 (to 235.3 W/m^2). You’re saying this is not correct?
OK, I see the discrepancy. When I refer to post albedo power, I mean globally averaged post albedo power, i.e. TSI/4*(1-0.3) or about 240 W/m^2.
So getting back the original question, how can 3.7 W/m^2 of additional power from GHG ‘forcing’ have a 3x greater ability to warm the surface the same amount of additional post albedo power from the Sun, especially since each addition incident watt from the Sun causes proportionally less and less warming in the system?
Please support this claim with some numbers or a literature citation.
When the surface temperature increases, the temperature of the atmosphere increases. That means the surface temperature must increase even more to achieve a net increase in flux. The reason the surface temperature increases doesn’t matter. Forcing of the same magnitude from an increase in TSI or an increase in CO2 will have the same effect on surface temperature. I am completely unaware of any factor of 3 difference between ghg forcing or solar forcing.
For clear sky, US76 atmosphere in MODTRAN, it requires an increase in surface temperature of 1.12 C to increase the TOA emission by 3.7 W/m². That increase in temperature causes an increase in emission from the surface of 6 W/m². That’s in the absence of any feedbacks. Doubling CO2 from 280 to 560 ppmv requires an increase of 0.98 C to restore radiative balance at 13 km. The forcing change calculated by MODTRAN at 13 km (tropopause) is only 3.4 W/m², probably because the stratosphere wasn’t allowed to equilibrate. There is no factor of three here. There is no reason I know of to believe that feedbacks are proportional to anything other than the change in temperature.
Dewitt,
“Any increase in TOA or tropopause forcing from any source will increase the surface temperature by much more than the increase in temperature at the tropopause. Or to put it another way, the increase in radiative flux at the surface must increase faster than the increase of flux at the tropopause. Any feedback, such as increased water vapor at higher temperature depends only on the surface temperature, not the reason why the surface temperature increased.”
Let me elaborate on l what I’m asking in series of separate questions:
Do you agree that the 240 W/m^2 post albedo solar flux is forcing the climate system?
Do you agree that the 240 W/m^2 forcing the system from the Sun results a net increase at the surface of about 390 W/m^2?
Do you agree that this accounts for all the physical processes and feedbacks in the system?
If not, why haven’t the feedbacks fully manifested themselves after billions of years of incident energy from the Sun?
Do you agree that in order to amplify +3.7 W/m^2 from 2xCO2 into +3C requires an net increase of 16.6 W/m^2?
Do you agree that 390/240 = 1.625?
Do you agree that 16.6/3.7 = 4.5
Do you agree that 4.5 is nearly 3x greater than 1.625?
I should add one more question:
Do you agree that watts of GHG ‘forcing’ and watts of solar forcing must obey the same physics?
Dewitt,
“For clear sky, US76 atmosphere in MODTRAN, it requires an increase in surface temperature of 1.12 C to increase the TOA emission by 3.7 W/m². That increase in temperature causes an increase in emission from the surface of 6 W/m².”
Yes, and 3.7 W/m^2 x 1.625 = 6 W/m^2. Do you see how the so-called ‘no-feedback’ response of about 1.1 C is derived from the surface response to solar forcing (390/240 = 1.625)?
RW,
Do you agree that the energy flux at the surface is 490 W/m^2?
Why don’t you agree that’s the number to use, instead of 390 W/m^2?
No, I do not agree that the net energy flux at the surface is 490 W/m^2, as if it were, the surface would be emitting 490 W/m^2 and not 390 W/m^2.
I do agree that in addition to the radiative flux at the surface there is about 100 W/m^2 of non-radiative flux from latent heat and thermals. However, this flux originates from the surface, and to the extent that non-radiative flux leaves the surface, it also returns to the surface somewhere else (mostly as the temperature component of precipitation, wind, weather, etc). If there is an imbalance – say more non-radiative flux is leaving the surface than is returning to the surface on average, non-radiative flux is just being traded off for radiative flux at the surface, requiring the surface to emit less to achieve equilibrium output power at the TOA.
I should more technically correct say:
No, I do not agree that the net energy flux at the surface is 490 W/m^2, as if it were, the radiative flux at the surface would be 490 W/m^2 and not 390 W/m^2.
So you agree there is 390 W/m² radiative flux and in addition 100 W/m² non-radiative flux, but do not agree that the total is 490. Good one.
lgl,
“So you agree there is 390 W/m² radiative flux and in addition 100 W/m² non-radiative flux, but do not agree that the total is 490. Good one.”
The net energy flux entering and leaving the surface is 390 W/m^2 in the steady-state. Why is this so hard to understand? If this were not the case, and the net energy flux at the surface was 490 W/m^2, the planet would be in the process of warming to 32 C from 15C. If it were less than 390, it would be in the process of cooling to some temperature lower than 15C.
Do you understand the basic T^4 relationship between temperature and emitted power. Whatever temperature a body is radiating at (in this case the surface of the Earth), the amount of energy it is radiating has to be continually replaced or else the body will gain or loss energy and subsequently warm up or cool down.
I should more correctly say if “the net energy flux entering the surface was 490 W/m^2 with the surface still radiatively emitting 390 W/m^2, the planet would be in the process of warming to 32C from 15C.”
There is 490 W/m^2 radiative downward and 390 radiative + 100 non-radiative upward, so the solar is amplified to 490 W/m^2 and that’s the number to use.
One more time and I’m done.
We’ve been through this before. The net energy flux entering and leaving the surface is less than 1 W/m². If you split between incoming solar and outgoing thermal, it’s ~168 W/m² solar in and 66 W/m² radiative and 102 W/m² convective out. Gross energy in and out is 492 W/m² (168 + 324 W/m² in and 390 + 102 W/m² out). Convective heat transfer keeps the surface cooler than it would otherwise be. Convection happens because a radiative heat transfer only atmospheric temperature profile is unstable. Your apparent inability to understand this as well as add and subtract correctly makes further discussion pointless.
But the interesting discussion is RWs method. What’s wrong with finding the amplification of todays climate system (492/168 or whatever it is) and then assume that the next additional watt, from solar, CO2 or whatever, will see roughly the same amplification?
Igl,
RW has no method. You should read his comments on the ‘The Mystery of Tau-Mizkolczi-Part Four-Emissivity’ thread starting here:
http://scienceofdoom.com/2011/05/01/the-mystery-of-tau-%e2%80%93-miskolczi-%e2%80%93-part-four-%e2%80%93-emissivity/#comment-11568
He can’t work his way through the K&T97 or FK&T2009 energy balances. He insists they are double counting somewhere in spite of all attempts to show that they aren’t. It amounts to an idée fixe so any further discussion is pointless.
RW:
Don’t bother restating your point or asking your question again. As I have already promised I will just delete your repetitions. It’s only because others have come and answered that I feel bad about deleting your recent comments.
No more. Zip it up. Start your own blog.
Dewitt Payne,
“Convective heat transfer keeps the surface cooler than it would otherwise be.”
Yes I totally agree with this. I’m not sure exactly why you think this is in conflict with anything I’ve said, but I tried to explain it among other things and apparently failed. I’m no longer ‘allowed’ to discuss this any further. Sorry.
[...] unmanageable if I were to repeat them in every post. However, for now I’ll mention the recent Science of Doom and Isaac Held posts, and then begin listing some of the difficulties I see (particularly without [...]
DeWitt Payne
Thanks, RW does have a method but insisting on using the wrong numbers so everybody get bored before he gets to the core issue, unfortunately, because the method is very interesting imo.
so they are basing global warming on increases of the wind mixing waves, changing the reflectivity of the local surface? of water in shoals. Not counting the convectional currents of the streams or the up/downwelling of mixing, or how the clouds change the apparant reflectivity of the oceans and land masses. Dumb.
Jim,
Have you read this article?
Who is basing global warming on what?
This article is about measuring something important about climate, and whether the measurement has a systematic bias.
If you have something to comment on that topic, or a question to ask about that topic, please go ahead.
If you want to sound off about something, please visit another blog. There are many better blogs for sounding off and they have larger and more encouraging audiences.
SoD
If climate sensitivity is a variable, can this be shown by regression analysis of empirical data? Or from first principles, by looking at the physics equations governing the phenomenon?
Here’s an interesting paper from MIT on models and uncertainty. It was intended to assess economic models but the discussion on the levels of uncertainty also applies to climate models.
http://web.mit.edu/alo/www/Papers/physics8.pdf
I suspect the uncertainty in climate sensitivity falls under Level 3 (without sufficient data) or Level 4. Can this be proven from first principles? There may be a mismatch betweeen climate models and the phenomenon they are describing. If so, the models and their results may not be useful.
Roy,
From the understanding I have so far, the variation in measurements of climate sensitivity could be said to demonstrate this (that sensitivity is not a constant).
But I’m not clear.
Unfortunately, for the last many weeks “first life” has caught up with me and I have almost no time to think about this properly.
SoD
How is climate sensitivity as you define it related to the “climate sensitivity” as a change in temperature per doubling of atmospheric CO2? If the former is a variable, does it follow the latter is also variable?
If climate sensitivity is variable, can we determine its upper and lower limits and the shape of the probability curve through statistical analysis?
The MIT paper particularly Sections 3, 4 and 6.1 describes the types of uncertainty amenable to statistical analysis – whether it is possible to determine the correct probability curve. We often take it for granted that this is true, which leads to wrong models and wrong predictions.
[...] speaking a climate science blog; others (notable RealClimate, also notably James Annan, Tamino, Science of Doom) were covering that territory. Nor was it one of the many climate policy blogs. Rather its focus [...]
My apologies, I don’t often visit.
I don’t agree with much in the headline post.
1.”First, what do we mean by “climate sensitivity”?
In simple terms this parameter should tell us how much more radiation (“flux”) escapes to space for each 1°C increase in surface temperature.”
This assertion assumes a non-equilibrium planet. In an equilibrium planet, flux out=flux in. So unless flux in changes, flux out won’t either.
If you assume a non-equilibrium planet (one which is in the process of warming or cooling to make flux in = flux out) you can get any number you care to choose for sensitivity.
So I don’t much like your definition of this term, which i have always thought of as a consequence/drive ie, the equilibrium change in surface temp/ change in (ugly term)”forcing”.
2.”If the average surface temperature of the earth increased by 1°C and the radiation to space consequently increased by 3.3 W/m², this would be approximately “zero feedback”.”
This amounts to a sensitivity (in my terms) of 0.3DegC/W/m^2. The surface sensitivity is actually half to one third of that – 0.095 to 0.15 DegC/W/m^2 (depending on evaporation change, noting that evaporation change is not a feedback but a direct determinant of surface temperature. This range is supported by direct evidence from the seasonal behaviour of the planet, see below.) Perhaps you could point me to where you calculated your zero feedback sensitivity.(even eliminating evaporation change from the calculation I only get about 0.2DegC/W/m^2).
3. It seems to me that TOA (note: NOT tropopausal, so NOT Radiative Forcing) flux changes don’t matter to the Surface, which is largely de-coupled from the TOA by:
a. The highly variable stratosphere, which accounts for 8-30% of the atmosphere. This region seems to be adapting to local flux imbalances at least on an hourly basis.
b. The highly variable tropopause, which from day to day can change by several kilometres in height (temperate/polar zones, and by a kilometre in the tropics) and by kilometres in depth, with consequential temperature variability.
c. clouds
d. the difficulty TOA has in heating the surface. The surface responds only to the following:
1). Absorbed Sunlight
2). Back-Radiation received at the surface. (the change in this is nothing like the same as a radiative imbalance at the TOA.)
[The diagram in IPCC AR4 WG1 Chapter 2 Fig 2.2 purports to show how the Tropopause temperature influences the surface. I have recently looked at Sonde measurements trying to find confirmation of the process illustrated in that diagram, but have found no support for the claimed process, whatever it is (could be magic...) It is apparent from sonde measurements that atmospheric flux imbalances result in temperature change at the point of imbalance, but do not propagate downwards in the manner suggested by the IPCC diagram.]
4. Where I live, the average solar forcing changes by 132W/m^2 from winter to summer, resulting in a change in average temperature from July to January of 16DegC, for a sensitivity of 0.12DegC/W/m^2. This is in my view, strong confirmation that an insignificant change in “Radiative Forcing” (ie stuff happening at the Tropopause not the TOA – how do they calculate that when the Tropopause is bouncing around all the time?) of 3 or 4 W/m^2 will have very little effect down here where the real people live.
Apologies if these matters have already been raised.
Colin Davidson,
This is less about the specifics of your question today but I was thinking of many of your specific past questions when writing Radiative Forcing and the Surface Energy Balance.
It seems that you have raised similar questions here so that article might be worth a read.
Thankyou S_O_D for your helpful reply. I spotted that thread after writing my contribution above, and will be posting on it. Thanks for spending your valuable time on this.
[...] a meridian scholarship blog; others (notable RealClimate, also particularly James Annan, Tamino, Science of Doom) were covering that territory. Nor was it one of a many meridian process blogs. Rather a [...]
SoD,
In the spirit of fairness, can I at least get you to address my point about how designating the 1.1C as the ‘zero-feedback’ starting point (or so-called ‘Planck response’ of about 3.3 W/m^2 per 1 degree of warming) arbitrarily separates the physical processes and feedbacks in the system that will act on additional ‘forcings’ or imbalances, like from increased GHGs, from those physical processes and feedbacks that maintain and control the planet’s energy balance from the forcing of the Sun?
[...] In Part One I created a Matlab model which reproduced the same problems as Spencer & Braswell (2008) had found. This model had one layer (an “ocean slab” model) to represent the MLD with a “noise” flux into the deeper ocean (and a radiative noise flux at top of atmosphere). Murphy & Forster claimed that longer time periods require an MLD of increased depth to “model” the extra heat flow into the deeper ocean over time: Because heat slowly penetrates deeper into the ocean, an appropriate depth for heat capacity depends on the length of the period over which Eq. (1) is being applied (Watterson 2000; Held et al. 2010). For 80-yr global climate model runs, Gregory (2000) derived an optimum mixed layer depth of 150 m. Watterson (2000) found an initial global heat capacity equivalent to a mixed layer of 200 m and larger values for longer simulations. [...]
To me the whole formulation of radiative forcing is wrong.
If I understand it, the radiative forcing of a gas is the change in W/m2 emited out of the atmosphere due to the gas being present (all other things being constant) or perhaps not completely present but due to the change in concentration since the year 1750. Here is the fundamental problem with the approach: The value in W/m^2 is proportional to the radiation emited by the ground surface, and thus it depends on the ground temperature. The values used to measure sensitivity ought to be intrinsic quantities, not the result of a multiplication by the quantity you are trying to find in the first place.
The way I think of it, at the top of the atmosphere you have the net downward solar radiation S = So/4*(1-A) with A=albedo, the transmitted ground radiation G*trans where trans is a transmission factor, and the upwards energy emitted by the Atmosphere. This is turn is proportional to a factor Ctop times the Ground radiation. Then
So/4*(1-A) = G*trans + G*Ctop = G*(trans + Ctop)
We can then solve for the ratio of G/So as
G/So = 1/4*(1-A)/(Ctop + trans)
This way the terms A, trans and Ctop are independent of the ground radiation or temperature (as well as solar) and one can can get the sensitivity of trans and Ctop versus increases in greenhouse gas concentration, and thus the sensitivity of the ground temperature to them.
In order to analyze the atmosphere I would need to know from published ‘radiative forcing’ numbers the ground temperature assumed when the analysis was done, and the ‘base concentration at year 1750′ from which it was derived. It seems that the radiative forcing method ofuscates the problem of calculating a ground temperature rather than bringing light to it.
Wouldn’t help. Forcing alone doesn’t tell you all that much. You need the climate sensitivity. But the climate sensitivity should also be a function of temperature also as it takes a smaller forcing at a lower temperature to increase the temperature by 1 degree. I think. Not to mention that the forcing isn’t all that sensitive to surface temperature. A quick and dirty with MODTRAN tropical atmosphere has the forcing reduced from 4.2 to 3.8 W/m² when the surface temperature is dropped 10C.
[...] plenty of criticism (see my “Radiation and Climate Sensitivity” link to the right, as well as this series by [...]
Sod, or anyone else,
Question 1: Since the colder air is, the less water vapor it can hold, is it true that it takes less energy to raise a cold air mass a given delta T than raising warmer air mass the same delta T? given the same RH?
Question 2: If the answer to Question 1 is yes, should the non-uniformity of the global average temperature anomaly be taken into account to determine climate sensitivity?
1. Assuming constant RH, yes. The converse is true too. It takes more energy to cool warm air by one degree than it takes to cool air at lower temperature by 1 degree.
2. Yes, and it is in the GCM’s. That, IMO, is also one of the reasons for polar amplification, i.e. the temperature changes faster at the poles than at the equator. That would be the absolute local temperature, though, rather than the local anomaly. In fact, it’s one of the reasons you need something as complex as a GCM to estimate climate sensitivity. Unfortunately, GCM’s have other problems, like accounting for the effect of aerosols when we don’t completely understand them and don’t have a historical record that’s worth a dime.
Thank you!
Yes, I have wondered as well how we could know aerosol concentrations in the more distant past, and how reliable/uncertain the data is.