Guest Post by Willis Eschenbach
In my last post, entitled Advection, I was discussing the online MODTRAN Infrared Light In The Atmosphere model. A commenter pointed out that in the past I’d wondered about why the MODTRAN results showed that a doubling of CO2 caused a clear-sky top-of-atmosphere (TOA) decrease in upwelling longwave (LW) radiation of less than the canonical value of 3.7 watts per square meter (W/m2) per doubling of CO2. Here’s that data.
Figure 1. MODTRAN results for several doublings of CO2, clear-sky only, measured at the top of the atmosphere (TOA). Units are watts per square meter (W/m2).
To figure out exactly why these values were so low, I went back to the paper giving the 3.7 W/m2 value, New estimates of radiative forcing due to well-mixed greenhouse gases, by Myhre et al. I also recalled that in my earlier thread, commenters had mentioned that there were two “top-of-atmosphere” definitions. One of them was what I’d used for Figure 1, looking down from 70 km above the surface. And the other definition of “top-of-atmosphere” was the tropopause. Upon re-reading Myhre and doing some further research, I confirmed that the measurements and model results giving the canonical value of 3.7 W/m2 per doubling were taken, not at the actual top of the atmosphere (TOA), but at the tropopause.
The tropopause is the boundary between the troposphere and the stratosphere. It is the location where the temperature of the atmosphere stops getting colder with altitude. The tropopause is at different altitudes at different times and locations.
The MODTRAN model offers a graph of the atmospheric temperature profile at various locations and seasons. Here’s the profile for what is called the “US Standard Atmosphere”.
Figure 2. Profile showing temperature versus altitude, US Standard Atmosphere
My calculations for Figure 1 were done from 70 km looking down … but as you can see, at that location the tropopause in Figure 2 is only at 11 km.
So I redid my MODTRAN runs shown in Figure 1, this time measuring from the appropriate tropopause levels at each location. You have to take two measurements when calculating longwave changes at the tropopause—one looking upwards and one looking downwards. The final answer is the net of the two changes.
With that as a prologue, here are my results. I’ve compared them to the results shown in Table 1 of the Myhre et al. paper. My average results calculated as in the Myhre et al. paper give a troposphere clear-sky increase in longwave (LW) absorption resulting from a doubling of CO2 of 4.97 watts per square meter (W/m2). This is extremely close to the Myhre et al. Table 1 figure of 5.04 W/m2 per doubling—it’s less than 0.1 W/m2 difference. And adding in the good agreement with the CERES figures noted in my last post, these results give me confidence in the MODTRAN model.
Figure 3. As in Figure 1, except measured at the tropopause rather than from 70 km up at the top of the atmosphere (TOA).
There were a couple of surprising things about Figure 3. First, there is a slight reduction in the change per doubling as the absolute value of the atmospheric CO2 level increases. Unexpected. Presumably, this reflects a gradual saturation of the absorption bands. However, it’s not large enough to affect most calculations.
Second, and more importantly, I did not expect such a large difference between measurements taken at the two levels. The TOA measurements average about 52% smaller than the tropopause measurements.
This is interesting because of the theory of why a CO2 increase leads to surface warming. The theory goes like this:
• The amount of atmospheric CO2 is increasing.
• This absorbs more upwelling longwave radiation, which leads to unbalanced radiation at the top of the atmosphere (TOA). This is the TOA balance between incoming sunlight (after some of the sunlight is reflected back to space) and outgoing longwave radiation from the surface and the atmosphere.
• In order to restore the balance so that incoming radiation equals outbound radiation, the surface perforce must, has to, is required to warm up until there’s enough additional upwelling longwave to restore the balance.
I’ve pointed out the problem with this theory, which is that there are a number of other ways to restore the TOA balance. These include:
• Increased cloud or surface reflections can reduce the amount of incoming sunlight.
• Increased absorption of sunlight by the atmospheric aerosols and clouds can lead to greater upwelling longwave.
• Increases in the number or duration of thunderstorms move additional surface heat into the troposphere, moving it above some of the greenhouse gases, and leading to increased upwelling TOA longwave.
• Increases in the amount of energy advected from the tropics to the poles increase the upwelling TOA longwave
• A change in the fraction of atmospheric radiation going upwards vs. downwards can lead to increased upwelling radiation.
So there is no requirement that surface temperatures increase in response to increasing CO2. Increasing surface temperatures are only one among a number of ways to restore the TOA radiation balance.
With that as prologue, the insight for me from the big difference between TOA and troposphere measurements is that I’ve been thinking that the imbalance at the actual TOA from a doubling of CO2 would be 3.7 W/m2 … but in fact, it is only about half of that, about 1.9 W/m2.
Now, as I pointed out just above, there are a variety of ways that the TOA radiation balance can be restored. So how much of that is from surface warming?
Well, here’s the relationship between the surface temperature and the upwelling TOA longwave.
Figure 4. Scatterplot, average upwelling TOA longwave versus surface temperature, 1° latitude by 1° longitude gridcells.
As you might expect, over much of the planet as the surface warms, the upwelling TOA longwave increases. This makes sense, a warmer surface radiates more longwave, so you’d think there would be increasing upwelling TOA longwave.
But at temperatures above about 26°C, the situation changes rapidly. Above that temperature, the upwelling TOA longwave drops very rapidly with increasing temperature.
I ascribe this to the action of tropical thunderstorms. These form preferentially at temperatures above ~ 26°C. Here’s a look at the effect using two very different datasets.
Figure 5. Rainfall from tropical thunderstorms versus sea surface temperatures. Red dots are from the Tropical Rainfall Measuring Mission. Blue dots are from the TAO/TRITON moored ocean buoy array.
And what is the long-term net of all of this over the entire globe? Figure 6 shows that result.
Figure 6. Scatterplot, monthly top-of-atmosphere upwelling longwave (TOA LW) versus surface temperature.
[UPDATE] An alert and statistics-savvy commenter pointed out that my use of ordinary least squares (OLS) linear regression underestimated the slope of the trend line. I’ve redone Figure 6 using Deming regression, which gives a correct slope. His comment is here, my response below it. My profound thanks to him, this will help me in many areas. Always more for me to learn …]
Other things being equal (which they never are), according to the CERES data a 1°C increase in global average temperature leads to a 3 W/m2 increase in upwelling TOA LW.
It’s worth noting in this context that because we are dealing with radiation in the atmosphere, things happen at the speed of light. A cross-correlation analysis shows that there is no delay between monthly changes in surface temperature and monthly changes in TOA longwave.
Figure 7. Cross-correlation, monthly top-of-atmosphere upwelling longwave (TOA LW) and surface temperature. Positive values show TOA LW lagging surface temperature, negative values show surface temperature lagging TOA LW. Overall, there is no lag between the two.
Since there is no lag in this, and since it directly relates surface temperature to TOA longwave radiation changes, it would seem to me that this would give a good estimate for the equilibrium climate sensitivity (ECS) of 0.6°C per doubling of CO2 … but what do I know, I was born yesterday.
Next, the calculated decrease in TOA upwelling LW ascribable to the increase in CO2 over the 21-year period is about -0.3 W/m2. The change in surface temperature over the period is ~ 0.4°C. This has increased the TOA LW by ~ 1.2 W/m2 … meaning that the surface is warming more than four times as fast as would be required to offset the TOA imbalance.
Why is the surface warming faster than the CO2 increase would suggest? Well, the main reason is the increase in the amount of sunlight absorbed by the surface. That solar energy has increased by 1.5 W/m2 over the 21-year period of the CERES record … as I said, other things are never equal.
My very best regards to all,
w.
PS: In analyses such as this one, it is generally useful to keep in mind what I modestly call “Willis’s First Rule Of Climate”, which states
“In climate, everything is connected to everything else … which in turn is connected to everything else … except when it isn’t.”
MY USUAL: I can defend my own words, but not your interpretation of my words. When you comment, please QUOTE THE EXACT WORDS that you are discussing. This avoids endless misunderstandings.
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1. Clearly the TOA (mesopause) forcing is the relevant parameter for overall climate system sensitivity.
2. For comparison, Wijngaarden and Happer (W&H) calculate forcings per doubling CO2 in the Standard Atmosphere of 5.5 W/m2 at the tropopause, reducing to 3.0 W/m2 at the mesopause, and provide an explanation of the difference. These values are close to the Standard Atmosphere values shown in Figures 1 and 3 in the post. W&H refer to the Standard Atmosphere as a Mediterranean model; they also calculate spectral intensities for the Sahara and for Wintertime poles, but unfortunately omit to give forcings for these different regions.
3. The above are clear sky forcings. The effect of clouds, which cover two thirds of the sky, needs to be taken into account. Since greenhouse gases impact the outgoing longwave from cloud tops to a much lesser extent (due to lower densities of GHGs at altitude, and the smaller temperature differential between cloud tops and the radiating layers above) one can expect the climate system sensitivity above clouds to be considerably reduced from that in clear skies. The modelling of clouds is not well developed, but their effect is examined observationally in Dubal & Vahrenholt (D&V). Drawing on observations in D&V, one can estimate an all-sky ECS of only 40-45% of the clear sky effect.
4. This would give an estimate for all-sky radiative forcing per doubling of CO2 of 40-45% of 3.0 W/m2 or about 1.2-1.35 W/m2. This compares with the 1.9 W/m2 estimated in the post. Either way, the observational data points to a much lower ECS than that in mainstream climate models.
D&V: Dübal, H.R. and Vahrenholt, F., 2021. Radiative Energy Flux Variation from 2001–2020. Atmosphere, 12(10), p.1297.
W&H : van Wijngaarden, W.A. and Happer, W., 2020. Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases. arXiv preprint arXiv:2006.03098.
Thanks, OG. I looked at the situation with clouds by way of the MODTRAN model. Although the absolute values per CO2 doubling are smaller with various kinds of clouds, I found that the TOA value for different kinds of clouds as a proportion of the tropospheric value remained about the same, a bit above 50%.
I suspect this is because the overwhelming majority of clouds are below the tropopause. Thus, the situation above the clouds, both at the tropopause and from there on up, is clear air. So the kind of clouds would (and does) affect the absolute amount of LW making it up to the tropopause, but the proportion remains ~ the same.
w.
Hi Willis, what is het CERES 1,5 W/m2 increased solar radiation source? (link) It is puzzling why someone would use the tropopause radiation imbalance? That just makes no sense.
The source of the increased solar radiation is the CERES dataset. The link to the dataset is at the bottom of Figs. 4,6 and 7 above. As to why use the tropopause radiation imbalance, I have no clue. It’s not possible to measure it directly as you can with the TOA imbalance, so it seems like a less-than-helpful figure.
w.
Alexander, it’s complicated making sense of it all.
See Myhre 1998 if interested enough & you have studied atm. radiation details enough, the spectral line-by-line calculations developed & widely used for climate studies prior to CERES data (Clough 1995) was computationally expensive for intercomparison of radiation schemes. Sure, as you imply full definition of radiation forcing does include stratospheric temperature adjustment.
So, back in those days a first order result was obtained by treating the stratospheric temperatures as being allowed to adjust (downward a bit) to the radiative perturbation of say, added ppm CO2 to compare the influence of radiatively active components on Earth’s energy balance.
The line-by-line radiative transfer method (LBLRTM) iteratively balancing each layer of the atm. was shown back then to be reasonably good enough globally by using 3 temperature profiles for the computation (tropical & NH,SH extratropical).
For example, if you want to consume some Myhre spinach, the absorption of solar radiation in the troposphere yields a weak positive radiative forcing at the tropopause but the absorption in the stratosphere dominates for -0.11 W/m^2 forcing. The shortwave absorption due to added CO2 reduces longwave cooling of the stratosphere increasing the longwave radiative flux from the stratosphere to the troposphere contributing to a positive forcing of 0.05 W/m^2. The net global forcing at tropopause then due to inclusion of solar absorption by CO2 is -0.06 W/m^2. At least back then.
As Willis notes 9:05am, CERES data measured by radiometers takes into account all of these processes over time as the experiment is observing nature rather than doing LBLRTM temperature profile computations to find changes over time which Loeb et. al. publishes for decadal changes in water vapor, CO2 & 6 other well mixed infrared-active gases, clouds, surface temperature so forth (their Fig. 3).
We should be constantly mindful of declining solar activity, as evidenced by very high levels of galactic radiation. Changes since the beginning of the 25th cycle are small. If this trend continues there will be significant changes in the chemistry of the stratosphere at high latitudes.
The effects of the changes are already evident in Alaska and western Canada.
The circulation over Alaska is still blocked, which is why temperatures are so low in Alaska and central Canada.
“but what do I know, I was born yesterday.”
You said that a few days ago.
It must be nearly a week already.
Excellent post BTW – clearly a prodigy! 🙂
Nice digging by Willis as usual. One problem is here he is making the classic error of doing least squares to fit a linear regression to a scatter plot. This defies the conditions required for OLS of having minimal errors in the abscissa ( x axis ).
What happens when doing this is called regression dilution and leads to incorrect, under-estimated value of the slope. One way to verify it’s wrong is to swap the axes. It will not give the same answer and in fact will distorted towards the other variable.
This is no rigorously better way to do this without having some more information about that nature and relative magnitude of the variable errors on both x and y. One quick hack it to eyeball the slope. Horrible as this may sound it is actually better the known to be wrong and visibly wrong misapplication of OLS .
My MkI eyeball tells me the slope here in fig 6. is nearer to 3W/m2/K . That lowers ECS.
This is why climatologists always do this flawed analysis with temperature on x axis, despite their assumption that it is radiation which is the controlled variable as we are seeking to find out the resulting temp change. Doing the flawed OLS with temp on x , assures an exaggerated estimation of ECS.
I’ve been banging on about this fundamental error for over a decade, Sad to see even climate skeptics are still propagating it.
Here’s an article detailing this I wrote in 2014:
https://climategrog.wordpress.com/2014/03/08/on-inappropriate-use-of-ols/
This graph shows the two extremes of incorrect OLS descibed above on such a graph of data with significant error in both axes:
If OLS worked in this situation both of those fitted lines would be the same !
Thanks, Greg. That is a most fascinating objection, and one I’d never heard of. Your linked post explains it very well. And a bit of testing shows that you are correct. My use of OLS linear regression was wrong.
There is, however, a regression method which allows for a more accurate trend line. It is called “Deming regression”, and is used when the errors in both X and Y are known.
In the case of Figure 6, there are two sources of error in each dataset (TOA LW and temperature). One is the error in the area-weighted averageing of the gridcells. The other is the error in the removal of the seasonal variations. As usual they add in quadrature.
I’ve calculated those errors, figured out the Deming regression, and redone my Figure 6 and subsequent text. You’ll laugh. You said:
The Deming regression including the errors gives a slope of 3.03 W/m2 per °C … just what you said.
And as you pointed out, this means that the ECS is 1.9/3.0 = 0.6°C per doubling of CO2 …
Much appreciated, always more to learn. I love writing for the web, my mistakes rarely last long.
w.
Hi, Willis — BLUE: best linear unbiased estimator. That is what OLS gives you. Best means that it has the smallest variance of all linear unbiased estimators, linear is because Y = a + b X + e is the linear model you estimate to find the true relationship Y = A + B X, and unbiased because the OLS estimator, b, is unbiased: E(b) = B.
The issue Greg is raising is due to a fundamental misunderstanding of what a regression does. In a classical regression, the X variables are taken to be strictly exogenous. The classical example is where different amounts of fertilizer are applied to a crop and crop yield is the dependent variable Y.
Since the experimenter wants to see how X affects Y, the errors in the regression are due to things which are beyond the control of the experimenter. So the linear formulation is that Y = a + b X + e, where the error e has expectation of E(e) = 0 and it is assumed that E(X*e) = 0 as well. That is, there is no correlation between the X variables and the errors e. This is what it means to be strictly exogenous.
In the scatter plot example where the author in the blog Greg linked to switched the X and Y variables to estimate X = (Y-a-e)/b = c + d Y + v, the errors in Y have been interpreted as being errors in X, with E(v)=0 (which naturally follows from b being a constant and E(e)=0). But now E(v*Y) is not equal to zero, since the errors v=e/b, and the errors e were due to things that affected Y.
In general, if you have reason to believe that the expectation E(X*e) is not zero, which your statement that everything is related suggests might be true, this is an “errors in variables” problem, and it is much more difficult so solve than is being suggested.
1. How many Degrees of Freedom does the climate system have?
2. To what degree is one favored in relation to all others?
3. Is this incorporated into the Climate Models?
For example. The earth can shed more energy by increasing temperature variance while the average remains unchanged.
Conversely the earth can raise its average temperature by reducing variance without any change in energy in or out.
I submit that these are probabilistic properties that cannot be calculated deterministically.
The LIA can be perfectly explained as a change in the variance in the temperature field, without the slightest change in forcings.
That is exactly why modelling is extremely difficult and an ongoing process.
How many Degrees of Freedom does the climate system have?
Climate is fluid flow. When it’s turbulent i.e. high dimensional chaos, then it has almost infinite degrees of freedom.
But what makes interesting pattern emerge is when the dimensionality is reduced, by for instance internal feedbacks (excitability) and external periodic forcing from astrophysical sources. Low dimensional borderline chaos is where pattern emerges.
Like “climate change”, TOA is a theoretical construct that has meaning only in context.
Thus, like climate change, it can be both True and False and Null all at the same time.
Accounting for valid surface energy constraints and using a sound conceptual understanding we can determine all important energy components knowing only surface temperature and measured OLR. These represent the lower and upper boundary conditions, respectively.
Here I will demonstrate why Kiehl-Trenberth US standard atmosphere flux diagram is wrong when applied to the global climate system.
See my comments up-thread for more context.
All units are in watts per square meter.
Say OLR is measured = 240.
At 15C air temperature; surface upward flux density must be around 375 at hemispheric emissivity = 0.96.
https://www.omnicalculator.com/physics/stefan-boltzmann-law
Trenberth lists 390. This is where consensus climate science goes horribly wrong. 390 upward surface flux density has no physical basis at 15C earth.
Atmospheric emission = surface upward flux / 2
Atmospheric emission = 375/2 = 188
Trenberth lists 165 + 30 = 195
IR window = OLR [minus] atmospheric emission
IR window = 240 – 188
IR window = 52
Trenberth lists 40. Gross underestimation of IR window is the result of a poorly defined TOA boundary condition in consensus climate science. The IR window is substantially larger than commonly assumed..
Atmospheric absorbed flux = surface upward flux [minus] IR window
Atmospheric absorbed flux = 375 – 52.5
Atmospheric absorbed flux = 323
Trenberth lists 350
Accounting for logarithmic total column density profile (pressure profile):
Total column IR opacity = ln (Atmospheric absorbed flux / IR window)
Total column IR opacity = ln (323 / 52)
Total column IR opacity = 1.83
Total column IR opacity is a unitless ratio of surface flux absorbed in the atmosphere vs surface flux transmitted through the IR window.
The climate system is constrained by:
1) surface upward flux density
2) total column IR opacity.
You will find the total column IR opacity around 1.8 remains practically invariable regardless of climate i.e. latitude, season, or global climate change scenarios.
Conceptually, assuming no change in mass, turbulent energy flux K adapts to distribute energy exactly where it’s required to minimize temperature (or to maximize entropy).
The observed nature of the system indicates no change to total IR opacity regardless of the conditions observed. A truly remarkable finding.
The system achieves this through dynamic sensible and latent heat flux distribution throughout the atmosphere. It is constrained by the density profile of the atmosphere. Cloud dynamics are a critical second order consequence achieving efficient solutions.
Comparing spot OLR changes to surface flux from earth observation systems such as CERES are thus mostly influenced by surface flux straight up through the atmospheric window.
Using the same concepts –
To calculate change in OLR from 1 C surface temperature increase:
At 16 C the surface upward flux must be around 380 at emissivity 0.96
https://www.omnicalculator.com/physics/stefan-boltzmann-law
Change in OLR = (380-375) / Total column IR opacity
Change in OLR = 5 / 1.83
Change in OLR = 2.7 watts per square meter.
JCM
Find below the faulty standard atmosphere flux profile.
All simpified models are both wrong and useless, average temperature when emissivity is a T4 function has no meaning. And water vapor quantity and distribution and condensation is what mainly determines the IR window. The only proof of the pudding is the increase in ocean heat content and melting of ice, everthing else is just a model.
JCM, when you reduced the surface emissivity from the rounded value Trenberth used, you forgot to change the surface reflectivity back to balance since:
global surface emissivity + reflectivity + transmissivity = 1.0
Conceptually the radiative surface emissivity is only influencing the IR window portion. In this case you could make a minor adjustment to reflectivity in the IR window fraction if you wish (assuming all else remains equal). However you’ve hit on the most interesting bit – the bulk of surface upward flux density delivered to the atmosphere is not radiative in nature, it is the result of turbulent eddy diffusion. “Surface radiation” is a misnomer. Surface energy balance concepts must maintain continuity between surface temperature and air. Convection delivers the bulk of heat (sensible and latent heat) to the radiating height. The mistake is interpreting the nature of surface flux as only radiative in nature. I used the Kielh Trenberth diagram, which is not ideal, in an attempt to merge the concepts.
Where Is The Top Of The Atmosphere?
“. A commenter pointed out that in the past I’d wondered about why the MODTRAN results showed that a doubling of CO2 caused a clear-sky top-of-atmosphere (TOA) decrease in upwelling longwave (LW) radiation of less than the canonical value of 3.7 watts per square meter (W/m2) per doubling of CO2.
To figure out exactly why these values were so low, I went back to the paper giving the 3.7 W/m2 value, New estimates of radiative forcing due to well-mixed greenhouse gases, by Mhyre et al.
–
I also recalled that in my earlier thread, commenters had mentioned that there were two “top-of-atmosphere” definitions. One of them was what I’d used for Figure 1, looking down from 70 km above the surface. And the other definition of “top-of-atmosphere” was the tropopause.
–
Upon re-reading Mhyre and doing some further research, I confirmed that the measurements and model results giving the canonical value of 3.7 W/m2 per doubling were taken, not at the actual top of the atmosphere (TOA), but at the tropopause.
My calculations for Figure 1 were done from 70 km looking down … but as you can see, at that location the tropopause in Figure 2 is only at 11 km.”
–
So at least two definitions.
I have a third.
Leaving the question
–
What is the TOA presuming it exists.
We’re talking about the TOA radiation balance, where at steady-state the incoming energy matches the outgoing energy.
For that definition, 70 km altitude works fine, because up that high, downwelling LW radiation is only about 0.05 W/m2, lost in the noise.
w.
My naive assumption is that the TOA is, as usually stated, the height of the atmosphere where the incoming radiation equals the exiting radiation.
–
This is therefore the height at which the temperature that would give that radiation to space equals the actual surface temperature that would exist on the planet surface with no atmosphere for that amount of received radiation.
i.e. the solar radiation minus the albedo and atmospheric absorption effects
–
I also pictured the TOA as a balloon of various heights down even to surface level on the dark side with no incoming radiation.
Unfortunately that assumption was punctured when it was pointed out that with no incoming radiation it was pretty hard to even define a TOA on the dark side as there is no balance.
–
The best way out of the dilemma was to imagine a TOA for a world with the 24 hour input spread over the whole globe which does give a conceptual average TOA.
Which is what I believe you are using?
–
A height of 11 kilometers would then seem to be in that ballpark.
–
Note for Willis.
Wiki Total Solar Irradiance(TSI) is a measure of the solar power over all wavelengths per unit area incident on the Earth’s upper atmosphere.
but
The solar constant is a conventional measure of mean TSI at a distance of one astronomical unit (AU).
The SI unit of irradiance is watt per square metre (W/m2 = Wm−2).
The separation of Earth from the sun can be denoted RE and the mean distance can be denoted R0, approximately 1 astronomical unit (AU).
The solar constant is denoted S0. The solar flux density (insolation) onto a plane tangent to the sphere of the Earth, but above the bulk of the atmosphere (elevation 100 km or greater)
[Here they specify, as I said the plane is at the mid level of the earths distance from the sun.
Then they cleverly say it is above the atmosphere but not between the earth and the sun]
Of course the amount of energy that can hit the earth on a plane tangent to the earth and sideways above its atmosphere is zilch.
Average annual solar radiation arriving at the top of the Earth’s atmosphere is roughly 1361 W/m2.
on the plane next to earth at earths midpoint level
The average annual solar radiation arriving at the top of the Earth’s atmosphere (1361 W/m2) represents the power per unit area of solar irradiance across the spherical surface surrounding the sun with a radius equal to the distance to the Earth (1 AU). This means that the approximately circular disc of the Earth, as viewed from the sun, receives a roughly stable 1361 W/m2 at all times.
So it is the earth’s disc surface area that is considered to be irradiated. not the toa above the earth between the earth and the sun.
Because the Earth is approximately spherical, osphere, averaged over the entire surface of the Earth, is simply divided by four to get 340 W/m2. In other words, averaged over the year and the day, the Earth’s atmosphere receives 340 W/m2 from the sun. This figure is important in radiative forcing.
TSI is for the earths surface at the space level TSI on a plane lateral to the earth
The earth has atmosphere outside this disc which is also heated.
The energy budget worked out this way is fictitious and allows a top of earth imbalance that does not exist.
You mention a virtual upper boundary that is the effective height where the bulk of upward radiative flux originates from.
Physically this is the zone where non-radiative and radiative flux are roughly equal. It is the zone where net radiative flux takes over from K. It’s turbulent but if you like it can be pictured as the temperature somewhere in the range 5-10km.
However, this zone is not the height where downward IR radiation is zero and so it’s not very helpful if you’re trying to detect overall IR greenhouse enhancement. It’s arbitrary to choose a level somewhere in the middle of the upper troposphere, no?
I agree with the author that if you want a mental picture then somewhere around 70km-100km seems a reasonable boundary where there is no more emitted LW radiation to consider.
Invoking physical boundary conditions from my perspective –
Using 0.4C CERES surface temperature increase mentioned in the article:
0.4C is empirically associated with surface upward flux density change of roughly 2.1 watts per square meter.
Change in OLR = 2.1 watts per square meter / 1.83
Change in OLR = 1.15 watts per square meter
This largely approximates the increase OLR by ~1.2 w/m2 indicated in the article. From my perspective there is no need to invoke changes to trace gases here.
“The mistake is interpreting the nature of surface flux as only radiative in nature.”
There is no mistake, JCM, if you look at the Trenberth cartoon you posted 11:43pm, find there are thermals (convection) and evapo-transpiration surface flux considered also so the nature of surface flux is NOT only radiative.
The downdraft flux and condensation flux returning to surface are components of the 324 downward flux equal and opposite to the updrafts and evapo-transpiraton in the multi annual period because these two fluxes do not cross the TOA control volume to deep space as does radiation.
If you properly add in the surface reflectivity .04 to your 0.96 surface emissivity then you will recover Trenberth’s numbers – this is so hard to do accurately & so not needed no one has made the effort to do so that I have come across.
For a better treatment breaking out the water cycle component in the ~324 downward flux summation see L’Ecuyer et. al. 2015 energy budget Vol. 28 Journal of Climate Fig. 4 p. 8335.
There is no need to partition the various fluxes to observe changes to optical thickness or greenhouse factor. The 1.83 ratio can be observed very easily.
My proposal is to simplify the problem to upper and lower boundary conditions. I broke out some internal components in my comment to illustrate the point and to explain why.
Observed average OLR and surface temperature continues to follow the same ratio through the observational period. We can argue about internal partitioning but it won’t change the simple observation.
OLR and surface upward flux are bound and so there has been no observable change to net column flux properties. It will be difficult to see this viewed from the current common perspective.
Addendum – it is quite apparent many visitors to this website are very loyal to the enhanced greenhouse effect hypothesis and will staunchly defend its assumptions. I understand different perspectives will ruffle some feathers. That’s what it’s all about.
Thanks. This seminal analysis by Willis should get one spellcheck:
It’s Myhre, not Mhyre, (or Myrhe as in one of the comments)
In the beautiful Norwegian language, the ‘h’ works as a softener.
https://www.researchgate.net/profile/Gunnar-Myhre
Thanks, fixed. I hate typos and misspellings.
w.
Willis,
See guest post by Dr. Tim Ball here on August 29,2015, “Where is the Top of the Atmosphere?” commenting on Bob Tisdale’s then recent post on this subject.
There is real confusion as no one has a consistent definition of TOA.
Most papers seem to be suggesting mid to upper troposphere or the tropopause. Sir John Houghton in his book “Global Warming: the Complete Briefing” in discussing the Greenhouse Effect nominates the TOA as a height between 5 and 10 km above the Earth ( but that does not allow for variations you discuss around the globe).
As Tim and Bob show there is no consistent definition which only adds to the uncertainties in the “enhanced greenhouse effect “.