I think this is wrong. We have the CET measurements that show very little change. But we also have sea level measurements that show an increase. Perhaps some more melting across the earth, but certainly some ocean warming since LIA. Impossible to say how great impact CO2 had on this.. ]]>

Mike: At your blog, you wrote (with my emphasis):

“From 1750 to 1920 CO2 increased from 277 to 307 ppm (roughly) and the earth cooled slightly. Interestingly solar irradiance increased by one watt per square meter during this period. From 1940 to 1965 solar irradiance increased as did earth’s average annual temperature. Since about 1970, temperature change has been steadily upward. THE LINK BETWEEN CO2 CONCENTRATION AND AVERAGE GLOBAL SURFACE TEMPERATURE DOES NOT CORRELATE. What other man made causes could be directly responsible?”

Radiative fluxes entering and exiting the atmosphere are effected by CO2 (and to a lesser extend other GHGs), anthropogenic and volcanic aerosols, changing solar irradiation, and anthropogenic changes in surface albedo (aka land use). We can only determine whether CO2 has or has not caused warming FROM OBSERVATIONS when the warming from CO2 is large and these other factors are small or we can correct for the effect of these other factors. We try to quantify the effect CO2 and these other factors by measuring or calculating their effect (called radiative forcing) on the net radiative flux crossing the top of the atmosphere (TOA). The periods you have chosen to focus on involve small and highly uncertain changes in temperature and forcing. These periods can’t prove anything.

In the last half-century (1970-2020), we have the best data on warming and changes in GHGs and other forcing. The planet has warmed slightly less than 1.0 degC in this period and CO2 has increased from 325 ppm to 415 ppm, a 1.28-fold increase, about 1/3 of a doubling. (1.28^3 = 2.1) With two more 1.28-fold increases, might expect about 3 degC of warming for a doubling of CO2 (crudely in line with what the IPCC projects), IF nothing else influenced that first 1.0 degC of warming and nothing else influences subsequent warming.

When all of the factors that influence radiative heat transfer entering and exiting the atmosphere are accounted for we can do a better job of calculating our planet’s “climate sensitivity” to radiative forcing (in W/m2). Then we can use radiative transfer calculations to determine that a doubling of CO2 causes a roughly 3.5 W/m2 reduction in radiative cooling to space to convert radiative forcing in W/m2 to “doublings of CO2”. We can calculate the expected warming when equilibrium (ECS) has been reached and an insignificant amount of heat is flowing into the ocean or the warming when forcing stops (TCR) but the ocean is still being warmed by the atmosphere and the atmosphere cooled by the ocean. Such calculations are called energy balance models and they include all of the uncertainties in forcing and warming. Energy balance models show central estimates climate sensitivity at the low end of AR5’s range and the 90% confidence interval is nowhere near zero. The latest energy balance results come from skeptics Lewis and Curry (2018) and the authors of the climate sensitivity chapter of AR6. They are proof the CO2 causes warming.

https://journals.ametsoc.org/view/journals/clim/31/15/jcli-d-17-0667.1.xm

If you could do the same calculation over some of the periods you chose – with less warming and much more uncertainly about forcing and warming, the confidence interval will be enormous – meaning you would haven’t proven anything.

There is still the problem of “unforced” variability or chaos. If climate can warm or cool without any forcing, how do we know that some or all of the 1 degC of warming in the last half-century wasn’t caused by unforced variability OR that a larger amount of warming wasn’t negated by unforced variability? We don’t! Fortunately, the proxy record for the last ten millennia doesn’t provide much precedent for unforced or unforced GLOBAL change approaching 1 degC, and the odds of that happening over the last half century – precisely when GHGs rose most rapidly – are low. We suspect that some historic variability such as the LIA was at least partially forced by weak solar activity and volcanoes. Ice core records from Greenland show an MWP, RWP and MinoanWP (2 degC warmer), but those same warm periods are not found in Antarctic Ice cores and other areas. So this variability does not appear to be global in extent. Furthermore, we know that variability at high latitudes is amplified by surface albedo feedback and greater than global variability at low latitudes.

The clearest example of unforced variability I know of is El Nino, where global temperature can increase 0.3 degC in six months and fall 0.3 degC over the next six months – without any major change in the radiative fluxes across the TOA. El Ninos are caused in part by a chaotic slowing in upwell of deep cold water off the coast of Peru and downwelling of warm water in the Western Pacific. The AMO may be a much slower form of natural variability associated with changes in the MOC in the Atlantic Ocean, but we’ve got good data on only to oscillation (of 65 years). It is believed that more than half of the warming from 1920 to 1945 (perhaps 0.3 degC) was due to unforced variability, as was the Pause in warming in the 2000s.

Fortunately, we don’t need to rely on the complications forcing and an observed warming to determine that rising GHGs cause warming. Radiative transfer calculations show that – if nothing else changes – rising GHGs slow the rate at which thermal IR escapes to space. These calculations are grounded in quantum mechanism and have been thoroughly validated in the laboratory and in the atmosphere. The law of conservation of energy demands that this slowing must cause the planet to warm somewhere below the TOA until a balance between incoming and outgoing radiation is restored.

The problem you discuss of radiation traveling at an angle to the surface is easily solved by the “two-stream approximation” – breaking the radiative fluxes in the atmosphere into three vector components: one traveling in +z direction (upward), one in the -z direction, and ignoring the horizontal components that cancel and neither heat nor cool the planet. Then you integrate over hemispheres, resulting in a PI/2 greater flux than the simple flux perpendicular to a plane. Such calculations are common when using Planck’s Law. You can read (and criticize) the Wikipedia article I wrote on how Schwarzschild Equation of Radiation Transfer is used in climate science and the subject is also discussed here at ScienceofDoom.

https://en.wikipedia.org/wiki/Schwarzschild%27s_equation_for_radiative_transfer

If you imagine a thin layer of atmosphere, the GHG’s it contains emit equal amounts of thermal IR in the upward and downward directions, and absorb the same FRACTION of the radiation passing up or down through it, However, upward radiation from the generally warmer atmosphere below is more intense than the downward flux from the cooler atmosphere above. So the outward flux in the troposphere (where most absorption and emission occurs) decreases with altitude and this decrease gets larger in magnitude as the concentration of GHG’s rises.

Radiation transfer calculations are done with layers of atmosphere thin enough that net absorption and emission produces change in intensity (dI) that is much smaller than the intensity of the incoming radiation (I). In this case, numerical integration of the changing flux with altitude isn’t effected by the overlapping absorption bands of water vapor and CO2.

]]>Reading the linked page is a total waste of time if you actually want to know anything about atmospheric radiative transfer and how it results in the greenhouse effect.

]]>http://www.resistorcfd.com/articles/climate-change-spoiler-its-not-co2

]]>You explain these things better than I thought possible! ]]>

Jan: 239 W/m2 is used because it was the best estimate of the average amount of radiation being absorbed (post-albedo). And emitted by the planet assuming a steady state before rising GHGs.

Most of what you have written is correct. There are multiple ways to answer this question.

A doubling of CO2 was calculated by Myhre to reduce LWR radiative cooling to space by 3.7 W/m2. The calculation assumes nothing else changes and is sometimes referred to as an instantaneous doubling. Under this hypothetical situation, the law of conservation of energy demands that temperature rise (somewhere below the tope of the atmosphere or TOA). That rise will continue until the planet emits 3.7 W/m2 and no radiative imbalance at the TOA exists.

To determine how much warming is needed to eliminate this imbalance, we need to know how much more radiation the planet emits for each degC its temperature rises. This is called the climate feedback parameter (W/m2/K).

As you noted, one can postulate that the Earth emits 239 W/m2 because it behaves like a blackbody at 255:

W = -oT^4

dW/dT = -4oT^3 = -3.76 W/m2/K

According to this model, the 3.7 W/m2 radiative imbalance from 2XCO2 will be negated by 0.98 K of warming. (By convention, the negative sign represents heat lost by the planet, though this convention is sometimes ignored.)

As you noted, others (presumably including this post) postulate a graybody model for the Earth, where emission of 239 W/m2 is the result of a surface temperature of 288 K and an emissivity of 0.615 (or slight variants of these values).

W = -eoT^4

dW/dT = -4oeT^3 = -3.33 W/m2

According to this model, the 3.7 W/m2 radiative imbalance from 2XCO2 will be negated by 1.11 K of warming.

A few postulate a model where the Earth behaves like at blackbody at 288, but this model doesn’t explain why the Earth emits 239 W/m2. Most people would call this “wrong”, but technically one is free to postulate any model one wants.

Climate models divide the planet up into roughly a million grid cells with realistic temperatures and calculate how much more radiation they absorb and emit. From their output, climate scientists have determined that a warming planet emits 3.21 W/m2/K (+/-0.05 W/m2/K) more radiation to space – assuming nothing else changes. According to this model, the 3.7 W/m2 radiative imbalance from 2XCO2 will be negated by 1.15 K of warming. This is what most people call the no-feedbacks climate sensitivity.

If you want to be more sophisticated, the following model I devised may be useful. Others explain this differently. The planet’s radiative imbalance (I) is:

I = (S/4)*(1-a) – eoTs^4

where a is albedo, S is incoming solar radiation, Ts is surface temperature and e is the planet’s effective emissivity given an average Ts of 288 K.

dI/dTs = -4eoTs^3 – (oTs^4)*(de/dTs) – (S/4)*(da/dTs)

dI/dTs is the climate feedback parameter. Here emissivity hasn’t been treated as a constant. The first term is called Planck feedback and is -3.3 W/m2. The third term is the change in reflection of SWR by clouds and the surface, called cloud SWR and ice albedo feedbacks. The sum of the first and second terms is called LWR feedback. The second term includes: a) the effect on emissivity of rising humidity (water vapor is a GHG reducing emissivity) with temperature, b) the change in emissivity due rising humidity causing more warming higher in the atmosphere than at the surface, and c) the change in emissivity of clouds due to a change in their altitude/temperature or composition. These are called water vapor, lapse rate and cloud LWR feedbacks. (And while we are being more sophisticated, the composition of atmosphere predicted by climate model changes with warming and those changes result in a doubling of CO2 producing an effective forcing (reduction of radiative cooling to space) from 2.4 to 4.4 W/m2.)

No one knows the correct values for de/dTs, da/dTs, or feedbacks, but they can be abstracted from the output of climate models. Most climate models predict dI/dTs is around -1 W/m2/K. Current forcing is about 2.5 W/m2 and ocean heat uptake is about 0.7 W/m2, so current warming of roughly 1 degK is sending about 1.8 W/m2 more radiation to space (emission of LWR and reflection of SWR). That’s -1.8 W/m2/K; almost half as much warming at steady state as predicted by climate models. This approach is called an energy balance model.

Assuming I haven’t made any mistakes, all of these answers begin with different models/assumptions and are as “correct” or “wrong” as the assumptions on which they are based. Confusion arises because different people use different assumptions without making them clear.

]]>I would like to discuss the following section:

Tnew4/Told4 = (239 + 3.7)/239

where Tnew = the temperature we want to determine, Told = 15°C or 288K

We get Tnew = 289.1K or a 1.1°C increase.

Why do you take the value of 239? The current temperature is not because of the solar radiation of 239 W/m2, its due to the solar radiation of 239 W/m2 + the current radiation forcing of 157 W/m2 which brings it to 396 W/m2. You are going to raise the total energy warming the planet from this value of 396 W/m2 to 399.7 W/m2.

So we get

Tnew4/Told4 = (396 + 3.7)/396

where Tnew = the temperature we want to determine, Told = 15°C or 288K

We get Tnew = 288.67K or a 0.67°C increase.

What you are doing is calculating the ratio by which an earth without an atmosphere would increase given an extra 3.7 W/m^2. Then you multiply that ratio with the temperature of the earth with an atmosphere to get to the end value.

Off course it requires way less energy to heat non greenhouse gas -18 degree Earth than it does to heat pre industrial revolution +15 degree greenhouse earth.

Put differently the 239 comes from how much the sun shines on the top of the atmosphere and how much the earth radiates into space from the top of the atmosphere. This value is in equilibrium as you explained in another post. Obviously when we get more greenhouse gasses this value will not change! It will be the 396 W/m^2 that will change. So this should show in your calculations.

I also looked at calculations I came across at other places that try to derive the climate sensitivity parameter from the Boltzmann equation.

I came across this: landa = Ts / 4*sigma*Te^4

Here: http://web.ma.utexas.edu/mp_arc/c/11/11-16.pdf

She used Ts = 288 and Te = 255, again I would argue that 255 (temperature of a blackbody radiation 239 W/m^2) has no place in these calculations and it should also equate to 288. (289 is closer if I take your value of 396 btw)

Then that equation simplifies to landa = 1 / 4*sigma*T^3

Similar to the one I found here:

clivebest.com/blog/?p=4923

Where he uses an emissivity factor to make the earth a greybody instead of a blackbody.

Now you wrote on another page that the earth could be seen as close to a blackbody. So if we take the simplified formula and T = 289 then that solves for landa to 0.1827. Significantly lower than the 0.3 commonly quoted.

This could only come close to 0.3 (but not quite, 0.285) if we use an emissivity of 0.64 which wikipedia claims of the earth taking cloud cover into account.

But would this not already be effectively a feedback loop of the water vapor?

And even when not half of the atmosphere by mass (pressure, same thing if you think about it) lies under 5000 meter altitude. So half of the radiative forcing should take place here under the clouds (assuming that the average cloud lies at 5000 meter) and thus the emissivity that matters for that half at least is that of the earth’s surface which is quite close to 1, lets say 0.95. So the total emissivity should be somewhere in between 0.64 and 0.95 then.

However clouds are vapor and does not absorb the same wavelengths as CO2 albeit there’s some overlap as you showed in part 1. Thus assigning a lower emissivity to the earth due to the clouds seems to be a mistake from the getgo. The source of the radiation is the Earth and giving it a lower emissivity (which would increase the effect of CO2) because it already has gasses surrounding it that traps radiation that the CO2 cant trap a second time seems illogical to say the least.

Thus the question remains. Where does the 1-1.2 degree no-feedback calculation comes from? Because I get different figures using two different, albeit it similar methods.

Thank you for your attention.

I hope you can shine a good light on this.

Regards,

Jan

Bruce asked: Is it possible to follow heat emitted using satellites over time? If so, is it possible to demonstrate that the “CO2 bite” has become larger as more CO2 has been added to the atmosphere?

Let’s do some simple calculations to determine if what you ask is possible. Our satellites in space show that the planet is emitting an average of about 240 W/m2 of heat (thermal infrared or LWR). CO2 is near 400 ppm and increasing about 2 ppm/yr or 5%/decade. At that rate it would take 14 decades to double (1.05^14 = 20) or 20 decades using linear rather than exponential growth. According to laboratory measurements of radiation, a doubling of CO2 will reduce radiative cooling to space by 3.7 W/m2 or 0.26 W/m2/decade. Requires measuring an 0.1% change in 240 W/m2/decade – from space.

Even worse, the planet is warming (because of that reduction in emission of heat to space). A warmer planet emits more heat to space, compensating with some lag for the reduction caused by CO2.

Even worse, the 240 W/m2 average we do measure varies with the seasons (almost 10 W/m2) and weather and phenomena like ENSO.

No, we can’t measure what you would like us to measure.

What we can do is use data from laboratory measurements to predict what we should “see” at various locations on the planet. “See” means measure the radiation intensity at all wavelengths coming down from the sky to the surface or up from the Earth to space. The former is easier to do. First, a radiosonde is sent to measure the temperature and humidity at all altitudes overhead. Then the spectrum of radiation reaching the surface is compared with what we calculate based on laboratory measurements. This has been done from Antarctica to the tropics, producing changes in downward radiation of more than 100 W/m2 due to temperature differences and large changes in the spectrum due to changes in water vapor. Agreement between theory and experiment with these large changes should give you confidence we can calculate small changes. SOD provided this link to compare theory and experiment.

https://scienceofdoom.com/2010/11/01/theory-and-experiment-atmospheric-radiation/

In general, it is a bad idea to expect to confirm the physics of climate change by observing the planet. The climate change you are seeking is changing extremely slowly, weather changes chaotically, large El Ninos and La Ninas are massive disruptions.

]]>Bruce,

It’s a good question but it’s not as simple as you might think to do this experimentally.

1. Satellites measuring outgoing longwave radiation (OLR) across the spectrum are rare. Well, over the last 15 years there has been the AIRS satellite, but prior to that it was just occasional measurements.

2. The total radiance at each wavelength actually depends on the surface temperature as well as how much the CO2 takes out of the spectrum. It also depends on the absorption by the water vapor continuum in this range of wavelengths (this is hard to explain in a sentence or two but more in the series Visualizing Atmospheric Radiation.

Now perhaps you are wondering whether the whole idea of CO2 absorption is quite speculative. Not at all. It’s very repeatable and boring to put radiation of different wavelengths through gases with different proportions of CO2 and get exactly the same amount of absorption each time. For example, if you want bedtime reading you can read *Journal of Quantitive Spectroscopy and Radiative Transfer* where there are decades of papers on this subject by people who do these kind of measurements.

Likewise, if we know the surface temperature, the atmospheric temperature profile and the concentration of CO2, water vapor and other GHGs, we can calculate the spectrum of radiation at the top of the atmosphere and compare it with satellite measurements. The results match, which is why the theory of radiative transfer is fundamental physics (and used in all kinds of measurements).

For example, this comparison of theory and experiment is shown in Theory and Experiment – Atmospheric Radiation:

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