The Greenhouse Effect, A Summary of Wijngaarden and Happer

By Andy May

This post was updated 9/24/2021 to reflect reader comments.

The phrase “greenhouse effect,” often abbreviated as “GHE,” is very ambiguous. It applies to Earth’s surface temperature, and has never been observed or measured, only modeled. To make matters worse, it has numerous possible components, and the relative contributions of the possible components are unknown. Basic physics suggests that Earth’s surface is warmer than it would be with a transparent atmosphere, that is no greenhouse gases (GHGs), clouds, or oceans. If we assume Earth is a blackbody, then subtract the solar energy reflected, from the hypothetically non-existent clouds, atmosphere, land, ice, and oceans; we can calculate a surface temperature of 254K or -19°C. The actual average temperature today is about 288.7K or roughly 15.5°C. This modeled difference of 35°C is often called the overall greenhouse effect.

A blackbody is usually defined as a perfectly black cavity kept at a constant temperature. All energy that enters the cavity is absorbed by the cavity walls, and they emit exactly the same amount of energy, but the wavelength of the emitted radiation is not the same as the energy captured. Instead, the emitted radiation has a wavelength determined by the cavity temperature, which is held constant. The Earth is nothing like this. It isn’t black and both the atmosphere and the oceans absorb and redistribute solar energy, often the absorbed energy is circulated for a long time, even centuries or millennia, before it is reemitted. A blackbody absorbs and reemits energy with a delay of less than a second. Earth’s surface temperature is not constant, like a blackbody’s temperature, it varies a lot by latitude, altitude, season, and/or ocean depth. The Moon has a calculated blackbody temperature of 270K, no atmosphere or oceans, and an average temperature, at the equator and low latitudes, of around 215K, so even the Moon is not an ideal blackbody.

Some unknown portion of the overall GHE is probably due to atmospheric greenhouse gases (GHGs). These include, CO2, H2O, CH4, N2O, and O3. Dr. William Wijngaarden and Dr. Will Happer examine the likely influence of these greenhouse gases using the HITRAN line-by-line molecular transmission and absorption database maintained at Harvard University (Wijngaarden & Happer, 2020). We discuss Wijngaarden and Happer’s important paper in this post and refer to it as W&H. HITRAN stands for high-resolution transmission molecular absorption. The database compiles spectroscopic parameters that computer programmers can use to model the transmission and emission of light in the atmosphere. W&H use the database to model a hypothetical mid-latitude temperature and GHG atmospheric profile to derive a representative climate sensitivity to doubling the gases. We have previously written about the GHE and will not cover the same ground in this post, which is mostly about the W&H model.

Dr. Clive Best also studied the HITRAN database, but just for CO2 (Best, 2013). Best also investigated the effect of gravity or air pressure on Earth’s surface temperature and concluded that they must contribute something to the overall greenhouse effect but was unable to model the amount. According to the second law of thermodynamics, a thermally isolated atmosphere will reach a constant temperature throughout its height if entropy remains constant. For a closed system that does not exchange heat or work with the surroundings, entropy can only increase. Earth’s atmosphere is not closed, since it is being heated by the Sun and losing heat by radiating to space.

Also, gravity does positive and negative work on the atmosphere, it does positive work on air parcels that sink. The work causes their temperature to rise and it can cause their entropy to reduce. But, since reducing entropy means taking heat out of the system, a cooling effect, which is stronger? This constant battle of contradictory forces keeps the entropy per kilogram of air approximately constant in the troposphere. The entropy of the stratosphere increases with altitude due to warming by ozone and stronger ultraviolet radiation than the troposphere receives. As temperature increases, entropy increases and radiation emissions from the GHGs increase. The overall proportions of surface warming due to GHGs, and gravity-induced warming, if any, remains unknown.

As far as recent—past 120 years or so—warming is concerned, gravity has not changed. However, the CO2 added to the atmosphere has increased the surface pressure slightly, since CO2 is 50% denser than dry air. Measurements suggest that the total water vapor in the atmosphere has decreased slightly, but these measurements are disputed due to the quality of the instruments used. Water vapor is 40% less dense than dry air, so how much the surface air pressure has changed due to differences in these two important molecules is unknown.

In this post we will ignore the effects of gravity and surface air pressure, even though gravity causes the Sun to fuse hydrogen into helium and emit the sunlight that warms our planet. Trying to figure out how much gravity contributes to the overall GHE, and recent warming only gives me a headache, and it creates furious arguments in the comments. The reason for the furious arguments, and my headaches, is that it is a complicated thermodynamic argument, and no one really understands thermodynamics. So, we just acknowledge it must have some effect on the total GHE and leave it at that.

Gravity has no direct effect on radiation transfer, but since gravity determines how the air pressure changes with altitude, there is an indirect effect because the air pressure influences the density of greenhouse-gas molecules. Thus, it also has a large effect on their total capture cross sections that contribute to the opacity of the atmosphere. For cloud-free air, the radiation flux is determined by only two quantities, how the opacity of the atmosphere varies with altitude and how the temperature varies with altitude. W&H took the altitude profiles of both temperature and opacity from experimental observations. The HITRAN data is based on observations. It is not theoretical data.

Because Earth’s atmosphere is transparent to most solar radiation and the Earth’s surface is opaque, the surface absorbs twice as much radiation as the atmosphere. Per the laws of thermodynamics, a planet tries to emit as much radiation as it receives. If Earth emits more than it receives, it cools; if it emits less, it warms. The global average temperature of Earth varies about three degrees every year, it is just over 12 degrees in January and just under 16 degrees in July. The Earth’s temperature controls the type of radiation it emits, and it emits mostly in the thermal infrared. The range of emitted frequencies, plotted as wavenumbers, with units of 1/cm, are shown in Figure 1.

Figure 1. The computed outgoing radiation flux spectrum from Earth, with a temperature of 288.7K. The red, green and black curves are the emitted radiation as modified by CO2 (in various concentrations) and H2O, O3, CH4, and N2O, the main GHGs, in their present concentrations. The blue curve is the flux with no GHGs in the atmosphere. The black curve represents the flux with 400 ppm CO2, today’s concentration. The green is with no CO2 at all, and the red is with CO2 doubled (800 ppm). The x axis is frequency in wavenumber units and the flux is in (mW cm)/m2. The additional forcing caused by doubling CO2, is the integrated area of the distance between the black line and the red line, the major differences are highlighted in yellow. The rest of the figure is explained in the text. The data used is from HITRAN and the figure is very similar to Figure 4 in (Wijngaarden & Happer, 2020).

The frequency and the power emitted by molecules are determined largely by the molecule’s kinetic temperature. In Figure 1, if the atmosphere is transparent and contains no infrared absorbing molecules, like CO2, the 288.7K emission spectrum would look like the blue curve. The y axis in Figure 1 is the spectral flux, or the amount of energy passing through the top of the atmosphere per unit frequency, in this case frequency is expressed as a wavenumber, or the number of waves per cm. Mathematically, ѵ (frequency) is the inverse of the wavelength.

A perfectly transparent atmosphere would radiate all surface emitted energy according to the blue line in Figure 1. All the curves plotted overlay in the atmospheric window (“Atm window”) from 824 to 975 cm-1. In this window the surface radiation can go straight to space, so it is labeled 0 km. This means the emission temperature (as determined from the spectral flux) reflects the modeled surface temperature of 288.7K or 15.5°C. Other example departures from the ideal Planck brightness blue curve, are labeled with the approximate altitude of the emissions, based on their brightness temperature. At these locations the atmosphere below these altitudes can be considered opaque to surface radiation due to the combination of GHGs modeled.

The green curve is the computed spectrum with all the greenhouses gases present, in their current concentrations, except for CO2. The black and red lines are the computed energy flux for CO2 concentrations of 400 ppm and 800 ppm respectively. The area difference between the green line and the black line is representative of the CO2-caused warming from zero CO2 to today’s concentration of 400 ppm. The area difference between 400 and 800 ppm, is much smaller and will result in much less warming.

The marked altitude of 84.8 km, in the middle of the CO2 caused divot in the energy curve, means that the emissions at that frequency range, roughly 609 to 800 cm-1, come from that altitude. Below that altitude, CO2 blocks the radiation at those frequencies. In this critical CO2 region of the spectrum, CO2 is saturated and cannot block anymore radiation. 84.8 km is nearly the top of the atmosphere, very high in the mesosphere. Additional CO2 makes the divot a little wider though, as the red curve illustrates and the widening causes a bit more radiation at the edges of the enlarged divot to be blocked.

As CO2 doubles from today’s concentration, the radiation emission level moves upward at all altitudes. As it moves upward in the troposphere, if cloud cover does not change, the emission temperature decreases, and the amount of energy emitted decreases. Since less energy is emitted to space, Earth’s surface should warm. When the sky is clear, radiation fluxes can be calculated accurately, but the conversion to a temperature change can get complicated. Emission height is strongly dependent upon frequency, as Figure 1 shows, and an average emission height has little meaning, just as a global average temperature has little practical meaning.

But at higher altitudes, in the middle stratosphere, temperature begins to warm with altitude. The warming is due to an increase in ozone (O3) as shown by the dotted red line in the right-hand graph of Figure 2. The increase in unattenuated solar ultraviolet light with altitude also has a warming effect. This means as the emission moves higher, more energy is emitted. This results in cooling, and we see this effect at the bottom of the CO2 divot in Figure 1. The red and the black curves reverse their positions and adding CO2 causes cooling. The reason why is illustrated in Figure 2.

Figure 2. The atmospheric temperature and GHG concentration profiles used by W&H in their emissions model. CO2 is a very stable molecule and is present in about the same concentration at all altitudes, the other GHGs vary in concentration with altitude. Source: (Wijngaarden & Happer, 2020).

The left graph in Figure 2 shows the atmospheric temperature profile used for the W&H model. In the real world, the temperature profile varies a lot from location to location and with time, especially in the troposphere, but W&H use a single set of values that are representative of the “standard atmosphere” in the mid-latitudes for their model.

There is very little H2O above the tropopause and N2O and CH4, already minor greenhouse gases in the troposphere, also decrease. In the stratosphere ozone (O3) warming is dominant and temperature increases, until the mesosphere is reached where ozone decreases rapidly and CO2 cooling begins to dominate. At the top of the mesosphere, roughly 86 km, changes in the energy flux are negligible, so W&H call this the top of the atmosphere or TOA.

Convection is minimal above the tropopause, but in the troposphere, it provides about half of the total heat transfer from the surface to the tropopause. As Figure 1 shows, except for the atmospheric window, the lower troposphere (below 2.8 km) is opaque to Earth’s OLR, or outgoing longwave (infrared) radiation, except in the IR window. The evaporation of water transports much of the surface emitted thermal energy, as latent heat, to higher altitudes where it can be radiated away from Earth. Thermal energy emissions, released from condensing water vapor, begin to appear at the base of low-level clouds, and continue throughout the cloud. Clouds are a very important component of Earth’s cooling system but cannot currently be modeled, so they are not included in the W&H model.

Clouds are included in the IPCC general circulation models (GCMs), but the IPCC assumes the cloud parameters and impact, they cannot calculate them. The IPCC AR6 report acknowledges that “clouds remain the largest contribution to overall uncertainty in climate feedbacks (high confidence).” (IPCC, 2021, pp. TS-59). While researchers are trying to model clouds, we share their high confidence that clouds are the largest source of uncertainty in computing the impact of humans on climate change.

The W&H emissions model is a clear sky model and only accurate above the clouds and in areas where there are few clouds, such as the poles and over deserts. Clouds excluded, W&H do try and account for GHG warming feedbacks. They investigated three cases, fixed relative humidity with a constant tropospheric lapse rate, fixed relative humidity with a variable lapse rate, and fixed absolute humidity. The resulting climate sensitivity values are shown in Table 1.

Table 1. The W&H modeled climate sensitivity values for three scenarios.

W&H also compared their resulting emissions calculations for three specific areas, the Sahara Desert, the Mediterranean and Antarctica. The comparison is shown in Figure 3.

Figure 3. The W&H models on the left, compared to satellite measurements on the right. The modeled values are very similar to the measurements. Source: (Wijngaarden & Happer, 2020).

The intensity values plotted in Figure 3 are different than the spectral flux values given in Figure 1 by 1/pi. The spectral flux values are energy passing an elevation in all directions, the values in Figure 3 are for brightness or intensity measured by a satellite. The difference is just in the units, they both measure emissions from Earth. The red Planck brightness curves in the left graphs are characteristic surface temperatures for the locations indicated, 320K (47°C) for the Sahara Desert, 288.7K (15.5°C) for the Mediterranean, and 190K (-83°C) for Antarctica. Notice the CO2 and H2O emission temperatures in Antarctica are warmer than the surface in the atmospheric window, this means the air above the ground is warmer than the ground and that the GHGs are cooling, not warming the air.

Summary and Conclusions

In summary, W&H have provided us with a detailed and accurate emissions model that shows only modest warming (2.2 to 2.3°C), inclusive of likely water vapor feedback, but not counting the feedback due to cloudiness changes. Both the magnitude and sign of net cloud feedback to surface warming are unknown. Lindzen has shown it is likely negative (cooling) in the tropics, but outside the tropics no one knows.

The water vapor feedback to surface warming is also very unclear, Ferenc Miskolczi (2014) has written:

“As long as the Earth has unlimited water supply (in the oceans) with its three phases permanently present in the atmosphere and two phases on the ground surface, the stability of the planetary climate will be controlled by the equations [see paper, page 19]. These two equations, together with the Clausius-Clapeyron equation, will regulate the transfer of the latent heat through the boundary layer in such a way that the net amount maintains the planetary radiative balance.” (Miskolczi, 2014).

Miskolczi, and others have found that total water vapor in the atmosphere has gone down in the past 70 years, although this is questioned. The work by W&H on radiation emissions suggests that future warming due to GHGs will be modest. Speculation about the warming feedback due to clouds and changes in total water vapor is just that, speculation.

The results of the study are summarized in Table 2.

Table 2. Modeled parameters for each GHG in the W&H study. The current flux at 11 km and 86 km for each GHG are shown, then the values if they are doubled, and removed from the atmosphere, and finally the percentage change in forcing (W/m2) if the current concentration is doubled. Only CO2, H2O and O3 change significantly when doubled.

Table 2 shows that the main GHGs are CO2, H2O and O3, doubling the methane or N2O concentration changes the outgoing forcing by less than one percent. Due to the properties of water vapor, its atmospheric concentration is very unlikely to double, but if it did, it would only increase the forcing by eight percent at 11 km. Doubling CO2 only increases the forcing by four percent at 11 km.

The combined current 11 km and 86 km forcing values in the table are not the sum of the individual values due to overlap. It is very clear from this table that all GHGs are saturated and adding to the current concentrations will make very little difference. Doubling CO2 will cause the stratosphere to cool about 10°C, but the changes in surface temperatures from this model are all less than 2.3°C, as shown in Table 1. This is much less than the preferred IPCC AR6 value of 3°C (IPCC, 2021, pp. TS-57). Considering that the current net effect of clouds is cooling and it seems likely that total water vapor in the atmosphere is decreasing or staying flat, these results suggest we have little to worry about regarding increasing GHGs.

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Published by Andy May

Petrophysicist, details available here:

26 thoughts on “The Greenhouse Effect, A Summary of Wijngaarden and Happer

  1. QUOTE: Both the magnitude and sign of net cloud feedback to surface warming is unknown. Lindzen has shown it is likely negative (cooling) in the tropics, but outside the tropics no one knows.

    It should not be in doubt that cloud cools. Global cloud cover peaks in December when heating of the atmosphere by the landmasses is least. Cloud cover is least in July- August. That’s when solar irradiance is 6.7% weaker due to orbital distance. And yet, the Earth is warmest in July-August when heating of the atmosphere by the vast landmasses of the northern hemisphere is at its peak.

    The Earth is particularly sensitive to change in cloud albedo in December and adjacent months because solar irradiance is most intense at this time, the sun is overhead the tropic of Capricorn and more than 90% of the illuminated surface is ocean.

    Heating of the atmosphere from any source should be of interest. The heating power of ozone, due to its low partial pressure, is a function of atmospheric density and change in its partial pressure, because unlike CO2 its far from saturation.

    As surface pressure falls in the Antarctic trough and the Aleutian Low, it builds in the mid latitudes and across the Pacific driving upwelling which cools the surface of the ocean. Conjunctionally, ozone is gathered by the lows in high latitudes and circulated by the jet streams into the upper troposphere in the mid latitudes where the partial pressure of water vapour is relatively invariable. This causes the air above 500 hPa to warm at a rate that is a multiple of that at the surface. Upper troposphere cloud cover must be affected. More sunlight streams into the ocean as it cools due to upwelling. Lo and behold, when the upwelling ceases, surface temperature is discovered to be warmer.

    Geography matters. It’s more important than any other factor. Projecting the possibility of a warming globe on the basis of a model that ignores cloud, the primary driver of the Earths albedo and its energy budget is never going to be useful.

    1. Erl, I agree. The net feedback to surface warming should be cooling. Sometimes this means fewer clouds, as with the high level cirrus clouds that Lindzen studied and sometimes it will be more clouds. But, the effect of clouds and how they form and disappear overall is unknown. What we do know is that over the past 20 years more clouds means cooler. They have had a net cooling effect overall. This suggests they will be a net negative feedback, but the IPCC takes the opposite view.

      1. I found your blog, Erl; very nice! I’ve added a link to it on my site, here (near my link to Andy’s blog):

        Andy, van Wijngaarden and Happer have written two papers together. You cite the 2020 paper, which can be found here:

        They also have a newer (2021) paper; here’s a preprint:

        I was very pleased to see you write, “Emission height is strongly dependent upon frequency, as Figure 1 shows, and an average emission height has little meaning.” That is correct, and it is a point of confusion for the great majority of climate alarmists, including both RC (Ray Bradley) and SkS (Dana Nuccitelli).

        RC/Bradley, SkS/Nuccitelli, and most others err by describing emission height as a single number. In fact, it is a function of wavelength. If you oversimplify it as some sort of average, it no longer “works” to describe how emissions and temperatures change with changes in CO2 concentration.

        However, Ken Rice at ATTP gets it right:

        Between about 13 and 17 microns, the emission’s coming from a region with temperatures close to 220K – so, near the troposphere/stratosphere boundary.

        That “boundary” is called the tropopause, because that’s where the temperature lapse rate pauses. One nit: the wavelength range over which CO2’s emission height is approximately the tropopause is a bit narrower than Rice describes; it’s about 14.2 to 15.8 µm rather than 13 to 17 µm. (Note: Rice is one of the smarter climate alarmists, but I cannot recommend his blog, because he and his colleague, “Willard,” frequently censor it, to enforce their point of view.)

        The tropopause is the coldest altitude in either the troposphere or stratosphere. The lapse rate there is zero, and the temperature does not continue to decrease with increasing altitude.

        Adding CO2 to the atmosphere raises emission heights over the full CO2 emission band, but for emissions between about 14.2 µm to 15.8 µm (i.e., most of CO2’s emissions), raising emission height does not lower emission temperature, so it doesn’t reduce emission intensity, and has no “greenhouse warming” effect.

        It is only at the fringes of CO2’s emission band, where CO2 absorbs (and emits) weakly, that CO2’s emission heights are below the tropopause. Within those fringes, raising emission heights lowers emission temperatures, which reduces radiative emissions and causes the so-called “greenhouse warming” effect. Additional CO2 does not deepen the “15 µm CO2 notch” in Earth’s emission spectrum, but it does broaden the notch slightly. You can see that in this graph is from van Wijingaarden and Happer (2021), which is derived from line-by-line spectral calculations. The black trace is the emission curve for CO2 = 400 ppmv. The red trace is for CO2 = 800 ppmv. (I added the flashing purple ovals.)

        The difference between the red and black traces is the calculated effect at the mesopause (i.e., approx. TOA) of a doubling of CO2 concentration.

        As you can see, the difference is about 277 – 274 = 3 W/m². They give a more precise figure of 2.97 W/m² in their Table 2:

        To put that radiative forcing into perspective, it is calculated that a uniform global temperature increase of 1°C would increase radiant heat loss from the surface of the Earth by about 1.4% (variously estimated to be 3.1 to 3.7 W/m² or 3.1 to 3.3 W/m² in the CMIP5 models (the 8th column) — it’s complicated).

        W/r/t cloud feedbacks, I classify them as “unknown sign” on my list of climate feedbacks. This is what I say about them:

        Cloud Feedback (Overall). Clouds are the elephant in the living room. They’re obviously extremely important, but they are very poorly understood. High, wispy cirrus clouds have a warming effect, because they are made of ice crystals, which makes them much more nearly opaque to outgoing longwave infrared than to incoming visible and near-IR solar radiation. Lower clouds, which are made of liquid water droplets, have a strong cooling effect in daytime, but a warming effect at night. How clouds are affected by warming or cooling climate is very complex. See: [1] [2] [3] [4] [5] [6] [7] [8] [9] [and AR5 sections –]

        I hope the formatting of this comment isn’t too badly botched. Whenever I click the “Preview” button I get an error message: “The connection to the server has been interrupted. Please reconnect.”

        1. Hi Dave,
          Thanks for the comment. It was held in pending due to the number of links, but is out now.

          I agree with all your points, especially about clouds. I didn’t know about Wijngaarden and Happer’s 2021 paper so that link was very welcomed, thanks.

          Writing about the GHE is extremely tough, as you know, but this one came out well, thankfully.


  2. Hi Andy May,

    I have a couple of observations after reading your post. First, the energy from the sun to earth balances the energy from the earth to space (neglecting core cooling). Space is at a constant temperature. If the earth receives more energy from the sun than the earth’s temperature goes up to maintain the energy balance. If, due to atmospheric changes say, more energy goes to space than comes in from the sun, the earth will cool.
    This is a function of temperature to the fourth power. Adding the above may make it easier to follow your discussion on earth’s temperature.

    Second, Wein’s Law provides an estimate of the peak spectral irradiance emitted by a black body. For a temperature of 288.7 K the peak is 10.04 micro meters or 1.004 times ten to the minus five or 1.004 times ten to the minus three centimeters. The Frequency is the reciprocal of the wave length or 1004. This would shift the spectral radiance curve to the right. The resulting figure would look more like the one in my post ( ) flipped on the horizontal.

    Also, I have added a discussion about the interaction of water vapor and the very low temperatures caused by carbon dioxide energy absorption at part of the electromagnetic spectrum.

    Thanks for your contributions to the very important discussion of our planet’s atmosphere.


  3. The calculations of climate sensitivity in Wijngaarden and Happer is based on a clear sky model. However, only about 1/3 of the Earth’s surface is clear sky – the remaining 2/3 is cloudy. The calculations in the paper don’t apply to the areas of cloudy skies. As a result, I don’t see how the climate sensitivity figures in the paper can have any real meaning, even without taking into account changes in cloudiness brought about by the increase in CO2 (etc) concentration. I suspect that an attempt to calcuate what is happening in the cloudy regions would be extremely difficult, if not impossible.

    The paper does show that polar regions, especially Antarctica, operate very differently due to the major temperature inversion present there. Their calculation of a negative climate sensitivity in those regions is very clear, although these regions account for a very small part of the Earth’s surface (8% or so in total).

    The climate sensitivity figures calculated by this paper and its predecessors are often quoted in the debates on climate change. Unfortunately, the limited applicability of these figures to the real world is not generally appreciated.

    1. Mike, Well stated! Thank you.

      You are correct and I can assure you that Will Happer agrees with you. Will and William are working on the cloud problem, but do not have a solution yet. Models are important, but we need to be aware of their limitations.

  4. The GHE have been observed several times. It is very odd how you fail to mention this.


    First Direct Observation of Carbon Dioxide’s Increasing Greenhouse Effect at the Earth’s Surface

    “the critical link between c02 concentrations and the addition of energy to the system, or the greenhouse effect […] and further confirmation that the calculations used in today’s climate models are on track when it comes to representing the impact of CO2.”

    Science have known about the greenhouse effect for 200 years, and it has been possible to calculate how much it would amount to by making calculations on radiation spectra. Based on this, the correlation between CO2 concentration and temperature increase has been calculated, and found that it is in good agreement with what you actually measure.

    Here they have managed to insert instruments “in the middle”, and actually measure what happens to the spectra. It is a demanding exercise. IR spectrometers with very high accuracy are challenging to keep in operation, partly because they have to be cooled. But here they have managed it.

    1. Roger, Thanks for the links I had not seen Kramer’s paper before, but I have read Feldman’s. Some points:
      1. No one denies that human CO2 emissions have some impact on climate, it is how big is the impact and whether the feedbacks to additional CO2 are positive or negative and how big they are that is in dispute.
      2. Both papers are model based, they use observations to estimate a TOA radiation imbalance and then attempt to parse the imbalance with a model to determine how much is due to human CO2 emissions and how much is natural. The models, as usual, assume all excess is due to humans and that natural factors over the study period net to zero.
      3. By discounting possible solar variations, they assume it is humans and thus, the result is humans. Neither paper should have passed peer review.
      4. Both find a human influence of about 0.2 W/m2 per decade. This is a change in temperature of 0.009 deg C. Even if true it is hardly alarming.

      The changes at the TOA are due to surface warming, which no one disputes. It is the relative causes, solar or human, that is in dispute. Everyone agrees some is human, the disagreement is mostly how much is due to the Sun and how much is feedback and whether the feedbacks are positive or negative.

    2. Roger, Here is a pretty good critique of Kramer, et al.
      The meat of it is this:
      “Not only that, but to give an accurate result regarding human influence, the “radiation kernels” have to include all of the factors that go into the radiation balance. From Figure 2 above, we can see that these include the amount of solar radiation absorbed by the atmosphere (including the clouds), the sensible heat lost by the surface, the latent heat lost by the surface, and the longwave radiation emitted by the surface.

      However, I find no indication that they have included all of the relevant variables.”

      Radiative kernels are the model they are using to produce their “observations.” They ignore the Sun and other natural factors, just like the IPCC GCMs.

      1. Like Feldman’s results, Kramer’s results are a lot closer to those of van Wijngaarden & Happer than to Myhre and the IPCC. (Also like Feldman, Kramer unfortunately fails to mention that fact in the paper.)

        Kramer et al (preprint) reported a TOA radiative forcing change of 0.53±0.11 W/m² from 2003 to 2018, of which they attribute 0.43±0.10 W/m² to rising GHG concentrations, and 0.10±0.05 W/m² to air pollution abatement (though they note that the latter “may have a greater direct impact than inferred by [their analysis], which does not include aerosol cloud albedo effects…“).

        Per Mauna Loa measurements, average atmospheric CO2 concentration rose from 375.98 ppmv in 2003 to 408.72 ppmv in 2018. log2(408.72/375.98) = 0.12046, so that increase was about 12% of a doubling.

        CH4 concentration rose from 1.7774 ppmv in 2003 to 1.8573 in 2018. According to MODTRAN, the CH4 increase should have accounted for about 298.488 – 298.426 = 0.062 W/m². If CO2 and consequent feedbacks accounted for the rest, that leaves 0.43±0.10 – 0.06 = 0.37±0.10 W/m², from a 12% CO2 forcing increase (due to an 8.7% CO2 concentration increase).

        So ERF at TOA from a doubling of CO2 + feedbacks should be (0.37±0.11) / 0.12046 = 3.07±0.83 W/m². That’s substantially less than the Myhre 1998 and IPCC (TAR & later) estimates for radiative forcing from CO2 alone, without feedbacks (3.7±0.4 W/m² per doubling).

        Kramer’s result isn’t directly comparable to their figures, because his result includes the effects of feedbacks, but if feedbacks had no net effect then his result would imply 𝞪 is 4.43 ±1.20 (compared to Myhre’s 5.35 ±0.58). If net temperature feedbacks are positive/amplifying (as the IPCC assumes), then Kramer’s result is even farther from what the IPCC assumes.

        To get a feel for what such RF values imply for temperatures, consider that it is calculated that a uniform global temperature increase of 1°C would increase radiant heat loss from the surface of the Earth by about 1.4% (variously estimated to be 3.1 to 3.7 W/m², or 3.1 to 3.3 W/m² in the CMIP5 models — it’s complicated). So a 3 W/m² forcing increase (including feedbacks) should result in a bit less than 1°C of average eventual warming. So +0.53 W/m² over 1.5 decades should yield a warming trend of about +0.11°C/decade, which is about right.

        That relation also gives us a way to estimate warming that is “still in the pipeline,” due to current TOA radiative imbalance. That’s more or less the temperature difference resulting from the difference between ECS and TCR (except, from all forcings, not just CO2).

        TOA radiative imbalance is probably <1 W/m². It is variously estimated as 0.6 to 0.8 W/m². NASA’s latest radiation balance diagram shows it as 340.4 – (77.0 + 22.9 + 239.9) = 0.6 W/m² (but their previous version gave a range from 0.6 to 0.8 W/m²):

        0.6 to 0.8 W/m² represents only about 0.2°C of eventual warming “in the pipe” (which is negligible, for practical purposes).

        See also: and

        1. Dave, Pretty good explanation of what they did.

          You mention it, but I would like to reinforce the point that they assume that there are no natural factors contributing to the surface warming, that all warming is due to humans, so concluding that humans did it is circular. Considering the Pause and 1944-1976, natural factors (as yet unidentified) are possibly 50% of the total climate “forcing.” Thus, your numbers are 2X actual. I also think your deg C/W/m^2 value is a bit high. 0.5 W/m^2 is probably more like 0.02 deg. C, but either way – insignificant. And the warming rate per W/m^2 estimates are all over the map. Too many unknowns.

          1. I don’t have a good enough understanding of what they did to be able to critique it. That would require, at the very least, studying CERES, AIRS, and MERRA-2, which I did not do. I only looked at the results which they reported.

            However, the significance of Kramer’s statement that aerosol reduction (air pollution abatement) “may have a greater direct impact than inferred by [their analysis], which does not include aerosol cloud albedo effects…” is that they suspect that the 0.43±0.10 W/m² forcing which they attributed to GHGs is on the high side.

            Another source of plausible distortion is their endpoints: 2003 and 2018. Here’s a graph of ENSO, in which I’ve highlighted those two years:


            Do you see it? The left half of that 15-year period had more La Niña years, and the right half had the 2015-16 “super El Niño.” But I don’t know how that could have affected their analysis.

  5. William Happer is a climate change denier specialising in MRI imaging. He has no training in climate science. He is also Chairman of the Board of Directors of the George C. Marshall Institute and is on the Academic Advisory Council of the Global Warming Policy Foundation, a denier think tank.

    Greenpeace exposes sceptics hired to cast doubt on climate science

    “Sting operation uncovers two prominent climate sceptics available for hire by the hour to write reports on the benefits of rising CO2 levels and coal.”

    “Happer wrote in an email that his fee was $250 an hour and that it would require four days of work – a total of $8,000. “Depending on how extensive a document you have in mind, the time required or cost could be more or less, but I hope this gives you some idea of what I would expect if we were to proceed on some mutually agreeable course,” he wrote.”

    “Our research reveals that professors at prestigious universities can be sponsored by foreign fossil fuel companies to write reports that sow doubt about climate change and that this sponsorship will then be kept secret,” said John Sauven, the director of Greenpeace UK. “Down the years, how many scientific reports that sowed public doubt on climate change were actually funded by oil, coal and gas companies? This investigation shows how they do it, now we need to know when and where they did it.”

    1. Dr. Happer is not an MRI researcher. He is an expert at the interaction of radiation and the atmosphere and famous for his invention the sodium guide star. He is an expert in climate science and atmospheric physics for this reason and was a co-author of one of the very first large studies of the effect of CO2 on warming in 1981 and has studied climate science and CO2 ever since.

      The so-called sting by Greenpeace and the article they wrote for the Guardian, New York Times, etc. was false. Happer agreed to write the article for the Greenpeace spy only if they agreed with his views and he sent him articles expressing his view. Once the spy agreed that their views coincided, then Happer said his usual fee was $250/hr and he did not want it for himself, he wanted it donated to the CO2 coalition. Greenpeace is not an honest organization, as I explain here:

      1. Actually, among his many other accomplishments, Prof. Happer did make a major contribution to medical imaging technology, through the use of spin-polarized gases when imaging lungs. (It’s far beyond my ken.) His advance has doubtless saved many lives, but it tends to be forgotten because he is more famous for inventing “perhaps the most spectacular, revolutionary advance in ground-based astronomy since the invention of photography.”

        Prof. Happer has published over 200 peer-reviewed scientific papers. He’s a fellow of the American Physical Society, and the American Association for the Advancement of Science, and he is a member of the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society. He was awarded the Alfred P. Sloan fellowship, an Alexander von Humboldt award, the Broida Prize, and the 1999 Davisson-Germer Prize of the American Physical Society.

        What has Roger [no last name] accomplished? Won a ribbon for his prize lima beans at the County Fair, perhaps?

        Prof. Happer has a long-established habit of generously donating his fees to various charities, such as the CO2 Coalition and the UNC Physics Department. In keeping with that habit, when Greenpeace activists lied about their identity to Prof. Happer, and solicited him to write a “white paper” about the costs and benefits of fossil fuel use, he asked them to NOT pay him, but to donate his fee to charity.

        Greenpeace ran their “sting” to try to bait Prof. Happer into agreeing to do something unethical — and failed spectacularly. The activists approached Prof. Happer, lied about their identities, and offered to hire him to write a report about the beneficial effects of CO2 emissions. He agreed to do so, but he refused to take their money. Instead, he asked that his fee be donated to charity!

        The report which he was asked to write was what I would call a “whitepaper” or monograph. There was never any suggestion that the information in it would be anything other than completely scientifically accurate. If there had been, then Prof. Happer would not have entertained the idea of writing it.

        The Greenpeace activists lied, and Dr. Happer never did, yet climate activists like Roger want you to believe that that impugns Dr. Happer’s integrity. I hope it’s obvious how absurd that is.

        For Greenpeace and Roger to pretend that Prof. Happer’s generosity was unethical is, indeed, proof of corruption — but Greenpeace’s and Roger’s, not Prof. Happer’s.

        1. Thanks Dave for correcting me. I was unaware that Dr. Happer had done MRI research. In his long and brilliant career he has done so much it is hard to keep track of. Thanks again for commenting.

  6. Andy,

    Thank you for your summary paper of the Happer and Wijngaarden paper on the greenhouse effect. Summaries like yours are needed so that people who are not physicists can better understand the important conclusions of their paper.

    I re-posted your article on our website. See the link below.

    Congratulations on your excellent website. We will promote it on our website and in our newsletter sent to people in 124 countries.

    John Shanahan
    Founder of website:
    Denver, Colorado

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