CO₂ and downwelling longwave radiation

In 2015, Feldman, Collins, Gero, Torn, Mlawer, and Shippert published a scientific letter titled “Observational determination of surface radiative forcing by CO₂ from 2000 to 2010.” This study was notable because it offered direct observational confirmation of the relationship between local variations in atmospheric CO₂ concentration, and the radiative flux of downwelling longwave radiation (DLR) at the surface.

The results in Feldman (2015), as I will refer to it, confirmed that climate models accurately describe the relationship between the atmospheric CO₂ concentration and atmospheric radiation incident on Earth’s surface.

Climate skeptics routinely question the validity of such models, and demand empirical (i.e., observational) or experimental evidence of the validity of such models. This study provides an example of empirical confirmation.

Unfortunately, the topic the study addresses is complex enough that it’s not necessarily easy for non-scientists to understand the meaning of the results of the study. Nonetheless, I’ll try to explain what I understand to be the significance of the results.

In particular, I’ll do what I can to address a question asked by a reader comment on this site. The reader noted:

[It] isn’t the case [that CO₂ really is the main driver for the rapid global warming since the 1970s], as the numbers provided in the Abstract to the Feldman et al. Letter make clear. If you work through the math, those numbers indicate that the upper limit on the relative contribution of the increased CO₂-based forcing occurring during the decade-long study period is only about ten percent (10%) of the total increase in radiative forcing occurring during that decade-long study period. That number is a far cry from the approximately 90% figure that the IPCC has estimated for the effective forcing from all of the long-lived trace greenhouse gases combined, relative to the total radiative forcing.

The reader points out an interesting aspect of the findings. It’s understandable why they might believe they’ve identified a discrepancy between the mainstream climate change narrative and the findings of Feldman (2015). 

Yet… they haven’t identified a discrepancy. 

Yes, Feldman (2015) indicated that the observed increase in DLR directly due to changes in CO₂ concentration constitute “approximately ten percent of the trend in downwelling longwave radiation.” 

However, these findings are fully consistent with mainstream climate models. Feldman (2018) write in their abstract:

These results confirm theoretical predictions of the atmospheric greenhouse effect due to anthropogenic emissions, and provide empirical evidence of how rising CO₂ levels, mediated by temporal variations due to photosynthesis and respiration, are affecting the surface energy balance.

Feldman (2015) also says their observations “thoroughly corroborated radiative transfer calculations” (which are a central component of all climate models).

In other words, what Feldman (2015) observed matched the predictions of the same climate models which tell us that “CO₂ really is the main driver for the rapid global warming since the 1970s.” This match between predictions and observations falsifies the reader’s impression that the findings of Feldman (2018) were somehow inconsistent with climate models and the mainstream narrative about climate change.

So, the results of Feldman (2015) are fully consistent with climate models. 

The results are only inconsistent with what the reader imagines the results “should have been,” based on their interpretation of IPCC statements, and likely based on an incomplete understanding of how climate operates.

All that remains is to unpack why what happens with DLR (and was predicted to happen with DLR) differs from what the reader expected.

I suspect there are a few main sources of confusion:

1. Many people don’t understand the distinction between climate change “drivers” and climate change “feedbacks.” (This distinction is subtle but extremely important.)
2. The technical term “forcing” has significantly different meanings in different contexts.
3. There can be differences between how quantities relate regionally vs. how they relate globally.

I’ll unpack these issues in the following sections.

Climate change drivers and feedbacks

Let’s consider a non-climate example first.

• Suppose there is a room where there is a sound system with a microphone, audio amplifier, and speakers. Somebody steps up to the microphone, and starts speaking with an audio volume of 60 decibels. The audio system boosts the volume to 70 decibels.
• What is the cause of the sound that is present in the room? Most of the sound present is due to the sound system. However, if the person weren’t speaking, there would be no sound in the room. So, although the speaker is only directly responsible for 60 decibels of sound, they are indirectly the cause of the full 70 decibels.
• One could say that the person’s voice is the “driver” of the sound level in the room, while the sound system provides a “feedback” which amplifies the direct effect of the speaker’s voice.

Something similar happens when it comes to planetary temperature changes.

Planetary temperature is primarily determined by two things:

• the rate at which heat arrives; and
• the rate at which heat leaves.

As temperature increases, this increases the rate at which heat leaves. Temperature tends to move towards a level at which the rate of heat leaving equals the rate of heat arriving, so that there is no net accumulation of thermal energy.

The rate at which heat arrives is set by the intensity of the Sun, Earth’s distance from the Sun, and planetary “albedo”, i.e., how much sunlight Earth reflects back into space. 

The rate of heat leaves is set by the temperature of the surface and the planetary “effective emissivity”, i.e., how much thermal radiation escapes to space, for a given surface temperature. Planetary effective emissivity, , is a product of the emissivity of Earth’s surface, , and the atmospheric modification to emissivity, , where is called the normalized greenhouse effect. The greenhouse effect is really just a measure of how much less thermal radiation reaches space, compared to how much thermal radiation leaves Earth’s surface.

The greenhouse effect, , gets bigger in response to any of the following:

• An increase in the concentration of “persistent” greenhouse gases like CO₂ and methane.
• An increase in absolute humidity, i.e., the concentration of water vapor. (I describe water vapor as a “responsive” greenhouse gas, because its concentration responds to temperature changes.)
• An increase in the magnitude of the lapse rate, i.e., the rate of decrease in air temperature with increasing altitude. The lapse rate is typically about 6.5℃/km, but varies between different places and times. If the lapse rate was zero, the greenhouse effect would also be zero.

The situation with the greenhouse effect is a bit like the situation with sound levels in a room. Most of the changes in the greenhouse effect are the direct result of changes in humidity or the atmospheric temperature profile. The direct effect on the greenhouse effect of changes in persistent greenhouse gas concentrations is always only a small part of the total change. However, humidity and atmospheric temperature profile only change if something else changes first, leading to humidity and the temperature profile changing.

So, increasing the concentration of persistent greenhouse gases is a “driver” of changes in the greenhouse effect, and in temperature, while water vapor and lapse rate changes act as climate “feedbacks” which amplify any warming initiated by a climate change “driver.”

Altogether, planetary temperature can be understood as resulting from three categories of processes:

• Changes in “driver” variables, such as the concentration of CO₂, the concentration of aerosols in the atmosphere, the intensity of the Sun, volcanic eruptions, etc.
• Changes in “responsive” variables, such as humidity, lapse rate, cloud coverage, ice extent, etc., which respond to changes and either amplify those changes (usually), or mitigate those changes (occasionally).
• Natural fluctuations in relevant variables. These fluctuations occur within a limited range, and over limited periods of time. Such fluctuations can make the relationship between drivers and the observed temperatures a bit loose in the short term, so that sometimes the effects of changing driver variables are only visible over longer time periods.

When climate scientists say that the rapidly increasing global temperature is mostly driven by the increase in the atmospheric concentration of CO₂ and other human-produced greenhouse gases, they:

• Do NOT mean that CO₂ etc. directly leads to the majority of increases in the greenhouse effect and global temperature. (Most of the change happens as the result of climate “feedbacks” which amplify the effects of increasing CO₂ etc.)
• Mean that CO₂ etc. are “drivers” of the change, which are indirectly responsible for most of the change―in the sense that the change would not and could not be happening if it were not for human emissions of CO₂ and other greenhouse gases.

Understanding how the results of Feldman (2015) are consistent with the assertion that increasing global temperatures are almost entirely the result of human activities critically depends on understanding this distinction between climate drivers and climate feedbacks.

Different uses of the term “forcing”

I find it rather regrettable that Feldman (2015) and some other sources refer to downwelling longwave radiation (DLR) emitted by the atmosphere towards the surface as “surface forcing.”

This usage is quite different from the more common way that the term “radiative forcing” is used by climate scientists:

• At the top-of-atmosphere, TOA radiative forcing includes only the direct effects of climate change “drivers”; the indirect effects associated with climate feedbacks are excluded.
• In contrast, measured DLR includes the effects of both “drivers” and “feedbacks.”

Thus, I think it tends to be rather confusing to associate DLR with “surface forcing.”

There is also another way in which I find the term “surface forcing” misleading:

• TOA radiative forcing includes the full direct effect of the change in “drivers” on the total planetary energy balance.
• In contrast, changes in DLR constitute only an incomplete portion of the effects of changes in the greenhouse effect on the surface energy balance.

The reason why looking at DLR offers a very incomplete view of surface energetics is because a majority of energy loss from the surface is associated with non-radiative heat transfer via convection and thermals. While you might naively think that convection and thermals are independent of the greenhouse effect, it can be shown that the rate of non-radiative surface cooling is strongly driven by the overall greenhouse effect. If the atmosphere wasn’t busy radiating longwave radiation from the upper troposphere, there would be much less convective air circulation. So, changes in the greenhouse effect impact both DLR and non-radiative surface cooling. Thus, examining DLR alone offers an incomplete characterization of the effects of increasing the concentration of CO₂.

I urge readers to avoid thinking of downwelling longwave radiation as “surface forcing.” That terminology introduces unnecessary confusion, since the usage is so different from other uses of the term “forcing.”

Thinking about energetics at the surface, instead of at TOA, is tricky and error-prone. The textbook Principles of Planetary Climate by R. T. Peirrehumbert refers to overly focusing on surface energetics as the “Surface Budget Fallacy,” because such a focus so often leads to erroneous reasoning.

Size of the split between direct effects and feedback

A majority of changes in global temperature are associated with the effects of “climate feedbacks” rather than with the direct effects of changes in “climate drivers.”

Thus, the direct effect of doubling the atmospheric concentration of CO₂ is generally expected to be an increase in global mean temperature of around 1.4℃.¹Even according to the calculations of climate skeptic W. Happer However, when feedback is taken into account, the IPCC anticipates a global temperature rise of 2.5-4.0℃.²This is the estimate of “likely” Environmental Climate Sensitivity (ECS) from p. 1007 of the 2021 IPCC AR6 WG1 report.

So, at a global level, climate feedbacks are expected to roughly double or triple the temperature rise directly attributable to increases in atmospheric CO₂. 

Yet, the size of this division between direct and feedback effects should not be taken to apply to every aspect of what happens in climate. The split is likely to be different if one looks at another variable, such as DLR, instead of looking at global temperature. Even more importantly, the split can be very different if one is considering regional effects instead of global effects.

Felman (2015) reported on regional effects, measured in the U.S. Southern Great Plains region (SGP) and on the North Slope of Alaska (NSA).

Regional effects are strongly affected by changes in global circulation of air and water, which transfer heat between regions.

Feldman (2015) reported:

Over the length of the observation period (2000–2010), the modelled spectra at both SGP and NSA are dominated by trends associated with the temperature and humidity structure of the atmosphere rather than the smaller signal from CO₂.

In other words, the changes in observed DLR were mostly due to changes in humidity, lapse rate, and overall temperature, i.e., “feedback” processes, rather than the changes in CO₂ concentration.

They further cite evidence from other researchers that

the water-vapour feedback enhances greenhouse gas forcing at the surface by a factor of three.

Globally, other anthropogenic greenhouse gases are estimated to increase the total greenhouse forcing by an additional 23 percent beyond that from CO₂ alone.

Combining those estimates, other factors need to explain a remaining factor of 2.7 in order to account for CO₂ directly accounting for only 10 percent of changes in DLR. [This particular argument is, however, on very shaky ground, as discussed in an “update” below.]

Based on what Feldman (2015) reported, this factor was likely due to changes in the temperature structure of the atmosphere (i.e., lapse rate and overall temperature). Such regional changes could easily have been the result of changes in atmospheric circulation―or even the result of changes in the TOA greenhouse effect (in which case CO₂ may have been partly responsible in an indirect way). 

Thus, while we haven’t personally reproduced the analysis in Feldman (2015), it is at least understandable how a full analysis could plausibly lead to a prediction of regional changes in DLR being only 10 percent due to the direct effect of local changes in CO₂ concentration.

Pitfalls in interpreting data

The scientific method for validating or falsifying a scientific theory involves:

1. Applying the scientific theory to determine what the theory quantitatively predicts in a particular experimental or natural context.
2. Collecting data.
3. Comparing the predictions with the data and checking for statistically-significant discrepancies between the predictions and the observations.

In my experience, all too often, amateur scientists and bloggers follow a very different process for interpreting data:

1. Review data
2. Assume you know what the theory would predict for those conditions, without actually applying the theory to do any calculations.
3. If the data doesn’t subjectively “look like” your unverified guess of predictions, declare the theory to have been “falsified.”

This common procedure has no scientific validity whatsoever.

Time and time again, I have analyzed experiments alleged to have falsified some scientific theory. Yet, when I do the steps associated with a proper analysis, I routinely find that the theory predicted exactly what was actually observed (contrary to others’ unverified assumptions about what the theory would predict)―or that the data had too little statistical significance to allow any meaningful conclusion at all to be reached.

Conclusions

In the case of the results of Feldman (2015), I understand why someone not versed in the science might mistakenly assume that “if climate models are correct, then CO₂ increases should have fully accounted for the increases in DLR.”

However, it’s simply not safe to rely on such assumptions. Naive assumptions about how complex systems work are almost always wrong.

Feldman (2015) reported that their results matched the predictions of climate models. I see every reason to believe that assessment.

Many changes in climate, particularly local changes, are dominated by the effects of  “climate feedbacks” rather than by the direct effects of “climate drivers.” That is what is consistently predicted by climate models, and what is observed.

Yet, the important influence of climate feedbacks does not contradict the premise that climate drivers bear ultimate responsibility for observed changes.

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So, do the findings of Feldman (2015) establish or falsify the claim that human CO₂ emissions have been the main driver of recent climate change?

Neither.

• To establish such a claim requires more than the results of any one study. That sort of conclusion only becomes clear as one joins together many complementary lines of evidence―as climate scientists did decades ago, leading to a conclusion that is now well-established, despite climate skeptics having a wildly different impression.
• To falsify the claim, one would have to show that the models which indicate that anthropogenic CO₂ is responsible for current global warmings would have predicted something different than what was observed. However, Feldman (2015) reports that their findings corroborated the models. So, even if the findings don’t match some readers’s naive expectations, there is no evidence that findings are in any way inconsistent with the mainstream narrative about global warming.

Thus, my take is that Feldman (2015), by itself, neither verifies nor falsifies any broad conclusions.

Yet, the findings of Feldman (2015) do affirm the credibility of key portions of climate models, and in particular, the radiation transfer models that are at their heart.

UPDATE

Upon reading the initial version of this essay, a reader comment reasonably questioned whether the research finding that in Europe “the water-vapour feedback enhances greenhouse gas forcing at the surface by a factor of three” is really applicable to what happens in the U.S. Southern Great Plains (SGP) and on the North Slope of Alaska (NSA).

That’s a fair question.

In general, one needs to be very careful about mixing data associated with different regions or different time periods.  Sometimes such a hybrid result is meaningful, and sometime it yields nonsense.

In the current situation, mixing data veers towards the latter. Mixing data in this way can offer a “just so” story about how things might work (which is basically what I offered above). But, in the absence of much more study, such combining of unmatched data usually should not be taken very seriously as offering a narrative of how things actually work in practice.

Of course, the statement that stimulated this entire essay is subject to very similar problems.

Feldman (2015) had indicated that their observed trend in CO₂-related DLR corresponded to “approximately ten percent of the trend in downwelling longwave radiation.”  However, examining their references, we find that this statement compares:

• Feldman (2015)’s clear-sky CO₂-related DLR trends for the period 2000-2010 in the SGP and NSA regions.
• Global-mean DLR trends under all-sky conditions for the periods 1992-2000 and 1973-2008, and under clear-sky conditions for the period 1964-1990.

Thus, the statement compares local trends for one time period to global-mean trends over very different time periods. Moreover, most of the global data took into account clouds, unlike the observations in Feldman (2015).

Thus, the premise that CO₂ accounted for “approximately 10 percent” of an overall trend may now be seen to be extremely questionable as to its significance.

Feldman (2015) found that CO₂ concentration changes accounted for a 0.2 ±0.07 W/m²/decade increase in DLR over the period 2000-2010. When I analyze NASA CERES EBAFv4.2 clear-sky data for the period 2001-2011,³Data wasn’t available for early 2000. I restricted my analysis to years for which a full year of data was available. I compute a global trend in DLR of only 0.28 ±0.56 W/m²/decade. Note the huge uncertainty, meaning that there was really no clear global trend for that particular 10-year period.

By shifting to a comparison with a period that largely overlaps the measurement period of Feldman (2015), suddenly the result becomes one in which the measured regional CO₂-related increase in DLR doesn’t differ from the total global DLR trend in any statistically significant way.

We went from thinking that CO₂ only accounted for 10 percent of the trend to thinking it could conceivably account for 100% of the trend.

How could changing the measurement period make such a large difference? To see this, let’s look at a plot of mean-global clear-sky DLR.

Note that this chart plots the 12-month rolling average of fluxes, to eliminate seasonal variations.

Looking at this plot, it should be evident that trying to draw a straight line to approximate the DLR curve will yield very different slopes depending on precisely which range of years is considered. While there is a significant upward trend over 22 years, the perceived trend can vary wildly between different sub-periods. It should be no surprise that the global trend during the period over which Feldman (2015) did their measurements was not necessarily representative of more long-term trends.

In the chart, I also plotted a scaled version of surface-emitted longwave radiation flux (SLR). SLR basically corresponds to surface temperature. It can be seen that there is a high correlation between DLR and SLR or temperature. This makes sense because DLR represents thermal radiation emitted by the near-surface atmosphere. When the surface is warmer, the air will typically also be warmer, and so the atmosphere will emit more thermal radiation downward. Thus, variations in DLR can be driven by any factor that affects temperature.

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Up to this point, we have been comparing the regional trends in Feldman (2015) to global trends. Is this a safe and meaningful comparison? 

Not remotely! 

Consider the chart below, which shows regional trends in clear-sky DLR, based on CERES data.

From this map, we see that the global average clear-sky DLR trend for 2001-2011 was 0.28 W/m²/decade. Yet, in different places on the globe, the regional trend varied from -24.6 to +13.5 W/m²/decade. The rate at which the global mean changes is tiny in comparison to the rate of change in particular regions.

Why would regional variations be so large?

The answer is that atmospheric and oceanic circulation each transport enormous amounts of heat laterally, from one place to another. Changes in circulation can easily drive major changes in regional phenomena.

When we compute global averages, the effect of lateral heat transport largely disappears. Instead of seeing heat transport between regions, we only see net heat transport between Earth and space. (Or between the surface and the deep ocean; I believe that fluctuations in heat transfer within the oceans is likely what is responsible for most fluctuations in global-mean values.)

Thus, global averages are subject to much smaller fluctuations than are regional values.

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So, what does this say about the significance of Feldman (2015)? I think it tells us:

• Any notion that Feldman (2015) tells us what fraction of changes in DLR are attributable to CO₂ should not be taken seriously. Hence, Feldman (2015) in no way falsifies assertions that increases in CO₂ and other greenhouse gases are the primary cause of global warming. (Neither does Feldman (2015), by itself, prove this claim.)
• As stated previously, Feldman (2015) does offer confirmation that atmospheric radiative transfer models accurately describe how CO₂ affects radiative transfer within the atmosphere.

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Afterthought:

Note that DLR is, in my opinion, a terrible quantity to focus our attention on, if we are trying to understand overall climate trends.

This is because surface cooling is determined by both DLR and non-radiative surface cooling (i.e., convection and thermals). So, when we look at DLR, we are only looking at a very incomplete piece of the surface-energetics puzzle.

In contrast, when we look at the TOA normalized greenhouse effect, , we are looking at a complete characterization of the efficiency of cooling to space.

Below are a chart and a trend-map for the clear-sky normalized greenhouse effect.

While this quantity, , also exhibits fluctuations over time and variation between regions, the variations are not as extreme as they were for DLR. (The map does relate to a longer averaging period, 2001-2022, instead of 2001-2011; however, even when the same averaging period is used, the trend in varies less than the trend in DLR.)

I believe that looking at the normalized greenhouse effect, , tells a more complete and consistent story than does looking at DLR.

• 1
  Even according to the calculations of climate skeptic W. Happer
• 2
  This is the estimate of “likely” Environmental Climate Sensitivity (ECS) from p. 1007 of the 2021 IPCC AR6 WG1 report.
• 3
  Data wasn’t available for early 2000. I restricted my analysis to years for which a full year of data was available.