Study: Climate models underestimate cooling effect of daily cloud cycle

From PRINCETON UNIVERSITY:

Princeton University researchers have found that the climate models scientists use to project future conditions on our planet underestimate the cooling effect that clouds have on a daily — and even hourly — basis, particularly over land.

The researchers report in the journal Nature Communications Dec. 22 that models tend to factor in too much of the sun’s daily heat, which results in warmer, drier conditions than might actually occur. The researchers found that inaccuracies in accounting for the diurnal, or daily, cloud cycle did not seem to invalidate climate projections, but they did increase the margin of error for a crucial tool scientists use to understand how climate change will affect us.

“It’s important to get the right result for the right reason,” said corresponding author Amilcare Porporato, a professor of civil and environmental engineering and the Princeton Environmental Institute. “These errors can trickle down into other changes, such as projecting fewer and weaker storms. We hope that our results are useful for improving how clouds are modeled, which would improve the calibration of climate models and make the results much more reliable.”

Porporato and first author Jun Yin, a postdoctoral research associate in civil and environmental engineering, found that not accurately capturing the daily cloud cycle has the sun bombarding Earth with an extra 1-2 watts of energy per square meter. The increased carbon dioxide in the atmosphere since the start of the Industrial Age is estimated to produce an extra 3.7 watts of energy per square meter. “The error here is half of that, so in that sense it becomes substantial,” Porporato said.

Yin and Porporato undertook their study after attending a seminar on cloud coverage and climate sensitivity. “The speaker talked a lot about where the clouds are, but not when,” Yin said. “We thought the timing was just as important and we were surprised to find there were fewer studies on that.”

Clouds change during the day and from day-to-day. Climate models do a good job of capturing the average cloud coverage, Yin said, but they miss important peaks in actual cloud coverage. These peaks can have a dramatic effect on daily conditions, such as in the early afternoon during the hottest part of the day.

“Climate scientists have the clouds, but they miss the timing,” Porporato said. “There’s a strong sensitivity between the daily cloud cycle and temperature. It’s like a person putting on a blanket at night or using a parasol during the day. If you miss that, it makes a huge difference.”

The researchers used satellite images from 1986-2005 to calculate the average diurnal cycles of clouds in each season worldwide. Yin analyzed the cloud coverage at three-hour intervals, looking at more than 6,000 points on the globe measuring 175 miles by 175 miles each.

Yin and Porporato compared the averages they came up with to those from nine climate models used by climate scientists. The majority of models have the thickest coverage occurring in the morning over the land rather than in the early afternoon when clouds shield the Earth from the sun’s most intense heat. “A small difference in timing can have a big radiative impact,” Yin said.

The researchers used both reanalysis data and satellite images from 1986-2005 to calculate the average diurnal cycles of clouds in each season worldwide. The reanalysis (above) shows (left to right) the mean (average), standard deviation (amplitude) and phase (timing) of global cloud coverage by season. The color scale indicates low (blue) to high (red) coverage, amplitude and timing. The majority of models suggest that clouds are thickest over land in the early morning. The Princeton study showed, however, that cloud coverage peaks more frequently in the afternoon. CREDIT Image by Jun Yin, Department of Civil and Environmental Engineering

The researchers plan to explore the effect different types of clouds have on climate-model projections, as well as how cloud cycles influence the year-to-year variation of Earth’s temperature, especially in relation to extreme rainfall.

Gabriel Katul, professor of hydrology and micrometeorology at Duke University, said that “the significance is quite high” of accurately modeling the daily cloud cycle. Katul was not involved in the research but is familiar with it.

The cloud cycle can indicate deficiencies in the characterization of surface heating and atmospheric water vapor, both of which are necessary for cloud formation, he said. Both factors also govern how the lowest portion of Earth’s atmosphere — known as the atmospheric boundary layer — interacts with the planet’s surface.

“The modeling of boundary-layer growth and collapse is fraught with difficulties because it involves complex processes that must be overly simplified in climate models,” Katul said. “So, exploring the timing of cloud formation and cloud thickness is significant at the diurnal scale precisely because those timescales are the most relevant to boundary-layer dynamics and surface-atmosphere heat and water-vapor exchange.”

When it comes to clouds, climate models have typically focused on mechanisms, spatial areas and timescales — such as air pollution and microphysics, hundreds of square kilometers, and seasons, respectively — that are larger and more generalized, Katul said. “There are practical reasons why data-model comparisons were conducted in a manner that masked the diurnal variation in clouds,” he said. “Diurnal variation was somewhat masked by the fact that much of the climate-model performance was reported over longer-term and larger-scale averages.”

By capturing the timing and thickness of the daily cloud cycle on a global scale, however, Yin and Porporato have provided scientists with a tool for confirming if climate models aptly portray cloud formation and the interaction between clouds and the atmosphere.

“The global coverage and emphasis on both ‘timing’ and ‘amount’ are notable. As far as I am aware, this is the first study to explore this manifold of models in such a coherent way,” Katul said. “I am sure this type of work will offer new perspectives to improve the representation of clouds. I would not be surprised to see this paper highly cited in future IPCC [U.N. Intergovernmental Panel on Climate Change] reports.”

###

The paper, “Diurnal cloud cycle biases in climate models,” was published online Dec. 22 by Nature Communications.

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87 thoughts on “Study: Climate models underestimate cooling effect of daily cloud cycle

    • That’s exactly what I was thinking. Maybe Willis could co-author a paper with them. Oh wait it would never get published if he was a co-author!

    • Well, frankly, no, that’s not enough. But, Willis did raise good questions and did some research to support his thinking. In my opinion, a model that does not have a realistic cloud cover is unrealistic and can be tossed without further consideration. Why those models live, is beyond my imagination.

      • But not my imagination…
        The models live because they produce the future warming signal that AGW proponents calim should be there.
        Without their hypothesised catastroprophecies, their models wouldn’t suit their purpose

      • Indeed!

        I can hypothesize that Martians will invade the World and cause the extinction of humanity but modeling such a war wouldn’t make it any more viable than what the AGW proponents claim in their modeling.

      • Scenerio
        Small Asteroid strikes Mars
        A piece of Mars is ejected into space and travels to Earth
        On this piece is a Martian Bacterium that doesn’t exist on Earth but is deadly to 99% of the populace.
        Who wins the war of the worlds??

    • The big difference in Willis’ post was that he was looking at diurnal cloud cover in the tropics over the ocean. In the long run, I think Willis’ analysis is much more important as I think a lot of heating of the earth is short wave radiation penetrating up to 30 meters in the oceans. If you develop in the hottest part of the day over the water, that’s a lot of heat not ending up in the earths biggest heat sink.

    • Exactly my thought – I certainly hope the Princeton authors referenced and gave credit for Willis’ work as published here!

      • Well, I elieve that clouds are wet. Very, very wet.

        My proof: I’ve actually walked through them…

      • What? How do you dare present hard fact as proof? a proof takes a paper, a “scientist” title, a few pal to sign the paper with you, and a few other pals to have it peer-reviewed and accepted.

  1. “the researchers found that inaccuracies in accounting for the diurnal, or daily, cloud cycle did not seem to invalidate climate projections, but they did increase the margin of error”

    It’s telling how afraid researchers are of contradicting the orthodoxy and being labeled a denier, even when there research directly refutes the warmist doctrine.

    • Haha yes, there is a high barrier in saying anything contrarian. And a price must be paid by kowtowing the supposed Konsensus.

    • In my mind it pretty much does invalidate climate projections, in my business it would be like saying “we know price plays a role in the adoption and use of mobile data packages, but we’re pretty much going to ignore it in our market projection models.”

    • I picked up on that as well.
      The error is 25 to 50% of the total heating from CO2, but don’t worry, the pre-ordained results are not invalidated.

  2. ‘ The researchers found that inaccuracies in accounting for the diurnal, or daily, cloud cycle did not seem to invalidate climate projections, but they did increase the margin of error for a crucial tool scientists use to understand how climate change will affect us.‘

    As a non-scientist my question is: how much inaccuracy does it take to invalidation projections? From what I gather from reading WUWT the projections are already invalid due to always being incorrect.

  3. From the article: “The increased carbon dioxide in the atmosphere since the start of the Industrial Age is estimated to produce an extra 3.7 watts of energy per square meter.”

    And how does atmospheric CO2 “produce” energy?

    • And 3.7 is about 1% of the extra “back” long wave energy.

      Vary cloud effect by 1% and the whole 3.7 is swamped. This one paper, in a real world, would halt all the model speculation.

      • What you stated is, or should be, obvious/common knowledge. The variable cloud input (guesses) will control the whole thing. And it’s sad that any new study or paper would be necessary to change direction of this mess.

        It seems that the authors statement, “It’s important to get the right result for the right reason, these errors can trickle down into other changes, such as projecting fewer and weaker storms ….”, shows that they were less interested in finding/showing modeling errors than they were in figuring out how to get the model to predict more bad stuff.

  4. I’m no expert, but the C02 big lie is the foundation for totalitarian control of all humanity. So cooling clouds? What cooling clouds? Endless funds support junk science to justify psychotic elites’ control of the planet. And the continued failure to call it what it is makes their unspeakable success more likely.

  5. Now we have an idea of how hot the models run…. anyone punched this new number into a GCM to see the effect? It might be enough to kill the ‘it’s the carbon wot did it’ from the Science Is Always Settled brigade….

  6. CAGW advicates’ feigned ignorance of clouds’ impact on climate is their get-out-of-jail-free card.

    All IPCC’s AR reports carefully mention that climate models ensembles can’t simulating cloud cover, and even express uncertainty of whether clouds have a net warming or net cooling effect on earth’s climate.. (settled science, anyone?)

    When the CAGW hypothesis is finally tossed on the trash heap of failed ideas, and Congrssional and Senate Hearings are held to determine why $trillions were wasted on CAGW, former CAGW advocates will blame their “ignorance” of cloud dynamics for CAGW’s demise…

    Plausible deniability is already baked in the cake..

  7. Sigh. The simplest mechanisms.
    I’ve tried to explain this sort of thing to some of my green-indoctrinated friends in just these terms – greenhouse gases are a moderating effect – they warm up a cold day, and cool off a warm day – simply by blocking the sun. (Insert Joni Mitchell lyrics).
    Nice to see some of these studies catching up to the simple observations of a layman.

      • Around 49% of the heating effect of the Sun is in the non visible near infrared, water vapour absorbs lots of it.

      • ‘Almost all of the energy from the sun arrives as visible light. CO2 doesn’t block any of that.’

        I should specified water vapor, not C02, which in the form of clouds, is a semi-tangible object that causes shade, physically blocking sunlight – water vapor being the primary greenhouse gas.

        Just a quibble.

      • Water vapour alone blocks considerable amounts of solar near infrared from reaching the surface, because it has big absorption bands in the near infrared.

    • /www.tripadvisor.com/LocationPhotoDirectLink-g51867-d3661743-i168484673-South_Jetty_County_Park-Florence_Oregon.html

      Good cloud pic; “both sides” (ignore the ad)

  8. The fact that there are a plethora of different models that the IPCC supports is evidence that a lot of guess work is involved. Until th IPCC comes out and states which model is correct we can only conclude that all of the models are wrong and hence do not provide reliable results. In general the models all beg the question becaue CO2 based warming is hard coded in. The reality is that there is no real evidence that CO2 has any effect on climate and plenty of scientific rational to support the idea that the climate sensivity of CO2 is zero.

  9. “The researchers report in the journal Nature Communications Dec. 22 that models tend to factor in too much of the sun’s daily heat, which results in warmer, drier conditions than might actually occur.”

    But didnt the models predict all of these colder, wetter conditions as part of global warming?? They keep telling us how accurate the models are…

    “…not accurately capturing the daily cloud cycle has the sun bombarding Earth with an extra 1-2 watts of energy per square meter. The increased carbon dioxide in the atmosphere since the start of the Industrial Age is estimated to produce an extra 3.7 watts of energy per square meter. “The error here is half of that, so in that sense it becomes substantial,” Porporato said.”

    Ya think?? Does Trenberth know about this?? :)

  10. List of things that CAGW priests say aren’t important enough to study because they don’t understand them and therefore can’t be studied because they can’t possibly be important enough to study to try to understand because shut up:

    1) the sun
    2) clouds
    3) etc.

    • In the interests of accuracy, it needs to be noted that Willis did not invent the cloud hypothesis, but he made a good deduction all the same. Many of us have been the ‘first person we know’ to make a deduction, but the world turns out to be a bigger place than we thought. Doesn’t take anything away from the actual achievement though……

      • Brett Keane January 10, 2018 at 11:19 pm

        In the interests of accuracy, it needs to be noted that Willis did not invent the cloud hypothesis, but he made a good deduction all the same.

        In the interests of accuracy, as far as I know I was the first to suggest that the TIMING of the daily emergence of the tropical cumulus field and thunderstorms are crucial to the global temperature regulation … just as this paper confirms.

        Also in the interests of accuracy, when you accuse a man of not inventing something, it’s common courtesy to point out who you think DID invent it …

        w.

      • Ramanathan and Collins (1991) and Lindzen (2001) both investigated mechanisms involving cirrus clouds. Willis’s investigation involved the timing of afternoon thunderstorm formation. Cirrus clouds and thunderheads are very different.

  11. “…models tend to factor in too much of the sun’s daily heat, which results in warmer, drier conditions than might actually occur. The researchers found that inaccuracies in accounting for the diurnal, or daily, cloud cycle did not seem to invalidate climate projections…”

    Well the climate projections already run too warm, and when corrected for this failure, they’ll run even warmer. How much more invalidated can you get?

  12. This is yet another example of the sky is falling crowd trying to justify their existence. There is no correlation between carbon dioxide and global warming. There is no global warming. There is weather. And there is a bunch of left wing elitist do holders who want to save is from ourselves. I don’t want to be saved I want to be left alone. Your study is just one more example of junk science and fake news. Please go away.

  13. Maybe the geniuses who wrote many of the climate models have never heard of “fair-weather cumulus” clouds.

    These are clouds that form during generally sunny weather in spring or summer. Away from a storm or weather front that results in totally overcast skies, a day can dawn with totally clear skies, but by late morning, small cumulus clouds tend to form (from upward convection of warm, humid air due to solar heating, which can form clouds when the temperature of the surrounding air reaches its dew point). These clouds tend to grown larger and more numerous around midday and early afternoon, then start to disperse in late afternoon when the lower sun angle no longer produces enough vertical convection to replenish the moisture in the clouds. By sunset, very few of these clouds are left.

    Since clouds tend to cool the surface during daylight hours by reflecting sunlight, but help to retain heat at night, failure to take into account “fair-weather cumulus” clouds will neglect an important cooling effect during generally sunny, dry days, but clear skies at night would allow maximum cooling. These clouds also tend to be most prevalent from late morning to mid-afternoon, when sun angles are relatively high, and they can reflect the most energy away from the earth’s surface.

    Many weather stations have hourly measurements of cloud cover (eighths or tenths of the sky covered by clouds). It would not be too difficult to use these measurements to estimate cloud cover as a function of local time for generally sunny days, and estimate the amount of sunlight reflected by the clouds. But since that would make the models predict LESS warming and a less frightening future, such effects are ignored in climate models, because the goal is to BE AFRAID, BE VERY AFRAID.

  14. From the abstract: While this model tuning does not seem to invalidate climate
    projections because of the limited DCC response to global warming, it may potentially
    increase the uncertainty of climate predictions.

    That is a curiously worded sentence. Nearly everyone gets the implication that the model error may lead to overprediction of warming, but the sentence focuses instead on the change in diurnal cloud cover that is consequent on warming.

    • looks like they just said climate projections are ok…..and climate predictions are even more uncertain
      …I have no idea what they mean by projections and predictions…thought it was the same thing

      • Difference between projections and predictions:
        When I project a thing through the window, I predict it will eventually fall down.
        Except if it is money.

      • One can project a trend by extending it. A specific outcome at a specific future time would be a prediction, but that outcome is determined by the trend plus fluctuation. Thus, predictions are inherently more difficult. (This is why we can’t accurately predict weather more than a couple of weeks out, but can project climate trends — with short-term fluctuations smoothed away — decades out.)

  15. The increased carbon dioxide in the atmosphere since the start of the Industrial Age is estimated to produce an extra 3.7 watts of energy per square meter.“. Isn’t 3.7 the figure for doubled CO2? If so then their finding is even more important, because CO2 isn’t anywhere near doubling yet.

    • It is ok with this 3.7W/m2, but they forget that the Earth has warmed up since then and radiates nearly the same amount more. What if they made a balance now, with the existing CO2 and the existing temperature?

    • Right. The 3.7 watts per square meter claim is false. The number is from model claims for sensitivity for doubled CO2 with positive water feedback. The measured change in watts per square meter at the surface from 300 ppm to 400 ppm is zero. Satellite measured outgoing longwave radiation has not changed since 1979.

      • @bw
        To be fair, the GHG theory do NOT pretend that outgoing longwave radiation would change. It would just stay the same, the increase in surface temperature resulting only from the higher average emission altitude (combine it with lapse rate, and you get higher surface temperature).

  16. Global warming/climate change can do practically anything it seems.

    Ironically, climate models can’t do anything.

  17. Over 100 models by (I suspect) 200 + “climate scientists” and they all (but one apparently) are grossly wrong. This should be the scandal of the millennium. How many research $’s went down the gurglar? If this form of group think and collusion occurred in the finance industry heads would roll. Its a disgrace.

    There is a BIG lesson here for future generations

    m

  18. does this mean there wasn’t any “missing” heat at all then ? if so, was the karl paper just a pile of junk like i originally assumed ?

  19. I do not understand what has to do with climate sensitivity to changes in CO2 content. The 2 watts/m^2 stays the same it seems. The climate models error is in underestimating the negative feedback of increased ocean evaporation causing more clouds. Besides loss solar energy to the surface, more radiation to space from latent heat transferred to clouds. And the atmospheric window from high clouds is much higher because of reduced water vapor content. Climate models have evaporation increase at only about 3%/C rather that 6%/C
    from simple theory. The reason: they overestimate absolute humidity change with temperature.

  20. Well I once checked the daily “cloud cycle” for myself, based on a huge data set of NCEI. So it is the USA only, but I’d very surprised if it looked much different on a global scale.

    And as we are talking about clouds, there is something much more important. It is the essential question if clouds are cooling or heating over all. I know, that both sides are pretty much relying on the believe that clouds would be cooling the planet.
    The skeptics like to argue, that a (likely) increase in cloud cover due to increased temperatures, would counter the heating thus be a negative feedback. For the apologetic position however cooling clouds are mandatory to argue even the GHE itself. If clouds had a neutral or even heating effect, there would not be much left over for GHGs to do. Anyhow..

    So what I wanted to find out is, what temperatures are given the cloud condition.The data provided by the NCEI hereto are anything but perfect, and would deserve a lengthy discussion, which I will skip for the time being. The result looks like this:

    Clear and overcast skies are the coldest situations, the highest temperatures are yielded with intermediate cloudiness. Otherwise the curve is almost symmetric. But there are a couple of things to note here.
    1. Rain-chill. Rain, as it comes from high above is cold and will drop temperatures quite quickly (depending on the prevalent temperature). It is a well observable phenomenon. But rain is correlated to strong levels cloudiness and therefor is lowering the average temperature in these situations.
    2. Air pressure. Air pressure will have an impact on temperatures, because of the adiabatic lapse rate. As air pressure is also related to cloudiness, we have another bias here.
    3. The NCEI data only provide information on clouds up to 12.000ft (because it is about aviation). It is being argued however, that high clouds would have a much stronger GHE than low clouds. If that is so, we will have another bias.

    All 3 points of which mean, that temperatures will be relatively lower with strong cloudiness because of other reasons than their radial impact. In other words, these data suggest, that clouds must have a heating, not a cooling effect.

    • Daytime clouds reflect sunlight, the surface heating rate is reduced.
      Night clouds absorb OLR, the surface cooling rate is reduced.

    • Nice data for USA, but the important data is rather tropical area than whole USA, and ocean rather than land. And I would be very surprised if it looks the same as USA.

    • ” these data suggest, that clouds must have a heating, not a cooling effect.”
      Clouds are the main part of Earth albedo, without them Earth would receive ~20% more energy. Huge cooling effect.
      On the other hand, clouds are part of the water cycle, which has a huge dampening effect on temperature, and yields a higher average temperature, because of 4th power law of radiation. Water reduce temperature (in summer, at day time) by turning into steam, and increase it (at night, in winter) by turning from steam to liquid or even ice. And it transports heat from hot place (tropics) to cold one (poles).
      All in all, clouds are neither cooling nor heating the Earth, the are a huge negative feedback that stabilize the temperature to it current level

    • Btw. I forgot to name the 4th point despite highlighting it explicitly. As the diurnal pattern shows, we have “peak cloudiness” during the coldest daytime in the morning, while temperatures will be much higher at dusk.

  21. Alright if climate modeling is way to much on the high side why don’t realists start creating models that look more accurate than the current mess? Wouldn’t that give the first modeler to do that some instant cred?

  22. Okay, who can tell me how the GCMs “handle” clouds? Is cloud cover calculated from first principles, based on temperature, pressure, wind velocity and humidity? Or is it estimated stochasticaly, using historical cloud data, and then imposed on the grid? Or somewhere in between?

    • GCM handle clouds like they handle everything:
      Remember it is just impossible to calculate climate, this sort of chaotic things run amok in no time. Even a perfect model would only result in something observed in recent time, like a really green Greenland or frozen Thames most of winters, depending on the run. Useless for the purpose.
      That’s were “anomaly” enter: we know the whole thing is not linear, but let’s use the linear tool nonetheless.
      You take recent historical data (clouds or whatever), add some forcing, pretend you know how it turns into more of this and less of that (” temperature, pressure, wind velocity and humidity”, and voilà: you get, among other things, a new cloud cover, slightly different from the historical data you began with.

  23. Really all this talk to say ‘climate models are currently not fit for purpose’ or in the vernacular:

    Climate Models Suck.

  24. I wonder how long it will be before this study is dismissed because it was done by engineers not climate scientists who will say leave it to the “experts”?

  25. So if they include this new data in the models and rerun them backwards from matching current measured temperatures won’t the models be running cool at the original start point as at that point there was already elelvated CO2?

  26. This Nature paper fits well with my Energy and Environment paper:
    DOI: 10.1177/0958305X16686488
    Blog version at http://climatesense-norpag.blogspot.com/2017/02/the-coming-cooling-usefully-accurate_17.html
    See for example Fig 11

    Fig.11 Tropical cloud cover and global air temperature (29)
    “The global millennial temperature rising trend seen in Fig11 (29) from 1984 to the peak and trend inversion point in the Hadcrut3 data at 2003/4 is the inverse correlative of the Tropical Cloud Cover fall from 1984 to the Millennial trend change at 2002. The lags in these trends from the solar activity peak at 1991-Fig 10 – are 12 and 11 years respectively. These correlations suggest possible teleconnections between the GCR flux, clouds and global temperatures.
    By contrast, the lag between the solar activity peak at 1991 and the Arctic sea ice volume minimum is 21 years (30). It is simple and natural to correlate the cycle 22 low in the neutron count (high solar activity) in 1991 with the millennial temperature peak and trend inversion in the RSS in 2003 with the solar activity 1991 Golden Spike, and to project forward a probable general temperature decline for the coming decades and centuries. Lags differ between data sets because of the real geographical area differences, proxy data point selection differences and instrumental differences between different proxy time series. ”
    See also Fig10
    .”……….it is reasonable to conclude that the solar activity millennial maximum peaked with a solar activity “Golden Spike” in Cycle 22 at about 1991.

    Fig. 10 Oulu Neutron Monitor data (27)
    The connection between solar “activity” and climate is poorly understood and highly controversial. Solar “activity” encompasses changes in solar magnetic field strength, IMF, GCRs, TSI, EUV, solar wind density and velocity, CMEs, proton events, etc. The idea of using the neutron count and the 10Be record as the most useful proxy for changing solar activity and temperature forecasting is agnostic as to the physical mechanisms involved. Having said that, however, it seems likely that the three main solar activity related climate drivers are the changing GCR flux – via the changes in cloud cover and natural aerosols (optical depth), the changing EUV radiation producing top down effects via the Ozone layer, and the changing TSI – especially on millennial and centennial scales. The effect on observed emergent behaviors i.e. global temperature trends of the combination of these solar drivers will vary non-linearly depending on the particular phases of the eccentricity, obliquity and precession orbital cycles at any particular time convolved with the phases of the millennial, centennial and decadal solar activity cycles and changes in the earth’s magnetic field. Because of the thermal inertia of the oceans there is a varying lag between the solar activity peak and the corresponding peak in the different climate metrics. There is a 13+/- year delay between the solar activity “Golden Spike” 1991 peak and the millennial cyclic “Golden Spike” temperature peak seen in the RSS data at 2003 in Fig. 4. It has been independently estimated that there is about a 12-year lag between the cosmic ray flux and the temperature data – Fig. 3 in Usoskin (28). “

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