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Earth is heating at a rate equivalent to five atomic bombs per second

Posted on 6 February 2020 by dana1981

This is a re-post from the Bulletin of the Atomic Scientists

The heat absorbed in Earth’s oceans reached a new record in 2019, found a recent study published in the journal Advances in Atmospheric Sciences. Despite the fact that this has been the case for almost every year over the past decade, this information dominated the news cycle, with some particularly viral headlines noting that the amount of energy accumulating in the oceans is equivalent to detonating five Hiroshima atomic bombs per second, every second over the past 25 years.

While stunning, this isn’t a new analogy. After we published a paper about Earth’s energy accumulation in 2012, my colleagues and I at Skeptical Science created a website called that provided a widget that websites can include on their homepages to illustrate the amount of heat accumulating on Earth as compared to the energy in the Hiroshima atomic bomb. The widget also uses other analogies to get the idea across, such as how the amount of heat accumulated compares to the energy in Hurricane Sandy, or 6.0 magnitude earthquakes, or Big Bens full of dynamite, or millions of lightning bolts. Improved ocean heat measurements have since revised the rate of warming upwards from four to five ‘Hiros’ per second. (For the record, as of the writing of this article, our climate has accumulated the equivalent of a total of more than 2.8 billion Hiroshima bombs’ worth of heat since 1998.)

Our team wasn’t the first to use this analogy. In 2010, oceanographer John Lyman compared the rate of ocean warming to atomic bombs, and James Hansen used the Hiroshima atomic bomb analogy in his February 2012 TED talk. One might say that the comparison has come under heat, however. Some criticize the analogy for exploiting or being insensitive to the horrors suffered by the people of Hiroshima. Others have complained that the analogy is imperfect, as all analogies are, by definition.

On the other hand, the use of Hiros has one major upside. Earth and especially its oceans have been accumulating such a vast amount of heat due to human-caused global warming that it’s difficult to comprehend. Most people have little if any sense what 10 zettajoules per year—the amount of heat energy absorbed per year by the Earth—means. That’s why climate communicators have searched for a metric of comparison that the public can grasp. It’s relatively easy to visualize five atomic bombs detonating every second, and consequently comprehend the vast amount of energy being absorbed by the Earth’s climate system.

For those who nevertheless object to the Hiros analogy, perhaps microwaves offer a more palatable comparison. The heat accumulating in Earth’s oceans over the past 25 years is also equivalent to every person now on Earth running 35 standard household microwave ovens nonstop during Justin Bieber’s entire lifetime.

Critically, the rate of global heating is also accelerating. During the prior 25 years (1968–1992), the oceans only warmed at a rate equivalent to one Hiroshima bomb detonation per second, or 7.7 billion people each running 10 microwaves nonstop during that quarter-century period.

The good news: the rate at which we’ve been adding heat to Earth’s climate hasn’t changed much over the past two decades. The bad news: to avoid a potential climate catastrophe, global heating needs to begin declining soon and rapidly, which will require international implementation of numerous ambitious climate policies.

So far, many governments appear more inclined to keep increasing fossil fuel extraction than taking the necessary steps to slow global heating. Political leaders in many countries can implement these destructive policies without fear of losing power because too few people grasp the urgency of the climate crisis. Perhaps visualizing global heating as five atomic bomb detonations per second will help convey that sense of urgency to more people.

[Updated article on Feb 25, 2024 to fix the link to the 4hiroshima website]

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Comments 1 to 21:

  1. You could always change it to xyz tons of gun powder exploding per second. This would be an impressively huge number.

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  2. No doubt, the Earth is warming. But the number of Hiroshima bombs per second is uncertain. Most recent estimates of Earths energy imbalance is approx. 0.7 W/m2 (Hohnson et al. 2016), while the sum of all positive and negative forcings is in most papers, even Wikipedia, somewhere at 2 W/m2 or more. I have no idea, which figure is right or more reliable. Can anybody help me?

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  3. Eschwarzbach @2 ,

    Please please please be careful to avoid typo errors in critical information ~ such as the scientific author's name.  From your own moniker, I assumed the author might be German or Scandinavian but I eventually circled back to the common English name Johnson.  And a great host of papers.

    I did find a  Johnson et al, 2016 ~ with planetary energy connection.  But no Extract.  Can you supply the paper's Extract for the readers here?  Thanks.

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  4. eschwarzbach @2,

    Like Eclectoic @3, I presuime you meant to cite Johnson, Lyman & Loeb (2016) 'Improving estimates of Earth's energy imbalance' [full text] who do estimate the global energy imbalance 2005-15 as being "0.71±0.10 W m^-2" (which I calculate as 4 Hiroshima's/second). The OP cites Cheng et al (2020) which puts the annual increase in ocean heat content (the bulk of global warming due to the imbalance is ocean warming) for 2015-19 at 19ZJ = 1.2 Wm^-2.

    The net global forcing is a different number of which the energy imbalance is but a part. Additional to the imbalance is the extra energy leaking out into space because the globe is now hotter than it was pre-industrial. If the warming-so-far is 1ºC, and ECS=3ºC for a doubling of CO2 (3.7Wm^-2), the climate forcing required to support that 1ºC warming would be 0.8Wm^-2. From this, using Cheng et al, we can infer a net global forcing of roughly 2Wm^-2.

    Of course, the difficulty with directly assessing the value of net forcing is the negative component. The positive component is relatively exact with NOAA's AGGI standing at 3Wm^-2 (2015-18) suggesting a negative forcing of roughly 1Wm^-2.

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  5. "...compares to the energy in Hurricane Sandy, or 6.0 magnitude earthquakes, or Big Bens full of dynamite, or millions of lightning bolts."


    Why not keep it simple, in degrees C.  So it is ~0.09 C/decade, less than the capability of the instruments to differentiate.


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    Moderator Response:

    [DB]  "So it is ~0.09 C/decade, less than the capability of the instruments to differentiate"

    Incorrect.  Couple with the power of large numbers and using mathematical averagingScientists have quantified the warming caused by human activities since preindustrial times and compared that to natural temperature forcings.

    Changes in the sun's output falling on the Earth from 1750-2011 are about 0.05 Watts/meter squared.

    By comparison, human activities from 1750-2011 warm the Earth by about 2.83 Watts/meter squared (AR5, WG1, Chapter 8, section 8.3.2, p. 676).

    What this means is that the warming driven by the GHGs coming from the human burning of fossil fuels since 1750 is over 50 times greater than the slight extra warming coming from the Sun itself over that same time interval.

    In the early 20th century human activities caused about one-third of the observed warming and most of the rest was due to low volcanic activity. Since about 1950 it's all humans and their activities.

    Further, the detection of the human fingerprint in the observed tropospheric warming caused by the increase in atmospheric concentration of greenhouse gases like CO2 has reached 6-sigma levels of accuracy.

    Please cite credible for sources for claims running counter to the published science.  Thanks!

  6. Color me old, but I prefer units of <ChristmasTreeLights>/<square meter>. Easier to visualize. 1.2W/m^2 is roughly 10 mini incandesent lights per square meter of land — UL won't let us string them over water — or nearly one of the older 5 W bulbs we so fondly remember. Countinuous, 24/7, throughout the year.

    The problem with Hiros/second is they're so effervescent. That, and they are used by many of the No Nukes! contigent to simultaneously whip up anti-nuclear power sentiment, and consquent excuse to frack more gas and burn more coal.

    So I stick with ChistmasTrees/m^2. They're a constant reminder and are carbon neutral.   

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  7. Franklefkin @5 ,

    Yay !    0.09 C/decade sounds good.  Or even 0.14 C/decade . . . or maybe 0.20 C/decade  (depending on which decade you wish to ignore).

    Trouble is, the pesky ole planet - a.k.a. the real physical world - keeps on responding to the increasing heat, rather than to the kitchen-thermometer figure showing on the cupboard door.   World ice keeps melting, world sea level keeps rising . . . gosh, it's almost enough to make ordinary folks think we got ourselves a real problem!

    Easier to go with the parable of the frog in the warming pot of water ~  just hang around, eyes closed, saying nothing . . . until we croak    ;-)

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  8. Ed Leaver @6 ,

    I am appalled at your suggestion.

    Surely you were meaning to say <FestivusTreeLights>   [for Seinfeld fans]

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  9. Sorry for the terrible typo Hohnson/Johnson. Thanks MA Rodger @4 for the explanation and providing the pdf of Cheng´s et al 2020 paper, describing the accelerating Earths heating from 0.38 W m^-2 over the last 60 years to 1.2 W m^-2 in the last 5 years and the large hike in 2019 (table 1). Am I right, that the total forcing is just a "could be" in absence of extra energy leaking out into space due to a hotter globe?

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  10. eschwarzbach @9,

    Yes, although I think it is "would be" rather than "could be".

    The definitions of Climate Forcing tend not to help in respect of AGW as they describe a Forcing as the energy imbalance at the top of the atmosphere. So this NOAA webpage says "The difference between incoming and outgoing radiation is known as a planet’s radiative forcing (RF)." Such a definition is fine if it concerns a one-off event. But when it is an on-going process like AGW, it becomes confusing as the TOA energy imbalance will never match the total applied Forcing as the climate will be reacting to the imbalance before it is fully applied.

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  11. Mod response @# 5

    You say I am incorrect, yet fail to state what you feel (or what you determine credible sources state) the actual temp rise of the oceans per decade is!

    What is it?

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  12. franklefkin @11,

    You ask for "the actual temp rise of the oceans per decade" having been told-off for suggesting @5 that some unspecified "it" was warming at "~0.09 C/decade" adding that this rate was "less than the capability of the instruments to differentiate." Note that your definition of ocean temperature here is still not complete.

    According to NOAA data, global SST has been rising at +0.13ºC/decade, a value evidently within "the capability of the instruments to differentiate."

    Mind, the usual quantity which those suffering denial over AGW seem to enjoy bandying-about is the average increase in temperature for the entirety of the ocean's waters. That is a simple calculation. By taking the 0-2000m dOHC as representative of the entire ocean (again a value evidently within "the capability of the instruments to differentiate."), over the last 5 years we get +107 ZJperDecade /(1.4e21kg x 4200J/ºC) = +0.02ºC/decade.

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  13. Franklefkin @11 , to add to MA Rodger's comment :-

    the moderator was not referring to the ocean temperature rise, but to the heating (from global warming) of the ocean.

    You were incorrect ~ in stating that the instruments could not determine a small temperature change (such as the 0.09 figure you yourself nominated).  Was this the point you wish to dispute?

    The ocean covers 70% of the planetary surface, and has an average depth of around 4,000 meters.  The ocean is warming, but not uniformly from 0.1 meter down to 4,000 meters of depth.  Therefore there is little point in trying to specify an average oceanic temperature rise in degrees per year or per decade.  OHC (ocean heat content) is the logical measurement.  Was this another point you wish to dispute?  

    "Metrology" arguments would belong in a different thread than this one.

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    Moderator Response:

    [DB] You make sage points, but the user to which you are responding is a sock puppet and has thus recused itself from further participation here.

  14. I've been keeping an eye on the increasing rise in global tempature, and decided to do a bit of investigating after Antartica's new record of 65 degrees. Little did I expect to stumble upon such researched conversation, and better yet, the intellectual slamming nearly brought tears of joy to my eyes. Reading through this banter made my day, and has left me more educated about our collective crisis. You may see my contribution to this thread as a waste, and I don't care, but for your average Joe the comparison to Atomic bombs helps put things into perspective. In case your were curious about the opinion of a "lesser" mind. 

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  15. Thanks, Moderator @13 , for the sockpuppet notification.

    I won't ask which rather puerile puppeteer it was.   Being an optimist at heart, when I see a comment containing undertones of passive-aggression & deliberate fatuousness . . . I nevertheless think there's a 20% chance the comment comes from a clumsily laconic innocent.  In this case, perhaps closer to a 10% chance, though !

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  16. I use the Hiroshima atomic bomb (HB) analogy as an energy ruler when talking about climate change energies.  The energy in the HB is listed as 12,000 tons of TNT (trinitrotoluene) and 1 ton of TNT is listed as 4.2 gigajoules (4,200,000,000 tons = billions).  That works out to 5x10^13 joules = 50,000,000,000,000 joules (trillions).  The difference in the HB and climate energy is intensity.  Assume the HB energy is released in 1 second.  That is enough energy to level a 6 mile^2 area.  In Hiroshima 140,000 people died and in Nagasaki 80,000 people died (about half by radiation poisoning), which shows the deadly result of intense energy.  Climate change energy is larger but not usually so intense, released over decades, centuries, mellinia, etc.

    Assume 40 Gigaton of CO2 released in 1 year = 8x10^14 moles of CO2.  Use octane, C8H18, as a proxy for all fossil fuels then 1x10^8 moles of octane were burned (Hcomb = 5,000,000 joules/mole).  That works out to 5x10^20 joules released in 1 year of fossil fuel burning (500, joules = 500 quintillion).  Divide 5x10^20 joules/year FF combustion by 5x10^13 joules/bombs/year = 10,000,000 bombs/year FF combustion.  If there are 32,000,000 seconds/year then that energy = 1 HB every 3 seconds.  

    Next use the Stefen-Boltzmaann Law to calculate the energy if earth's temperature is 288K.  Energy = (5.7x10-8 W/(m^2 T^4))xT^4 which is 392 W/m^2.  Do the same for T = 289oC (1oC increase in earth's temperature) and I get 398 W/m^2.  That is a difference of 6 W/m^2.  I calculate about 5.2x10^14 m^2 as the area of earth and 3.2x10^7 seconds in a year for a total increase in energy for 1oC for the earth in one year of 1x10^23 joules (100, joules = 100 sextillion joules).  Compare that to all of the energy of all fossil fuel combustion in 1 year = 1x10^23 joules / 5x10^20 joules = 200/1 ratio.  Instead of 1 HB every 3 seconds it comes out to 62 HB every second for the extra energy from 1oC increase in earth's temperature.  Look at it another way.  If you eat 2,000 calories a day, you would have to up your calorie intake to 200 x 2,000 = 400,000 calories a day (every day).  Pretty intense eating.  If you do the calculation for 2oC increase, it comes out to a 370/1 ratio (116 HB per second) and a 3oC increase comes out to 580/1 increase in energy (181 HB per second).  Also, you'd have to eat the equivalent of over 1,000,000 calories /day for a 3oC increase in energy.  Some different ways of looking at the energy of climate change.  Hope my calculations are correct.  

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  17. rip71749 @16,

    Your arithmetic look fine although the numbers you input are not those I would use.

    While the yield of the Hiroshima bomb is not known with any certainty, the usual figure bandied about is a little higher than the figure you use at 6.3e13 J.

    Conversely, your calculation of FF energy production is well done given the approximations you run with. Using BP's FF energy use for 2018, it works out at 4.92e20 J for the year.

    I'm not sure of the value of your 200:1 ratio. Your sixty-two bombs-per-second is calculated using, not the global energy imbalance or the climate forcing, but the extra IR emissions up from the surface resulting from a +1ºC temperature rise. We do see such a rise but it results from many years of FF burning. If calculated for +1ºC at the top of the atmosphere, the well-known 3.7Wm^-2 value would appear rather than the 6Wm^-2 for the higher surface temperatures. The surface value is not a net value, of course, as there is an equally large increase in the back-radiation coming down from the atmosphere which has also heated by +1ºC. The five bombs per second of the OP is calculated using the global energy imbalance, a far smaller quantity.

    Perhaps more meaningful than the 200:1, an interesting calculation is the time required for the climate forcing from the resulting GHGs to trap an equivalent amount of energy as produced from the FF burning. Assuming those 2018 emissions were responsible for a 2.25ppm CO2 increase (mind if there had been no emissions through the year, the level of atmospheric CO2 would have dropped, so the 'responsible' level is entirely academic), the forcing would be some 0.03Wm^-2, globally 1.5e13 W. Thus the forcing would accumulate energy globally equal to the annual FF power generated every 385 days.

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  18. Thank you MA Rodger.  I have been trying to educate myself on CC over the past few years, pretty much working in a vacuum, on my own.  I'm not quite clear on your energy balance from the 1oC increase in temp.  Your 3.7Wm ^-2 seems reasonable as a new equilibrium loss to space of energy from the extra energy gained from the greenhouse effect.  I view the CO2 levels as a savings account that pays out interest in heat (currently paying 1oC each year, but not carried over).  Because we add an extra small amount of CO2 each year we get an extra 'small' amount of extra heat, that slowly accumulates over the decades, centuries etc (so maybe we will reach 2oC, 3oC or higher this century).  Of course not all of that heat is from CO2, but its additional effects on ocean H2O (and possibly CH4 from warmer permafrost and peat).  So the extra energy seems to me to be calculatable from the Stefen Boltzmann Law, as I did above.  It seems to me the sun comes out every day and warms the earth according to the 'current' conditions of the earth and currently that is running 1oC warmer than recent centuries.  The large energy value does not seem unreasonable given that the entire earth is warmed 1oC higher.  As I understand it we are getting about (0.7)x(342 W/m^2) = 240 W/m^2 from the sun and the 3.7 W/m^2 you mention above is the new equilibrium value from the extra energy of the greenhouse effect.  I am assuming that we are leaking more energy than recieved at any particular moment because some of the incoming energy is 'saved' in its warming effect from the greenhouse gases.  I'm not sure why my delta = 6 W/m^2 value is not valid and my 200/1 ratio is not accurate.  My calculation really does not say anything about how the 1oC increase came about, but the extra energy does seem correct (to me).  A CC denier could claim that the extra energy was from Milankovitch cycles or sun spots ot cosmic rays or something else, but those seem to have been discounted from what I have read.  To me, it seems the extra energy added from burning all the fossil fuels each year seems pretty trivial (the 200/1 ratio).  The problem energy is the energy from the greenhouse gases (H2O, CO2, CH4, etc) absorbing IR radiation and bouncing it around the atmosphere before it reaches equilibrium on its way out to space.  

    Also, I did do a calculation on how fast the Greenland ice could melt with temperature increases of earth of 1oC, 2oC and 3oC.  I assumed there was 680,000 miles^3 of ice.  I assumed it started at -1oC to calculate the energy to heat it 1oC (to compare with the energy to melt it all).  The heat capacity of ice is about 2.1 joules/(gm oC) and I got a value of 5.8xx10^21 joules.  Next, I caluated the energy to melt the ice using a heat of fusion of 334 joules/gram and came out with a value of 9.3x10^23 joules.  Because melting is so much more energy I ignored any warming of the ice from lower temperature and only used the energy to melt the ice.  I compared that with my energy calculated to warm the earth 1oC (1.0^23 joules), 2oC (1.9x10^23 joules) and 3oC (2.9x10^23 joules).  I estimated that the area of Greenland was 1/280 the area of earth and used that to 'crudely' estimate the amount energy available to warm the ice in Greenland with those above energies from 1oC, 2oC and 3oC.  My thinking is 9.3x10^23 joules to melt the GL ice divided by (1/280) of the extra energy from 1oC (or 2oC or 3oC) increase in energy.  So I came out with 2600 years to melt GL ice with 1oC increase in temp, 1370 years to melt GL ice with 2oC increase and 900oC with 3oC increase in temp.  I'm guessing that we will see at least a 3oC increase in temp (or higher, since we are not doing anything), so I went with the 3oC increase.  Also, I have read that we are heating the Arctic 2-3 times faster than the rest of earth.  If we assume a 24 foot sea level rise from the GL ice and simplistically plot out a straight line for 900 years we would see a 2.7 foot rise in sea level by 100 years, 2120 (or 2.1 foot rise in sea level by 2100).  Those seem pretty conservative estimates because I did not consider any melt from the west Antarctic sheet or from pumped out ground water from around the world.  

    I am sorry for deluge of estimations, but this has been bottled up inside me for a few years, since I am working on my own, and I'm jumping at the chance that you can provide some feedback in case I am going off the tracks.  This is the first time I have posted on Skeptical Scientist, but the 'atomic bomb' reference caught my attention since I had also used a Hiroshima atomic bome as an energy ruler.  Also, I had read the Hiroshima abomic bomb was 12,000 tond TNT  (called little boy) and the Nagasaki was 15,000 tons of TNT (called fat man), so that may be the difference in size of atomic bombs.  The biggest US nuclear bomb was castle bravo at 130 Megatons in 1954.  The Russian created the biggest nuclear bomb ever, the Tsar Bomba in 1961, at 50 Megatons (the heigth of the blast actually reached the edge of earth/space, over 211,000 feet).  That's a whole other problem.  Again, I thank you for the taking the time to provide feedback.

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  19. RIP71749,

    In general it is a waste of time to do your own calculations.  You will be much better informed by reading more peer reviewed papers.  Articles at SkS are a good place to start.

    As for the melting of Greenland I saw a calculation once but cannot find it to cite.  I get very different numbers than you. 

    First of all, you cannot use the Boltzman equation to calculate the energy absorbed so you are off at the start.

    I will use 2, 850,000 km3 of ice which is the same as yours.  I get 2.685E21 cm3 of ice.  Times 330j/gm times 0.9g/cm3.  That is 8E23 joules absorbed to melt the ice (ignoring the energy to increase the temperature) close to your number (did you account for the lower density of ice compared to water? please show your work).

    You calculate the energy absorbed by using the energy imbalance of 3.7 W/m2 times the surface area of the Earth of 5.1E14m2 =2E15w times the number of seconds in a year (3E7) = 5.7 E22 joules per year absorbed.  It would take about 10 years to melt all the ice in Greenland.  If more CO2 is released the energy imbalance will increase and the speed of ice melt increases.

    I might have a mistake since the calculation is not peer reviewed.  I remember the calculation as showing the energy to melt Greenland was absorbed in a single year but it was a  very long time ago and I probably remember it incorrectly.

    This number can be GOOGLED if you look hard enough.

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  20. Michael,

    Thanks for the reply.  Actually, I think our numbers are pretty similar.  If I adjust for the density of ice (as you suggest), I get almost exactly the same as you for the energy to melt the GL ice.  You use 3.7 W/m2 for the imbalance and I used 6 W/m2 as the extra energy from a 1oC increase in temp.  If all the 'extra' energy went into melting GL ice I calculated it was about 9+ years and you get about 10 years, so we are pretty close.  I went a little farther and said that GL was 1/280 of earth's area and used that amount of energy to warm the ice (x3 because I assumed that earth would warm at least that much this century and the Artic is warming faster) and came out with 900 years to melt all of the ice in GL (assuming no further increase in temp and everything otherwise stays constant and continues in a linear fasion - no doubt false).  That would produce a SLR of just over 2 feet by 2100, which seems pretty realistic, ignoring any other melting ice in the world.  I used a little more ice than you (should melt longer) but I also used more energy than you (should melt faster).  I'm not sure why you say the Stefan Boltzmann equation is not valid.  It's a pretty simple equation "energy = constant x temp^4".  I'm only looking for 1 significant figure to convince myself about what I'm reading is happening, and this seems to give it to me.  I greatly appreciate your comments.  I actually feel better about what I did because of what you did (maybe false confidence?).  

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  21. rip71749,
    Regarding the energy from burning fossil fuels, there is an SkS graphic illustrating the relative size of the various global energy inputs.

    I feel that 3.7Wm^-2 figure requires some further explaining. It is the value of Climate Forcing, the global energy imbalance, that would result from a doubling of CO2 which, without feedbacks, would result in a global temperature increase of +1ºC. These values are explained by the solar warming (less albedo) being globally 240Wm^-2 which thus gives an effective planetary temperature of (240/5.67e-8)^0.25 = 255K. Add 3.7Wm^-2 and it becomes 256K. These values, of course, apply high up in the atmosphere but the temperature increase from any forcing also applies to the surface temperatures as the lapse rate acts in a linear fashion down through the atmosphere.

    Additional to the initial forcing, there are feedbacks which increase the warming. They act as the global temperature rises, this temperature rise meaning the initial climate forcing is being equalised. Thus the feedbacks do not appear as an increased energy imbalance but instead extend the temperature effect of the climate forcing as it equalises with rising temperature.

    Now, at any particular time during AGW (where the Climate Forcing is applied slowly over a period and not all at once) the energy imbalance which is warming the globe (and so theoretically available to melt Greenland ice) will be far smaller than the accumulative Climate Forcing since pre-industrial times. Much of this Climate Forcing (and as negative forcings are poorly defined, the value of net Forcing since pre-industrial is imprecisely known but it is usually quoted as very roughly 2Wm^-2) will have been balanced by the global temperature increase since pre-industrial. It is solely the remaining energy imbalance that is available for melting ice caps, this running presently at something like 1Wm^-2.
    From the imbalance, there is then perhaps something like 16ZJ/year entering the climate which, if it could be brought to bear on Greenland's ice, would melt Greenland in something like 50 years. Of course, getting all that energy imbalance to Greenland would be impossible but if the ice were to set off across the oceans, it does become possible. Indeed, having melting icebergs bobbing about at lower latitudes would lower the global temperature and this will increase the global energy imbalance. (This is the mechanism behind the hypothesis set out in Hansen et al 2016.)

    Hope all that makes sense.

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