Earth is Heating at a Rate of 1,150,000 Hiroshima Bombs Every Day

Have you ever relied on the media for facts and then been disappointed to find out the information is either out-of-date or just plain wrong? Well, that happened to me yesterday as I was working on a Twitter post. I recalled reading a headline about comparing the rate of heating of the planet to a number of Hiroshima bombs per second. I wanted to just multiply that number by 86,400 (the number of seconds in a day) to get the number of Hiroshima bombs per day. My idea was to accompany that with a nice archival picture of a nuclear explosion and everything would be in place for a viral Tweet.

So, I went looking for the answer.  Here is some of what I found:

There are lots more — a simple Google search on “Hiroshima, climate change” will get you started.  I went with 350,000 Hiroshima nuclear bombs per day, to err safely on the low side.  Here is the tweet. That’s just over four Hiroshima nuclear bombs per second. And all seemed good with the tweet until someone rightfully commented that I should show my work.  Well, I can do that! And surprise surprise. The media got it wrong.

It all comes down to what’s known as the Earth Energy Imbalance (EEI). This is the difference between the amount of incoming solar radiation that heats the planet and the outgoing thermal radiation that escapes back into space. As one group of scientists put it in a recent paper, “The absolute value of EEI represents the most fundamental metric defining the status of global climate change, and will be more useful than using global surface temperature.” Unlike weather, which changes wildly from year to year, the EEI is a direct measurement of the rate of heating of the planet. Heat in minus heat out. Couldn’t be any simpler than that.  If you want to take a deeper dive, here is a good article on the topic.

The EEI is measured in units of Watts per square meter (W/m²).  The most recent number for the EEI as published by NASA is 1.64 W/m², from March 2021 through February 2022. The graph to the left shows the EEI over time, click on it to make it larger (thank you Leon Simmons for posting this).

Let’s put this number into perspective. If you think of an ancient 100 Watt incandescent lightbulb and the heat that gives off (they got very hot), imagine gridding off the planet into (roughly) 26’x26′ squares and having one 100 Watt lightbulb in the center of that square all over the planet — including the oceans and poles.  Imagine every single one of those lightbulbs was turned on and left on, every day, 365 days per year.  That’s approximately the current rate of heating.

Okay, keeping the value EEI = 1.64 W/m² in mind, let’s do the math.

First question — how many square meters on planet Earth?  If we assume the planet is a sphere with a radius of 6,371,000 meters, then by using the equation for the surface area of a sphere (A = 4πr²), we get a surface area of 5.100 × 10¹⁴ m².  (I hope you are using Google to double check me).  The correct answer is slightly larger than this, owing to geographic features that generate additional surface area — but we will ignore this slight additional surface area, so we can be sure that we are not overestimating the global EEI.

Multiplying, this leads to a global planetary energy imbalance of (1.64 Watts/m²) × (5.100 × 10¹⁴ m²) = 8.365 × 10¹⁴ Watts.

Now one Watt is the same as one Joule per second, where the physical unit “Joule” is the direct measurement of energy. So we get a global EEI of 8.365 × 10¹⁴ Joules per second.  This is such a large number that physicists have come to the rescue by creating the “terajoule,” which is one trillion (10¹²) Joules.  So, a simple division gives a global EEI of 836.5 terajoules per second.

And here is the easy part. How many terajoules in a Hiroshima bomb?  You can Google that and find numbers quoted from 50 to 75.  But we want to be precise here as a point of reference — the Hiroshima bomb was measured as being equivalent to 15 kilotons of TNT. Even though the actual explosion has never been pinned down, we can pin down 15 kilotons of TNT.  Google it yourself: “terajoules in 15000 tons of TNT.” This number comes out to 62.76 terajoules.

Okay — one Hiroshima bomb = 62.76 terajoules.  The global EEI is 836.5 terajoules per second.  Converting EEI to Hiroshima bombs is now simple division.  The global EEI is 836.5/62.76 = 13.33 Hiroshimas per second.

That’s right!  The number of Hiroshimas going off every second on the planet is not 4 or 5 or 6 or 7 — it’s 13.33.

Multiplying 13.33 by the number of seconds in a day (86,400), we get 1,151,587 Hiroshimas per day.  Because there were only three significant figures in the original EEI, we will round down to three significant figures, to get 1,150,000 Hiroshimas per day.

According to NOAA (and other sources, once again Google is your friend) the oceans absorb about 90% of this excess energy. Easy math: 90% of 13.3 is 12.0. If we restrict to the heating of the oceans, then they are heating at a rate of about 12.0 Hiroshimas per second or about 1,040,000 Hiroshimas per day.

Summarizing for the headlines — feel free to use this CNN, MSNBC, FOX, ABC, CBS, NBC, NYTIMES, WAPO, TRUTH SOCIAL, ALEX JONES, ETC.:

“The planet is currently heating at the rate of over 13.3 Hiroshima nuclear bombs per second, or over 1,150,000 Hiroshima nuclear bombs per day.”

“The oceans are currently heating at the rate of over 12 Hiroshima nuclear bombs per second.”

The EEI is changing all the time and is mostly getting larger. If you want to keep up on the latest numbers, here are the simple equations you can use for the next mainstream media article you write:

Hiroshima bombs per second = 8.12 × EEI

Hiroshima bombs per day = 701500 × EEI

Hiroshima bombs per second in the oceans = 7.31 × EEI

Addendum

For those who object to the Hiroshima bomb comparison (for any number of valid reasons) here are others.

The current EEI is equivalent to 697,000,000,000 microwave ovens running on high (1200 Watts), full time, 24 hours a day.  This is about 88 microwaves for every person on the planet.

The current EEI is equivalent to about seven hurricane Katrinas at landfall per second (Katrina was estimated to be about 120 terajoules at landfall).

The current EEI is equivalent to each person on the planet having 1045 100-Watt lightbulbs burning full time, 24 hours a day.

The current EEI is equivalent to 446,100,000,000 hand-held hair driers running on high (1875 Watts), full time, 24 hours a day. This is about 55 hair dryers for every person on the planet.

Eliot Jacobson, Ph.D.

Retired professor of mathematics and computer science, retired casino consultant, now a full time volunteer, husband and grandfather. Know-it-all doomer. Born in the year 316 ppm CO2.

9 thoughts on “Earth is Heating at a Rate of 1,150,000 Hiroshima Bombs Every Day

  • May 25, 2022 at 11:59 am
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    Thanks for this lucid explanation Eliot. It’s 1.64 joules per second over every square meter, spread over the entire planet, 24 hours/day. When it’s night here, somebody in Kenya is getting 3 joules per second on their square meters. (???)

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      • July 10, 2022 at 2:35 am
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        I like the fact you bring it down to a Universal principle – thermodynamics
        It stops the “ I don’t believe we can measure global temperatures that accurately “ argument in its tracks

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  • May 29, 2022 at 12:23 pm
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    The LA Times Editorial section today had an article by an arctic ecology professor in Alaska who likes to take her kids to frozen lakes and show them the methane gas by lighting gas bubbles under the ice on fire. When asked by her kids if she is worried she says she tells them she’s not worried. It just means humans will have to cut back even more on their emissions and change their attitude to adapt to the changing climate. Don’t worry so much, Eliot. Light the gas on fire so you can see the Hiroshimas in action with fun fire balls! Math is so boring when you could be doing fun science projects instead!

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  • June 3, 2022 at 3:04 pm
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    Can you calculate what is the normal, “background” sun’s radiating the Earth?

    13.3 H. bombs per second sure seems like quite a lot.
    Then you realize the “solar constant” irrradiating the planet is like 11,190 every second.

    (Is that figure correct?)

    I don’t mean to make light of the 13.3 — but it does give a bit more clarity, the context of what we’re up against.

    My personal favorite techno-scheme involves building bunches of OTEC plants.
    A proven technology, EACH large *endothermic* plant puts out 100,000 gallons of 39°F (!) per *second* — while producing useful sustainable, baseload, electricity for the developing world.

    Converting excess heat INTO needed power seems like a great choice.

    (“We’re saving our own lives.”)
    We build them — creating cooling now — and just charge for the ongoing maintenance and upkeep. (They run forever with never a charge for fuel.)

    Not a new technology, (over a century); running right now in Hawaii — [link deleted]. More popular recently: the largest OTEC plant in the world is currently under construction in China.

    I realize this does not fit the meta-narrative of your blog…
    And definitely OTEC is not the whole answer for global warming,
    but add in the meers (reflective mirroring)
    and Marine Cloud Brightening …
    and …
    and ….

    And it seems to me like we still may have a shot at making it through *this* closing door.

    Likely? Oh, No. Seriously? Definitely not.

    (You hear people look long at the facts, shake their heads, say,
    “…it’d take a miracle!”
    And then you raise your head up a bit, take a deeper into our history, and realize our path has been *strewn* with ‘miracles’ !
    Recent example: would *anyone* have bet we humans could make it through a half-dozen DECADES without triggering WWIII and our “mutually assured destruction” ? )

    But is it still possible that we maybe *could* squeeze through this Fermi Great Filter?
    “Yes!” is my answer.

    Don’t foreclose on humanity too soon.

    Joanna Macy’s parting words at the end of one her workshops, 25 years ago:

    “Do not be seduced by despair.”

    Thank you for your good and important work.

    I appreciate your holding up the dark clear mirror to those blithely assuming that certainly WE could not possibly be responsible for this 6th Great Extinction.

    Thank you for your service.

    Reply
    • July 25, 2022 at 11:17 am
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      Homo sapiens, also known as vertebrate mammals, were not around for the other 5 mass extinction events. Are you suggesting that humans caused the 6th extinction event currently unfolding on the planet and therefore can stop it?

      Reply
  • July 8, 2022 at 11:54 pm
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    Or, “95% of the carbon dioxide can be out of the atmosphere by 2050” see Peter Fiekowsky’s book, Climate Restoration. Whoa!! If we aim for 300 ppm –by 2050– turns out we *can* do that… Speed and Scale…

    Reply
  • July 10, 2022 at 6:22 pm
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    The numbers should shock people into action but we are being blocked by the wealthy corporate elite who still are attached to having more money that they can ever use and to causing so many more emissions through personal lifestyles (like private jets) as well as their corporate activities. Can we inspire people to create co-ops and transition the economy in a more equitable way as we transition to a renewable energy future? We don’t need to let the wealthy determine our fate. So co-ops, please, and also, please vote! So we can have the benefit of Build Back Better legislations and other changes and incentives that we need government to do.

    Reply
  • July 15, 2022 at 9:20 am
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    To my knowledge the Hiroshima, ” Hiro”, analogy was first refined by Joe Romm durning the “Climate Progress Blog ” era ~12 years ago. During that era the EEI was computed at 4 Hiros/sec. With much less refined data and none of the additional Methane and other escalating assorted greenhouse gasses incorporated for lack of data. It clearly needed updating. “Skeptical Science” still has that graphic running at 4H/s.
    Thank you Eliot,

    Reply

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