Earth's energy imbalance

Global surface air temperatures have risen less rapidly over the past 15 years than the previous few decades. The causes of this ‘hiatus’ have been much debated. However, just considering surface temperatures does not tell the whole story – a new analysis using satellite & ocean observations confirms that the Earth is still gaining energy overall.

Understanding how Earth is currently heating up helps us to gauge how much the planet is going to warm in the future. The bottom line is that Allan et al. (2014, open access) find that the Earth gained 0.62 ± 0.43 Wm−2 (uncertainties at 90% confidence level) between 2000-2012. This amounts to 320 ± 220 TW of energy, which is:

  • about 20x the total global energy generated by humans1
  • about half a day’s worth of solar energy every year2
  • equivalent to every person worldwide using 20 kettles each to heat the oceans continuously3

In addition, atmospheric model simulations using observed sea surface temperatures and radiative forcings are able to capture variations in this heating rate due to natural factors such as volcanoes (which cool the planet) and changes in the ocean relating to El Niño/La Niña (which have both cooling and heating effects) – see Figure below.

It was also found that heating of the planet increased from the 1985-1999 period (0.34 ± 0.67 Wm−2) to the 2000-2012 period (0.62 ± 0.43 Wm−2), despite slowing in the rate of surface warming. This suggests that the extra energy is warming deeper layers of the ocean.

Changes in Earth’s yearly average heating rate in observations and simulations 1985-2013. All lines were adjusted to match the observed average heating rate over the 2005-2010 period. [Taken from factsheet about Allan et al. (2014)]

1 20 ± 14x global energy generation of 16TW in 2006
2 16 ± 11 hours based on solar constant of 1360Wm−2
3 23 ± 16 kettles of 2kW each

Thanks to Richard Allan for providing some of the text & the figure.

Allan, R., Liu, C., Loeb, N., Palmer, M., Roberts, M., Smith, D., & Vidale, P. (2014). Changes in global net radiative imbalance 1985-2012 Geophysical Research Letters DOI: 10.1002/2014GL060962

About Ed Hawkins

Climate scientist in the National Centre for Atmospheric Science (NCAS) at the University of Reading. IPCC AR5 Contributing Author. Can be found on twitter too: @ed_hawkins

18 thoughts on “Earth's energy imbalance

  1. Thanks for the write-up Ed!

    Just to add that only atmospheric simulations which are given realistic observed sea surface temperature and radiative forcings (“AMIP” experiments) are able to reproduce the observed variability in the energy budget. Fully coupled climate simulations, which are used to make future projections, can simulate the changes in response to radiative forcings (including natural effects from volcanic eruptions and human caused factors such as greenhouse gas emissions) but are not designed to capture the timings of natural ocean “weather”, generating their own El Nino and La Nina events randomly in time.

  2. Hi,

    I am having difficulty interpreting the following:

    “Over the 1985–1999 period mean N (0.34 ± 0.67 Wm−2) is lower than for the 2000–2012 period (0.62 ± 0.43 Wm−2, uncertainties at 90% confidence level) despite the slower rate of surface temperature rise since 2000. ”

    The confidence intervals appear to be too wide to be our uncertainty in the inferred mean. They seem to be more like the visually apparent variation about the mean in the data themselves.

    How should one interpret that statement?

    I presume the following gives a clue:

    “Calculating z scores and applying a two-tail test to annual values, N is significantly larger in the 2000–2009 period than the 1985–1989 period at the 90% confidence level for UPSCALE (z = 3.1), CMIP5 (z = 2.4), and the OBS reconstruction (z = 1.8, also applicable when replacing the 2000–2009 period with 2000–2012) but not for the AMIP5 ensemble (z = 0.6, applying to the shorter 2000–2008 period).”

    but I am not sure what that clue is. Perhaps it is the “annual” bit.

    The z scores of 1.8 (and above) seem at odds with the stated uncertainty intervals of the means themselves. I don’t doubt the z scores but I would have thought that they would be compatible with much smaller estimates in the uncertainty of the inferred means.

  3. Dear Alexander,

    Good point. Most of the uncertainty relates to the ocean heating data and is the same sign and magnitude for both periods. The difference between the 0.67 Wm-2 and 0.43 Wm-2 is more relevant to the variability. So the changes are only a bit bigger than the uncertainty, you are correct. Sorry if any of this is garbled as I’m away on holiday at the moment.

    Best Wishes,

    Richard Allan

  4. An addition to Alexander Harvey’s comment: Using the error propagation formula for f=A-B, ie. σf^2= σA^2+ σB ^2 gives in this case that the increase in the imbalance value is

    f=0.28 ± 0.80 W/m2.

    (f=0.62-0.34=0.28; The uncertainty= (0.67^2+0.43^2)^0.5=0.80).

    Thus the mean value of the increase between the 1985–1999 period and the the 2000–2012 period is very much in the middle of the uncertainty interval.

    1. Sorrry, not well said, should be that the value zero for the increase is very much in the middle of the unceartainty ineterval.

    2. Dear Pehr,

      Thank you for making this point. I think you are right that the change in net imbalance may not be significant.

      However, as I mentioned, part of the uncertainty for each period relates to the ocean heating data to which the time series is anchored and so is of identical sign and magnitude for each period (±0.43 W/m2 at the 90% confidence level). In the paper I estimated an additional structural uncertainty for the earlier period 1985-1999 of ±0.24 W/m2 which I think is directly relevant to the change in the imbalance between the periods 1985-1999 and 2000-2012.

      If this is correct, and you may have a better method, the estimated change in net heating is of similar magnitude to the uncertainty, f=0.28 ± 0.24 W/m2, so I think you are both right that we should be cautious about the significance of the increase in net radiative heating but it suggests to me that it is unlikely Earth’s heating rate has diminished.

      Best Wishes,

      Richard Allan

      1. Dear Richard,

        Thanks for a prompt reply!

        I have no better method and I agree that there is definitely support for stating that it is unlikely that the imbalance has diminished. On the other hand I guess that it will take a long time before the last word about this imbalance has been said in the scientific literature.

        Best wishes,

        Pehr Björnbom

  5. The earth continues to gain energy, but this fact tells us very little about how much surface temperatures are going to warm in the next few decades. Climate policies are based on coupled climate models, not “AMIP” experiments with inputted observed sea surface temperatures. The fact that most of the warming is going into the oceans rather than the atmosphere implies that transient climate response is small. The oceans are such a huge heat sink that the tiny deep ocean temperature changes (0.02 C since 2004 in the 700 to 2000 m layer) will have insignificant affects on surface temperature over this century.

    I calculated the net flux from the CMIP5 multi-model mean from Climate Explorer as follows:
    1985 – 1999 0.70 W/m2
    2000 – 2012 0.97 W/m2

    The Allan et al 2014 analysis shows the average net flux for the period 1985 to 1999 was only 49% of the CMIP5 multi-model mean, and the net flux for the period 2000 to 2012 was only 64% of the CMIP5 multi-model mean. This implies that equilibrium climate sensitivity (ECS) is only 1.6 to 2.0 C (assuming an CMIPS ECS 0f 3.2). The middle value of 1.8 C for ECS translates to a transient climate response of only 1.2 C for double CO2, from Otto et al data. This would cause no problems, but great benefits for people.

    1. Hi Ken,

      Actually I agree with you: the magnitude of the net radiative imbalance (or Earth’s overall heating rate) does not tell us too much about current and future climate change on its own. There is also a large uncertainty on the size of the imbalance which we estimated in our journal article as:
      1985-1999: 0.34 ± 0.67 W/m2
      2000–2012: 0.62 ± 0.43 W/m2, [“±” is 90% confidence range]
      So your estimates above from the CMIP5 simulations are within the sizable uncertainty range of our observational estimates:

      It’s important to also note that almost all of this additional heat is absorbed by the oceans since they are by far the largest heat store in the climate system. It’s only the upper mixed layers that influence the surface and therefore atmospheric temperature, so how much of the heat that accumulates here is important. In some decades heat flux to deeper layers may become small due to fluctuations in ocean circulation leading to faster surface warming while in others, like the recent period, the heat flux to deeper levels can increase leading to slower surface warming.

      What I think may be more relevant for understanding current warming is the changes in the net imbalance. We find that this increases slightly between the two periods, +0.28 ± 0.24 W/m2 (the difference between the two uncertainty estimates above relates to the inhomogeneity in the time series). It’s interesting that your calculations show a similar increase in CMIP5 simulations over the period. This is probably partly explained by the eruption of Mt. Pinatubo in the earlier period but also the rising greenhouse gas concentrations (the simulations include all the main radiative forcings, natural and anthropogenic).

      We also looked at CMIP5 coupled simulations in our article (albeit a subset) and found a similar increase to you. However, there is also a large spread in the magnitude of the net radiative imbalance between different models and perhaps this is relevant to the realism of ocean heat uptake in the simulations which is an area of active work, e.g.:

      The net imbalance relates to the history of radiative forcing, ocean heat uptake and climate sensitivity. And even with a relatively low climate sensitivity, the projections under the current trajectory of emissions (RCP8.5) are still likely to produce a sizeable magnitude of warming compared to the 4 or 5 degrees Celsius global warming since the last glacial maximum 20,000 years ago and given the potentially large future human-caused increases in greenhouse gas concentrations (and given an increase of 2 degrees Celsius above pre-industrial is considered dangerous for some parts of the climate system):

      I think the climate explorer site you used is great. I couldn’t find an easy way of calculating the net imbalance (incoming solar:rsdt minus outgoing longwave:rlut minus outgoing shortwave:rsut) on the site for the two periods using the historical and rcp experiments but I guess you found a clever way:

      Anyway, thanks for your comments and I’ll have a think about your estimates of equilibrium and transient climate sensitivity.

      Best Wishes,

      Richard Allan

    2. Ken, Richard,

      If you look at TOA flux in the earliest decades (1861-1880) of the CMIP mean you’ll find it has a positive imbalance of about 0.3W/m2. As far as I’m aware it’s not considered likely that such a persistent imbalance existed at that time, so why are CMIP GCMs tending to show this? Drift may be a cause in some models. I’ve also seen an indication in one model write-up that the “top of the atmosphere” at which these fluxes are “sensed” are not strictly at the very top so a zero imbalance will report as a positive figure.

      Either way, within the logic of CMIP modelling it makes most sense, I think, to consider the true model predicted imbalance to be the one given minus the imbalance in the preindustrial control run. Using the Climate Explorer preindustrial control model mean I get an average imbalance of about +0.35W/m2, which would indicate a CMIP5 predicted imbalance of +0.35W/m2 over 1985-1999 and +0.62W/m2 over 2000-2012. Unsettlingly close 🙂

      1. Hi Paul,

        Thanks for your comment – good point!

        In the supplementary material attached to the paper by Otto et al. (2013) they estimate a net imbalance of about 0.1 W/m2 for the 1860-1879 period but even accounting for this I agree that your analysis seems to imply good agreement between the CMIP5 model mean net imbalance and our observational estimate.

        It would be useful to look at the spread in estimates of net imbalance from the models though. Even accounting for pre-industrial drifts I expect the range will still be quite large and probably mainly reflects differences in how efficiently the models uptake heat to the deeper ocean. I just found a nice analysis in a blog by Troy Masters on this.

        Best Wishes,


  6. @ken made the argument that with the bulk of heating (energy) going into to deep oceans, we are unlikely to see a profound negative impact on surface temperatures and, by extension, human habitation. I was curious of the authors’ and experts’ thoughts on this claim. Is the ocean that significant of a buffer to the impacts of warming, or will warmer oceans translate through various ecosystems and still produce ill effects?

    1. Hi MJ – good question.
      If Earth had no oceans it would rapidly (over a number of weeks) arrive at a new equilibrium temperature in response to a radiative forcing. The large capacity for water to take up heat mean that it takes many decades for the climate to fully respond to a radiative forcing. The oceans have always been up-taking heat and this rate of heat uptake is what determines the rate of climate change in response to rising concentrations of greenhouse gases. For more details see this post:

      Most of the excess heat from the radiative imbalance, primarily caused by emissions of greenhouse gases through human activity, initially accumulates in the upper mixed layers of the ocean which influence the surface temperature. It is a much slower process subducting heat (either through more heat going down or less heat diffusing upward) below the mixed layers and into the abyss. It turns out that natural fluctuations in the oceans (a kind of ocean weather, much slower than atmospheric weather) alters this heat flux from decade to decade. So in some decades more of the accumulating heat from rising greenhouse gases warms the mixed layer (adding to surface temperature rise) than usual and in other decades more of the heat penetrates to deeper layer and so warms the mixed layer less (suppressing the surface temperature increases. These year to year and decade to decade fluctuations, which vertically redistribute energy in the oceans, add lumps and bumps to the surface temperature record. So the bottom line is that while this natural variability can temporarily suppress the surface warming rate in some decades, in others it will compound it and lead to a surge in global surface temperatures. Only over many decades does the anthropogenic greenhouse gas induced warming rate become clear and this is determined by (i) how sensitive the climate is to a radiative forcing, (ii) how quickly the deep ocean uptakes heat and, most crucially, how rapidly atmospheric greenhouse gas concentrations are rising (or falling) in the atmosphere. These issues are thoroughly dealt with in the IPCC reports:

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