A CERES of fortunate events…

The CERES estimates of the top-of-atmosphere radiative fluxes are available from 2001 to the present. That is long enough to see that there has been a noticeable trend in the Earth’s Energy Imbalance (EEI), mostly driven by a reduction in the solar radiation reflected by the planet, while the outgoing long wave radiation does not appear to contribute much. But what can be causing this?

A paper last year (Goode et al., 2021) also reported on a two decade estimate of Earthshine measurements which appear to confirm a small decrease in albedo (and decrease in reflected short wave (SW) radiation). While the two measurements are subtly different due to the distinct geometries, they do show sufficient coherence to give us some confidence that they are real.

Comparison of CERES SWup trends (blue) with inferred changes in Earthshine (black).

Similarly, Loeb et al. (2021) show that the trends in the EEI derived from CERES match what you get from the changes in ocean heat content.

Satellite-derived trends in EEI compared to estimates from changes in ocean heat (Loeb et al., 2021).

A few people have started to interpret the dominance of the SW trends to imply that the overall trends in climate are not (despite copious evidence) being driven by the rise in greenhouse gases (for instance, the rather poorly argued and seemingly un-copyedited Dübal and Vahrenholt (2021)) but these simplistic interpretations are seriously confused.

We can explore the issues and pitfalls of this using the ‘simple model’ of the greenhouse effect we explored back in 2007. At that time, we said:

You should think of these kinds of exercises as simple flim-flam detectors – if someone tries to convince you that they can do a simple calculation and prove everyone else wrong, think about what the same calculation would be in this more straightforward system and see whether the idea holds up. If it does, it might work in the real world (no guarantee though) – but if it doesn’t, then it’s most probably garbage.

A simple model with feedbacks

The simplest model for the greenhouse effect. Two layers, albedo, and one LW absorber.

It’s unlikely(?) that you remember that post, but the simple model has an albedo and an atmospheric absorption that together control the surface temperature. We discussed radiative forcings and the possibility of feedbacks that change the albedo (a SW feedback) or the absorption (a LW feedback). The point was that since this is the simplest possible model of the greenhouse effect, you can use it to test some basic things – like the notion of radiative forcing, or the difference between climatological fluxes and climate sensitivity. We can also use it to explore the possible explanations for the CERES trends (assuming for the sake of argument that they are robust, though there may still be some residual uncertainty in the retrievals and there is also an impact from the specific history of El Niño/La Niña).

Over the two decades of these changes, there is no apparent correlation to solar activity or galactic cosmic rays, so the source of the trends are most likely internal, so let’s see if the results are possibly consistent with feedbacks to the main sources of climate trends in recent decades – the rise in greenhouse gases and the recent decline (regionally) in atmospheric aerosols.

The observed downward trend in albedo (an increase in absorbed shortwave radiation by around 0.5 W/m2) is dominated by clouds – less or thinner clouds than previously, possibly aided and abetted by decreases in reflective aerosols. You will however recall clouds have impacts on the LW absorption too, so changes in clouds (depending on where they are) will likely have both SW and LW effects.

So let’s set up a case where, in the simple model, the albedo responds to temperature, but so do the LW absorbers (water vapour and clouds). To make things easier for the math, let’s actually make them linear in G\equiv \sigma T^4_{surf} (just to avoid all the quartic roots etc.). The basic equations are:

Surface:  (1-a) S_0/4 + \lambda A = G
Atmosphere: \lambda G = 2 \lambda A
Planet:  (1-a) S_0/4 = \lambda A + (1-\lambda) G

which just reflect the energy conservation at each level, with S_0 is the solar input, a is the albedo and \lambda is the LW absorption. The solution for the surface flux is just G=0.25 (1-a) S_0/(1-0.5\lambda). For quasi-realistic values of surface temp (15ºC), albedo (29%) and solar irradiance (1360 W/m2), we get that G=391, \lambda=0.767.

To build in the GHG and aerosol forcings ,and feedbacks on temperature we can define:

SW forcing + SW feedback: a = a_0 + \Delta a + a' (\Delta G/G_0)
LW forcing + feedback: \lambda =  2 F_{toa}/G_0 + \lambda_0 + \lambda' (\Delta G/G_0)

where F_{toa} is the LW radiative forcing imposed by the increase in GHGs, \Delta a is the change in albedo from aerosols, and \Delta G is the (small) change in the upward LW radiation (consistent with the increase in surface temperature) from the basic state (denoted by the G_0 subscript). The total radiative forcing is F_{toa}- 0.25 \Delta a S_0.

With these definitions, we can simply write down the change in the reflected SW and outward LW in this model.

Change in reflected SW:  = (a' \Delta G/G_0 + \Delta a) S_0/4
Change in outwards LW:  \approx - F_{toa} (1 + \Delta G/G_0) + \Delta G (1 - 0.5 \lambda_0 - 0.5 \lambda')

You should be able to see the effect of the LW forcing acting on the total temperature, the SW forcing acting on the reflected SW, and then the change in upward fluxes acted on by the existing greenhouse effect and then the feedbacks in both SW and LW. We can therefore use the observed changes to try to identify the net SW and LW feedbacks.

Over the last 20 years the LW radiative forcing change from well-mixed greenhouse gases is around 0.7 W/m2, while the warming from 2000 to 2020 is just a bit less than 0.5ºC, equivalent to a change in G of about 2.7 W/m2. The change in reflected SW is negative, but we don’t have a great estimate of how much of that is due to aerosols and how much to clouds (or surface changes), so the observations instead define a relationship between the coefficient a' and \Delta a as \Delta a + 2.7/391 a' = - 0.5*4*/1360 = -0.0015 (totaling to a net change of albedo of -0.15%). If we assume there is no change in outward LW we can calculate \lambda' = 0.711. This leads to a change in absorption of [tex]\lambda’ \Delta G/G_0 = 0.005[\tex], e.g. from 0.767 to 0.772. Thus despite the increased GHG forcing (which decreases the outgoing LW), the increase in the surface upward flux modified by the LW feedbacks, can be enough to effectively cancel out the net change in LW.

Given the simplicity of this model – notably a single atmospheric layer, no regional effects, no internal variability – and the uncertainty in the aerosol effect, we can’t really translate these numbers into precise feedbacks (for instance, if there is no aerosol effect, we’d get a 1 W/m2/ºC positive shortwave feedback and 1.3 W/m2/ºC net longwave effect, both of which are pretty large, while if the aerosols were 50% of the SW effect, it would be a more reasonable ~0.5 W/m2/ºC positive SW feedback). But qualitatively, it demonstrates how impacts to the long-wave radiation combined with cloud feedbacks can lead to big shifts in SW and almost no shift in LW at the top of the atmosphere. That conclusion stands in stark contrast to what you’d conclude if you don’t consider feedbacks at all in the analyses.

Where do we go from here?

The ability to analyse trends from the Earth’s radiation data is new, and opens up many avenues for further research. Some analyses are already appearing (for instance, Raghuraman et al (2021) and Quaas et al (2022)), and in the next few months, a group of climate modelers will be putting together a proposal for more targeted simulations (varying aerosols, models, and other forcings) that will allow for a more detailed comparison of models to the observations and help in the attribution of what’s causing them (there is an abstract at Fall AGU for instance).

Shiv Priyam Ragahuraman gave a recent webinar on the results from his paper which is worth watching:

Unfortunately, there are also some changes happening to the observation side. The satellites that CERES instruments are on, the NASA Aqua and Terra platforms, are now starting to drift in their orbits, and it’s not clear how (or if) they will contribute to the long-term records going forward. Fortunately, there are additional CERES instruments on Suomi-NPP (launched in 2011) and NOAA-20 (launched in 2017) that can be used.

It’s nonetheless clear to me that maintaining the continuity of this data product will be of major importance in constraining the feedbacks to climate change, and the longer the time-series available, the better.


  1. P.R. Goode, E. Pallé, A. Shoumko, S. Shoumko, P. Montañes‐Rodriguez, and S.E. Koonin, “Earth’s Albedo 1998–2017 as Measured From Earthshine”, Geophysical Research Letters, vol. 48, 2021.

  2. N.G. Loeb, G.C. Johnson, T.J. Thorsen, J.M. Lyman, F.G. Rose, and S. Kato, “Satellite and Ocean Data Reveal Marked Increase in Earth’s Heating Rate”, Geophysical Research Letters, vol. 48, 2021.

  3. H. Dübal, and F. Vahrenholt, “Radiative Energy Flux Variation from 2001–2020”, Atmosphere, vol. 12, pp. 1297, 2021.

  4. S.P. Raghuraman, D. Paynter, and V. Ramaswamy, “Anthropogenic forcing and response yield observed positive trend in Earth’s energy imbalance”, Nature Communications, vol. 12, 2021.

  5. J. Quaas, H. Jia, C. Smith, A.L. Albright, W. Aas, N. Bellouin, O. Boucher, M. Doutriaux-Boucher, P.M. Forster, D. Grosvenor, S. Jenkins, Z. Klimont, N.G. Loeb, X. Ma, V. Naik, F. Paulot, P. Stier, M. Wild, G. Myhre, and M. Schulz, “Robust evidence for reversal in the aerosol effective climate forcing trend”, 2022.

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