Summary for Policymakers

The Earth’s annual mean surface temperature can change, basically, from two different reasons: external and internal. External change is if the absorbed solar energy is increasing or decreasing; for example, the Sun’s radiation is changing, or the Earth’s albedo is changing (including any change in the cloud cover or in the surface shortwave reflectivity). Internal change is if more greenhouse gas in the atmosphere (water vapour, carbon dioxide, methane, etc.) absorb more thermal radiation emitted by the Earth’s surface and radiates also more back to the surface.

The magnitudes of these energy flows are generally well-known: the top-of-the-atmosphere (TOA) fluxes, both solar (shortwave) and terrestrial (longwave) are measured by satellite systems, the atmospheric and surface fluxes are partly observed, partly modelled and computed. Well-known graphical representations of the global mean energy budget are given in the IPCC Working Group I assessment reports; below is the latest (AR5, 2013):

The same group of scientists produced a similar diagram for the cloudless regions of the surface, the so-called clear-sky case (Wild et al. 2016). TOA and surface data come from independent observations:

Our results in this webpage can be explained with a recognition from the clear-sky diagram above. Let us calculate how much energy is absorbed by the Earth’s surface in the annual global clear-sky mean: 

As incoming solar radiation at TOA is 340 watts per square meter (W/m2), after atmospheric absorptions and all the reflections, 216 W/m2 is  absorbed by the surface. From 398 W/m2 surface thermal emission some part leaves the system through the ‘atmospheric window’, the others are being absorbed by the greenhouse gases. These gases re-emit this energy upward and downward; the thermal downward radiation that is reaching surface is, according to computation models and surface radiation measurement systems, 314 W/m2. All together the surface has 216 + 314 = 530 W/m2 energy income. The uncertainty of these data is about ± 4 W/m2.

These data can also be found in the data tables as presented by NASA CERES (Clouds and the Earth’s Radiant Energy System) science team on their webpage (EBAF stands for the Energy Balanced and Filled product). Below we give a table with detailed data for one climate year. Here Surface Net Shortwave stands for downward minus reflected solar radiation:

The surface energy income, according to these data, in annual mean, for clear-sky, is:

214.34 + 316.28 = 530.62 W/m2.

Now our recognition is the following. Let us compare this value to the clear-sky TOA outgoing longwave flux. In principle, they are independent. Downward solar radiation and solar reflection depend on atmospheric aerosol content and surface albedo; downward atmospheric thermal emission is thought to be depending on the greenhouse gas concentration. The more greenhouse gas in the air, the more downward radiation to the surface, the ruling theory says; anthropogenic global warming is thought to be enhancement of the greenhouse effect without any increase in the TOA fluxes. 

So we do not expect any peculiar connection to the outgoing thermal TOA flux. But still, let’s make the comparison: in the table below we give the clear-sky outgoing longwave radiation (OLR-clear) for the months of a climate year:

To our greatest surprise, the difference of 2OLR(clear) and the surface energy income is only 0.58 W/m2. What is this, a funny coincidence? Not too likely, mainly if we look at the difference. This value is said to be the energy imbalance of the system. Read what the CERES website (Data Quality Summary) has to say:

"Despite recent improvements in satellite instrument calibration and the algorithms used to determine SW and LW outgoing top-of-atmosphere (TOA) radiative fluxes, a sizeable imbalance persists in the average global net radiation at the TOA from CERES satellite observations. With the most recent CERES Edition3 Instrument calibration improvements, the SYN1deg_Edition3 net imbalance is ~3.4 W m-2, much larger than the expected observed ocean heating rate ~0.58 W m-2 (Loeb et al. 2012a).”

"In the current version, the global annual mean values are adjusted such that the July 2005–June 2010 mean net TOA flux is 0.58 ± 0.38 W/m2."  

That is, this 0.58 W/m2 is a result of adjustment. So we can write:

This means that the equality is EXACT!

Contrary to the expectations, the sum of solar absorbed flux and thermal absorbed flux at the surface seems to be regulated on a planetary level in the annual global mean, creating an unequivocal interconnection between the surface and the TOA fluxes - at least, in the clear-sky part of the atmosphere.

(Our additions in green.)


The situation becomes even more interesting if we examine the all-sky case (this is the name for the average meteorological conditions of cloudless and cloudy scenes). Here another quantity should be introduced: the difference of clear-sky and all-sky outgoing TOA thermal fluxes, 266 – 239 = 27 W/m2, which is the reduction in the thermal emission of the climate system in the presence of clouds. It is called longwave cloud radiative effect, LWCRE, termed also the greenhouse effect of clouds.

Using the all-sky data of Figure 2.11 of the IPCC (2013) diagram above, the surface energy income is:  

161 + 342 = 503 W/m2. 

It is balanced by radiative (398) and turbulent (84+20 latent plus sensible) heat flows. Now let us compare again this value to the TOA fluxes: 

503 = 2 × 239 + 25.

Is it possible that the difference to 2OLR, 25 W/m2, is LWCRE? It is, at least, within the error bar. But we have found a more recent graphical arrangement of the global fluxes, where the equality is exact. The diagram below is from a 2015 publication of Stephens and L’Ecuyer with the original figure legend, who made adjustments to the earlier mean values based on global hydrological cycle assessments. 

Let’s see:

Solar absorbed by surface = DSR – USW = 163 W/m2, downward longwave radiation, DLR = 344 W/m2. The surface energy income is 163 + 344 = 507 W/m2. (There is a +4 W/m2 difference to the IPCC 2013 value). OLR = 240 W/m2, therefore

507 = 2 × 240 + 27 W/m2.

As LWCRE is not indicated here, we can refer to an earlier study of the same authors, where the longwave cloud effect is given as 26.6 W/m2 (Stephens, Wild, Loeb, Kato, L'Ecuyer et al. 2012, Nature Geoscience).

Now what we have:

Surface energy income: 

507 W/m2 = 2 OLR + LWCRE + 0.4 W/m2. 

The difference is also there in the diagram, termed Net Absorbed (called imbalance in the IPCC diagrams). The equality is exact again, now in the all-sky mean!

This is really interesting. If these equalities are true, the accepted theory is in big trouble since the surface energy budget is unequivocally predetermined by the TOA fluxes, and only external forces can modify its magnitude:

(Our additions: green arrows, textbox, and mini-diagram with the LW cloud effect from Stephens et al. 2012)


We were looking for a possible theoretical analogy for the Energy(surface) = 2OLR situation, and found an evident example: it is described by textbooks as the ‘simplest greenhouse model’, a planet closed into a single-layer ‘glass shell’ atmosphere. The figure below is from Marshall and Plumb (2008), Chapter 2: The global energy balance, Section 2.3: The greenhouse effect.

It is assumed that the atmospheric layer is completely transparent to the incoming solar radiation and completely opaque to the terrestrial upward radiation. The layer radiates in all directions equally so that half goes up and half goes down. Because the half that goes up must be equal to the incoming solar flux, the total flux from the surface is equal to twice the outgoing radiation flux:

S = 2A,

that is,

E(SFC) = 2OLR.

Is it possible that the cloudless part of the Earth's real atmosphere mimics (follows) the maximum absorption model of a closed single-layer ‘glass shell’-atmosphere?

Is it possible that in the all-sky mean, the Earth real atmosphere mimics (follows) the maximum absorption model of a closed single-layer ‘glass shell’-atmosphere, with the difference of one cloud longwave effect?

According to the observations yes, it is not only possible but the equalities are exact and look like this:

E(SFC, clear) = 2OLR(clear)

E(SFC, all) = 2OLR(all)  + LWCRE


We projected some of our basic observations to a figure from the joint report of the UK Royal Society - US National Academy of Sciences (2014) [our additions in textboxes, and a 'shell' around the atmosphere]: 


The following scheme below is intended to represent the idea that, according to the data, the importance of the internal composition of the atmosphere seems to be fading away, and the role of the boundary conditions is strengthened in the determination of the surface energy budget:

We propose a possible conceptual framework in the Medium ('Fugue') page, discussed further in the Introduction section to the main site.


Since the greenhouse effect of clouds, LWCRE, appears to be an important quantity here, it can be anticipated that it will be a component of other flux elements in the system. And really, a thorough check of the observed fluxes reveals the following integer multiple pattern:

After analysing the non-observable flux elements as window radiation and atmospheric upward longwave emission, inserting their values from published computations, the all-sky table can be extended to all fluxes, and, in a separate table, the clear-sky fluxes also can be written in this way:


Let us project our theoretical values on the observed CERES data, published by Loeb et al. (2016, Clim Dyn, 46:3239–3257, DOI 10.1007/s00382-015-2766-z), blue in W m-2, underlined red in units as above (typical uncertainties as in the diagrams):

The same on Wild et al. (2015, Clim Dyn, 44:3393-3429, DOI 10.1007/s00382-014-2430-z) Table 3:


Here are also our values for clear-sky:


Cavity radiation, closed at the upper boundary as well,
the leak in the greenhouse gas greenhouse effect (atmospheric window)
is closed by the greenhouse effect of clouds (LW CRE).
Wave numbers are integral multiples of a unit flux.

The flux structure propagating within this 'closed box' (constrained between the TOA and surface boundaries) might be illustrated as 'waves', having wave-numbers as integer multiples of a unit value - like in this simple schematic animation (left border: surface, right border: TOA); B = 1 unit, C = 2 units, D = 3 units etc.:




The surface-TOA interconnection and the integer flux structure together give us a coherent new picture about the work of our climate system: we collected these results into a new energy budget diagram and poster.


Policy recommendations? Let's understand first what the data tell us. We do believe, with high confidence, that the system is much more constrained than previously thought.


A brief Summary can be find at the end of the Medium page:

The Medium page itself gives an overview of the data (Fugue):

An introduction with a possible conceptual framework:

History, Results, Discussion, the new diagram and poster on the main site:

The take away message (Marble Earth):