We show that the annual global mean energy flow data, measured by the CERES instruments onboard Aqua and Terra satellites for the time period 2000 - 2015, published in the CERES EBAF surface Data Quality Summary Edition 2.8 (March 27, 2015) have a very peculiar feature. 


Absorbed energy at the surface = Downward solar minus reflected solar plus absorbed longwave (emitted downward by atmospheric greenhouse gases and the clouds).

Main values are from Table 4-1, the uncertainty ranges (plus/minus one standard deviation) from Table 4-2 of CERES EBAF surface DQS Ed2.8; all in watts per square meter (W/m2).

Clear-sky (cloudless region):

Surface SW down = 243.9 (+/-5)

Surface SW up = 29.7 (+/-3)

Surface LW down = 316.0 (+/-7)

Surface energy absorbed = SW down - SW up + LW down = 243.9 - 29.7 + 316.0 = 530.2 W/m2.

TOA outgoing LW (Outgoing Longwave Radiation, OLR) = 265.8 W/m2.

Let us observe:

530.2 = 2 x 265.8 (– 1.4)

E(SRF, clear) = 2OLR(clear)  (-1.4 W/m2)


All-sky (average clear + cloudy atmospheric conditions):

Surface SW down = 186.4 (+/-5)

Surface SW up = 24.1 (+/-3)

Surface LW down = 345.1 (+/-7)

Surface energy absorbed = 186.4 - 24.1 + 345.1 = 507.4 W/m2.

TOA outgoing LW = 239.6 W/m2.


507.4 = 2 x 239.6 + 28.2.

Long Wave Cloud Radiative Effect, LWCRE (known also as The greenhouse effect of clouds):

LWCRE = 265.8 - 239.6 = 26.2.

E(SRF, all) = 2OLR(all) + LWCRE  (+2.0 W/m2)


The simplest greenhouse model for a planet with a single-layer SW transparent, LW-opaque, non-turbulent atmosphere (the so-called "glass-shell" geometry: no other energy exchange between the planet's surface and the atmosphere than radiation):

Example in the textbook of Marshall-Plumb (2008), Chapter 2: The global energy balance, Section 2.3: The greenhouse effect,  Fig. 2-7 and Eq. 2-8 below:

 E(SRF) = 2OLR


It can be seen also in the latest published energy budget study of Stephens and L'Ecuyer 2015:


SW absorbed = 185 - 22 = 163 W/m2

LW absorbed = 344 W/m2

OLR = 240 W/m2

LWCRE = 26.6 W/m2 (see Stephens, L'Ecuyer et al. 2012 Nat Geosci, see below)

163 + 344 = 507 = 2 x 240 + 26.6 + 0.4

E(SRF, all) = 2OLR + LWCRE (+IMB)


It shows that the surface energy balance is constrained to TOA, contrary to the differences:

The Earth's semi-transparent SW, quasi-opaque LW, turbulent atmosphere mimics the glass shell geometry with the help of the greenhouse effect of clouds (LWCRE).

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

E(SRF, all) = 2OLR(clear) - LWCRE = 2OLR(all) + LWCRE


Schematic view representing the concept of a
partially LW-transparent ('leaky') atmosphere:


Schematic view representing the concept of the
role of LWCRE in the 'closed-shell' geometry:



ATMOSPHERIC version of the same relationship can be recognized in the updated energy balance diagram of Stephens, L'Ecuyer, Loeb, Kato, Wild et al. 2012, Nat Geosci (our additions are: green arrow and textboxes):



The same can be observed also in the NASA Langley Research Center's Global Energy Budget poster, 2014 June (our additions: yellow and red arrows and white text boxes):

ASR: Absorbed Solar Radiation; OLR: Outgoing Longwave Radiation; CTS: Cooling-To-Space (Atmospheric upward LW emission); 
DLR: (Downward Longwave Radiation by atmosphere and clouds, termed also back-radiation)

The atmospheric energy budget is constrained to the energy flows at TOA:


But this is not the case in the Martian thin, but full-CO2 atmosphere:



1. An LWCRE-modulated INTEGER structure in the fluxes:

To get a better understanding of the LWCRE-modulated integer flux structure, solve the Climate Sudoku:

Hint: ASR = 9 = 240 W/m2. Calculate the surface and atmospheric energy balance! 

(LWCRE = 1 = 26.6 W/m2)

Surface: SW abs + LW abs = LW out + Turbulent

Atmosphere: SW abs + LW abs + Turbulent = LW emitted up + LW emitted down




2. The total cloud cover is constrained to planetary emissivity:

The cloud-covered part of the surface radiates the amount of OLR(all),

the total single-layer IR-opaque cloud area fraction is unequivocally connected to the planetary emissivity (all-sky transfer function):

beta = f(all)


3. A symmetrical and constrained albedo at 

albedo = 1 - sin 45 = 1 - √2/2 = 0.293


4. The normalized greenhouse factor is stable at g(all) = 2/5.

The greenhouse effect is defined as the difference of the two boundary LW radiations: G = surface upward longwave emission minus TOA outgoing LW radiation, G = ULW - OLR, and the normalized greenhouse factor is g(all) = G(all) / ULW. With OLR(all) = 239.4 W/m2 and ULW = 399 W/m2, we have g(all) = 2/5 = 0.4. This value is pre-determined by the pattern, and cannot change (except tiny fluctuations, 'vibrations' - with unknown size and time-scale). There is no enhanced (elevated, increased) greenhouse effect from change in the atmospheric trace-gas composition.

How this stability is achieved and maintained? 

Adding CO2 -> Increased atmospheric LW absorption -> Immediate (instantaneous? 10 days [one hydrological cycle]? seasonal? annual?) radiative constraint from the E(SRF, clear) = 2OLR(clear) and E(SRF, all) = 2OLR(all) + LWCRE geometric relationships -> Reserved greenhouse factors.

The temperature loop is missing from the feedback chain.


Energy budget poster:

(open in new tab to enlarge):


But if the energy budget is constrained, why is there global warming?

Because recently all of the parameters are slighly above their equilibrium position.

Planetary emissivity is 0.6005, cloud area fraction is about 0.605, and albedo is 0.293,

insetad of ep = beta = 0.6 and albedo = 1 - sin45 = 0.29289.

The system must slowly warm to reach the required equilibrium.

Continue in the Medium section, or in the main site: Foreword, Abstract, Introduction.