Earth's Energy Flows


by Miklos Zagoni


miklos.zagoni@earthenergyflows.com



Are you familiar with this energy balance diagram?

(Stephens et al.2012)

 

Let's focus on the longwave part:



 

Clear-sky emission to space (266.4) and all-sky outgoing longwave radiation (239.7) differ, by definition, by one longwave cloud radiative effect, LWCRE (26.7, each in Wm-2).  But the fact that their absolute value is an integer multiple of LWCRE, with a difference of 0.6 Wm-2, which is the TOA imbalance, is a surprise!


Also for the upward and the downward emissions at the surface, with a difference of 1.5 Wm-2 !


And that the surface emission itself can be expressed as an integer multiple of LWCRE, which is the greatest surprise! Surface longwave upward emission, as a definite multiple integer of the TOA LW cloud effect? That sounds crazy, or at least implausible—but history taught science is not about plausibility but validity, and this, at least on this diagram, seems valid!



Taking the values from the diagram: If LWCRE = 1 unit (shown in red bold typeface) = 26.7 Wm-2, then OLR(all-sky = 9 units, OLR(clear-sky) = 10 units (difference = 0.6 Wm-2; same as the TOA imbalance), DLR(clear-sky) = 12 units, and DLR(all-sky) = 13 units (difference is 1.5 Wm-2), and surface upward emission is 1 units, with a difference of only 2.5 Wm-2, contrary to the far larger uncertainties noted on the diagram.


Really interesting!


Next year, the IPCC (2013) report showed the following diagram; let's first deal with the shortwave irradiances:



Using the same unit flux of 1 = LWCRE = 26.7 Wm-2, incoming solar radiation is 51 units (= 1361.7 Wm-2) on the intercepting cross-section disk to incoming solar radiation (that is, before division by four for spherical weighting, see Fig. 2.2 from Hartmann: Global Physical Climatology, 1994)





and 51/4 units = 340.4 Wm-2 on the sphere. From this, 15/4 units = 100.1 Wm-2 is reflected and 36/4 units = 240.3 Wm-2 is emitted as outgoing longwave radiation. Furter, 3 units = 80.1 Wm-2 is absorbed in the atmosphere and 6 units = 160.2 Wm-2 is absorbed in the surface. These shortwave integer positions are extremely close, within 1 Wm-2 to the shown values given by the IPCC AR5 (2013) report (based on Wild et al. 2013).



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Next year, Norman Loeb published this estimate, based on more than a decade of CERES data:



Here the novelty is that with this very slightly refined unit flux of 26.67 Wm-2, at the TOA each of the difference is zero! Atmospheric longwave cooling differs only by 0.3 Wm-2, and that all the components are within their noted range of uncertainty, even the components of the convective flux, separately.


Below I show a recent publication (Wild 2020, Clim Dyn) comparing clear-sky and all-sky data from four different sources: CMIP6 model mean (in red), CMIP5 model mean (pink), Martin Wild's own estimate, and Seiji Kato's CERES data from a previous data product (EBAF Edition 4.0, 2018).


 

Clear-sky: Incoming solar: 340; reflected solar: 53, outgoing longwave: 267; solar absorbed atmosphere: 73, solar down surface: 247, solar absorbed surface: 214, thermal up surface: 398, thermal down surface: 314-318.

 

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All-sky: Incoming solar: 340; reflected solar: 100, outgoing longwave: 239; solar absorbed atmosphere: 80, solar down surface: 187, solar absorbed surface: 160, thermal up surface: 398, thermal down surface: 344

 

***

 

I will show that these energy flow components in the annual global mean clear-sky and all-sky diagrams may be derived from simple geometric considerations, without referring to the atmospheric gaseous composition or reflective properties.

 

The starting point of the deduction is the simplest greenhouse model, consisting og a surface and a solar-transparent, infrared-opaque atmospheric layer — as for example is shown in Hartmann (1994), Global Physical Climatology, Fig. 2.3:

 



 

 

PART TWO

 

GEOMETRIC DEDUCTION

 

Further details:

Zagoni, M.: Trenberth’s (2022) Greenhouse Geometry, EGU General Assembly 2024, Vienna, Austria, 14–19 Apr 2024, EGU24-7

https://doi.org/10.5194/egusphere-egu24-7

 

Supplementary Material (video) (2:20:35):

https://www.earthenergyflows.com/Zagoni-EGU2024-Trenberths-Greenhouse-Geometry_Full-v03-480.mp4