 |
Earth's
Energy Flows by Miklos Zagoni Eotvos Lorand University Budapest, Hungary miklos.zagoni@earthenergyflows.com |
 |
|
I. INTRODUCTION
On this page, I will demonstrate that the Earth's annual global mean energy flow system adheres to the simplest greenhouse geometry as described, for example, in Dr. Kevin E. Trenberth's recent book, "The Changing Flow of Energy Through the Climate System" (Cambridge University Press, 2022). • I
will demonstrate that the fundamental equations given
by Dr. Trenberth to describe his model are direct consequences of Karl
Schwarzschild's (1906) two-stream radiative transfer equation.
• I
will point out that the geometric model represents the simplest
arithmetic ratios of 1 :
2 : 3 : 4, or their extended version, 1 : 2 : 3 : 4 : 6 : 8. I
will prove on published datasets that the Earth's global mean
clear-sky energy flow system accurately satisfies these ratios.
• I will demonstrate that this
clear-sky integer system can be extended to the all-sky system in a
single step. By using the difference between clear-sky and all-sky
outgoing longwave radiation—referred to as the longwave cloud radiative
effect (LWCRE) at the top of the atmosphere (TOA)—as one unit, the
all-sky energy flow system also reveals a simple integer ratio
structure, with small integers as multiples of LWCRE. This system
satisfies the corresponding radiative transfer constraint equations for
both clear-sky and all-sky conditions.
I will prove that the first of these fundamental equations is a direct one-step consequence of Schwarzschild's original (1906) equation. This equation has been consistently reproduced in standard university textbooks on atmospheric physics and radiation—from Goody (1964, Oxford) to Houghton (2002, Cambridge) and Ambaum (2021, RMetSoc)—but is notably absent from climate change literature, including studies and assessments from Manabe-Strickler (1964) to the IPCC reports (1990–2021). • I will demonstrate that the
all-sky and clear-sky global mean integer energy flow systems are
accurately reflected in reliable energy budgets, including over 30
years of GEWEX datasets, 24 years of NASA CERES satellite observations,
and two decades of CMIP climate models cited in IPCC reports.
• An unexpected discovery is that solar reflections—both clear-sky and all-sky—precisely occupy integer positions within the global mean energy flow system. This allows the Total Solar Irradiance (TSI) to have a defined integer position as the foundation of this unified system. • The aim of the work is to present these recognized relationships among the observed data, and offer the corresponding theoretical equations. I do not want to go into speculations on how the channels of human influence on the climate system should be reconsidered in light of these recognitions. The historical development of these observations followed a reverse order. I first identified integer ratio systems in published global energy budgets (e.g., Stevens and Schwarz, 2012; Stephens et al., 2012; Wild et al., 2013; Loeb, 2014). I then located the corresponding equations in the history of radiative transfer (e.g., Schwarzschild, 1906) and validated the system using recent data from GEWEX (2023), NASA CERES (2024), and CMIP6 (2024). Encountering Dr. Trenberth's greenhouse geometry in his recent book was a significant and confirming moment. II. PRESENTATIONS Trenberth's Greenhouse Geometry I.: The
Physical Science Basis (video, 1:16:09)
Trenberth's Greenhouse Geometry II,: Implications (video, 1:11:21) Trenberth's Greenhouse Geometry and its Representation on the Earth's Atmosphere (AMS 2025 Annual Meeting Poster) A Constraint on Convection (AMS 2025 Annual Meeting Poster) Modeling and Observing Global Energy and Water Cycles by GEWEX (AGU 2024 Fall Meeting iPoster) What's Next for Science: Theoretical Understanding of Atmospheric Convection on Global Scales (AGU 2024 Fall Meeting iPoster) Trenberth's (2022) Greenhouse Geometry (EGU 2024 General Assembly talk) Patterns in the CERES Global Mean Data (NASA CERES Science Team Meeting talk, 2017 NASA GSFC) Observing and Modeling Earth's Energy Flows, Ten Years Later (Earth Radiation Budget Workshop / NASA CERES/Libera Science Team Meeting talk, Max Planck Institute, Hamburg, Germany, 2022) III. HISTORY
My first encounter with the integer system: Stephens et al. (2012, Nature Geosci.) (video, 4 min) * * * The second, next year: Wild et al. (2013, Clim.Dyn., IPCC AR5) (video, 3 min) * * * The third, next year: Loeb (2014, NASA CERES) (video, 1 min) IV. THEORY, PART I. TRENBERTH'S GREENHOUSE GEOMETRY (video, 18:32) V. THEORY, PART II. EQUATIONS (video, 20 min) VI. THEORY, PART III. GEOMETRIC DEDUCTION (video, 9 min) For more of the theory, see the full video: Trenberth's Greenhouse Geometry, The Physical Science Basis VII. TAKE AWAY / BOTTOM LINE Stephens et al. (2023, GEWEX, BAMS), Wild et al. (2024 Nature Comm.,), CERES (2024) (video, 2 min 20 sec) * * * A note on Total Solar Irradiance (as the basis of the unit flux): PLAIN LANGUAGE SUMMARY The
"plate-state" of Dr Trenberth's greenhouse geometry is not a mere
analogy. According to observed data, the Earth's atmosphere follows
precisely the requirements of this simple model. The "greenhouse"
concept is better than previously thought: the atmosphere acts like
a pane-of-glass: probably on the radiative background defined by CO2,
the unlimited amount of greenhouse
gas (water vapor) condensed in the ocean, via the evaporation —
cloud-formation — precipitation process, is able to generate and maintain
the transparency/opacity ratio prescribed by radiative
transfer principles. The resulted global mean energy flow system
serves as a theoretical stationary geometric equilibrium state against
which temporal vibrations or permanent (systematic) deviations may be
considered. The mechanisms of possible anthropogenic perturbations on this quantal structure should be carefully re-examined.
* * *
 |