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By Philip Mulholland and Stephen Wilde

A fundamental concept at the heart of climate science is the contention that the solar energy that the disk of the Earth intercepts from the Sun’s irradiance must be diluted by a factor of 4.  This is because the surface area of a globe is 4 times the interception area of the disk silhouette (Wilde and Mulholland, 2020a).

This geometric relationship of divide by 4 for the insolation energy creates the absurd paradox that the Sun shines directly onto the surface of the Earth at night. The correct assertion is that the solar energy power intensity is collected over the full surface area of a lit hemisphere (divide by 2) and that it is the thermal radiant exhaust flux that leaves from the full surface area of the globe (divide by 4).

In between these two geometric relationships of energy collection and departure back to space lies the Atmospheric Reservoir, the Earth’s gaseous coating within which all climate processes occur. The following table and figure adapted from the canonical model of Kiehl and Trenberth (1997) are used to illustrate a model in which the fundamental realities of a lit (day) and unlit (night) hemisphere are retained as the irreducible logical minimum geometric relationship for the energy budget of the Earth’s climate.

Table 1: The Atmospheric Reservoir Energy Recycling Process for a single Lit Hemisphere Model.

In the following figure the parameters have been adjusted by using hemisphere dependent thermal exhaust flux values of 200 W/m2 (day) and 270 W/m2 (night) based on a Dynamic Atmosphere Energy Transport model of the Earth’s Climate (Wilde and Mulholland, 2020b).

Figure 1: The Atmospheric Reservoir Energy Recycling Process.

Key Features of the Diagram

  1. It demonstrates that the concept of the Atmospheric Reservoir can be made to work for a Lit Hemisphere (Divide by 2) Solar Irradiance.
  2. It shows how the Atmospheric Reservoir behaves as both a store and a transporter of energy.
  3. All captured fluxes are doubled by the process of infinite geometric recycling (the half lost; half retained process by which an infinite series of halves of halves sums to one).
  4. In the daytime the Troposphere expands as it stores potential energy with work done against gravity.
  5. Potential energy cannot be radiated away so the daytime loss at the Top of the Atmosphere (TOA) is reduced as the atmosphere expands.
  6. During the night the Troposphere contracts as it cools, this converts potential energy back into kinetic energy which accounts for the enhanced night-time loss of energy to space.
  7. The atmospheric reservoir gross value of 780 W/m2 is halved to the 390 W/m2 canonical value because the surface area of the emitting globe is twice that of the solar collection hemisphere.
  8. The daytime processes of thermals and evapo-transpiration are driven primarily by direct solar energy and so do not occur at night (lots of caveats here: if the surface is moist then the evaporation process can also occur at night e.g. land versus sea, moist tropical forest versus dry desert, weather systems advection etc).
  9. The Earth’s surface is a huge slow release storage radiator that emits its captured solar energy at night and in the winter.
  10. The bypass radiation occurs both during the day and at night at the same rate (40 W/m2) as in the canonical model because of the same surface area issue of collection versus emission as listed in point 7.

The Lungs of Gaia

One could liken the process of the daytime capture of solar energy that causes the atmosphere to expand, followed by the night-time contraction of the atmosphere as it cools – to the Earth ‘breathing’. The atmosphere being the lungs of our planet which expand and contract over the course of a 24-hour cycle, and in doing so varies the supply of potential energy back to the surface. This rhythmic process acts to maintain hydrostatic equilibrium for the atmosphere as a whole by matching thermal radiant energy out to space with high frequency radiant energy coming in from the sun.

References

Kiehl, J.T and K.E. Trenberth, 1997. Earth’s Annual Global Mean Energy BudgetBulletin of the American Meteorological Society, Vol. 78 (2), 197-208

Wilde, S.P.R. and Mulholland, P., 2020a. An Analysis of the Earth’s Energy Budget. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 54-64. doi: 10.11648/j.ijaos.20200402.12

https://www.researchgate.net/publication/344539740_An_Analysis_of_the_Earth’s_Energy_Budget

Wilde, S.P.R. and Mulholland, P., 2020b. Return to Earth: A New Mathematical Model of the Earth’s Climate. International Journal of Atmospheric and Oceanic Sciences. Vol. 4, No. 2, 2020, pp. 36-53. doi: 10.11648/j.ijaos.20200402.11

https://www.researchgate.net/publication/342109625_Return_to_Earth_A_New_Mathematical_Model_of_the_Earth’s_Climate

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