Radiant Energy Transfer Surface to Atmosphere
Written by Pierre R Latour PhD PE
This article gives radiator properties for net radiant energy flow from the cooler to the warmer
α1 εo < α0 ε1, to disprove the greenhouse gas theory. It explains why radiant energy flows two way. Flow from Earth’s surface absorbed by atmosphere exceeds that from atmosphere absorbed by surface.
Introduction of more atmospheric CO2 increases atmosphere’s emissivity and absorptivity and probably cools atmosphere and surface slightly.
The Global Warming from Green House Gas (CO2) Theory, GHGT, controversy has been raging
since 1990 [1, 2]. Proponents say radiant energy transfers from colder atmosphere with CO2 to
Earths warmer surface, warming it (Fig. 1). Critics say since heat flows from higher temperature
to lower, this must be wrong and the whole GHGT a hoax.
Many global warming experts claim radiant energy is transferred between two radiators at a
rate proportional to their temperature difference (to power 4); much like thermal and
convective heat transfer. There is confusion between electromagnetic energy intensity from a
radiator (all matter emits) and energy transfer rate between two radiators (all matter absorbs,
transmits and reflects).This paper explains why this is only true in special, unrealistic cases. This allows the controversy to be resolved. More complete models have been published [3,4]
Radiant energy, em, is emitted from matter with intensity according to the Stefan-Boltzmann
equation, Ii = σ εi T4 , where Ii = radiant exitance, radiant emittance, emission intensity, w/m2,
rate per m2 , a function of wavelength i, T = surface temperature, deg K/100, εi = emissivity of
radiator, a physical property of matter, function of wavelength i. 0 < εi < 1, and σ = StefanBoltzmann fundamental constant of nature, 5.67 w/m2/(K/100)4
Many experts simplify with emissivity εi = 1 for both radiators, since emissivity is difficult to
determine. This is the black body assumption. This is a source of controversy. Real matter has εi< 1.
By integrating over all wavelengths, i, we can find a weighted average emissivity ε = ∫ εi di/I and
corresponding average emission intensity I = ∫ Ii di/i = ∫ σ εi T4 di/i = σ ε T4. Therefore I, w/m2 =
5.67 ε T4 where ε is the average emissivity of the emitter and T is emitter temperature. This is the
generalized Stefan-Boltzmann Equation for all matter radiators.
Radiant energy is absorbed by matter with intensity that is the absorption fraction of incident
radiation from the emitter. Ji = αi I0 = αi σ ε0 T04, where Ji = absorption intensity, w/m2, rate per m2, a function of wavelength i, I0 = emitter intensity, w/m2 T0 = emitter surface temperature, deg K/100, αi = absorptivity of absorber, a physical property of matter, function of wavelength i. 0 < αi < 1 ε0 = average emissivity of emitter σ = Stefan-Boltzmann fundamental constant of nature, 5.67 w/m2/(K/100)4
The remaining incident radiation is transmitted through radiator, β, and reflected to surroundings,
γ, such that α + β + γ = 1. Like emissivity, absorptivity has a spectrum of exitance vs. wavelength unique to each atom and molecule. By integrating over all wavelengths, i, we can find a weighted average absorptivity α1 = ∫ αi di/I and average absorption intensity J = ∫ Ji di/i = ∫ σ αi ε0 T0
4 di/i = σ α1 ε0 T04. J1 = σ α1 ε0 T04 , where α is average absorptivity and J is average absorption intensity. This is the fraction of incident em from emitter 0 absorbed by absorber 1.
Energy Transfer Rate Law
The driving force for net radiant energy transfer is an intensity difference between radiators, like a temperature difference for conduction and convection. In the latter two there is a temperature gradient through matter, transmitting the molecular/atomic kinetic energy (indicated by temperature). In the former case there is an electromagnetic energy field everywhere throughout space, transmitting electromagnetic energy among radiators in all directions by an intensity difference, gradient, among them.
The radiant energy transfer from radiator 0 to radiator 1 is intensity emitted by 0 and absorbed
by 1. The energy transfer from radiator 1 to radiator 0 is the intensity emitted by 1 and
absorbed by 0. This two-way energy transfer occurs simultaneously because radiation exists at
many frequencies. The net energy transfer from 0 to 1 is the first less the second 
For simplicity we assume steady state from here. For unsteady state, just include energy accumulation rate, mCpdT/dt, in the energy balance, input – output for the describing differential equation of the body of interest temperature. Latour  gives a rigorous model of changing interacting energy flows to estimate radiator temperature changes.
This is the general equation for net radiant energy transfer between dissimilar radiators. The
first term is the intensity from radiator 0 times the fraction absorbed by radiator 1, α1, i.e. flow
from 0 to 1. The second is the intensity from radiator 1 times the fraction absorbed by 0, α0, i.e.
flow from 1 to 0.
Here we have radiant energy flowing from the colder radiator T14 = 4 to the hotter radiator T0
4 =6, because the colder has higher emissivity and lower absorptivity. (This does not prove GHGT
Fig. 1 that net energy flows down from cold atmosphere to warmer surface. Just that it is
theoretically possible with some physical property combinations.)
Unsteady state transients
Energy balance of plate 0: Rate of accumulation in 0 equals input – output, where m0 Cp0 dT0/dt = Q0 – Q0,1 Q0 = thermal energy input to 0 Q0,1 = radiant energy transfer from 0 to 1 when Q0,1 > 0. Otherwise rate is from 1 to 0. m0 = mass of plate, kg Cp0 = heat capacity of plate, joule/T – g – s
t = time, s.
Rate of energy accumulation in 1 equals input – output, where m1 Cp1 dT1/dt = Q1 + Q0,1,
and where Q1 = thermal energy input to 1.
This is a pair of coupled ordinary differential equations. With appropriate T0 and T1 initial
conditions and specified input functions, Q0(t) and Q1(t), these can be solved for transient
changes in T0(t) and T1(t).
These can be combined by addition, eliminating the em terms, m0 Cp0 dT0/dt + m1 Cp1 dT1/dt =
Q0 + Q1. At steady state both derivatives are 0, and Q0 = – Q1.
Input rate = output rate = constant, naturally. One side is heated, and one side is refrigerated.
Each rate equals +- Q0,1, which need not be 0. T1 need not equal T0 at steady state when each is
Net radiant energy flows from 0 to 1; surface to atmosphere.
If radiating atmospheric CO2 increases, both ε1 and α1 increase. To determine the change in
these properties quantitively is beyond the scope of this paper.
Assume CO2 increases from 400 to 800 ppmv and atmosphere properties increase 0.1% to:
ε1 = 0.083006 * 1.001 = 0.083089
α1 = 0.402980 * 1.001 = 0.40701
Q0,1 = 0.06612 * 1.001 * 2.88 4
– 0.007263 * 1.001 * 2.554
= 0.066186 * 68.7971 – 0.007270 * 42.2825
= 4.55341 – 0.307406 = 4.24600 > 0 and > 4.24155
Both atmospheric emissivity and absorptivity increased with CO2 doubling, but emissivity
dominates. Net energy transfer rate from surface to atmosphere increased with CO2, which
would cool the surface. Connecting all interacting variables shows the same thing 
From the law of radiant energy transfer we have proven it can flow from the colder to warmer
radiator, depending on emissivity and absorptivity properties of both radiators. And we have
derived the specific physical property conditions of radiators where this can happen: the colder
radiator has higher emissivity and lower absorptivity than the hotter radiator.
When T0 > T1 and α1 εo < α0 ε1, radiant energy flows from 1 to 0, provided Q0,1 = α1 ε0 T0 4- α0 ε1T14 < 0
Using realistic average physical properties for Earth’s surface and atmosphere, we find energy
transfers from surface to atmosphere at a higher rate than the reverse with increasing CO2. This
indicates net global cooling by radiant energy transfer from increasing atmospheric CO2. This
contradicts the Green House Gas Theory.
1. Latour, P. R., “Undeniable and Unfalsifiable”, January 2014. https://principiascientific.org/undeniable-unfalsifiable.html/
2. Latour, P. E., “Physics Proves Cooling”, December 2014. https://principiascientific.org/physics-proves-radiating-gases-decrease-global-temperature.html/
3. Latour, P. R., “ChE Models Earth’s Temperature Response to Fuel Combustion”, July
4. Latour, P. R., “Radiation Physics Laws Give the Effect of CO2 on Earth’s Temperatures –
A Primer”, Principia Scientific International, February 2017. http://principiascientific.org/radiation-physics-laws-give-effect-co2-earths-temperatures-primer/
5. Latour, P. R., “Simultaneous Conduction and Radiation Energy Transfer”, March 2017.
Editor’s note: readers should be aware that our software does not reproduce super and subscripts correctly – the original PDF is here Radiant Energy Transfer Nov19 (2)
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