Paris Climate Agreement Beacon of Hope

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The Stefan-Boltzmann equation relates the temperature of an object to the rate at
which it is able to disperse energy:

PowerT=s

4

(1.3)

Power is used in Eq. 1.3 since Power is defined as Energy/Time, and the Stefan-
Boltzmann equation is based on the rate at which energy is dispersed; σ is the same
constant used in Eq. 1.1. In equilibrium, Earth’s surface releases (or radiates) energy
at the same rate it is supplied to the surface by the atmosphere. Hence Power in
Eq. 1.3 can be replaced with RF, where RF represents the atmospheric radiative
forcing of climate:

RF=sT

4

(1.4)

Those who have taken calculus will understand that upon taking the derivative of
Eq. 1.4 and re-arranging terms, it can be shown that:

D

s

T D

T

= RF

1

(^43)

(1.5)

where ΔRF represents a perturbation to the system (i.e., the rise in RF of climate
due to human release of GHGs) and ΔT represents the response (i.e., resulting rise
in global mean surface temperature).
Scientists use relations such as Eq. 1.5 to diagnose the output of climate models.

A common value for the term

1

4 sT^3

in Eq. 1.5 is 0.31 K/(W m−2), which is related

to the temperature at which Earth radiates to space (Bony et al. 2006 ). Substituting

this numerical value for

1

4 sT^3

into Eq. 1.5 leads to:

DDTR= 031. - 2 F

K

Wm

(1.6)

We now examine the quantitative consistency between the rise in temperature
(ΔT in Fig. 1.3) over the Anthropocene and the radiative forcing of climate attrib-
uted to humans (ΔRF in Fig. 1.3). The product 03 ./ 12 KWmW--^22 ́. 3 m is equal
to 0.7 K (which is the same as 0.7 °C),^9 quite close to the observed rise in GMST
(about 0.9 °C) over the course of the Anthropocene. As examined in detail in
Chap. 2 , the actual relationship between ΔT and ΔRF requires a consideration of
factors such as climate feedback (i.e., enhancement or diminution of the RF of cli-
mate imposed by humans due to changes in factors such as atmospheric humidity
and clouds) as well as the transport of heat from the atmosphere to the world’s
oceans, which specialists refer to as ocean heat export. It is likely, for instance, that
positive feedback (enhancement) of the direct RF of climate caused by humans is

(^9) Degrees Celsius and degrees Kelvin are identical when used to express temperature difference.
1.2 The Anthropocene

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