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François et al. Carbon Footprints 2026, 5, 22 Page 5 of 22

% 9 (C) = 0 9 2 9 (C) (1)
with AGFP (t) the Absolute Global Forcing Potential (W.m .kg ); c the time response function of an
-1
-2
j
j
impulse of the GHG j (dimensionless), a is the radiative efficiency of GHG j (W.m .kg ) and t the time
-1
-2
j
elapsed after the pulse emission .
[24]
The time decay law, or impulse response function, c(t) represents the degradation of the GHG j over the
j
time (or its reabsorption by biogeochemical mechanisms regarding the CO ):
2

 3 Õ C
 −
  1 0 + 1 = e g = , 9 = $ 2

2 9 (C) = (2)
==1
 C
 −
 4 g 9 ,
 ∀9 ≠ $ 2
with c the time response function of an impulse of the GHG j (dimensionless), τ the lifetime of the GHG j in
j
j
the atmosphere (years) and b and τ the carbon dioxide impulse response function parameters taken from .
[25]
n
n
Lifetimes of all GHGs are provided in an associated worksheet-based tool , under the “IPCC AR6”
[22]
worksheet based on [26,27] , b and τ are provided in the “Additional data” worksheet based on .
[25]
n
n
The Absolute Global Warming Potential (AGWP) is the instantaneous radiative forcing [Equation 2]
cumulated over a time T:
) )
∫ ∫
,% 9 ()) = % 9 (C)3C = 0 9 2 9 (C)3C (3)
0 0
with AGWP (T) the Absolute Global Warming Potential of GHG j cumulated over a time T
j
(W.m .yr.kg ) .
-1 [24]
-2
The GWP characterization factor is a relative metric based on the AGWP expressed relatively to the CO 2
chosen as the reference substance:
∫ )
,% 9 ()) 0 9 2 9 (C)3C
,% 9 ()) = = ∫ 0 (4)
()) )
,% $ 2 (C)3C
2 $ 2
0 $ 2 0
with GWP (T) the static Global Warming Potential characterization factor of GHG j over time T
j
(kg CO -eq) .
[24]
2
The Absolute Global Temperature Potential (AGTP) represents the temperature variation due to the
radiative forcing potential, expressed in Equation 5 . It is based on the AGFP and on a temperature
[24]
response function. Compared to the radiative forcing, a temperature variation is introduced that relies on the
climate impulse response R . This one is based on climatic layers models. In latest IPCC reports, AR5 and
θ
AR6, R is represented by a two exponential terms expression with a fast and a slow contribution, as
θ
expressed in Equation 6 .
[28]
∫ ) ∫ )
)% 9 ()) = % 9 (C)' \ () − C)3C = 0 9 2 9 (C)' \ () − C)3C (5)
0 0
with AGTP (T) the Absolute Global Temperature Potential of GHG j over a time T (K.kg ) and R (t) the
-1
θ
j
climate warming impulse response function (K.yr .m .W ) .
-1
2
-1 [24]