Page 55 - 2417

Page 8 of 22 François et al. Carbon Footprints 2026, 5, 22

Which finally leads to the unified expression:

) = ! + ) (14)

This condition is general to any impact category whenever compatibility is required between static and
dynamic approaches. This relationship had already been suggested and conceptually explained by although
[29]
it was not demonstrated. For partially dynamic approaches based on EPDs, Time Horizon of the Impact
(THI) = 100 years.

Dynamic GWP characterization factors
On a general basis, the agwp of a GHG j emitted at time t over an observation duration T can be deduced
i
from Equation 3 by introducing the time t at which the emission occurs:
i

∫
)−C 8
06F? 2 9 (C)3C (15)
8, 9 ()) = 0 9
0
where agwp (T) is the dynamic Absolute Global Warming Potential of GHG j emitted at time t and
i
i,j
cumulated over time T (W.m .yr .kg ).
-2
-1
-1
To obtain dynamic gwp characterization factor, one requires to divide dynamic agwp by the agwp of 1 kg of
the reference substance (carbon dioxide). Thus, considering the equivalence of notation between agwp 0,CO2
and AGWP , the dynamic gwp characterization factor of a GHG j emitted at time i and observed on a time
CO2
T can be expressed as follows:
∫ )−C 8 !
06F? ()) 2 9 (C)3C
8, 9 0 9 0
6F? 8, 9 ()) = = ∫ ) (16)
())
06F? 0, $ 2 0 $ 2 (C)3C
0 2 $ 2
where gwp (T) is the dynamic Global Warming Potential of GHG j emitted at time t and cumulated over
i
i,j
time T (kg CO -eq).
2
Dynamic GTP characterization factors
Like GWP, the dynamic agtp and gtp characterization factors can be expressed from the static AGTP and
GTP, Equations 5 and 7 respectively, by introducing the time of emission t as expressed in Equations 17 and
i
18:

∫
)−C 8 (17)
06C? 2 9 (C)R \ ( T − C 8 − C)3C
8, 9 ()) = 0 9
0
where agtp (T) is the dynamic Absolute Global Temperature Potential of GHG j emitted at time t and
i,j
i
cumulated over time T (K.kg ).
-1
∫ )−C 8 !
06C? 8, 9 ()) 0 9 0 2 9 (t)R \ ( ) − C 8 − C) 3C
6C? 8, 9 ()) = = ∫ ) (18)
())
06C? 0, $ 2 0 $ 2
2 $ 2 (C)R \ ( ) − C)3t
0
where gtp (T) is the dynamic Global Temperature Potential of GHG j emitted at time t and cumulated over
i
i,j
time T (kg CO -eq).
2
DELAY FACTORS
Definition
In order to compare and easily convert characterization factors from static to dynamic, the delay factors,
symbolized by α and β respectively for the gwp and gtp are defined as dimensionless coefficients representing