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François et al. Carbon Footprints 2026, 5, 22 Page 17 of 22

gwp100 = 1,642 kg CO eq (thus a 21% reduction compared to static indicator) and the dynamic present
2
method provides gwp100 = 2,001 kg CO eq (thus a 4% reduction compared to static indicator). The use of a
2
reduction coefficient that is identical for all GHGs (except refrigerating fluids) in the RE2020 also
overestimates the benefits of emissions spreading on climate change.

DISCUSSION
What is different compared to previous methods?
An important point of discussion concerns changes in the reference of dynamic indicators. Compared to
previous methods, this paper does not provide a new indicator, it only modifies the integration times in
order to ensure compatibility between static and dynamic indicators. As expressed in Equations 19 and 22 of
delay factors, the time T is the same entity at numerator and denominator. However, it does not have the
same value: T is defined by Equation 14, thus for static indicator T = THI because LCD = 0, whereas for
dynamic indicator T = LCD + THI. In the application to GWP100, T = LCD + 100 years, and thus T = 100
years for the static indicator. This ensures an identical integration time concerning the reference substance
CO at the denominator. In fact, delay factors do not depend on the CO reference as can be seen in
2
2
Equations 20 and 23. Compared to the previous method of Levasseur et al. , the change is that the
[13]
numerator of the characterization factor has a longer integration time than the LCD time. Compared to the
previous method of Ventura , the change is that the denominator of the characterization factor has a
[29]
shorter time, set to T = THI.

What can be learned from literal expressions of delay factors?
Equations 21 and 24 demonstrate that delay factors can be expressed in closed forms. These analytical
expressions increase their usability in various calculation programs. Furthermore, apart from the total
integration time and the different times of emissions, the values of the delay factors depend only on the
physicochemical constants of the GHGs:

α (T) only requires lifetimes for each GHGs, except for the CO that requires constants defined in its own
2
i,j
decay function [25]
β (T) also requires lifetimes and parameters of the CO decay function, yet more specifically parameters of
2
i,j
the climate warming impulse response function in Equation 6 available from .
[33]
Thus, the mathematical expressions of the delay factors (see Equations 21 and 24 do not depend on the
reference substance (CO ). Delay factors actually represent the ratio between the impact on climate change of
2
a GHG emitted at time t and up to the total observation time T, and the impact of the same GHG emitted at
i
time zero. These coefficients are dimensionless and thus represent the anticipated change in impact resulting
from the delay or dispersion of emissions, relative to an instantaneous emission at time zero.

What can be learned from behavior of delay factors?
Comparing results obtained for the two delay factors α and β corresponding respectively to the GWP and
GTP indicators provides interesting insights as they present opposite behaviors: delaying emission will
translate in a decrease of the GWP, whereas it will induce an increase of the GTP (except for GHGs with very
long lifetimes). Equivalently, α is based on cumulative radiative forcing and thus the shorter the integration
time, for a delayed emission, the lower the value of the GWP. In contrast, β is based on an instantaneous
temperature at a given point in time (T). Then higher results for GTP are expected when emissions are
greatly delayed.