This paper exposes flaws in the mathematical structure of the Global Warmin
g Potential (GWP) concept. These lead to errors when emissions changes in d
ifferent greenhouse gases are compared. The most fundamental problem is tha
t the unit impulse response functions from which GWPs, and many of their pr
oposed alternatives, are constructed provide an incomplete representation o
f the relationship between emissions and radiative forcing. Additional erro
rs occur when GWPs are used to compare finite-length emissions changes.