Return periods in current and future climate

The distribution functions for large rain events X_c in current climate is denoted F(x) = P{X_c ≤ x} and for large rain events X_f in a future climate G(x) = P{X_f ≤ x}. A climate factor k is introduced, and it is assumed that P{X_c ≤ x} = P{X_f ≤ k x} corresponding to G(k x) = F(x). If we further assume that the distribution functions F and G have exponential tails, the following simple transformation of the return period in current climate T_c to the corresponding return period in future climate T_f can be deduced

T_f = T_c^1/k

Applying a first order analysis on this equation with k as independent variable leads to a relation between the uncertainties of k and T_f. In terms of the coefficient of variations we get

CV{T_f} ≈ 1/ lnT_c CV{k}

This equation reveals that even with moderate uncertainty in k, the uncertainty in T_f is notably increased.