Trade-off and risk in mitigation options for aviation

A recently proposed method to statistically treat trade-offs and associated risks in aviation mitigation options (Prather et al., 2025) leaves, to this author's opinion, issues open for discussion. In particular, the method lacks a rigorous mathematical derivation and gives no precise mathematical definition of the central notion “trade-off ratio”. The derivation, which is given here, leads to an inequality that expresses the postulate that the total (summed-up) metric value, after a mitigation measure has been taken, must be smaller than the value of the same metric without mitigation. Surprisingly, neither the metric pair itself nor the basic (effective) radiative forcings appear in the inequality. However, if one enforces their presence or if one does not cancel them out like in the original method, uncertain quantities appear on both sides of the inequality, which renders it inadequate for its purpose. In contrast, the method in its “sensitivity form” may work in hindcast mode (that is, to estimate the probability whether a mitigation method was successful), if the changes of the effective radiative forcings due to the measure taken can be determined with sufficient precision, using a climate model with well defined weather patterns over the course of a year or longer.