A derivation error exists in the current implementation of the Johnson et al. (1942) modified Arrhenius function that affects leaf carbon balance models

Understanding biological temperature responses is crucial to predicting global carbon fluxes. The current approach to modeling photosynthetic temperature responses in large scale modeling efforts uses a modified Arrhenius equation. We rederived the modified Arrhenius equation from the source publication and uncovered a missing term that was dropped between 1942 and 2002. We compare fitted temperature response parameters between the new and old derivation of the modified Arrhenius equation. We find that most parameters are minimally affected, though small errors still exist. We then scaled the impact of these small errors to whole plant carbon balance and found that the impact of the rederivation of the Arrhenius on modelled daily carbon gain causes a meaningful deviation of ~1.8%. This suggests that the error in the derivation of the modified Arrhenius equation has impacted predictions of carbon fluxes at larger scales. We argue that it is time to move beyond the modified Arrhenius paradigm since the current implementation is categorically incorrect and to use more thermodynamically-grounded temperature response equations going forward.