A derivation error that affects carbon balance models exists in the current implementation of the modified Arrhenius...

Area of Science:

• Plant physiology
• Biogeochemical cycles
• Climate modeling

Background:

• Accurate modeling of biological temperature responses is essential for predicting global carbon fluxes.
• Current large-scale models use a modified Arrhenius equation to represent temperature responses of photosynthetic capacity.

Purpose of the Study:

• To rederive the modified Arrhenius equation and identify any discrepancies.
• To assess the impact of a previously overlooked term on temperature response parameters and carbon gain predictions.

Main Methods:

• Re-derivation of the modified Arrhenius equation from its 1942 source publication.
• Comparison of fitted temperature response parameters using the correct and erroneous derivations.
• Scaling the impact of derived parameter differences on whole-plant carbon balance.

Main Results:

• A critical term was found to be missing from the modified Arrhenius equation after 2002.
• While most parameters showed minimal changes, activation energy was substantially affected.
• The corrected equation led to a significant deviation of approximately 18% day⁻¹ in modeled daily carbon gain.

Conclusions:

• The error in the modified Arrhenius equation derivation has impacted the accuracy of carbon flux predictions in Earth System Models.
• Over 40% of current Earth System Models may contain this erroneous derivation, affecting large-scale predictions.
• Correction of the derivation error is recommended for future modeling efforts to improve the accuracy of global carbon flux predictions.