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

Abstract

Carbon-concentration and carbon-climate feedbacks in CMIP6 models, and their comparison to CMIP5 models. Biogeosciences

No need to switch the modified Arrhenius function back to the old form

“…1b). However, the results of Murphy & Stinziano (2020) in their Fig. 2 showed that there were often significant outliers in the plots of estimated parameter values (including k 25 ) of one model vs those of the other model.…”

“…Eqn 1 has also been used for the temperature response of photosynthetic CO 2 -diffusion parameters, mesophyll conductance (Bernacchi et al, 2002) and bundle sheath conductance (Yin et al, 2016). However, recently Murphy & Stinziano (2020) drew our attention to the original modified Arrhenius equation (Johnson et al, 1942), which, if expressed in a form similar to Eqn 1 with the parameter value at the reference temperature of 25°C, is as follows:…”

“…Compared with Eqn 1, Eqn 2 has an additional term, T/298. According to Murphy & Stinziano (2020), this additional term was omitted by Hall (1979) and Farquhar et al (1980), and since then, the form without the term, Eqn 1, has been predominantly used (e.g. Harley et al, 1992;Medlyn et al, 2002).…”

“…Harley et al, 1992;Medlyn et al, 2002). Murphy & Stinziano (2020) compared Eqn 1 and Eqn 2, and found that the estimated values of k 25 , H and S were affected minimally, whereas the values of E were impacted substantially by the omission. They then upscaled these impacts using a whole-plant model, and showed that these impacts extended to modelled daily carbon gain.…”

“…They then upscaled these impacts using a whole-plant model, and showed that these impacts extended to modelled daily carbon gain. Murphy & Stinziano (2020) believed that the process of simplifying 'generated an error that was propagated for over 40 years', and recommended that the omission error of Eqn 1, which has been used most notably in current large-scale models, should be corrected. Here, I argue that the omission is not an error.…”