Modelling assimilation and intercellular CO₂ from measured conductance: A synthesis of approaches

A spectrum of models that estimate assimilation rate A from intercellular carbon dioxide concentration (C_i) and measured stomatal conductance to CO₂ (g_c) were investigated using leaf-level gas exchange measurements. The gas exchange measurements were performed in a uniform loblolly pine stand (Pinus taeda L.) using the Free Air CO₂ Enrichment (FACE) facility under ambient and elevated atmospheric CO₂ for 3 years. These measurements were also used to test a newly proposed framework that combines basic properties of the A-C_i curve with a Fickian diffusion transport model to predict the relationship between C_i/C_a and g_c, where C_a is atmospheric carbon dioxide concentration. The widely used Ball-Berry model and five other models as well as the biochemical model proposed by Farquhar et al. (1980) were also reformulated to express variations in C_i/C_a as a function of their corresponding driving mechanisms. To assess the predictive capabilities of these approaches, their respective parameters were estimated from independent measurements of long-term stable carbon isotope determinations (δ¹³C), meteorological variables, and ensemble A-C_i curves. All eight approaches reproduced the measured A reasonably well, in an ensemble sense, from measured water vapour conductance and modeled C_i/C_a. However, the scatter in the instantaneous A estimates was sufficiently large for both ambient and elevated C_a to suggest that other transient processes were not explicitly resolved by all eight parameterizations. An important finding from our analysis is that added physiological complexity in modeling C_i/C_a (when g_c is known) need not always translate to increased accuracy in predicting A. Finally, the broader utility of these approaches to estimate assimilation and net ecosystem exchange is discussed in relation to elevated atmospheric CO₂.