The appropriate analytical solution for coupled leaf photosynthesis and stomatal conductance models for C3 plants

Models coupling photosynthesis (An) and stomatal conductance (Gs) have been widely used for their estimation since it was found that An and Gs are correlated. Although a cubic equation for An can be derived from the coupled An-Gs model for C3 plants and a method of obtaining analytical solutions has been proposed, these analytical solutions have several problems like no solutions, changes in appropriate solutions, and no physical and biological logic for selecting the appropriate solution. In this study, a method is proposed to solve these problems using a different expression of analytical solutions and imposing requirements. The proposed method was then numerically tested under a wide range of environmental conditions. By proving the existence and uniqueness of physically and biologically appropriate solutions, this study showed that the proposed method can solve all the above problems and can provide an appropriate analytical solution for each of environmental conditions tested. The proposed method can be used in various studies on photosynthesis and stomatal conductance in the future.