Photosynthesis diffusion

Governing equations

The net CO\(_2\) assimilation due to biological demand must match the diffusion of CO\(_2\) from the surrounding air to the leaf surface and into the leaf, and is given by

\[\begin{equation} \label{eqn_an_diffusion} A_n = g_{bc} (c_a - c_s) = g_{sc} (c_s - c_i) = g_{\ell c} (c_a - c_i) \end{equation}\]

where \(c_a\) [\(\mu\)mol {CO\(_2\)} mol\(^{-1}\)] is the atmospheric CO\(_2\), \(c_s\) [\(\mu\)mol CO\(_2\) mol\(^{-1}\)] is the leaf surface CO\(_2\), \(c_i\) [\(\mu\)mol CO\(_2\) mol\(^{-1}\)] is the intercellular CO\(_2\), \(g_{bc}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the boundary conductance of CO\(_2\), \(g_{sc}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the stomatal conductance of CO\(_2\), and \(g_{\ell c}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the leaf conductance of CO\(_2\).

Similarly, the transpiration of flux, \(E\) [mol H\(_2\)O m\(^{-2}\)o s\(^{-1}\)], is given as \begin{equation} E = g_{bw} (q_a - q_s) = g_{sw} (q_s - q_i) = g_{\ell w} (q_a - q_i) \end{equation}

where \(q_a\) [\(\mu\)mol H\(_2\)O mol\(^{-1}\)] is the atmospheric H\(_2\)O, \(q_s\) [\(\mu\)mol H\(_2\)O mol\(^{-1}\)] is the leaf surface H\(_2\)O, \(q_i\) [\(\mu\)mol H\(_2\)O mol\(^{-1}\)] is the intercellular H\(_2\)O, \(g_{bc}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the boundary conductance of H\(_2\)O, \(g_{sc}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the stomatal conductance of H\(_2\)O, and \(g_{\ell c}\) [mol m\(^{-1}\) s\(^{-2}\)o] is the leaf conductance of H\(_2\)O. The leaf conductances can be written in terms of boundary and stomatal conductances as

\[\begin{eqnarray} \label{eqn_glc} g_{\ell c} &= \frac{1}{g_{bc}^{-1} + g_{sc}^{-1}} \\[0.4em] g_{\ell w} &= \frac{1}{g_{bw}^{-1} + g_{sw}^{-1}} \end{eqnarray}\]

It is assumed that \(g_{sc} = g_{sw}/1.6\). Using equations \eqref{eqn_an_diffusion} and \eqref{eqn_glc}, \(c_i\) can be given as

\[\begin{equation} \label{eqn_ci_diff} c_i = c_a - \frac{A_n}{g_{\ell c}} \end{equation}\]