# Using Stochastic Ray Tracing to Simulate a Dense Time Series of Gross Primary Productivity
## 5 Conclusions
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Units \({}^{*}\)** & **Description** \\ \hline \(\alpha\) & \(\mu\)mol- C \(\mu\)mol\({}^{-1}\)- photons & quantum yield \\ \(\alpha_{opt}\) & \(\mu\)mol- C \(\mu\)mol\({}^{-1}\)- photons & theoretical optimum for quantum yield \\ \(\beta_{h}\) & \% & sensitivity of \(P_{max}\) to changes in \(h\) \\ \(\beta_{D}\) & \({}^{\circ}\)C days & sensitivity of \(P_{max}\) to changes in \(D\) \\ \(\beta_{E}\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\) & sensitivity of \(P_{max}\) to changes in \(E_{el}\) \\ \(\beta_{T}\) & \({}^{\circ}\)C & sensitivity of \(P_{max}\) to changes in \(T\) \\ \(\gamma_{h}\) & & lag in response of \(P_{max}\) to changes in \(h\) \\ \(\gamma_{T}\) & & lag in response of \(P_{max}\) to changes in \(T\) \\ \(\theta\) & radians & zenith angle \\ \(\Theta\) & & vector of model parameters \\ \(\rho\) & & reflectance \\ \(\tau_{c}\), \(\tau_{k}\) & & collided and un-collided transmittance, respectively \\ \(\phi\) & radians & azimuth angle \\ \(\chi\) & & duration of initial linear response for eq. 2 \\ \(\omega\) & steradians & solid angle; \([\delta\omega\) = \(\{\)sin\(\omega\)-\(\delta\)\(\delta\)\(\phi\)\(\phi\) \\ \(\Omega\) & steradians & projected solid angle; \([\)cos\(\theta\)-\(\omega\)\(\phi\)\(\phi\) \\ \(A_{p}\) & m\({}^{2}\) & area of facet \(p\) (solid portion for porous facets) \\ \(A_{ref}\) & m\({}^{2}\) & area of reference plane \\ \(D\) & \({}^{\circ}\)C days & growing degree days \\ \(D_{mod}\) & \(D\) modifier \\ \(D_{opt}\) & \({}^{\circ}\)C days & optimal growing degree day for photosynthesis \\ \(E\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\) & photosynthetically active radiation (irradiance) \\ \(E_{ic}\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\) & \(E\) incident on the canopy \\ \(E_{ac}\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\) & \(E\) absorbed by the canopy \\ \(E_{el}\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\) & \(E\) absorbed by a canopy element \\ \(E_{mol}\) & & \(E_{el}\) modifier \\ \(h\) & \% & relative humidity \\ \(h_{mod}\) & & \(h\) modifier \\ \(k_{mb}\) & & exponential N-allocation coefficient \\ \(L\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\). sr\({}^{-1}\) & radiance \\ \(L_{ic}\) & \(\mu\)mol- photons m\({}^{-2}\)- s\({}^{-1}\). sr\({}^{-1}\) & radiance at reference plane above canopy \\ \(P_{abs}\) & & absorption probability \\ \(P_{g}\) & \(\mu\)mol- C \(\cdot\) m\({}^{-2}\)- s\({}^{-1}\) & gross primary productivity \\ \(P_{g}^{\mu}\) & \(\mu\)mol- C \(\cdot\) m\({}^{-2}\)- s\({}^{-1}\) & \(P_{g}\)at cloud level \\ \(P_{gl}\) & \(\mu\)mol- C \(\cdot\) m\({}^{-2}\)- s\({}^{-1}\) & \(P_{g}\) at canopy element level \\ \(P_{max}\) & \(\mu\)mol- C \(\cdot\) m\({}^{-2}\). s\({}^{-1}\) & photosynthetic capacity at leaf (\(p_{l}\)) level \\ \(P_{opt}\) & \(\mu\)mol- C \(\cdot\) m\({}^{-2}\). s\({}^{-1}\) & optimal photosynthetic capacity at leaf (\(p_{l}\)) level \\ \(p_{l}\), \(P_{u}\), \(P_{b}\) & & scene element (_i.e.,_ facet) \\ \(T\) & \({}^{\circ}\)C & air temperature \\ \(T_{mod}\) & \({}^{\circ}\)C & \(T\) modifier \\ \hline \hline \end{tabular}   
\({}^{*}\) Where the dimensions are not specified, the quantities are dimensionless.