Chapter 14 Day-level results

In the preceeding chapters we detailed how the model performs canopy and soil energy balances for subdaily time steps and how transpiration and photosynthesis values are determined for any given substep. This chapter indicates how these are aggregated at the daily scale and how other day-level model outputs are calculated.

14.1 Photosynthesis and transpiration

Cohort’s transpiration \(Tr_{i,t}\) (eq. (12.1)) are added across subdaily steps to yield daily transpiration (\(Tr_{i}\), in \(mm\,H_2O\)): \[\begin{equation} Tr_{i} = \sum_{t=1}^{n_t} {Tr_{i,t}} \end{equation}\] An the same for water extraction \(Ex_{i,s,t}\) for each soil layer \(s\) (eq.(12.2)): \[\begin{equation} Ex_{i,s} = \sum_{t=1}^{n_t} {Ex_{i,s,t}} \end{equation}\] \(Ex_{i,s}\) are substracted from the water content of the corresponding soil layer, closing the soil water balance of the day (eq. (7.1)).

Daily values of net carbon assimilation for plant cohorts are obtained similarly. \(A_{n, i, t}\) (eq. (12.3)) are added across subdaily steps to obtain \(A_{n,i}\), the daily net assimilation at the cohort level (in \(g\,C·m^{-2}\)): \[\begin{equation} A_{n,i} = \sum_{t=1}^{n_t} {A_{n,i,t}} \end{equation}\]

14.2 Plant water potentials and relative water contents

Because the model determines optimum transpiration for every subdaily time step, this leads to a daily sequence of leaf water potential (\(\Psi_{leaf,i,t}\)), stem water potential (\(\Psi_{stem,i,t}\)), root crown water potential (\(\Psi_{rootcrown,i,t}\)) and root surface water potential (\(\Psi_{rootcrown,i,s,t}\)) values for each plant cohort \(i\) (and soil layer \(s\) in the last case). The model defines the following daily water potentials for every cohort \(i\):

  • Pre-dawn leaf water potential (\(\Psi_{pd, i}\)): the maximum of \(\Psi_{leaf,i,t}\) values.
  • Pre-dawn shade leaf water potential (\(\Psi_{pd, i}^{shade}\)): the maximum of \(\Psi_{leaf,i,t}^{shade}\) values.
  • Pre-dawn sunlit leaf water potential (\(\Psi_{pd, i}^{sunlit}\)): the maximum of \(\Psi_{leaf,i,t}^{sunlit}\) values.
  • Mid-day leaf water potential (\(\Psi_{md, i}\)): the minimum of \(\Psi_{leaf,i,t}\) values.
  • Mid-day shade leaf water potential (\(\Psi_{md, i}^{shade}\)): the minimum of \(\Psi_{leaf,i,t}^{shade}\) values.
  • Mid-day sunlit leaf water potential (\(\Psi_{md, i}^{sunlit}\)): the minimum of \(\Psi_{leaf,i,t}^{sunlit}\) values.
  • Stem water potential (\(\Psi_{stem, i}\)): the minimum of \(\Psi_{stem,i,t}\) values.
  • Root-crown water potential (\(\Psi_{rootcrown, i}\)): the minimum of \(\Psi_{rootcrown,i,t}\) values.
  • Root surface water potentials (\(\Psi_{rootsurf, i,s}\)): the minimum of \(\Psi_{rootsurf,i,s,t}\) values for each soil layer \(s\).

Analogously, relative water content of stems and leaves is known for every subdaily time step, which results in a daily sequence of leaf relative water content (\(RWC_{leaf,i,t}\)) and stem relative water content (\(RWC_{stem,i,t}\)). These are summarized at the daily level for each plant cohort \(i\):

  • Leaf relative water content (\(RWC_{leaf, i}\)): the mean \(RWC_{leaf,i,t}\) values.
  • Stem relative water content (\(RWC_{stem, i}\)): the mean of \(RWC_{stem,i,t}\) values.

Finally, the daily sequence of slopes of the supply function (\(dE/d\Psi_{i,t}\)) is also averaged at the daily level:

  • Slope of the supply function (\(dE/d\Psi_{i}\)): the mean \(dE/d\Psi_{i,t}\) values.

14.3 Plant drought stress

In order to have an estimate of daily drought stress for the plant cohort, the model uses the stem vulnerability curve of the plant to find the conductance relative to maximum stem conductance and turns it into its complement:

\[\begin{equation} DDS_i = \phi_i \cdot \left( 1.0 - \frac{k_{stem, i}(\Psi_{rootcrown,i})}{k_{\max stem, i}}\right) = \phi_i \cdot \left(1.0 - e^{-(\Psi_{rootcrown,i}/d_{stem})^{c_{stem}}}\right) \end{equation}\] where \(\phi_i\) is the leaf phenological status. Note the use of \(\Psi_{rootcrown,i}\) (and not \(\Psi_{leaf,i}\)) to determine drought stress index. Thus the model tracks the degree of conductance decrease at the beginning of the stem as a measure of drought stress. This choice makes daily drought stress values of the Simple and Complex transpiration modes more comparable (because leaf mid-day water potentials are usually much more negative than soil water potentials) and is a sensible choice if one wants to run the model in irreversible cavitation mode (see below).