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 complement of relative whole-plant hydraulic conductance. In turn, the relative conductance is determined by dividing the current whole-plant hydraulic conductance by its maximum value:

\[\begin{equation} DDS = \phi \cdot \left( 1.0 - \frac{k_{plant}}{k_{\max plant}}\right) \end{equation}\] where \(\phi_i\) is the leaf phenological status, \(k_{plant, i}\) is the current whole-plant hydraulic conductance and \(k_{\max plant}\) is the maximum whole-plant conductance. Since \(k_{plant}\) varies through the day, average daily values are used for the determination of drought stress. Furthermore, remember than in the Sperry transpiration model we have that the whole-plant conductance is the slope of the vulnerability curve: \[\begin{equation} k_{plant} = dE/d\Psi \end{equation}\] In the Sureau sub-model, \(k_{plant}\) is estimated from the resistances across the hydraulic network (see 10.5.2).