Autotrophic Respiration
This page documents the autotrophic respiration model by Clark et al. [30], used in the JULES model. The ClimaLand code can be found here.
Model formulation
Autotrophic respiration of the canopy is partitioned into maintenance and growth components. At the canopy level, the respiration flux (mol CO$_2$ m$^{-2}$ s$^{-1}$) is
\[R_a = \Bigl(R_{pm} + R_g\Bigr)\; \frac{1 - \exp\!\left(-K \, LAI \, \Omega\right)}{K \, \Omega},\]
where $R_{pm}$ is the maintenance respiration (mol CO$_2$ m$^{-2}$ s$^{-1}$), $R_g$ is the growth respiration (mol CO$_2$ m$^{-2}$ s$^{-1}$), $K$ is the canopy extinction coefficient (–), $LAI$ is the leaf area index (m$^2$ leaf m$^{-2}$ ground), and $\Omega$ is a clumping factor (–).
Nitrogen allocation
Nitrogen is distributed among leaves, roots, and stems according to
\[S_c = \eta_{sl}\, h\, LAI \, H(SAI), \qquad R_c = \sigma_l \, RAI\]
\[n_m = \frac{Vc_{max25}}{n_e}, \qquad N_l = n_m \, \sigma_l \, LAI, \qquad N_r = \mu_r \, n_m \, R_c, \qquad N_s = \mu_s \, n_m \, S_c\]
where:
$H$ is the Heaviside function (–),
$Vc_{max25}$ is the leaf-level maximum carboxylation rate at 25 °C (mol CO$_2$ m$^{-2}$ s$^{-1}$),
$n_e$ is the conversion factor from $Vc_{max25}$ to nitrogen (mol CO$_2$ m$^{-2}$ s$^{-1}$ kg C$^{-1}$),
$\eta_{sl}$ is the live stem wood coefficient (kg C m$^{-3}$),
$h$ is the canopy height (m),
$\sigma_l$ is the specific leaf density (kg C m$^{-2}$ leaf),
$\mu_r$ is the root-to-leaf nitrogen ratio (–),
$\mu_s$ is the stem-to-leaf nitrogen ratio (–),
$N_l, N_r, N_s$ are the nitrogen contents in leaves, roots, and stems (kg N m$^{-2}$ ground),
$S_c$ is the stem carbon pool (kg C m$^{-2}$ ground),
$R_c$ is the root carbon pool (kg C m$^{-2}$ ground),
$n_m$ is the nitrogen per unit carboxylation capacity (kg N mol$^{-1}$ CO$_2$ m$^{2}$ s).
Maintenance respiration
\[R_{pm} = R_d \,\Bigl(\beta + \frac{N_r + N_s}{\max(N_l, \, \epsilon)}\Bigr),\]
where $R_d$ is a base respiration rate (mol CO$_2$ m$^{-2}$ s$^{-1}$), $\beta$ is a parameter scaling leaf respiration (–), and $\epsilon$ is machine epsilon (–) for numerical stability.
Growth respiration
\[R_g = R_{el} \, \Bigl(A_n - R_{pm}\Bigr),\]
where $R_{el}$ is the relative contribution of growth respiration (–), and $A_n$ is the net assimilation rate (mol CO$_2$ m$^{-2}$ s$^{-1}$).
Notes
- This formulation follows the approach used in large-scale ecosystem models such as JULES (Clark et al., 2011).
- Growth respiration is proportional to net assimilation after subtracting maintenance costs.
- Maintenance respiration scales with tissue nitrogen pools.