3.2. Gross Primary Productivity

ADELM estimates canopy gross primary productivity (GPP) using a simplified Farquhar-type formulation combining temperature regulation, CO2 diffusion limitation, and light limitation. The final flux is gpp_gCm2day [gC m-2 day-1; Flux: gross primary productivity].

See also

model.processes.photosynthesis.calculate_gpp()

Coupling to other components

1. Canopy photosynthetic capacity

The canopy-scale photosynthetic capacity combines the capacity coefficient photosynthesis_capacity_coefficient [default: 25 gC m-2 leaf day-1; Fixed parameter: leaf-scale photosynthetic assimilation capacity at optimum temperature], a peaked temperature-scaling function, and leaf area index lai [m2 m-2; Driver: leaf area index]:

(3.2.1)\[A_{\mathrm{can}} = \mathrm{LAI}\,A_{\mathrm{cap}}\,f_{T,\mathrm{cap}}(T_{\mathrm{a}})\]

The peaked temperature-scaling factor uses the optimum temperature photosynthesis_temperature_optimum [default: 30 degC; Fixed parameter: optimum temperature of the photosynthesis temperature response], the maximum temperature photosynthesis_temperature_maximum [default: 56 degC; Fixed parameter: upper temperature bound of the photosynthesis temperature response], and the curvature parameter photosynthesis_temperature_kurtosis [default: 0.183; Fixed parameter: shape parameter of the photosynthesis temperature response]:

(3.2.2)\[f_{T,\mathrm{cap}} = \left( \frac{T_{\mathrm{max,cap}} - T_{\mathrm{a}}}{T_{\mathrm{max,cap}} - T_{\mathrm{opt,cap}}} \right)^{k_{\mathrm{cap}}(T_{\mathrm{max,cap}} - T_{\mathrm{opt,cap}})} \exp\!\left[k_{\mathrm{cap}}\left(T_{\mathrm{a}} - T_{\mathrm{opt,cap}}\right)\right], \quad T_{\mathrm{a}} < T_{\mathrm{max,cap}}\]

and \(f_{T,\mathrm{cap}} = 0\) for \(T_{\mathrm{a}} \ge T_{\mathrm{max,cap}}\).

2. Temperature-dependent CO2 kinetics

The CO2 half-saturation constant \(K_{\mathrm{m}}\) and the CO2 compensation point \(\Gamma^*\) both follow an Arrhenius-type temperature response:

(3.2.3)\[K_{\mathrm{m}}(T_{\mathrm{a}}) = K_{\mathrm{m},0} \exp\!\left[k_{K_{\mathrm{m}}} \frac{T_{\mathrm{a}} - 25}{T_{\mathrm{a}} + 273.15}\right]\]
(3.2.4)\[\Gamma^*(T_{\mathrm{a}}) = \Gamma^*_0 \exp\!\left[k_{\Gamma} \frac{T_{\mathrm{a}} - 25}{T_{\mathrm{a}} + 273.15}\right]\]

where \(K_{\mathrm{m},0}\) (co2_michaelis_constant_25 [default: 404.9 ppm; Constant: rubisco Michaelis constant for CO2 at 25 degrees Celsius]) and \(k_{K_{\mathrm{m}}}\) (co2_michaelis_ha [default: 79430 J mol-1; Constant: activation energy of the Rubisco Michaelis constant for CO2]) are the reference value and activation energy of the half-saturation constant, and \(\Gamma^*_0\) (gammastar_25 [default: 42.75 ppm; Constant: photorespiratory CO2 compensation point at 25 degrees Celsius]) and \(k_{\Gamma}\) (gammastar_ha [default: 37830 J mol-1; Constant: activation energy of the photorespiratory CO2 compensation point]) are the corresponding quantities for the compensation point.

3. Conductance and internal CO2 concentration

The total canopy CO2 conductance is the series combination of stomatal and external conductances:

(3.2.5)\[g_{\mathrm{c,CO_2}} = \left( \frac{1}{g_{\mathrm{s,CO_2}}} + \frac{1}{g_{\mathrm{b,CO_2}}} \right)^{-1}\]

Here \(g_{\mathrm{s,CO_2}}\) is the canopy stomatal conductance on a CO2 basis, diagnosed from canopy_stomatal_conductance [mmol H2O m-2 s-1; Diagnostic: canopy-scale stomatal conductance to water vapour] with gs_ratio_co2_to_h2o [default: 0.625; Constant: ratio of CO2 to H2O molecular diffusivity through stomata]. \(g_{\mathrm{b,CO_2}}\) is the bulk canopy boundary-layer conductance on a CO2 basis, diagnosed from canopy_aerodynamic_conductance [m s-1; Diagnostic: effective aerodynamic conductance for water vapour transport between the canopy and the atmosphere] using air_molar_density [mol m-3; Diagnostic: molar concentration of air] and gb_ratio_co2_to_h2o [default: 0.729927; Constant: ratio of CO2 to H2O molecular diffusivity in the leaf boundary layer].

The canopy internal CO2 concentration \(C_{\mathrm{i,can}}\) is obtained from the positive root of

(3.2.6)\[C_{\mathrm{i,can}}^2 + b\,C_{\mathrm{i,can}} + c = 0\]

where \(C_{\mathrm{a}}\) (co2_ppm [ppm; Driver: atmospheric carbon dioxide concentration]) is the atmospheric CO2 concentration and

(3.2.7)\[b = \frac{A_{\mathrm{can}}}{g_{\mathrm{c,CO_2}}} - C_{\mathrm{a}} + K_{\mathrm{m}}, \qquad c = -C_{\mathrm{a}}\,K_{\mathrm{m}} - \frac{A_{\mathrm{can}}}{g_{\mathrm{c,CO_2}}}\,\Gamma^*\]

\(C_{\mathrm{i,can}}\) is clipped to the interval \([\Gamma^*, C_{\mathrm{a}}]\).

4. Diffusion-limited gross assimilation

The diffusion-limited gross assimilation is diagnosed from the total canopy CO2 conductance and the atmospheric-to-internal CO2 gradient:

(3.2.8)\[A_{\mathrm{d}} = g_{\mathrm{c,CO_2}}\left(C_{\mathrm{a}} - C_{\mathrm{i,can}}\right)\]

5. Light-limited gross assimilation

The light-limited gross assimilation is diagnosed from \(\mathrm{APAR}_{\mathrm{leaf}}\) (leaf_apar_Wm2 [W m-2; Flux: photosynthetically active radiation absorbed by leaf surfaces]) and the light-use efficiency \(\epsilon_{\mathrm{L}}\) (light_use_efficiency [default: 1.2 gC MJ-1; Fixed parameter: efficiency of converting leaf-absorbed photosynthetically active radiation into gross carbon assimilation]):

(3.2.9)\[A_{\mathrm{l}} = \epsilon_{\mathrm{L}}\, \frac{\mathrm{APAR}_{\mathrm{leaf}}}{10^6}\]

Here \(\mathrm{APAR}_{\mathrm{leaf}}\) is converted from W m⁻² to MJ m⁻² s⁻¹ so that it is consistent with the units of \(\epsilon_{\mathrm{L}}\).

6. Gross primary productivity

The instantaneous rates \(A_{\mathrm{l}}\) and \(A_{\mathrm{d}}\) are first scaled to daily fluxes by multiplying by seconds_per_day [default: 86400 s; Constant: number of seconds in one day]. The daily GPP (gpp_gCm2day [gC m-2 day-1; Flux: gross primary productivity]) is then obtained by solving the quadratic co-limitation equation (Collatz et al. 1991):

(3.2.10)\[\theta_{\mathrm{co}}\,\mathrm{GPP}^2 - (A_{\mathrm{l}} + A_{\mathrm{d}})\,\mathrm{GPP} + A_{\mathrm{l}}\,A_{\mathrm{d}} = 0\]

where \(\theta_{\mathrm{co}}\) is photosynthesis_colimitation_curvature [default: 0.95; Fixed parameter: colimitation curvature of photosynthesis by light and diffusion capacity]. Taking the smaller root gives

(3.2.11)\[\mathrm{GPP} = \frac{(A_{\mathrm{l}} + A_{\mathrm{d}}) - \sqrt{(A_{\mathrm{l}} + A_{\mathrm{d}})^2 - 4\,\theta_{\mathrm{co}}\,A_{\mathrm{l}}\,A_{\mathrm{d}}}}{2\,\theta_{\mathrm{co}}}\]