3.1. Stomatal Conductance

ADELM diagnoses canopy stomatal conductance with a Jarvis formulation that combines radiation, temperature, vapour-pressure deficit, and root-zone water status into a multiplicative stress response. The final diagnostic is canopy_stomatal_conductance [mmol H2O m-2 s-1; Diagnostic: canopy-scale stomatal conductance to water vapour].

See also

model.processes.photosynthesis.calculate_jarvis_gs()

Coupling to other components

1. Jarvis scheme

The Jarvis scheme diagnoses four dimensionless response factors and multiplies them to obtain the final stomatal limitation:

(3.1.1)\[f_{\mathrm{gs}} = f_{\mathrm{rad}}\,f_{\mathrm{temp}}\,f_{\mathrm{vpd}}\,f_{\psi}\]

Each factor varies between zero and one, so \(f_{\mathrm{gs}}\) progressively reduces conductance away from favourable conditions.

The Jarvis radiation response depends on incoming PAR incoming_par_Wm2 [W m-2; Flux: incoming photosynthetically active radiation at the canopy top] and the half-saturation parameter jarvis_radiation_half_saturation [W m-2; PFT-based parameter: absorbed PAR at which the stomatal radiation response reaches half its maximum]:

(3.1.2)\[f_{\mathrm{rad}} = \frac{\mathrm{PAR}_{\mathrm{in}}} {\mathrm{PAR}_{\mathrm{in}} + \mathrm{PAR}_{1/2}}\]

where \(\mathrm{PAR}_{\mathrm{in}}\) is incoming_par_Wm2 [W m-2; Flux: incoming photosynthetically active radiation at the canopy top] and \(\mathrm{PAR}_{1/2}\) is jarvis_radiation_half_saturation [W m-2; PFT-based parameter: absorbed PAR at which the stomatal radiation response reaches half its maximum].

The temperature response is a quadratic centered on the optimum temperature jarvis_temperature_optimum [default: 25 degC; Fixed parameter: air temperature at which stomatal conductance reaches its temperature-response maximum]:

(3.1.3)\[f_{\mathrm{temp}} = 1 - a_T\left(T_{\mathrm{opt,gs}} - T_{\mathrm{a}}\right)^2\]

where \(T_{\mathrm{opt,gs}}\) is jarvis_temperature_optimum [default: 25 degC; Fixed parameter: air temperature at which stomatal conductance reaches its temperature-response maximum], \(a_T\) is jarvis_temperature_curvature [default: 0.0016 degC-2; Fixed parameter: quadratic sensitivity of stomatal conductance to air temperature departure from the optimum], and \(T_{\mathrm{a}}\) is ta_degC [degC; Driver: near-surface air temperature]. The implementation clips \(f_{\mathrm{temp}}\) to the interval \([0,1]\).

The vapour-pressure-deficit response is

(3.1.4)\[f_{\mathrm{vpd}} = \frac{1}{1 + k_{\mathrm{vpd}}\,\mathrm{VPD}}\]

where \(k_{\mathrm{vpd}}\) is jarvis_vpd_sensitivity [kPa-1; PFT-based parameter: sensitivity of stomatal conductance to vapour pressure deficit] and \(\mathrm{VPD}\) is vpd_kPa [kPa; Driver: vapour pressure deficit].

The water-stress response is diagnosed from the root-zone soil water potential \(\psi_{\mathrm{root}}\) (root_zone_soil_water_potential [MPa; Diagnostic: mean soil water potential of the root zone]) with a sigmoid response:

(3.1.5)\[f_{\psi} = \frac{1}{1 + \exp\left[-k_{\psi}\left(\psi_{\mathrm{root}} - \psi_{\mathrm{soil},50}\right)\right]}\]

where \(\psi_{\mathrm{soil},50}\) is jarvis_water_potential_midpoint [default: -0.3 MPa; Fixed parameter: soil water potential at which stomatal conductance is reduced by half] and \(k_{\psi}\) is jarvis_water_potential_steepness [default: 3 MPa-1; Fixed parameter: steepness of the sigmoid stomatal response to soil water potential].

2. Canopy conductance

The Jarvis limitation is applied to a leaf conductance range between the minimum conductance \(g_{\mathrm{s,min}}\) (jarvis_min_stomatal_conductance [default: 10 mmol H2O m-2 s-1; Fixed parameter: lower bound on leaf stomatal conductance to water vapour]) and the maximum conductance \(g_{\mathrm{s,max}}\) (jarvis_max_stomatal_conductance [default: 500 mmol H2O m-2 s-1; Fixed parameter: upper bound on leaf stomatal conductance to water vapour]):

(3.1.6)\[g_{\mathrm{s,leaf}} = g_{\mathrm{s,min}} + \left(g_{\mathrm{s,max}} - g_{\mathrm{s,min}}\right)f_{\mathrm{gs}}\]

ADELM then scales this leaf-level quantity to canopy conductance with an effective leaf-area index:

(3.1.7)\[\begin{split}\mathrm{LAI}_{\mathrm{eff}} = \begin{cases} \mathrm{LAI}, & \mathrm{LAI} \le 2 \\ 2, & 2 < \mathrm{LAI} < 4 \\ 0.5\,\mathrm{LAI}, & \mathrm{LAI} \ge 4 \end{cases}\end{split}\]

where \(\mathrm{LAI}\) is lai [m2 m-2; Driver: leaf area index]. The final canopy stomatal conductance is

(3.1.8)\[g_{\mathrm{s,can}} = \mathrm{LAI}_{\mathrm{eff}}\,g_{\mathrm{s,leaf}}\]

and is diagnosed as canopy_stomatal_conductance [mmol H2O m-2 s-1; Diagnostic: canopy-scale stomatal conductance to water vapour].