2.9. Stomatal Resistance and Photosynthesis

2.9.1. Summary of CLM5.0 updates relative to the CLM4.5

We describe here the complete photosynthesis and stomatal conductance parameterizations that appear in CLM5.0. Corresponding information for CLM4.5 appeared in the CLM4.5 Technical Note (Oleson et al. 2013).

CLM5 includes the following new changes to photosynthesis and stomatal conductance:

  • Default stomatal conductance calculation uses the Medlyn conductance model

  • V_{c,max} and J_{max} at 25 oC: are now prognostic, and predicted via optimality by the LUNA model (Chapter 2.10)

  • Leaf N concentration and the fraction of leaf N in Rubisco used to calculate V_{cmax25} are determined by the LUNA model (Chapter 2.10)

  • Water stress is applied by the hydraulic conductance model (Chapter 2.11)

2.9.2. Introduction

Leaf stomatal resistance, which is needed for the water vapor flux (Chapter 2.5), is coupled to leaf photosynthesis similar to Collatz et al. (1991, 1992). These equations are solved separately for sunlit and shaded leaves using average absorbed photosynthetically active radiation for sunlit and shaded leaves [\phi ^{sun} ,\phi ^{sha} W m-2 (section 2.4.1)] to give sunlit and shaded stomatal resistance (r_{s}^{sun} ,r_{s}^{sha} s m-1) and photosynthesis (A^{sun} ,A^{sha} µmol CO2 m-2 s-1). Canopy photosynthesis is A^{sun} L^{sun} +A^{sha} L^{sha} , where L^{sun} and L^{sha} are the sunlit and shaded leaf area indices (section 2.4.1). Canopy conductance is \frac{1}{r_{b} +r_{s}^{sun} } L^{sun} +\frac{1}{r_{b} +r_{s}^{sha} } L^{sha} , where r_{b} is the leaf boundary layer resistance (section 2.5.3).

2.9.3. Stomatal resistance

CLM5 calculates stomatal conductance using the Medlyn stomatal conductance model (Medlyn et al. 2011). Previous versions of CLM calculated leaf stomatal resistance is using the Ball-Berry conductance model as described by Collatz et al. (1991) and implemented in global climate models (Sellers et al. 1996). The Medlyn model calculates stomatal conductance (i.e., the inverse of resistance) based on net leaf photosynthesis, the vapor pressure deficit, and the CO2 concentration at the leaf surface. Leaf stomatal resistance is:

(2.9.1)\frac{1}{r_{s} } =g_{s} = g_{o} + 1.6(1 + \frac{g_{1} }{\sqrt{D}}) \frac{A_{n} }{{c_{s} \mathord{\left/ {\vphantom {c_{s}  P_{atm} }} \right. \kern-\nulldelimiterspace} P_{atm} } }

where r_{s} is leaf stomatal resistance (s m2 \mumol-1), g_{o} is the minimum stomatal conductance (\mu mol m -2 s-1), A_{n} is leaf net photosynthesis (\mumol CO2 m-2 s-1), c_{s} is the CO2 partial pressure at the leaf surface (Pa), P_{atm} is the atmospheric pressure (Pa), and D is the vapor pressure deficit at the leaf surface (kPa). g_{1} is a plant functional type dependent parameter (Table 2.9.1) and are the same as those used in the CABLE model (de Kauwe et al. 2015).

The value for g_{o}=100 \mu mol m -2 s-1 for C3 and C4 plants. Photosynthesis is calculated for sunlit (A^{sun}) and shaded (A^{sha}) leaves to give r_{s}^{sun} and r_{s}^{sha}. Additionally, soil water influences stomatal resistance through plant hydraulic stress, detailed in the Plant Hydraulics chapter.

Resistance is converted from units of s m2 \mu mol-1 to s m-1 as: 1 s m-1 = 1\times 10^{-9} R_{gas} \frac{\theta _{atm} }{P_{atm} } \mu mol-1 m2 s, where R_{gas} is the universal gas constant (J K-1 kmol-1) (Table 2.2.7) and \theta _{atm} is the atmospheric potential temperature (K).

Table 2.9.1 Plant functional type (PFT) stomatal conductance parameters.



NET Temperate


NET Boreal


NDT Boreal


BET Tropical


BET temperate


BDT tropical


BDT temperate


BDT boreal


BES temperate


BDS temperate


BDS boreal


C3 arctic grass


C3 grass


C4 grass


Temperate Corn


Spring Wheat


Temperate Soybean








Tropical Corn


Tropical Soybean


2.9.4. Photosynthesis

Photosynthesis in C3 plants is based on the model of Farquhar et al. (1980). Photosynthesis in C4 plants is based on the model of Collatz et al. (1992). Bonan et al. (2011) describe the implementation, modified here. In its simplest form, leaf net photosynthesis after accounting for respiration (R_{d} ) is

(2.9.2)A_{n} =\min \left(A_{c} ,A_{j} ,A_{p} \right)-R_{d} .

The RuBP carboxylase (Rubisco) limited rate of carboxylation A_{c} (\mu mol CO2 m-2 s-1) is

(2.9.3)A_{c} =\left\{\begin{array}{l} {\frac{V_{c\max } \left(c_{i} -\Gamma _{\*} \right)}{c_{i} +K_{c} \left(1+{o_{i} \mathord{\left/ {\vphantom {o_{i}  K_{o} }} \right. \kern-\nulldelimiterspace} K_{o} } \right)} \qquad {\rm for\; C}_{{\rm 3}} {\rm \; plants}} \\ {V_{c\max } \qquad \qquad \qquad {\rm for\; C}_{{\rm 4}} {\rm \; plants}} \end{array}\right\}\qquad \qquad c_{i} -\Gamma _{\*} \ge 0.

The maximum rate of carboxylation allowed by the capacity to regenerate RuBP (i.e., the light-limited rate) A_{j} (\mu mol CO2 m-2 s-1) is

(2.9.4)A_{j} =\left\{\begin{array}{l} {\frac{J_{x}\left(c_{i} -\Gamma _{\*} \right)}{4c_{i} +8\Gamma _{\*} } \qquad \qquad {\rm for\; C}_{{\rm 3}} {\rm \; plants}} \\ {\alpha (4.6\phi )\qquad \qquad {\rm for\; C}_{{\rm 4}} {\rm \; plants}} \end{array}\right\}\qquad \qquad c_{i} -\Gamma _{\*} \ge 0.

The product-limited rate of carboxylation for C3 plants and the PEP carboxylase-limited rate of carboxylation for C4 plants A_{p} (\mu mol CO2 m-2 s-1) is

(2.9.5)A_{p} =\left\{\begin{array}{l} {3T_{p\qquad } \qquad \qquad {\rm for\; C}_{{\rm 3}} {\rm \; plants}} \\ {k_{p} \frac{c_{i} }{P_{atm} } \qquad \qquad \qquad {\rm for\; C}_{{\rm 4}} {\rm \; plants}} \end{array}\right\}.

In these equations, c_{i} is the internal leaf CO2 partial pressure (Pa) and o_{i} =0.20P_{atm} is the O2 partial pressure (Pa). K_{c} and K_{o} are the Michaelis-Menten constants (Pa) for CO2 and O2. \Gamma _{\*} (Pa) is the CO2 compensation point. V_{c\max } is the maximum rate of carboxylation (µmol m-2 s-1, Chapter 2.10) and J_{x} is the electron transport rate (µmol m-2 s-1). T_{p} is the triose phosphate utilization rate (µmol m-2 s-1), taken as T_{p} =0.167V_{c\max } so that A_{p} =0.5V_{c\max } for C3 plants (as in Collatz et al. 1992). For C4 plants, the light-limited rate A_{j} varies with \phi in relation to the quantum efficiency (\alpha =0.05 mol CO2 mol-1 photon). \phi is the absorbed photosynthetically active radiation (W m-2) (section 2.4.1) , which is converted to photosynthetic photon flux assuming 4.6 \mu mol photons per joule. k_{p} is the initial slope of C4 CO2 response curve.

For C3 plants, the electron transport rate depends on the photosynthetically active radiation absorbed by the leaf. A common expression is the smaller of the two roots of the equation

(2.9.6)\Theta _{PSII} J_{x}^{2} -\left(I_{PSII} +J_{\max } \right)J_{x}+I_{PSII} J_{\max } =0

where J_{\max } is the maximum potential rate of electron transport (\mumol m-2 s-1, Chapter 2.10), I_{PSII} is the light utilized in electron transport by photosystem II (µmol m-2 s-1), and \Theta _{PSII} is a curvature parameter. For a given amount of photosynthetically active radiation absorbed by a leaf (\phi, W m-2), converted to photosynthetic photon flux density with 4.6 \mumol J-1, the light utilized in electron transport is

(2.9.7)I_{PSII} =0.5\Phi _{PSII} (4.6\phi )

where \Phi _{PSII} is the quantum yield of photosystem II, and the term 0.5 arises because one photon is absorbed by each of the two photosystems to move one electron. Parameter values are \Theta _{PSII} = 0.7 and \Phi _{PSII} = 0.85. In calculating A_{j} (for both C3 and C4 plants), \phi =\phi ^{sun} for sunlit leaves and \phi =\phi ^{sha} for shaded leaves.

The model uses co-limitation as described by Collatz et al. (1991, 1992). The actual gross photosynthesis rate, A, is given by the smaller root of the equations

(2.9.8)\begin{array}{rcl} {\Theta _{cj} A_{i}^{2} -\left(A_{c} +A_{j} \right)A_{i} +A_{c} A_{j} } & {=} & {0} \\ {\Theta _{ip} A^{2} -\left(A_{i} +A_{p} \right)A+A_{i} A_{p} } & {=} & {0} \end{array} .

Values are \Theta _{cj} =0.98 and \Theta _{ip} =0.95 for C3 plants; and \Theta _{cj} =0.80and \Theta _{ip} =0.95 for C4 plants. A_{i} is the intermediate co-limited photosynthesis. A_{n} =A-R_{d} .

The parameters K_{c}, K_{o}, and \Gamma depend on temperature. Values at 25 o C are K_{c25} ={\rm 4}0{\rm 4}.{\rm 9}\times 10^{-6} P_{atm}, K_{o25} =278.4\times 10^{-3} P_{atm}, and \Gamma _{25} {\rm =42}.75\times 10^{-6} P_{atm}. V_{c\max }, J_{\max }, T_{p}, k_{p}, and R_{d} also vary with temperature.

J_{\max 25} at 25 oC: is calculated by the LUNA model (Chapter 2.10)

Parameter values at 25 oC are calculated from V_{c\max } at 25 oC:, including: T_{p25} =0.167V_{c\max 25}, and R_{d25} =0.015V_{c\max 25} (C3) and R_{d25} =0.025V_{c\max 25} (C4).

For C4 plants, k_{p25} =20000\; V_{c\max 25}.

However, when the biogeochemistry is active (the default mode), R_{d25} is calculated from leaf nitrogen as described in (Chapter 2.17)

The parameters V_{c\max 25}, J_{\max 25}, T_{p25}, k_{p25}, and R_{d25} are scaled over the canopy for sunlit and shaded leaves (section 2.9.5). In C3 plants, these are adjusted for leaf temperature, T_{v} (K), as:

(2.9.9)\begin{array}{rcl} {V_{c\max } } & {=} & {V_{c\max 25} \; f\left(T_{v} \right)f_{H} \left(T_{v} \right)} \\ {J_{\max } } & {=} & {J_{\max 25} \; f\left(T_{v} \right)f_{H} \left(T_{v} \right)} \\ {T_{p} } & {=} & {T_{p25} \; f\left(T_{v} \right)f_{H} \left(T_{v} \right)} \\ {R_{d} } & {=} & {R_{d25} \; f\left(T_{v} \right)f_{H} \left(T_{v} \right)} \\ {K_{c} } & {=} & {K_{c25} \; f\left(T_{v} \right)} \\ {K_{o} } & {=} & {K_{o25} \; f\left(T_{v} \right)} \\ {\Gamma } & {=} & {\Gamma _{25} \; f\left(T_{v} \right)} \end{array}

(2.9.10)f\left(T_{v} \right)=\; \exp \left[\frac{\Delta H_{a} }{298.15\times 0.001R_{gas} } \left(1-\frac{298.15}{T_{v} } \right)\right]


(2.9.11)f_{H} \left(T_{v} \right)=\frac{1+\exp \left(\frac{298.15\Delta S-\Delta H_{d} }{298.15\times 0.001R_{gas} } \right)}{1+\exp \left(\frac{\Delta ST_{v} -\Delta H_{d} }{0.001R_{gas} T_{v} } \right)}  .

Table 2.9.2 lists parameter values for \Delta H_{a} and \Delta H_{d} . \Delta S is calculated separately for V_{c\max } and J_{max } to allow for temperature acclimation of photosynthesis (see equation (2.9.15)), and \Delta S is 490 J mol -1 K -1 for R_d (Bonan et al. 2011, Lombardozzi et al. 2015). Because T_{p} as implemented here varies with V_{c\max } , T_{p} uses the same temperature parameters as V_{c\max} . For C4 plants,

(2.9.12)\begin{array}{l} {V_{c\max } =V_{c\max 25} \left[\frac{Q_{10} ^{(T_{v} -298.15)/10} }{f_{H} \left(T_{v} \right)f_{L} \left(T_{v} \right)} \right]} \\ {f_{H} \left(T_{v} \right)=1+\exp \left[s_{1} \left(T_{v} -s_{2} \right)\right]} \\ {f_{L} \left(T_{v} \right)=1+\exp \left[s_{3} \left(s_{4} -T_{v} \right)\right]} \end{array}

with Q_{10} =2, s_{1} =0.3K-1 s_{2} =313.15 K, s_{3} =0.2K-1, and s_{4} =288.15 K. Additionally,

(2.9.13)R_{d} =R_{d25} \left\{\frac{Q_{10} ^{(T_{v} -298.15)/10} }{1+\exp \left[s_{5} \left(T_{v} -s_{6} \right)\right]} \right\}

with Q_{10} =2, s_{5} =1.3 K-1 and s_{6} =328.15K, and

(2.9.14)k_{p} =k_{p25} \, Q_{10} ^{(T_{v} -298.15)/10}

with Q_{10} =2.

Table 2.9.2 Temperature dependence parameters for C3 photosynthesis.


\Delta H_{a} (J mol-1)

\Delta H_{d} (J mol-1)

V_{c\max }



J_{\max }













\Gamma _{\*}


In the model, acclimation is implemented as in Kattge and Knorr (2007). In this parameterization, V_{c\max } and J_{\max } vary with the plant growth temperature. This is achieved by allowing \Delta S to vary with growth temperature according to

(2.9.15)\begin{array}{l} {\Delta S=668.39-1.07(T_{10} -T_{f} )\qquad \qquad {\rm for\; }V_{c\max } } \\ {\Delta S=659.70-0.75(T_{10} -T_{f} )\qquad \qquad {\rm for\; }J_{\max } } \end{array}

The effect is to cause the temperature optimum of V_{c\max } and J_{\max } to increase with warmer temperatures. Additionally, the ratio J_{\max 25} /V_{c\max 25} at 25 oC decreases with growth temperature as

(2.9.16)J_{\max 25} /V_{c\max 25} =2.59-0.035(T_{10} -T_{f} ).

In these acclimation functions, T_{10} is the 10-day mean air temperature (K) and T_{f} is the freezing point of water (K). For lack of data, T_{p} acclimates similar to V_{c\max }. Acclimation is restricted over the temperature range T_{10} -T_{f} \ge 11oC and T_{10} -T_{f} \le 35oC.

2.9.5. Canopy scaling

When LUNA is on, the V_{c\max 25} for sun leaves is scaled to the shaded leaves J_{\max 25} , T_{p25} , k_{p25}, and R_{d25} scale similarly.

{V_{c\max 25 sha}} & {=} & {V_{c\max 25 sha} \frac{i_{v,sha}}{i_{v,sun}}}  \\
{J_{\max 25 sha}}  & {=} & {J_{\max 25 sun}  \frac{i_{v,sha}}{i_{v,sun}}}  \\
{T_{p sha}}        & {=} & {T_{p sun}        \frac{i_{v,sha}}{i_{v,sun}}}  \end{array}

Where i_{v,sun} and i_{v,sha} are the leaf-to-canopy scaling coefficients of the twostream radiation model, calculated as

(2.9.18)i_{v,sun} = \frac{(1 - e^{-(k_{n,ext}+k_{b,ext})*lai_e)} / (k_{n,ext}+k_{b,ext})}{f_{sun}*lai_e}\\
i_{v,sha} = \frac{(1 - e^{-(k_{n,ext}+k_{b,ext})*lai_e)} / (k_{n,ext}+k_{b,ext})}{(1 - f_{sun})*lai_e}

k_{n,ext} is the extinction coefficient for N through the canopy (0.3). k_{b,ext} is the direct beam extinction coefficient calculated in the surface albedo routine, and f_{sun} is the fraction of sunlit leaves, both derived from Chapter 2.3.

When LUNA is off, scaling defaults to the mechanism used in CLM4.5.

2.9.6. Numerical implementation

The CO2 partial pressure at the leaf surface, c_{s} (Pa), and the vapor pressure at the leaf surface, e_{s} (Pa), needed for the stomatal resistance model in equation (2.9.1), and the internal leaf CO2 partial pressure c_{i} (Pa), needed for the photosynthesis model in equations (2.9.2)-(2.9.4), are calculated assuming there is negligible capacity to store CO2 and water vapor at the leaf surface so that

(2.9.19)A_{n} =\frac{c_{a} -c_{i} }{\left(1.4r_{b} +1.6r_{s} \right)P_{atm} } =\frac{c_{a} -c_{s} }{1.4r_{b} P_{atm} } =\frac{c_{s} -c_{i} }{1.6r_{s} P_{atm} }

and the transpiration fluxes are related as

(2.9.20)\frac{e_{a} -e_{i} }{r_{b} +r_{s} } =\frac{e_{a} -e_{s} }{r_{b} } =\frac{e_{s} -e_{i} }{r_{s} }

where r_{b} is leaf boundary layer resistance (s m2 \mu mol-1) (section 2.5.3), the terms 1.4 and 1.6 are the ratios of diffusivity of CO2 to H2O for the leaf boundary layer resistance and stomatal resistance, c_{a} ={\rm CO}_{{\rm 2}} \left({\rm mol\; mol}^{{\rm -1}} \right), P_{atm} is the atmospheric CO2 partial pressure (Pa) calculated from CO2 concentration (ppmv), e_{i} is the saturation vapor pressure (Pa) evaluated at the leaf temperature T_{v} , and e_{a} is the vapor pressure of air (Pa). The vapor pressure of air in the plant canopy e_{a} (Pa) is determined from

(2.9.21)e_{a} =\frac{P_{atm} q_{s} }{0.622}

where q_{s} is the specific humidity of canopy air (kg kg-1, section 2.5.3). Equations and are solved for c_{s} and e_{s}

(2.9.22)c_{s} =c_{a} -1.4r_{b} P_{atm} A_{n}

(2.9.23)e_{s} =\frac{e_{a} r_{s} +e_{i} r_{b} }{r_{b} +r_{s} }

Substitution of equation (2.9.23) into equation (2.9.1) gives an expression for stomatal resistance (r_{s} ) as a function of photosynthesis (A_{n} ), given here in terms of conductance with g_{s} =1/r_{s} and g_{b} =1/r_{b}

(2.9.24)g_{s}^{2} + bg_{s} + c = 0


(2.9.25)b = 2(g_{o} * 10^{-6} + d) + \frac{(g_{1}d)^{2}}{g_{b}*10^{-6}D}

c = (g_{o}*10^{-6})^{2} + [2g_{o}*10^{-6} + d \frac{1-g_{1}^{2}} {D}]d


(2.9.26)d = \frac {1.6 A_{n}} {c_{s} / P_{atm} * 10^{6}}

D = \frac {e_{i} - e_{a}} {1000}

Stomatal conductance, as solved by equation (2.9.24) (mol m -2 s -1), is the larger of the two roots that satisfy the quadratic equation. Values for c_{i} are given by

(2.9.27)c_{i} =c_{a} -\left(1.4r_{b} +1.6r_{s} \right)P_{atm} A{}_{n}

The equations for c_{i} , c_{s} , r_{s} , and A_{n} are solved iteratively until c_{i} converges. Sun et al. (2012) pointed out that the CLM4 numerical approach does not always converge. Therefore, the model uses a hybrid algorithm that combines the secant method and Brent’s method to solve for c_{i} . The equation set is solved separately for sunlit (A_{n}^{sun} , r_{s}^{sun} ) and shaded (A_{n}^{sha} , r_{s}^{sha} ) leaves.