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

• and 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 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 [ , W m-2 (section 2.4.1)] to give sunlit and shaded stomatal resistance ( , s m-1) and photosynthesis ( , µmol CO2 m-2 s-1). Canopy photosynthesis is , where and are the sunlit and shaded leaf area indices (section 2.4.1). Canopy conductance is , where 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)

where is leaf stomatal resistance (s m2 mol-1), is the minimum stomatal conductance ( mol m -2 s-1), is leaf net photosynthesis (mol CO2 m-2 s-1), is the CO2 partial pressure at the leaf surface (Pa), is the atmospheric pressure (Pa), and is the vapor pressure deficit at the leaf surface (kPa). 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 mol m -2 s-1 for C3 and C4 plants. Photosynthesis is calculated for sunlit () and shaded () leaves to give and . Additionally, soil water influences stomatal resistance through plant hydraulic stress, detailed in the Plant Hydraulics chapter.

Resistance is converted from units of s m2 mol-1 to s m-1 as: 1 s m-1 = mol-1 m2 s, where is the universal gas constant (J K-1 kmol-1) (Table 2.2.7) and is the atmospheric potential temperature (K).

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

PFT

g1

NET Temperate

2.35

NET Boreal

2.35

NDT Boreal

2.35

BET Tropical

4.12

BET temperate

4.12

BDT tropical

4.45

BDT temperate

4.45

BDT boreal

4.45

BES temperate

4.70

BDS temperate

4.70

BDS boreal

4.70

C3 arctic grass

2.22

C3 grass

5.25

C4 grass

1.62

Temperate Corn

1.79

Spring Wheat

5.79

Temperate Soybean

5.79

Cotton

5.79

Rice

5.79

Sugarcane

1.79

Tropical Corn

1.79

Tropical Soybean

5.79

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 ( ) is

(2.9.2)

The RuBP carboxylase (Rubisco) limited rate of carboxylation ( mol CO2 m-2 s-1) is

(2.9.3)

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

(2.9.4)

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

(2.9.5)

In these equations, is the internal leaf CO2 partial pressure (Pa) and is the O2 partial pressure (Pa). and are the Michaelis-Menten constants (Pa) for CO2 and O2. (Pa) is the CO2 compensation point. is the maximum rate of carboxylation (µmol m-2 s-1, Chapter 2.10) and is the electron transport rate (µmol m-2 s-1). is the triose phosphate utilization rate (µmol m-2 s-1), taken as so that for C3 plants (as in Collatz et al. 1992). For C4 plants, the light-limited rate varies with in relation to the quantum efficiency ( mol CO2 mol-1 photon). is the absorbed photosynthetically active radiation (W m-2) (section 2.4.1) , which is converted to photosynthetic photon flux assuming 4.6 mol photons per joule. 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)

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

(2.9.7)

where 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 = 0.7 and = 0.85. In calculating (for both C3 and C4 plants), for sunlit leaves and for shaded leaves.

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

(2.9.8)

Values are and for C3 plants; and and for C4 plants. is the intermediate co-limited photosynthesis. .

The parameters , , and depend on temperature. Values at 25 o C are , , and . , , , , and also vary with temperature.

at 25 oC: is calculated by the LUNA model (Chapter 2.10)

Parameter values at 25 oC are calculated from at 25 oC:, including: , and (C3) and (C4).

For C4 plants, .

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

The parameters , , , , and are scaled over the canopy for sunlit and shaded leaves (section 2.9.5). In C3 plants, these are adjusted for leaf temperature, (K), as:

(2.9.9)

(2.9.10)

and

(2.9.11)

Table 2.9.2 lists parameter values for and . is calculated separately for and to allow for temperature acclimation of photosynthesis (see equation (2.9.15)), and is 490 J mol -1 K -1 for (Bonan et al. 2011, Lombardozzi et al. 2015). Because as implemented here varies with , uses the same temperature parameters as . For C4 plants,

(2.9.12)

with , K-1 K, K-1, and K. Additionally,

(2.9.13)

with , K-1 and K, and

(2.9.14)

with .

Table 2.9.2 Temperature dependence parameters for C3 photosynthesis.

Parameter

(J mol-1)

(J mol-1)

72000

200000

50000

200000

72000

200000

46390

150650

79430

36380

37830

In the model, acclimation is implemented as in Kattge and Knorr (2007). In this parameterization, and vary with the plant growth temperature. This is achieved by allowing to vary with growth temperature according to

(2.9.15)

The effect is to cause the temperature optimum of and to increase with warmer temperatures. Additionally, the ratio at 25 oC decreases with growth temperature as

(2.9.16)

In these acclimation functions, is the 10-day mean air temperature (K) and is the freezing point of water (K). For lack of data, acclimates similar to . Acclimation is restricted over the temperature range oC and oC.

2.9.5. Canopy scaling¶

When LUNA is on, the for sun leaves is scaled to the shaded leaves , , , and scale similarly.

(2.9.17)

Where and are the leaf-to-canopy scaling coefficients of the twostream radiation model, calculated as

(2.9.18)

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 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, (Pa), and the vapor pressure at the leaf surface, (Pa), needed for the stomatal resistance model in equation (2.9.1), and the internal leaf CO2 partial pressure (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)

and the transpiration fluxes are related as

(2.9.20)

where is leaf boundary layer resistance (s m2 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, , is the atmospheric CO2 partial pressure (Pa) calculated from CO2 concentration (ppmv), is the saturation vapor pressure (Pa) evaluated at the leaf temperature , and is the vapor pressure of air (Pa). The vapor pressure of air in the plant canopy (Pa) is determined from

(2.9.21)

where is the specific humidity of canopy air (kg kg-1, section 2.5.3). Equations and are solved for and

(2.9.22)

(2.9.23)

Substitution of equation (2.9.23) into equation (2.9.1) gives an expression for stomatal resistance ( ) as a function of photosynthesis ( ), given here in terms of conductance with and

(2.9.24)

where

(2.9.25)

and

(2.9.26)

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 are given by

(2.9.27)

The equations for , , , and are solved iteratively until 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 . The equation set is solved separately for sunlit ( , ) and shaded ( , ) leaves.