diff --git a/doc/source/tech_note/Photosynthesis/CLM50_Tech_Note_Photosynthesis.rst b/doc/source/tech_note/Photosynthesis/CLM50_Tech_Note_Photosynthesis.rst index d739751d7d..525751dd95 100644 --- a/doc/source/tech_note/Photosynthesis/CLM50_Tech_Note_Photosynthesis.rst +++ b/doc/source/tech_note/Photosynthesis/CLM50_Tech_Note_Photosynthesis.rst @@ -3,16 +3,14 @@ Stomatal Resistance and Photosynthesis ========================================= -Summary of CLM5.0 updates relative to the CLM4.5 ------------------------------------------------------ +History +------- -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 (:ref:`Oleson et al. 2013 `). - -CLM5 includes the following new changes to photosynthesis and stomatal conductance: +We describe here the complete photosynthesis and stomatal conductance parameterizations that appear in CLM6.0. In this version relative to CLM5, we have changed numerous parameter values, but have kept the algorithm unchanged. In CLM5 relative to CLM4.5, this section included the following updates: - Default stomatal conductance calculation uses the Medlyn conductance model -- :math:`V_{c,max}` and :math:`J_{max}` at 25 :sup:`\o`\ C: are now prognostic, and predicted via optimality by the LUNA model (Chapter :numref:`rst_Photosynthetic Capacity`) +- :math:`V_{c,max}` and :math:`J_{max}` at 25\ :sup:`\o`\ C: are now prognostic, and predicted via optimality by the LUNA model (Chapter :numref:`rst_Photosynthetic Capacity`) - Leaf N concentration and the fraction of leaf N in Rubisco used to calculate :math:`V_{cmax25}` are determined by the LUNA model (Chapter :numref:`rst_Photosynthetic Capacity`) @@ -28,16 +26,16 @@ Leaf stomatal resistance, which is needed for the water vapor flux (Chapter :num Stomatal resistance ----------------------- -CLM5 calculates stomatal conductance using the Medlyn stomatal conductance model (:ref:`Medlyn et al. 2011`). Previous versions of CLM calculated leaf stomatal resistance using the Ball-Berry conductance model as described by :ref:`Collatz et al. (1991)` and implemented in global climate models (:ref:`Sellers et al. 1996`). The Medlyn model calculates stomatal conductance (i.e., the inverse of resistance) based on net leaf photosynthesis, the leaf-to-air vapor pressure difference, and the CO\ :sub:`2` concentration at the leaf surface. Leaf stomatal resistance is: +Since CLM5 the model has calculated stomatal conductance using the Medlyn stomatal conductance model (:ref:`Medlyn et al. 2011`). Previous versions of CLM calculated leaf stomatal resistance using the Ball-Berry conductance model as described by :ref:`Collatz et al. (1991)` and implemented in global climate models (:ref:`Sellers et al. 1996`). The Medlyn model calculates stomatal conductance (i.e., the inverse of resistance) based on net leaf photosynthesis, the leaf-to-air vapor pressure difference, and the CO\ :sub:`2` concentration at the leaf surface. Leaf stomatal resistance is: .. math:: :label: 9.1 \frac{1}{r_{s} } =g_{s} = g_{o} + 1.6(1 + \frac{g_{1} }{\sqrt{D_{s}}}) \frac{A_{n} }{{c_{s} \mathord{\left/ {\vphantom {c_{s} P_{atm} }} \right.} P_{atm} } } -where :math:`r_{s}` is leaf stomatal resistance (s m\ :sup:`2` :math:`\mu`\ mol\ :sup:`-1`), :math:`g_{o}` is the minimum stomatal conductance (:math:`\mu` mol m :sup:`-2` s\ :sup:`-1`), :math:`A_{n}` is leaf net photosynthesis (:math:`\mu`\ mol CO\ :sub:`2` m\ :sup:`-2` s\ :sup:`-1`), :math:`c_{s}` is the CO\ :sub:`2` partial pressure at the leaf surface (Pa), :math:`P_{atm}` is the atmospheric pressure (Pa), and :math:`D_{s}=(e_{i}-e{_s})/1000` is the leaf-to-air vapor pressure difference at the leaf surface (kPa) where :math:`e_{i}` is the saturation vapor pressure (Pa) evaluated at the leaf temperature :math:`T_{v}`, and :math:`e_{s}` is the vapor pressure at the leaf surface (Pa). :math:`g_{1}` is a plant functional type dependent parameter (:numref:`Table Plant functional type (PFT) stomatal conductance parameters`) and is the same as those used in the CABLE model (:ref:`de Kauwe et al. 2015 `). +where :math:`r_{s}` is leaf stomatal resistance (s m\ :sup:`2` :math:`\mu`\ mol\ :sup:`-1`), :math:`A_{n}` is leaf net photosynthesis (:math:`\mu`\ mol CO\ :sub:`2` m\ :sup:`-2` s\ :sup:`-1`), :math:`c_{s}` is the CO\ :sub:`2` partial pressure at the leaf surface (Pa), :math:`P_{atm}` is the atmospheric pressure (Pa), and :math:`D_{s}=(e_{i}-e{_s})/1000` is the leaf-to-air vapor pressure difference at the leaf surface (kPa) where :math:`e_{i}` is the saturation vapor pressure (Pa) evaluated at the leaf temperature :math:`T_{v}`, and :math:`e_{s}` is the vapor pressure at the leaf surface (Pa). :math:`g_{o}` is plant functional type (pft)-dependent minimum stomatal conductance (:math:`\mu` mol m :sup:`-2` s\ :sup:`-1`) and :math:`g_{1}` is a pft-dependent parameter (:numref:`Table Plant functional type (PFT) stomatal conductance parameters`) with same values originally as in the CABLE model (:ref:`de Kauwe et al. 2015 `) but most values have been replaced in CLM6. -The value for :math:`g_{o}=100` :math:`\mu` mol m :sup:`-2` s\ :sup:`-1` for C\ :sub:`3` and C\ :sub:`4` plants. Photosynthesis is calculated for sunlit (:math:`A^{sun}`) and shaded (:math:`A^{sha}`) leaves to give :math:`r_{s}^{sun}` and :math:`r_{s}^{sha}`. Additionally, soil water influences stomatal resistance through plant hydraulic stress, detailed in the :ref:`rst_Plant Hydraulics` chapter. +Photosynthesis is calculated for sunlit (:math:`A^{sun}`) and shaded (:math:`A^{sha}`) leaves to give :math:`r_{s}^{sun}` and :math:`r_{s}^{sha}`. Additionally, soil water influences stomatal resistance through plant hydraulic stress, detailed in the :ref:`rst_Plant Hydraulics` chapter. Resistance is converted from units of s m\ :sup:`2` :math:`\mu` mol\ :sup:`-1` to s m\ :sup:`-1` as: 1 s m\ :sup:`-1` = :math:`1\times 10^{-9} R_{gas} \frac{\theta _{atm} }{P_{atm} }` :math:`\mu` mol\ :sup:`-1` m\ :sup:`2` s, where :math:`R_{gas}` is the universal gas constant (J K\ :sup:`-1` kmol\ :sup:`-1`) (:numref:`Table Physical constants`) and :math:`\theta _{atm}` is the atmospheric potential temperature (K). @@ -45,57 +43,59 @@ Resistance is converted from units of s m\ :sup:`2` :math:`\mu` mol\ :sup:`-1` t .. table:: Plant functional type (PFT) stomatal conductance parameters. - +----------------------------------+-------------------+ - | PFT | g\ :sub:`1` | - +==================================+===================+ - | 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 | - +----------------------------------+-------------------+ - | C\ :sub:`3` arctic grass | 2.22 | - +----------------------------------+-------------------+ - | C\ :sub:`3` grass | 5.25 | - +----------------------------------+-------------------+ - | C\ :sub:`4` 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 | - +----------------------------------+-------------------+ - | Miscanthus | 1.79 | - +----------------------------------+-------------------+ - | Switchgrass | 1.79 | - +----------------------------------+-------------------+ + +----------------------------------+-------------+------------------+ + | PFT | g\ :sub:`o` | g\ :sub:`1` | + +==================================+=============+==================+ + | NET Temperate | 110.93 | 2.35 | + +----------------------------------+-------------+------------------+ + | NET Boreal | 12500 | 2.57 | + +----------------------------------+-------------+------------------+ + | NDT Boreal | 1.00 | 2.09 | + +----------------------------------+-------------+------------------+ + | BET Tropical | 1733.21 | 3.50 | + +----------------------------------+-------------+------------------+ + | BET temperate | 102.24 | 4.12 | + +----------------------------------+-------------+------------------+ + | BDT tropical | 97.56 | 2.85 | + +----------------------------------+-------------+------------------+ + | BDT temperate | 100.40 | 4.45 | + +----------------------------------+-------------+------------------+ + | BDT boreal | 99.73 | 5.05 | + +----------------------------------+-------------+------------------+ + | BES temperate | 100.00 | 4.38 | + +----------------------------------+-------------+------------------+ + | BDS temperate | 100.00 | 4.70 | + +----------------------------------+-------------+------------------+ + | BDS boreal | 100.00 | 4.70 | + +----------------------------------+-------------+------------------+ + | C\ :sub:`3` arctic grass | 100.00 | 3.78 | + +----------------------------------+-------------+------------------+ + | C\ :sub:`3` grass | 5063.54 | 8.32 | + +----------------------------------+-------------+------------------+ + | C\ :sub:`4` grass | 100.00 | 1.62 | + +----------------------------------+-------------+------------------+ + | C\ :sub:`3` crop | 5063.54 | 9.17 | + +----------------------------------+-------------+------------------+ + | Temperate Corn | 100.00 | 1.79 | + +----------------------------------+-------------+------------------+ + | Spring Wheat | 100.00 | 5.79 | + +----------------------------------+-------------+------------------+ + | Temperate Soybean | 100.00 | 5.79 | + +----------------------------------+-------------+------------------+ + | Cotton | 100.00 | 5.79 | + +----------------------------------+-------------+------------------+ + | Rice | 100.00 | 5.79 | + +----------------------------------+-------------+------------------+ + | Sugarcane | 100.00 | 1.79 | + +----------------------------------+-------------+------------------+ + | Tropical Corn | 100.00 | 1.79 | + +----------------------------------+-------------+------------------+ + | Tropical Soybean | 100.00 | 5.79 | + +----------------------------------+-------------+------------------+ + | Miscanthus | 100.00 | 1.79 | + +----------------------------------+-------------+------------------+ + | Switchgrass | 100.00 | 1.79 | + +----------------------------------+-------------+------------------+ .. _Photosynthesis: @@ -105,18 +105,18 @@ Photosynthesis Photosynthesis in C\ :sub:`3` plants is based on the model of :ref:`Farquhar et al. (1980)`. Photosynthesis in C\ :sub:`4` plants is based on the model of :ref:`Collatz et al. (1992)`. :ref:`Bonan et al. (2011)` describe the implementation, modified here. In its simplest form, leaf net photosynthesis after accounting for respiration (:math:`R_{d}` ) is .. math:: - :label: 9.2 + :label: leaf_net_psn - A_{n} =\min \left(A_{c} ,A_{j} ,A_{p} \right)-R_{d} . + A_{n} =\min \left(A_{c} ,A_{j} ,A_{p} \right)-R_{d} The RuBP carboxylase (Rubisco) limited rate of carboxylation :math:`A_{c}` (:math:`\mu` \ mol CO\ :sub:`2` m\ :sup:`-2` s\ :sup:`-1`) is .. math:: - :label: 9.3 + :label: rubisco_lim_rate_of_carboxylation - 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.} 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. + A_{c} =\left\{\begin{array}{l} {\frac{\beta_{t} V_{c\max } \left(c_{i} -\Gamma _{*} \right)}{c_{i} +K_{c} \left(1+{o_{i} \mathord{\left/ {\vphantom {o_{i} K_{o} }} \right.} K_{o} } \right)} \qquad {\rm for\; C}_{{\rm 3}} {\rm \; plants}} \\ {\beta_{t} 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) :math:`A_{j}` (:math:`\mu` \ mol CO\ :sub:`2` m\ :sup:`-2` s\ :sup:`-1`) is +where :math:`\beta_{t} = \beta_{t,sun}` is the transpiration water stress for sunlit leaves and :math:`\beta_{t} = \beta_{t,sha}` for shaded leaves (Eqs. :eq:`beta_t_sun`, :eq:`beta_t_sha`). The maximum rate of carboxylation allowed by the capacity to regenerate RuBP (i.e., the light-limited rate) :math:`A_{j}` (:math:`\mu` \ mol CO\ :sub:`2` m\ :sup:`-2` s\ :sup:`-1`) is .. math:: :label: 9.4 @@ -128,9 +128,9 @@ The product-limited rate of carboxylation for C\ :sub:`3` plants and the PEP car .. math:: :label: 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\}. + 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, :math:`c_{i}` is the internal leaf CO\ :sub:`2` partial pressure (Pa) and :math:`o_{i} =0.20P_{atm}` is the O\ :sub:`2` partial pressure (Pa). :math:`K_{c}` and :math:`K_{o}` are the Michaelis-Menten constants (Pa) for CO\ :sub:`2` and O\ :sub:`2`. :math:`\Gamma _{*}` (Pa) is the CO\ :sub:`2` compensation point. :math:`V_{c\max }` is the maximum rate of carboxylation (µmol m\ :sup:`-2` s\ :sup:`-1`, Chapter :numref:`rst_Photosynthetic Capacity`) and :math:`J_{x}` is the electron transport rate (µmol m\ :sup:`-2` s\ :sup:`-1`). :math:`T_{p}` is the triose phosphate utilization rate (µmol m\ :sup:`-2` s\ :sup:`-1`), taken as :math:`T_{p} =0.167V_{c\max }` so that :math:`A_{p} =0.5V_{c\max }` for C\ :sub:`3` plants (as in :ref:`Collatz et al. 1992 `). For C\ :sub:`4` plants, the light-limited rate :math:`A_{j}` varies with :math:`\phi` in relation to the quantum efficiency (:math:`\alpha =0.05` mol CO\ :sub:`2` mol\ :sup:`-1` photon). :math:`\phi` is the absorbed photosynthetically active radiation (W m\ :sup:`-2`) (section :numref:`Solar Fluxes`), which is converted to photosynthetic photon flux assuming 4.6 :math:`\mu` \ mol photons per joule. :math:`k_{p}` is the initial slope of C\ :sub:`4` CO\ :sub:`2` response curve. +In these equations, :math:`c_{i}` is the internal leaf CO\ :sub:`2` partial pressure (Pa) and :math:`o_{i} =0.209P_{atm}` is the O\ :sub:`2` partial pressure (Pa) (where 0.209 is the value of the atmospheric O\ :sub:`2` molar ratio in mol/mol). :math:`K_{c}` and :math:`K_{o}` are the Michaelis-Menten constants (Pa) for CO\ :sub:`2` and O\ :sub:`2`. :math:`\Gamma _{*}` (Pa) is the CO\ :sub:`2` compensation point. :math:`V_{c\max }` is the maximum rate of carboxylation (µmol m\ :sup:`-2` s\ :sup:`-1`, Chapter :numref:`rst_Photosynthetic Capacity`) and :math:`J_{x}` is the electron transport rate (µmol m\ :sup:`-2` s\ :sup:`-1`). :math:`T_{p}` is the triose phosphate utilization rate (µmol m\ :sup:`-2` s\ :sup:`-1`), taken as :math:`T_{p} =0.167V_{c\max }` so that :math:`A_{p} =0.5V_{c\max }` for C\ :sub:`3` plants (as in :ref:`Collatz et al. 1992 `). For C\ :sub:`4` plants, the light-limited rate :math:`A_{j}` varies with :math:`\phi` in relation to the quantum efficiency (:math:`\alpha =0.05` mol CO\ :sub:`2` mol\ :sup:`-1` photon). :math:`\phi` is the absorbed photosynthetically active radiation (W m\ :sup:`-2`) (section :numref:`Solar Fluxes`), which is converted to photosynthetic photon flux assuming 4.6 :math:`\mu` \ mol photons per joule. :math:`k_{p}` is the initial slope of C\ :sub:`4` CO\ :sub:`2` response curve. For C\ :sub:`3` 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 @@ -146,30 +146,24 @@ where :math:`J_{\max }` is the maximum potential rate of electron transport (:ma I_{PSII} =0.5\Phi _{PSII} (4.6\phi ) -where :math:`\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 :math:`\Theta _{PSII}` \ = 0.7 and :math:`\Phi _{PSII}` \ = 0.85. In calculating :math:`A_{j}` (for both C\ :sub:`3` and C\ :sub:`4` plants), :math:`\phi =\phi ^{sun}` for sunlit leaves and :math:`\phi =\phi ^{sha}` for shaded leaves. +where :math:`\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 :math:`\Theta _{PSII}` \ = 0.7 and :math:`\Phi _{PSII} = 1 - f_{nps} = 0.85`, where :math:`f_{nps}` is the fraction of light absorbed by non-photosynthetic pigment. In calculating :math:`A_{j}` (for both C\ :sub:`3` and C\ :sub:`4` plants), :math:`\phi =\phi ^{sun}` for sunlit leaves and :math:`\phi =\phi ^{sha}` for shaded leaves. The model uses co-limitation as described by :ref:`Collatz et al. (1991, 1992) `. The actual gross photosynthesis rate, :math:`A`, is given by the smaller root of the equations .. math:: :label: 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 :math:`\Theta _{cj} =0.98` and :math:`\Theta _{ip} =0.95` for C\ :sub:`3` plants; and :math:`\Theta _{cj} =0.80`\ and :math:`\Theta _{ip} =0.95` for C\ :sub:`4` plants. :math:`A_{i}` is the intermediate co-limited photosynthesis. :math:`A_{n} =A-R_{d}`. + \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} -The parameters :math:`K_{c}`, :math:`K_{o}`, and :math:`\Gamma` depend on temperature. Values at 25 °C are :math:`K_{c25} ={\rm 4}0{\rm 4}.{\rm 9}\times 10^{-6} P_{atm}`, :math:`K_{o25} =278.4\times 10^{-3} P_{atm}`, and :math:`\Gamma _{25} {\rm =42}.75\times 10^{-6} P_{atm}`. :math:`V_{c\max }`, :math:`J_{\max }`, :math:`T_{p}`, :math:`k_{p}`, and :math:`R_{d}` also vary with temperature. +Values are :math:`\Theta _{cj} =0.9393` and :math:`\Theta _{ip} =0.95` for C\ :sub:`3` plants, :math:`\Theta _{cj} =0.80` and :math:`\Theta _{ip} =0.95` for C\ :sub:`4` plants, and :math:`\Theta _{cj} =0.98` for C\ :sub:`3` non-generic crops. :math:`A_{i}` is the intermediate co-limited photosynthesis. -:math:`J_{\max 25}` at 25 :sup:`\o`\ C: is calculated by the LUNA model (Chapter :numref:`rst_Photosynthetic Capacity`) +Now we write Eq. :eq:`leaf_net_psn` as :math:`A_{n} = A - \beta_{t} R_{d}` with :math:`\beta_{t}` as defined in Eq. :eq:`rubisco_lim_rate_of_carboxylation` to account for the effect of water stress on respiration. -Parameter values at 25 :sup:`\o`\ C are calculated from :math:`V_{c\max }` \ at 25 -:sup:`\o`\ C:, including: -:math:`T_{p25} =0.167V_{c\max 25}`, and -:math:`R_{d25} =0.015V_{c\max 25}` (C\ :sub:`3`) and -:math:`R_{d25} =0.025V_{c\max 25}` (C\ :sub:`4`). +The parameters :math:`K_{c}`, :math:`K_{o}`, and :math:`\Gamma` depend on temperature. Values at 25°C are :math:`K_{c25} ={\rm 4}0{\rm 4}.{\rm 9}\times 10^{-6} P_{atm}`, :math:`K_{o25} =278.4\times 10^{-3} P_{atm}`, and :math:`\Gamma _{25} {\rm =42}.75\times 10^{-6} P_{atm}`. -For C\ :sub:`4` plants, :math:`k_{p25} =20000\; V_{c\max 25}`. +:math:`V_{c\max }`, :math:`J_{\max }`, :math:`T_{p}`, :math:`k_{p}`, and :math:`R_{d}` also vary with temperature. :math:`J_{\max 25}` at 25\ :sup:`\o`\ C is calculated by the LUNA model (Chapter :numref:`rst_Photosynthetic Capacity`). -However, when the biogeochemistry is active (the default mode), :math:`R_{d25}` is calculated from leaf nitrogen as described in (Chapter :numref:`rst_Plant Respiration`) +Parameter values at 25\ :sup:`\o`\ C are calculated from :math:`V_{c\max }` \ at 25\ :sup:`\o`\ C, including: :math:`T_{p25} =0.167V_{c\max 25}`, :math:`R_{d25} =0.015V_{c\max 25}` (C\ :sub:`3`), and :math:`R_{d25} =0.025V_{c\max 25}` (C\ :sub:`4`). For C\ :sub:`4` plants, :math:`k_{p25} =20000\; V_{c\max 25}`. However, in active biogeochemistry mode (default), :math:`R_{d25}` is calculated from leaf nitrogen (see Chapter :numref:`rst_Plant Respiration`) The parameters :math:`V_{c\max 25}`, :math:`J_{\max 25}`, :math:`T_{p25}`, :math:`k_{p25}`, and :math:`R_{d25}` are scaled over the canopy for sunlit and shaded leaves (section :numref:`Canopy scaling`). In C\ :sub:`3` plants, these are adjusted for leaf temperature, :math:`T_{v}` (K), as: @@ -188,7 +182,7 @@ and .. math:: :label: 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)} . + 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)} :numref:`Table Temperature dependence parameters for C3 photosynthesis` lists parameter values for :math:`\Delta H_{a}` and :math:`\Delta H_{d}`. :math:`\Delta S` is calculated separately for :math:`V_{c\max }` and :math:`J_{max }` to allow for temperature acclimation of photosynthesis (see equation :eq:`9.16`), and :math:`\Delta S` is 490 J mol :sup:`-1` K :sup:`-1` for :math:`R_d` (:ref:`Bonan et al. 2011`, :ref:`Lombardozzi et al. 2015`). Because :math:`T_{p}` as implemented here varies with :math:`V_{c\max }`, :math:`T_{p}` uses the same temperature parameters as :math:`V_{c\max}`. For C\ :sub:`4` plants, @@ -246,12 +240,12 @@ In the model, acclimation is implemented as in :ref:`Kattge and Knorr (2007)