## 2.19.3. Carbon and Nitrogen Stoichiometry of New Growth[¶](#carbon-and-nitrogen-stoichiometry-of-new-growth "Permalink to this headline")
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After accounting for the carbon cost of maintenance respiration, the remaining carbon flux from photosynthesis which can be allocated to new growth (\\(CF\_{avail}\\), gC m\-2 s\-1) is

(2.19.6)[¶](#equation-19-6 "Permalink to this equation")\\\[CF\_{avail\\\_ alloc} =CF\_{GPP} -CF\_{GPP,mr} -CF\_{GPP,xs} .\\\]

Potential allocation to new growth is calculated for all of the plant carbon and nitrogen state variables based on specified C:N ratios for each tissue type and allometric parameters that relate allocation between various tissue types. The allometric parameters are defined as follows:

(2.19.7)[¶](#equation-19-7 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{l} {a\_{1} ={\\rm \\; ratio\\; of\\; new\\; fine\\; root\\; :\\; new\\; leaf\\; carbon\\; allocation}} \\\\ {a\_{2} ={\\rm \\; ratio\\; of\\; new\\; coarse\\; root\\; :\\; new\\; stem\\; carbon\\; allocation}} \\\\ {a\_{3} ={\\rm \\; ratio\\; of\\; new\\; stem\\; :\\; new\\; leaf\\; carbon\\; allocation}} \\\\ {a\_{4} ={\\rm \\; ratio\\; new\\; live\\; wood\\; :\\; new\\; total\\; wood\\; allocation}} \\\\ {g\_{1} ={\\rm ratio\\; of\\; growth\\; respiration\\; carbon\\; :\\; new\\; growth\\; carbon.\\; }} \\end{array}\\end{split}\\\]

Parameters \\(a\_{1}\\), \\(a\_{2}\\), and \\(a\_{4}\\) are defined as constants for a given PFT (Table 13.1), while \\(g\_{l }\\) = 0.3 (unitless) is prescribed as a constant for all PFTs, based on construction costs for a range of woody and non-woody tissues (Larcher, 1995).

The model includes a dynamic allocation scheme for woody vegetation (parameter \\(a\_{3}\\) = -1, [Table 2.19.1](#table-allocation-and-cn-ratio-parameters)), in which case the ratio for carbon allocation between new stem and new leaf increases with increasing net primary production (NPP), as

(2.19.8)[¶](#equation-19-8 "Permalink to this equation")\\\[a\_{3} =\\frac{2.7}{1+e^{-0.004NPP\_{ann} -300} } -0.4\\\]

where \\(NPP\_{ann}\\) is the annual sum of NPP from the previous year. This mechanism has the effect of increasing woody allocation in favorable growth environments (Allen et al., 2005; Vanninen and Makela, 2005) and during the phase of stand growth prior to canopy closure (Axelsson and Axelsson, 1986).

Table 2.19.1 Allocation and target carbon:nitrogen ratio parameters[¶](#id2 "Permalink to this table")         
| Plant functional type
 | \\(a\_{1}\\)

 | \\(a\_{2}\\)

 | \\(a\_{3}\\)

 | \\(a\_{4}\\)

 | \\(Target CN\_{leaf}\\)

 | \\(Target CN\_{fr}\\)

 | \\(Target CN\_{lw}\\)

 | \\(Target CN\_{dw}\\)

 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- |
| NET Temperate

 | 1

 | 0.3

 | \-1

 | 0.1

 | 35

 | 42

 | 50

 | 500

 |
| NET Boreal

 | 1

 | 0.3

 | \-1

 | 0.1

 | 40

 | 42

 | 50

 | 500

 |
| NDT Boreal

 | 1

 | 0.3

 | \-1

 | 0.1

 | 25

 | 42

 | 50

 | 500

 |
| BET Tropical

 | 1

 | 0.3

 | \-1

 | 0.1

 | 30

 | 42

 | 50

 | 500

 |
| BET temperate

 | 1

 | 0.3

 | \-1

 | 0.1

 | 30

 | 42

 | 50

 | 500

 |
| BDT tropical

 | 1

 | 0.3

 | \-1

 | 0.1

 | 25

 | 42

 | 50

 | 500

 |
| BDT temperate

 | 1

 | 0.3

 | \-1

 | 0.1

 | 25

 | 42

 | 50

 | 500

 |
| BDT boreal

 | 1

 | 0.3

 | \-1

 | 0.1

 | 25

 | 42

 | 50

 | 500

 |
| BES temperate

 | 1

 | 0.3

 | 0.2

 | 0.5

 | 30

 | 42

 | 50

 | 500

 |
| BDS temperate

 | 1

 | 0.3

 | 0.2

 | 0.5

 | 25

 | 42

 | 50

 | 500

 |
| BDS boreal C3 arctic grass

 | 1 1

 | 0.3 0

 | 0.2 0

 | 0.1 0

 | 25 25

 | 42 42

 | 50 0

 | 500 0

 |
| C3 grass

 | 2

 | 0

 | 0

 | 0

 | 25

 | 42

 | 0

 | 0

 |
| C4 grass

 | 2

 | 0

 | 0

 | 0

 | 25

 | 42

 | 0

 | 0

 |
| Crop R

 | 2

 | 0

 | 0

 | 0

 | 25

 | 42

 | 0

 | 0

 |
| Crop I

 | 2

 | 0

 | 0

 | 0

 | 25

 | 42

 | 0

 | 0

 |
| Corn R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Corn I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Temp Cereal R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Temp Cereal I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Winter Cereal R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Winter Cereal I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Soybean R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Soybean I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Miscanthus R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Miscanthus I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Switchgrass R

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |
| Switchgrass I

 | 2

 | 0

 | 0

 | 1

 | 25

 | 42

 | 50

 | 500

 |

Carbon to nitrogen ratios are defined for different tissue types as follows:

(2.19.9)[¶](#equation-19-9 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{l} {CN\_{leaf} =\\\_ {\\rm \\; C:N\\; for\\; leaf}} \\\\ {CN\_{fr} =\\\_ {\\rm \\; C:N\\; for\\; fine\\; root}} \\\\ {CN\_{lw} =\\\_ {\\rm \\; C:N\\; for\\; live\\; wood\\; (in\\; stem\\; and\\; coarse\\; root)}} \\\\ {CN\_{dw} =\\\_ {\\rm \\; C:N\\; for\\; dead\\; wood\\; (in\\; stem\\; and\\; coarse\\; root)}} \\end{array}\\end{split}\\\]

where all C:N parameters are defined as constants for a given PFT ([Table 2.19.1](#table-allocation-and-cn-ratio-parameters)).

Given values for the parameters in and, total carbon and nitrogen allocation to new growth ( \\(CF\_{alloc}\\), gC m\-2 s\-1, and \\(NF\_{alloc}\\), gN m\-2 s\-1, respectively) can be expressed as functions of new leaf carbon allocation (\\(CF\_{GPP,leaf}\\), gC m\-2 s\-1):

(2.19.10)[¶](#equation-19-10 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{l} {CF\_{alloc} =CF\_{GPP,leaf} {\\kern 1pt} C\_{allom} } \\\\ {NF\_{alloc} =CF\_{GPP,leaf} {\\kern 1pt} N\_{allom} } \\end{array}\\end{split}\\\]

where

(2.19.11)[¶](#equation-19-11 "Permalink to this equation")\\\[\\begin{split}\\begin{array}{l} {C\_{allom} =\\left\\{\\begin{array}{l} {\\left(1+g\_{1} \\right)\\left(1+a\_{1} +a\_{3} \\left(1+a\_{2} \\right)\\right)\\qquad {\\rm for\\; woody\\; PFT}} \\\\ {1+g\_{1} +a\_{1} \\left(1+g\_{1} \\right)\\qquad \\qquad {\\rm for\\; non-woody\\; PFT}} \\end{array}\\right. } \\\\ {} \\end{array}\\end{split}\\\]

(2.19.12)[¶](#equation-19-12 "Permalink to this equation")\\\[\\begin{split}N\_{allom} =\\left\\{\\begin{array}{l} {\\frac{1}{CN\_{leaf} } +\\frac{a\_{1} }{CN\_{fr} } +\\frac{a\_{3} a\_{4} \\left(1+a\_{2} \\right)}{CN\_{lw} } +} \\\\ {\\qquad \\frac{a\_{3} \\left(1-a\_{4} \\right)\\left(1+a\_{2} \\right)}{CN\_{dw} } \\qquad {\\rm for\\; woody\\; PFT}} \\\\ {\\frac{1}{CN\_{leaf} } +\\frac{a\_{1} }{CN\_{fr} } \\qquad \\qquad \\qquad {\\rm for\\; non-woody\\; PFT.}} \\end{array}\\right.\\end{split}\\\]

Since the C:N stoichiometry for new growth allocation is defined, from Eq., as \\(C\_{allom}\\)/ \\(N\_{allom}\\), the total carbon available for new growth allocation (\\(CF\_{avail\\\_alloc}\\)) can be used to calculate the total plant nitrogen demand for new growth ( \\(NF\_{plant\\\_demand}\\), gN m\-2 s\-1) as:

(2.19.13)[¶](#equation-19-13 "Permalink to this equation")\\\[NF\_{plant\\\_ demand} =CF\_{avail\\\_ alloc} \\frac{N\_{allom} }{C\_{allom} } .\\\]

