### 2.10.2.1. Plant Nitrogen[¶](#plant-nitrogen "Permalink to this headline")

The structure of the LUNA model is adapted from [Xu et al. (2012)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#xuetal2012), where the plant nitrogen at the leaf level ( \\(\\text{LNC}\_{a}\\); gN/ m 2 leaf) is divided into four pools: structural nitrogen( \\(N\_{\\text{str}}\\); gN/m 2 leaf), photosynthetic nitrogen ( \\(N\_{\\text{psn}}\\); gN/m 2 leaf), storage nitrogen( \\(N\_{\\text{store}}\\); gN/m 2 leaf), and respiratory nitrogen ( \\(N\_{\\text{resp}}\\); gN/m 2 leaf). Namely,

(2.10.1)[¶](#equation-10-1 "Permalink to this equation")\\\[ \\text{LNC}\_{a} = N\_{\\text{psn}} + N\_{\\text{str}}+ N\_{\\text{store}} + N\_{\\text{resp}}.\\\]

The photosynthetic nitrogen, \\(N\_{\\text{psn}}\\), is further divided into nitrogen for light capture ( \\(N\_{\\text{lc}}\\); gN/m 2 leaf), nitrogen for electron transport ( \\(N\_{\\text{et}}\\); gN/m 2 leaf), and nitrogen for carboxylation ( \\(N\_{\\text{cb}}\\); gN/m 2 leaf). Namely,

(2.10.2)[¶](#equation-10-2 "Permalink to this equation")\\\[ N\_{\\text{psn}} =N\_{\\text{et}} + N\_{\\text{cb}} + N\_{\\text{lc}}.\\\]

The structural nitrogen, \\(N\_{\\text{str}}\\), is calculated as the multiplication of leaf mass per unit area (\\(\\text{LMA}\\); g biomass/m 2 leaf), and the structural nitrogen content (\\(\\text{SNC}\\); gN/g biomass). Namely,

(2.10.3)[¶](#equation-10-3 "Permalink to this equation")\\\[ N\_{\\text{str}} = \\text{SNC} \\cdot \\text{LMA}\\\]

where \\(\\text{SNC}\\) is set to be fixed at 0.004 (gN/g biomass), based on data on C:N ratio from dead wood (White etal.,2000), and \\(\\text{LMA}\\) is the inverse of specific leaf area at the canopy top (\\(SLA\_{\\text{0}}\\)), a PFT-level parameter ([Table 2.10.1](#table-plant-functional-type-pft-leaf-n-parameters)).

Table 2.10.1 Plant functional type (PFT) leaf N parameters.[¶](#id5 "Permalink to this table")  
| PFT
 | \\(SLA\_{\\text{0}}\\)

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

 | 0.01000

 |
| NET Boreal

 | 0.01000

 |
| NDT Boreal

 | 0.02018

 |
| BET Tropical

 | 0.01900

 |
| BET temperate

 | 0.01900

 |
| BDT tropical

 | 0.03080

 |
| BDT temperate

 | 0.03080

 |
| BDT boreal

 | 0.03080

 |
| BES temperate

 | 0.01798

 |
| BDS temperate

 | 0.03072

 |
| BDS boreal

 | 0.02800

 |
| C3 arctic grass

 | 0.02100

 |
| C3 grass

 | 0.04024

 |
| C4 grass

 | 0.03846

 |
| Temperate Corn

 | 0.05000

 |
| Spring Wheat

 | 0.03500

 |
| Temperate Soybean

 | 0.03500

 |
| Cotton

 | 0.03500

 |
| Rice

 | 0.03500

 |
| Sugarcane

 | 0.05000

 |
| Tropical Corn

 | 0.05000

 |
| Tropical Soybean

 | 0.03500

 |
| Miscanthus

 | 0.03500

 |
| Switchgrass

 | 0.03500

 |

Notes: \\(SLA\_{\\text{0}}\\) is the specific leaf area at the canopy top (m 2 leaf/g biomass)

We assume that plants optimize their nitrogen allocations (i.e., \\(N\_{\\text{store}}\\), \\(N\_{\\text{resp}}\\), \\(N\_{\\text{lc}}\\), \\(N\_{\\text{et}}\\), \\(N\_{\\text{cb}}\\)) to maximize the photosynthetic carbon gain, defined as the gross photosynthesis ( \\(A\\) ) minus the maintenance respiration for photosynthetic enzymes ( \\(R\_{\\text{psn}}\\) ), under specific environmental conditions and given plant’s strategy of leaf nitrogen use. Namely, the solutions of nitrogen allocations { \\(N\_{\\text{store}}\\), \\(N\_{\\text{resp}}\\), \\(N\_{\\text{lc}}\\), \\(N\_{\\text{et}}\\), \\(N\_{\\text{cb}}\\) } can be estimated as follows,

(2.10.4)[¶](#equation-10-4 "Permalink to this equation")\\\[\\left\\{\\hat{N}\_{\\text{{store}}}, \\hat{N}\_{\\text{{resp}}}, \\hat{\\mathrm{N}}\_{\\text{lc}}, \\hat{N}\_{\\text{et}}, \\hat{\\mathrm{N}}\_{\\text{cb}} \\right\\} = \\underset{\\mathrm{N}\_{\\text{store}}\\,+\\,\\mathrm{N}\_{\\text{resp}}\\,+\\,\\mathrm{N}\_{\\text{lc}}\\,+\\,\\mathrm{N}\_{\\text{et}}\\,+\\,\\mathrm{N}\_{\\text{cb}}\\,<\\text{FNC}\_{\\mathrm{a}}}{\\text{argmax}} (A-R\_{\\text{psn}}),\\\]

where \\(\\text{FNC}\_{a}\\) is the functional nitrogen content defined as the total leaf nitrogen content ( \\(\\text{LNC}\_{a}\\)) minus the structural nitrogen content ( \\(N\_{\\text{str}}\\) ).

The gross photosynthesis, \\(A\\), was calculated with a coupled leaf gas exchange model based on the [Farquhar et al. (1980)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#farquharetal1980) model of photosynthesis and Ball–Berry-type stomatal conductance model (Ball et al. 1987). The maintenance respiration for photosynthetic enzymes, \\(R\_{\\text{psn}}\\), is calculated by the multiplication of total photosynthetic nitrogen ( \\(N\_{\\text{psn}}\\) ) and the maintenance respiration cost for photosynthetic enzymes.

