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2.18.5. Carbon expenditure on fixation and active uptake.¶
At each model timestep, the overall cost of N uptake is calculated (see below) in terms of C:N ratios. The available carbon (\(C_{avail}\), g m-2 s-1) is then allocated to two alternative outcomes, payment for N uptake, or conservation for growth. For each carbon conserved for growth, a corresponding quantity of N must be made available. In the case where the plant target C:N ratio is fixed, the partitioning between carbon for growth (\(C_{growth}\)) and carbon for N uptake (\(C_{nuptake}\)) is calculated by solving a system of simultaneous equations. First, the carbon available must equal the carbon spent on N uptake plus that saved for growth.
\[C_{growth}+C_{nuptake}=C_{avail}\]
Second, the nitrogen acquired from expenditure of N (left hand side of term below) must equal the N that is required to match the growth carbon (right hand side of term below).
\[C_{nuptake}/N_{cost} =C_{growth}/CN_{target}\]
The solution to these two equated terms can be used to estimate the ideal \(C_{nuptake}\) as follows,
\[C_{nuptake} =C_{tospend}/ ( (1.0+f_{gr}*(CN_{target} / N_{cost}) + 1) .\]
and the other C and N fluxes can be determined following the logic above.