## 2.10.3. Numerical scheme[¶](#numerical-scheme "Permalink to this headline")
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The LUNA model searches for the “optimal” nitrogen allocations for maximum net photosynthetic carbon gain by incrementally increase the nitrogen allocated for light capture (i.e., \\(N\_{\\text{lc}}\\)) (see [Ali et al. (2016)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#alietal2016) for details). We assume that plants only optimize the nitrogen allocation when they can grow (i.e., GPP>0.0). If GPP become zero under stress, then the LUNA model assume a certain amount of enzyme will decay at daily rates of 0.1, in view that the half-life time for photosynthetic enzymes are short (~7 days) (Suzuki et al. 2001). To avoid unrealistic low values of photosynthetic capacity, the decay is only limited to 50 percent of the original enzyme levels.
