### 2.10.2.3. Maximum rate of carboxylation[¶](#maximum-rate-of-carboxylation "Permalink to this headline")

The maximum rate of carboxylation at 25°C varies with foliage nitrogen concentration and specific leaf area and is calculated as in [Thornton and Zimmermann (2007)](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#thorntonzimmermann2007). At 25°C,

(2.10.11)[¶](#equation-10-11 "Permalink to this equation")\\\[ V\_{c\\max 25} = N\_{cb} NUE\_{V\_{c\\max 25}}\\\]

where \\(N\_{cb}\\) is nitrogen for carboxylation (g N m\-2 leaf, [Table 2.10.1](#table-plant-functional-type-pft-leaf-n-parameters)), and \\(NUE\_{V\_{c\\max 25}}\\) = 47.3 x 6.25 and is the nitrogen use efficiency for \\(V\_{c\\max 25}\\). The constant 47.3 is the specific Rubisco activity ( \\(\\mu\\) mol CO2 g\-1 Rubisco s\-1) measured at 25°C, and the constant 6.25 is the nitrogen binding factor for Rubisco (g Rubisco g\-1 N; [Rogers 2014](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/References/CLM50_Tech_Note_References.html#rogers2014)).

\\(V\_{c\\max 25}\\) additionally varies with daylength (\\(DYL\\)) using the function \\(f(DYL)\\), which introduces seasonal variation to \\(V\_{c\\max }\\)

(2.10.12)[¶](#equation-10-12 "Permalink to this equation")\\\[ f\\left(DYL\\right)=\\frac{\\left(DYL\\right)^{2} }{\\left(DYL\_{\\max } \\right)^{2} }\\\]

with \\(0.01\\le f\\left(DYL\\right)\\le 1\\). Daylength (seconds) is given by

(2.10.13)[¶](#equation-10-13 "Permalink to this equation")\\\[ DYL=2\\times 13750.9871\\cos ^{-1} \\left\[\\frac{-\\sin \\left(lat\\right)\\sin \\left(decl\\right)}{\\cos \\left(lat\\right)\\cos \\left(decl\\right)} \\right\]\\\]

where \\(lat\\) (latitude) and \\(decl\\) (declination angle) are from section [2.3.3](https://escomp.github.io/ctsm-docs/versions/master/html/tech_note/Surface_Albedos/CLM50_Tech_Note_Surface_Albedos.html#solar-zenith-angle). Maximum daylength (\\(DYL\_{\\max }\\) ) is calculated similarly but using the maximum declination angle for present-day orbital geometry (\\(\\pm\\)23.4667° \[\\(\\pm\\)0.409571 radians\], positive for Northern Hemisphere latitudes and negative for Southern Hemisphere).

