### 2.10.2.2. Maximum electron transport rate[¶](#maximum-electron-transport-rate "Permalink to this headline")

In the LUNA model, the maximum electron transport rate ( \\(J\_{\\text{max}}\\); \\({\\mu} mol\\) electron / m 2/s) is simulated to have a baseline allocation of nitrogen and additional nitrogen allocation to change depending on the average daytime photosynthetic active radiation (PAR; \\({\\mu} mol\\) electron / m 2/s), day length (hours) and air humidity. Specifically, the LUNA model has

(2.10.5)[¶](#equation-10-5 "Permalink to this equation")\\\[J\_{\\text{{max}}} = J\_{\\text{max}0} + J\_{\\text{max}b1} f\\left(\\text{day length} \\right)f\\left(\\text{humidity} \\right)\\alpha \\text{PAR}\\\]

The baseline electron transport rate, \\(J\_{\\text{max}0}\\), is calculated as follows,

(2.10.6)[¶](#equation-10-6 "Permalink to this equation")\\\[J\_{\\text{max}0} = J\_{\\text{max}b0}{\\text{FNC}}\_{\\mathrm{a}}{\\text{NUE}}\_{J\_{\\text{{max}}}}\\\]

where \\(J\_{\\text{max}b0}\\) (unitless) is the baseline proportion of nitrogen allocated for electron transport rate. \\({\\text{NUE}}\_{J\_{\\text{{max}}}}\\) ( \\({\\mu} mol\\) electron /s/g N) is the nitrogen use efficiency of \\(J\_{\\text{{max}}}\\). \\(J\_{\\text{max}b1}\\) (unitless) is a coefficient determining the response of the electron transport rate to amount of absorbed light (i.e., \\(\\alpha \\text{PAR}\\)). \\(f\\left(\\text{day length} \\right)\\) is a function specifies the impact of day length (hours) on \\(J\_{\\text{max}}\\) in view that longer day length has been demonstrated by previous studies to alter \\(V\_{\\mathrm{c}\\text{max}25}\\) and \\(J\_{\\text{max}25}\\) (Bauerle et al. 2012; Comstock and Ehleringer 1986) through photoperiod sensing and regulation (e.g., Song et al. 2013). Following Bauerle et al. (2012), \\(f\\left(\\text{day length} \\right)\\) is simulated as follows,

(2.10.7)[¶](#equation-10-7 "Permalink to this equation")\\\[f\\left(\\text{day length} \\right) = \\left(\\frac{\\text{day length}}{12} \\right)^{2}.\\\]

\\(f\\left(\\text{humidity} \\right)\\) represents the impact of air humidity on \\(J\_{\\text{{max}}}\\). We assume that higher humidity leads to higher \\(J\_{\\text{{max}}}\\) with less water limiation on stomta opening and that low relative humidity has a stronger impact on nitrogen allocation due to greater water limitation. When relative humidity (RH; unitless) is too low, we assume that plants are physiologically unable to reallocate nitrogen. We therefore assume that there exists a critical value of relative humidity ( \\(RH\_{0} = 0.25\\); unitless), below which there is no optimal nitrogen allocation. Based on the above assumptions, we have

(2.10.8)[¶](#equation-10-8 "Permalink to this equation")\\\[f\\left(\\text{humidity} \\right) = \\left(1-\\mathrm{e}^{\\left(-H \\frac{\\text{max}\\left(\\text{RH}-{\\text{RH}}\_{0}, 0 \\right)}{1-\\text{RH}\_{0}} \\right)} \\right),\\\]

where \\(H\\) (unitless) specifies the impact of relative humidity on electron transport rate.

The efficiency of light energy absorption (unitless), \\(\\alpha\\), is calculated depending on the amount of nitrogen allocated for light capture, \\(\\mathrm{N}\_{\\text{lc}}\\). Following Niinemets and Tenhunen (1997), the LUNA model has,

(2.10.9)[¶](#equation-10-9 "Permalink to this equation")\\\[\\alpha =\\frac{0.292}{1+\\frac{0.076}{\\mathrm{N}\_{\\text{lc}}C\_{b}}}\\\]

where 0.292 is the conversion factor from photon to electron. \\(C\_{b}\\) is the conversion factor (1.78) from nitrogen to chlorophyll. After we estimate \\(J\_{\\text{{max}}}\\), the actual electron transport rate with the daily maximum radiation ( \\(J\_{x}\\)) can be calculated using the empirical expression of leaf (1937),

(2.10.10)[¶](#equation-10-10 "Permalink to this equation")\\\[J\_{x} = \\frac{\\alpha \\text{PAR}\_{\\text{max}}} {\\left(1 + \\frac{\\alpha^{2}{\\text{PAR}}\_{\\text{{max}}}^{2}}{J\_{\\text{{max}}}^{2}} \\right)^{0.5}}\\\]

where \\(\\text{PAR}\_{\\text{{max}}}\\) ( \\(\\mu mol\\)/m 2/s) is the maximum photosynthetically active radiation during the day.

