/[MITgcm]/MITgcm_contrib/darwin/doc/equations.tex
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revision 1.1 by jahn, Mon Nov 24 21:59:58 2008 UTC revision 1.2 by jahn, Thu Sep 24 20:32:06 2009 UTC
# Line 147  $N_i^{lim}=\frac{N_i}{N_i+\kappa_{N_{ij} Line 147  $N_i^{lim}=\frac{N_i}{N_i+\kappa_{N_{ij}
147    
148  When we include the nitrogen as a potential limiting nutrient (EXP2) we  When we include the nitrogen as a potential limiting nutrient (EXP2) we
149  modify $N_i^{lim}$ to take into account the uptake inhibition caused by ammonium:  modify $N_i^{lim}$ to take into account the uptake inhibition caused by ammonium:
150  \[  \begin{align*}
151  N_N^{lim} = \frac{NO_3 + NO_2}{NO_3+NO_2+\kappa_{IN}} e^{-\psi NH_4}  N_N^{lim} &= \frac{NO_2}{NO_2+\kappa_{IN}} e^{-\psi NH_4}
152  +\frac{NH_4}{NH_4 + \kappa_{NH4}}  +\frac{NH_4}{NH_4 + \kappa_{NH4}}  && \text{(nsource=1)} \\
153  \]  N_N^{lim} &= \frac{NH_4}{NH_4 + \kappa_{NH4}}  && \text{(nsource=2)} \\
154    N_N^{lim} &= \frac{NO_3 + NO_2}{NO_3+NO_2+\kappa_{IN}} e^{-\psi NH_4}
155    +\frac{NH_4}{NH_4 + \kappa_{NH4}}  && \text{(nsource=3)}
156    \end{align*}
157  where $\psi$ reflects the inhibition and $\kappa_{IN}$ and $ \kappa_{NH4}$  where $\psi$ reflects the inhibition and $\kappa_{IN}$ and $ \kappa_{NH4}$
158  are the half saturation constant of $IN=NO_3+NO_2$ and $NH_4$ respectively.  are the half saturation constant of $IN=NO_3+NO_2$ and $NH_4$ respectively.
159    

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