.. _doc.meteor.reaclimit:

Modulation of reaction kinetics in module MET&OR
--------------------------------------------------

.. _f_arrhenius:

Kinetic Modulation with Temperature (Arrhenius function) 
++++++++++++++++++++++++++++++++++++++++++++++++++++++++

The Arrhenius law corrects the kinetics of the reaction as a function of temperature. User can choose between two different types:

   * **First Law called** :math:`\theta`
        
       | :math:`\mu_{T}=\mu_{T_{ref}} F_{Temp}`
       | :math:`F_{Temp}=\theta^{\frac{(T_T-{ref})}{\zeta}}`
       | avec :

              * :math:`T_{ref}` : reference temperature
              * :math:`\mu_{T_{ref}}` : kinetic max at reference temperature
              * :math:`T` : temperature at time t
              * :math:`\theta` : correction coefficient
              * :math:`\zeta` = 1 or 10 depending on law.

       | For chemical reactions, the law is often used with :math:`\zeta= 1`  and  :math:`T_{ref}` = 15 degC or 20 degC.
       | For biological reactions, the dependence is reported in terms of :math:`Q_{10}` which represents the ratio between reaction rates at 20 degC and at 10 degC; :math:`\theta` is then set equal to :math:`Q_{10}`, and :math:`\zeta` is equal to 10.


   * **Second Law called exponential law**

       | :math:`\mu_{T}=\mu_{T_{ref}} F_{Temp}`
       | :math:`F_{Temp}=\theta e^{-(\frac{(T_T-{ref})}{\sigma})^2}`
       | avec :

              * :math:`T_{ref}` : reference temperature
              * :math:`\mu_{T_{ref}}` : kinetic max at reference temperature
              * :math:`T` : temperature at time t
              * :math:`\sigma` : deviation
              * :math:`\theta` = 1 


.. _f_limiting:

Kinetic Limitation with a Monod function or an inhibiting function or with light radiation 
++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

+---------------------------------------------------------------------------------------------------+----------------------------------------------------------------+
| | These two functions vary according to the concentration of the limiting variable.               |                                                                |
| |                                                                                                 |     .. image:: FIG/METEOR/meteor_Flim_exple.jpg                |
| | For type **Monod function** : :math:`F_{L}` approaches 0, if the concentration is less than Ks  |                                                                |
| | The reaction does not occur or is reduced if the limiting variable is in low concentration.     |                                                                |
| |                                                                                                 |                                                                |
| | For type **Inhibit function**, the higher the concentration of the limiting variable becomes,   |                                                                |
| | the lower the reaction may develop. It is at full speed if the concentration is zero.           |                                                                |
| |                                                                                                 |                                                                |
+---------------------------------------------------------------------------------------------------+----------------------------------------------------------------+
| |                                                                                                 |     .. image:: FIG/METEOR/meteor_Fextinct_exple.jpg            |
| | The third limiting function is a **function of light**,                                         |                                                                |
| | It decreases with the depth according to an exponential law with an extinction coefficient      |                                                                |
| | (here :math:`\chi=0.1` )                                                                        |                                                                |
| |                                                                                                 |                                                                |
+---------------------------------------------------------------------------------------------------+----------------------------------------------------------------+


   * **Kinetic Limitation with a Monod**

       | :math:`F_{L1}=\frac{C_{lim}}{C_{lim}+K_s}`
       | avec :

              * :math:`F_{L1}`  : Limiting function (type 1 : Monod), [between 0 and 1 ]
              * :math:`C_{lim}` : Limiting concentration corresponding to this function and one reaction 
              * :math:`K_s` : Half saturation constant 


   * **Kinetic Limitation with an inhibiting function**

       | :math:`F_{L2}=\frac{K_s}{C_{lim}+K_s}`
       | avec :

              * :math:`F_{L2}`  : Limiting function (type 2 : Inhibit), [between 0 and 1 ]
              * :math:`C_{lim}` : Limiting concentration corresponding to this function and one reaction 
              * :math:`K_s` : Half saturation constant 


   * **Kinetic Limitation with light radiation** 

       | :math:`F_{L3}=e^{-a \chi z}`
       | avec :

              * :math:`F_{L3}`  : Limiting function (type 3 : Extinction), [between 0 and 1 ]
              * :math:`a` : parameter corresponding to this function and one reaction
              * :math:`\chi` : extinction coefficient 
              * :math:`z` : depth