pastas.recharge.Peterson
========================

.. toctree::
   :hidden:

   /api/pastas/recharge/Peterson.get_init_parameters
   /api/pastas/recharge/Peterson.simulate
   /api/pastas/recharge/Peterson.get_recharge
   /api/pastas/recharge/Peterson.get_water_balance

.. py:class:: pastas.recharge.Peterson



   
   Nonlinear recharge to the groundwater.

   Calculated based on :cite:t:`peterson_nonlinear_2014`.

   The water balance for the unsaturated zone reservoir is written as:

   .. math::

       \\frac{dS}{dt} = P_e - E_a - R

   where the fluxes $P_e$, $E_a$ and $R$ are calculated as:

   .. math::

       P_e = P \\left(1 - \\frac{S}{\\hat{S_{cap}}}\\right)^\\alpha

   .. math::

       E_a = E_p \\left(\\frac{S}{\\hat{S_{cap}}}\\right)^\\gamma

   .. math::

       R = \\hat{k_{sat}}\\left(\\frac{S}{\\hat{S_{cap}}}\\right)^{\\hat{\\beta}}

   with the parameters:

   .. math::

       \\hat{S_{cap}} = 10^{S_{cap}}; \\hat{k_{sat}} = 10^{k_{sat}}; \\hat{\\beta} =
       10^{\\beta}

   Note that the method currently uses forward Euler method to solve the ODE so
   significant water balance errors can occur.















   ..
       !! processed by numpydoc !!

   .. py:property:: nparam
      :type: int


      
      Number of parameters of the Peterson recharge model.
















      ..
          !! processed by numpydoc !!

Methods
-------

.. autoapisummary::

   pastas.recharge.Peterson.get_init_parameters
   pastas.recharge.Peterson.simulate
   pastas.recharge.Peterson.get_recharge
   pastas.recharge.Peterson.get_water_balance