.. _model_Vegetation:

``Vegetation`` — Simple Vegetation Model
========================================

This is a very simple implementation of a vegetation model. It is implemented as a stochastic cellular automaton on a grid, where the state of each cell is a double scalar representing the plant bio-mass on that cell. The only driver for a change in the plant bio-mass is rainfall, implemented as a Gauss-distributed random number drawn for each cell.

Model parameters
----------------

* ``rain_mean``\ : mean rainfall :math:`\langle r \rangle`
* ``rain_std``\ : rainfall standard deviation :math:`\sigma_r`
* ``growth_rate``\ : growth rate :math:`g`
* ``seeding_rate``\ : seeding rate :math:`s`

Growth process
--------------

In each time step, the plant bio-mass on a cell is increased according to a
logistic growth model. Let :math:`m_{t,i}` be the plant bio-mass on cell
:math:`i` at time :math:`t` and :math:`r_{t,i}` the rainfall at time :math:`t`
onto cell :math:`i`. The plant bio-mass at time :math:`t+1` is then determined
as

:math:`m_{t+1,i} = m_{t,i} + m_{t,i} \cdot g \cdot (1 - m_{t,i}/r_{t,i})`.

It is possible that the result yields a negative value. In this case, the
population density is silenty set to zero, :math:`m_{t+1,i} = 0`.

Seeding process
---------------

Since logistic growth will never start if the initial plant bio-mass is
zero, a seeding process is included into the model. If :math:`m_{t,i} = 0`, the
plant bio-mass at time :math:`t+1` is then determined as

:math:`m_{t+1,i} = s \cdot r_{t,i}`.

Default configuration parameters
--------------------------------

Below are the default configuration parameters of the model:

.. literalinclude:: ../../src/utopia/models/Vegetation/Vegetation_cfg.yml
   :language: yaml
   :start-after: ---

For these parameters and a grid size of 20 x 20, the system takes
roughly 50 time steps to reach a dynamic equilibrium, in which the
plant bio-mass on all cells fluctuates around 9.5.


Available plots
---------------
The following plot configurations are available for the ``Vegetation`` model:

Default Plot Configuration
^^^^^^^^^^^^^^^^^^^^^^^^^^
.. literalinclude:: ../../src/utopia/models/Vegetation/Vegetation_plots.yml
   :language: yaml
   :start-after: ---

Base Plot Configuration
^^^^^^^^^^^^^^^^^^^^^^^
.. literalinclude:: ../../src/utopia/models/Vegetation/Vegetation_base_plots.yml
   :language: yaml
   :start-after: ---

For available base plots, see :ref:`utopia_base_plots_ref`.