.. _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.