Forest fire and succession on a raster

Field: ecology · Zoo name: forest_fire · Module: modelly.zoo.forest_fire.model

A raster of cells, each empty, a tree, burning or burnt. At the start every cell holds a tree with probability density, or with its own probability from a cover raster, and the trees of the west edge are set alight. Every step a tree next to a burning cell (von Neumann neighbourhood) catches fire and a burning cell burns out. With growth > 0 empty and burnt cells grow a tree with that probability per step, and with lightning > 0 a tree is struck with that probability per step: the Drossel-Schwabl model of succession and disturbance.

How it is written

The state is one integer per cell, kept as a property layer of an OrthogonalVonNeumannGrid (model.layer, shaped (width, height) like the grid; model.state is the same array flattened in CellIndex row order). The spread is one sparse product per step, CellIndex.neighbor_sum, over the grid’s adjacency, so a 100 x 100 fire runs in a fraction of a second. A land-cover raster read with modelly.space.geo.RasterLayer gives the cover directly: ForestScenario(cover=layer.values) (the geo extra is needed only for reading the file, not for the model).

from modelly.zoo.forest_fire.model import ForestFire, ForestScenario

model = ForestFire(ForestScenario(rng=42, density=0.65))
model.run()  # stops when the fire is out
model.burnt_share(), model.spans()
model.datacollector.get_model_vars_dataframe()  # cells per state per step

Parameter	Default	Meaning
width, height	100, 100	raster size in cells
density	0.6	probability that a cell starts with a tree
cover	None	per-cell tree probability, shape (width, height), replaces density
growth	0.0	probability per step that an empty or burnt cell grows a tree
lightning	0.0	probability per step that a tree is struck
steps	2000	maximum run length of run()

Validation

Without growth and lightning the fire burns exactly the clusters of trees connected to the west edge, so the model is site percolation on the square lattice, whose threshold is p_c = 0.592746 (Newman and Ziff). On a 100 x 100 raster the transition is about L^(-3/4) ~ 0.03 wide.

tests/zoo/test_forest_fire.py checks, for three seeds, that at p_c - 0.15 the fire never reaches the east edge and burns under 10 % of the trees, and that at p_c + 0.15 it always reaches the east edge and burns over 90 %; that the mean burnt share rises with density; that a cover raster confines the trees; that succession mode keeps burning and conserves cells; and that the same seed gives the same fire.

References

• Drossel, B. and Schwabl, F. (1992). Self-organized critical forest-fire model. Physical Review Letters, 69(11), 1629-1632.

• Newman, M. E. J. and Ziff, R. M. (2000). Efficient Monte Carlo algorithm and high-precision results for percolation. Physical Review Letters, 85(19), 4104-4107.

• Stauffer, D. and Aharony, A. (1994). Introduction to Percolation Theory, 2nd ed. Taylor and Francis.

Start a project from it with modelly zoo copy forest_fire my_forest.