Burn Baby Burn!Burn Baby Burn!Prescribed Burning as a Silvicultural MethodPrescribed Burning as a Silvicultural Method

Dee Asbury & Erin Bodine

Math 164: Scientific Computing29 – April - 2003

MotivationMotivation

• History of wildfire suppression– Smokey-the-Bear Effect

• “Only you can prevent forest fires!”• Ideology: any forest fire is BAD!

– Shift of control burn• Suppress wildfires• Use control or prescribed burns to simulate natural forest

cycles

• Maintenance of forest diversity– Want to maintain a balance between the various tree

populations if a forest– Many tree species suffer without fire

• Ground litter too deep for shallow root trees• Fire replenishes nutrients in top soil• Seeds remain dormant, fire releases seeds from cones

The QuestionsThe Questions

• How can prescribed burns be used to maintain forest diversity?

• How will forest equilibrium be affected by fire suppression?

• Can we find an optimal burn frequency to yield desired forest dynamics?

The Biology:The Biology:A Hardwood and Pine Tree ForestA Hardwood and Pine Tree Forest

• Hardwoods – Fire Haters!– Hardwoods have a deep root system– Fire has phoenix effect on hardwoods– Spread rapidly

• Pine Trees – Fire Lovers!– Pine trees have a shallow root system– Fire causes pine cones to open– Pine trees have greater fire tolerance

• Dynamics– Hardwoods will crowd out pine trees!

The Model: An OverviewThe Model: An Overview

• The model uses time dependent transition matrices to calculate – annual tree populations – forest diversity

• The three transition matrices are – growth (G)– replacement (R) – death (D)

)()()()()()()1( ttttttt XDXRXGX

The Model: Growth MatrixThe Model: Growth Matrix

• Example of a growth matrix• Transition matrix models four height classes

1)(00

0)(1)(0

00)(1)(

000)(1

)(

3

32

21

1

tg

tgtg

tgtg

tg

tG

The Model: Replacement VectorThe Model: Replacement Vector

• Example of a replacement vector• All replacements occur in smallest height class

0

0

0

)()()()(

)()(

4321 trtrtrtr

tt XR

The Model: Death MatrixThe Model: Death Matrix

)(000

0)(00

00)(0

000)(

)(

4

3

2

1

td

td

td

td

tD

• Example of a death matrix• Transition matrix models four height classes

Results: Maximum Fire SuppressionResults: Maximum Fire Suppression

Results: Control BurnResults: Control Burn

Results: Control BurnResults: Control Burn

Results: Answers to the QuestionsResults: Answers to the Questions

• How can prescribed burns be used to maintain forest diversity?– Prescribed burns, at the appropriate frequency, can

maintain the desired forest diversity.

• How will forest equilibrium be affected by fire suppression?– In the pine/hardwood forest frequent fires will maintain a

pine forest, infrequent fires will maintain a hardwood forest.

• Can we find an optimal burn frequency to yield desired forest dynamics? – Close! Populations are slowly declining over time.

ExtensionsExtensions

• Model carrying capacities more accurately.

• Model effects of fire frequency on local wildlife.

• Model effect of fire frequency on biomass instead of tree populations.

• Add dynamics of shrubs and other flora.

• Add effects of other methods of silviculture (i.e. logging and thinning).