Burn Baby Burn!
Prescribed Burning as a Silvicultural Method
Dee Asbury & Erin Bodine
Math 164: Scientific Computing
29 – April - 2003
Motivation
• 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 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:
A 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 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)
X(t  1)  G (t ) X(t )  R (t ) X(t )  D(t ) X(t )
The Model: Growth Matrix
• Example of a growth matrix
• Transition matrix models four height classes
0
0
1  g1 (t )

0
 g1 (t ) 1  g 2 (t )
G (t )  
0
g 2 (t ) 1  g 3 (t )

 0
0
g 3 (t )

0

0
0


1
The Model: Replacement Vector
• Example of a replacement vector
• All replacements occur in smallest height class
 r1 (t )  r2 (t )  r3 (t )  r4 (t ) 


0


R (t ) X(t )  

0




0


The Model: Death Matrix
• Example of a death matrix
• Transition matrix models four height classes
0
0
0 
 d1 (t )


d 2 (t )
0
0 
 0
D(t )  

0
0
d 3 (t )
0


 0

0
0
d 4 (t ) 

Results: Maximum Fire Suppression
Results: Control Burn
Results: Control Burn
Results: 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.
Extensions
• 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).