Rabbit Rules An Application of Stephen Wolframs New Kind of Science to Fire Spread Modeling

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Rabbit Rules An Application of Stephen
Wolframs New Kind of Science to Fire Spread
Modeling

• Gary L. Achtemeier
• USDA Forest Service
• Athens, GA

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Background
The Rabbit Model described in the following PPT
slides was conceived following discussions during
and after a workshop on fire modeling held at
Tallahassee FL during March 2003. Considering the
enormous complexity of the fire spread/behavior
problem, one colleague expressed the need to
explore all ideas, whether conventional or
unconventional, to create an ensemble of fire
spread/behavior models that could be tested
against observed fire spread/behavior and against
each other. But the model effort would not stop
there. The models would have to be made
operational to be run with real-time and forecast
high-resolution weather data available through
FCAMMS.
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Background
The concept of a rule-driven fire
spread/behavior model that would be conceptually
unlike any of the existing models was laid out
during May 2003. The rule-driven model would be
the philosophical equivalent of a transformation
of coordinates. The resulting method for
understanding the fire spread/behavior problem
would be so radical that terminology must be
changed. The relationship between fire and fuels,
fuel consumption, and meteorology would be viewed
from an entirely different perspective, so much
so that fire-fuel-weather relationships would fit
a whole new matrix. The new perspective is cast
in terms of Rabbit Behavior because of a crude
parallel between fire behavior and rabbit
behavior.
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Background
By early June 2003, initial results from the
Rabbit Model were showing that the rule driven
concept had explanatory power and that further
development was justified. Another colleague
provided me with Stephen Wolframs 800 page
tome on rule-driven New Science and other
material on autonomous agents. This material
gave encouragement that the Rabbit Model concept
was based on principles set forth by leaders in
the field of new scientific thought. The slides
that follow were presented at the 5th Symposium
on Fire and Forest Meteorology held at Orlando FL
during November 2003.
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Purpose for the Rabbit Model Empirical Fire
Spread/Fire Behavior Models

• Are based on statistical equations between fire
  spread and measured variables
• Have skill at low to moderate wind speeds for
  which the equations have been derived
• Map fire spread through simple geometry
• Are transferable to operational models

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Purpose for the Rabbit Model Physical Fire
Spread/Fire Behavior Models

• Describe fire spread as heat transfer between
  burned and unburned fuels through coupled
  differential equations.
• Explain mathematically how combustion processes
  under various atmospheric conditions translates
  to fire behavior
• Explain coupled fire atmosphere feedbacks that
  can account for extreme fire behavior.
• Are enormously computationally intensive and thus
  are currently unsuitable for operational models.

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Purpose for the Rabbit Model Can a model be
designed to take advantage of .

• The simplicity and operational adaptability of
  the empirical fire spread models, and
• The robustness of the physical models

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Stephen Wolframs New Science

• Initial value problems described by complex
  partial differential equations can be recast as a
  set of simple computer programs and solved
  recursively.
• The computer programs can produce complex
  solutions such as fractal fire fronts, breaks in
  fire lines, waves (or bulges), heads, and
  flanking lines.
• Wolfram noted Over and over again the single
  most important principle that I have learned is
  that the best computer experiments are ones that
  are as simple and straightforward as possible.
  And the principle applies both to the structure
  of actual systems one studies - and to the
  procedures that one uses for studying them.
  (p.109.)

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The Rabbit Model.

• Follows Wolframs rules for computing
• But not cellular automata,
• Nor raster-based domains

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On Rabbit Behavior

• It is advisable to change terminology so that
  Rabbit rules will not be confused with
  mathematical and physical principles that govern
  empirical and physical fire spread models even
  though much physics is contained in the Rabbit
  Model.
• Fire behavior fire consumes fuel, fire leaps
  between adjacent fuel elements, fire spreads.
• Rabbit behavior rabbits eat food, rabbits jump,
  rabbits reproduce.

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Rules for Rabbit Vitality

• V1 - Rabbits eat
• V2 - Rabbits jump
• V3 - Rabbits reproduce

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This slide shows what happens when the three
Rules for Rabbit Vitality are coded as simple
subroutines. The subroutines were embedded in the
operational wind and smoke model, PB-Piedmont.
Click the left mouse button to view the initial
conditions and results of the application.

• Starting point
• 4 rabbits per generation
• 15 generations enough rabbits to circle the
  globe 200 times
• Computer saturated

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How to get rid of rabbits
Once fire burns over a bed of fuel, there remains
no fuel to support fire. The same principle
applies to our rabbits. Once the food supply is
exhausted, rabbits can no longer survive. As
there are three general rules for rabbit vitality
so there are three general rules that govern
rabbit mortality. These rules are presented and
demonstrated in the slides that follow.
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Rules for Rabbit Mortality

• M1 Rabbits are territorial a rabbit cannot
  jump onto a space occupied by another rabbit
• M2 Rabbits starve when jumping onto a space
  eaten by another rabbit
• M3 Rabbits starve when failing to jump off a
  space already eaten within a specified period of
  time.

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Application of the three rules for rabbit
mortality produces the pattern of rabbits (yellow
dots) shown below. Eaten-over areas are in black.
The solid green area represents uneaten food
which is uniformly distributed. There is no wind.
Click left mouse button to see the pattern of
spread of the rabbits.
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The distribution of rabbits at a later time. The
growth pattern is roughly circular with small
fractal/wave like structures that results from
the stochastic terms that govern jumping.
Small bulges due to stochastic jumping
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Rabbit Findings

• A rabbit is an autonomous agent
• Each rabbit is highly dependent on the location
  of its neighbors
• Each rabbit is dependent on the history of the
  spread of rabbits

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Other Rabbit Rules

• Terrain (T1) Rabbits enjoy jumping up hill
  rabbits are afraid to jump down hill.

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The terrain rule, T1, is programmed as a function
of slope multiplied by a coefficient called the
fear factor. A fear factor of no fear means
that terrain has no influence on rabbit behavior
and there results the circular spread pattern
shown on a previous slide. Here the fear factor
is morbid meaning that rabbits will only jump
uphill. The underlying graphic is that of a
mountain range in north Georgia. Dark greens
represent low elevation whites represent highest
elevation. Maximum elevation difference is 800 m
(2500 ft). Click the left mouse button 8 times
to follow the progression of the rabbits up the
mountain.
Fear Factor morbid
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With fear factor at morbid rabbits refused to
jump downhill. Once the food along all upslopes
was consumed, only downslopes remained. Since the
rabbits refused to jump downslope, they perished
according to Rabbit Mortality Rule M3. The result
is the eaten-over pattern shown on this
slide. Click left mouse button to continue to the
next example.
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With Fear Factor at cautious, rabbits will jump
downhill although they prefer to jump uphill.
This simulation shows how a simple terrain rule
T1 can yield an enormously complex rabbit spread
history. The features to watch for in the slides
to follow are rabbit runs and active
spots. Click the left mouse button 7 times to
follow the spread of rabbits over the complex
terrain of the north Georgia mountain.
Fear Factor cautious
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end
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Example of active spots Oregon June 30, 2003
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Other Rabbit Rules
The next section of our study of Rabbit
spread/behavior regards rabbit response to wind.
Unlike the terrain rule, there are no simple
rules that link rabbit behavior to wind speed.
How far rabbits are carried by the wind depends
upon how high rabbits jump (a measure of how long
rabbits are exposed to the wind) and how much the
rabbits weigh. A lightweight rabbit that jumps
high will be carried farther than a heavyweight
rabbit that is barely able to jump off the
ground. Thus the wind rules connect not only to
the magnitude of the wind speed but to the
characteristics of the food. Click left mouse
button to continue.
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Other Rabbit Rules

• Weather (W1) Rabbits are carried by the wind in
  proportion to how much they weigh and how high
  they jump.
• Food (F1) Rabbits gain weight in proportion to
  the water content of their food.
• Food (F2) Rabbits jump in proportion to the
  height of their food.

The next slide shows three examples of the
application of the wind rules with modifications
of the mortality rules. The salient feature is
the development of a head structure, a thicker
band of rabbits at the front edge of the area of
spreading rabbits. This feature results from the
carrying ahead a short distance from the spread
line a few rabbits to create local spotting.
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Mortality rules modified to permit survival if
there is an adjacent uneaten square.
Same as above but allowance for 15 survival rate
for rabbits that jump onto eaten squares.
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The application of the wind rules leads to the
tear drop structure frequently observed in
physical models of fire spread. The lack of
symmetry in the patterns is because the wind
fields generated by PB-Piedmont were shifting
slightly from northwesterly to westerly during
the period of simulation. The key feature of
these spread patterns is the thickness of the
heads at the leading edge of the spreading
rabbits. The ability of the Rabbit Model to
generate not only realistic patterns of spread
but also realistic patterns of thickness of the
spread zone is key to the next rule governing
rabbit/atmosphere feedback.
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Rabbit/Atmosphere Feedback Rule A1
Rabbits work up a sweat while eating, jumping,
and reproducing.
Rabbit gives off heat
Creates tiny low pressure anomaly
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The rabbit/atmosphere feedback rule posits that
each rabbit gives off heat as it does its rabbit
thing. Beneath the heat plume as it drifts away
downwind from the rabbit is a tiny
hydrostatically induced low pressure anomaly.
This low pressure anomaly is so weak that it has
no impact on the local wind field. However, when
these anomalies are summed over a large number of
rabbits, the low pressure center can be several
tenths of a millibar sufficient to turn and/or
reverse the winds downwind from the spreading
rabbits. The rabbit/atmosphere feedback rule
generates wind features and spread patterns
similar to those found in physical fire spread
models. In viewing the following 3 slides, note
the convergence zones along the flanks of the
rabbit lines and the weakened wind field in front
of the rabbit head.
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Rabbit/Atmosphere Feedback Initial winds are 5
m/sec (10 kts), base pressure 51 tenths mb. Grid
spacing 300 m, Time 8.0 min.
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Time 16 min
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Time 29 min
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The final simulation shows the response of the
wind/pressure field to the rabbit/atmosphere
feedback rule applied to a case of no wind. In
the slide that follows, a low pressure anomaly is
found at the center of the ring of spreading
rabbits. This low pressure center directs winds
to blow toward the front of rabbits. An
accompanying photograph of a ring fire in a
field shows the flame front being swept back
toward the center of the field by the inblowing
current of air to a single center of rising
smoke. In the second slide that follows, the
ring of rabbits has grown and the related wind
field has become more complex. An area of weak
divergence (subsidence) is found at the center of
the ring. Immediately behind the line of rabbits
are transient centers of low pressure. These
appear and disappear randomly as the rabbits
spread. They create centers of strong
convergence. They also cause local strengthening
of winds blowing toward the rabbit line and thus
do not necessarily increase the spread of
rabbits. They do contribute to the irregularity
of the rabbit line, however. The transient
pressure centers may have application to
instances of real grassland fire. Given uniformly
distributed fuels, linear theory predicts a flame
front of uniform height everywhere. The
rabbit/atmosphere feedback rule predicts the
appearance of centers of convergence that
concentrate volatile gases and locally increase
flame height. These flaming areas grow and
dissolve with no apparent relation to fuel
loading.
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Time 17 min
Rabbit/Atmosphere Feedback Effect of no ambient
wind. Photo courtesy of Brian Potter (EAMC)
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Time 89 min
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SummaryThe Rabbit Model.

• Simulates some of the features observed in
  physical models flattening of the head,
  convergence of wind along flanking line,
  weakening and/or reversal of winds ahead of fire.
• Simulates some of the features observed in fire
  spread highly irregular spread in complex
  terrain, head, flanking lines, and active
  spots.
• Appears sufficiently robust to merit continued
  development
• Fast

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SummaryBecause it is rule-based.

• The Rabbit Model should be considered as a
  screening model
• The goal is to make the Rabbit Model a baseline
  model the model for more sophisticated fire
  spread models to beat.
• The Rabbit Model is an addition to the
  operational PB-Piedmont Smoke Model.
• the Rabbit Model can be brought to operational
  capability relatively quickly through PB-Piedmont
  and FCAMMS.
• The next step is to validate the Rabbit Model
  with fire spread/behavior data from the
  Okefenokee fires of 2002 (FWS).