# Presentation: 209540

## “Rabbit Rules” – An Application of Stephen Wolfram’s “New Kind of Science” to Fire Spread Modeling

- “Rabbit Rules” – An Application of Stephen Wolfram’s “New Kind of Science” to Fire Spread Modeling

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

## 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.

## 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.

## 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 Wolfram’s 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.

## 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

## 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.

## 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

## Stephen Wolfram’s “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.)

## The Rabbit Model....

- Follows Wolfram’s rules for computing
- But not cellular automata,
- Nor raster-based domains

## 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.

## Rules for Rabbit Vitality

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

## 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

## 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.

## 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.

## 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.

## Small bulges due to stochastic jumping

- 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.

## 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

## Other Rabbit Rules

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

## Fear Factor – “morbid”

-                                                  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.

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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.

## Fear Factor – “cautious”

- 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.

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## Example of active spots – Oregon June 30, 2003

## 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.

## 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.”

## 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.

## 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.

## Rabbit/Atmosphere Feedback Rule A1

- Rabbit gives off heat

- Creates tiny low pressure anomaly

- Rabbits “work up a sweat” while eating, jumping, and reproducing.

## 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.”

## Rabbit/Atmosphere Feedback: Initial winds are 5 m/sec (10 kts), base pressure 51 tenths mb. Grid spacing 300 m, Time = 8.0 min.

## Time = 16 min

## Time = 29 min

## 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. 

- 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.

## Rabbit/Atmosphere Feedback: Effect of no ambient wind. Photo courtesy of Brian Potter (EAMC)

- Time = 17 min

## Time = 89 min

## SummaryThe 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

## SummaryBecause 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).