Spatially extended radiant heat fire model

Recent wildfire prevalence and destruction have led to new initiatives in the search for better land management techniques and prescriptions for controlled burns. With limited data on low-intensity prescribed burns, finding models that can represent fire behavior is of great importance to learning how to control fires with more accuracy while also maintaining the purpose for the burn, be it reducing fuels or managing the ecosystem. Here we use a data set of infrared temperatures collected in the New Jersey Pine Barrens from 2017 through 2020 to develop a model for very fine-scale fire behavior ($\approx 0.05 {\mathrm{m}}^2$). The model uses distributions from the data set to define five stages in fire behavior in a cellular automata framework. For each cell, the transition between each stage is probabilistically driven based on the radiant temperature values of the cell and its immediate neighbors in a coupled map lattice. With five distinct initial conditions, we performed 100 simulations and used the parameters derived from the data set to develop metrics for model verification. To validate the model, we also expanded it to include variables not in the data set that are important for fire behavior, e.g., fuel moisture levels and spotting ignitions. The model matches several metrics compared to the observational data set and exhibits behavioral characteristics expected from low-intensity wildfire behavior including a long and varied burn time for each cell after initial ignition, and lingering embers in the burn zone.

Figure 1

A schematic of the five stages that make up the life cycle of a burning cell; a definition of the five cellular automata output states.

Figure 2

Representation of how the radiant temperature changes in a specific cell over time beginning in stage two, warming, where Newton's law of cooling is applied, moving through the linear equations developed for stages three (rising) and four (falling) and ending in stage five, cooling; example of CML output for a single cell.

Figure 3

Truss setup in the New Jersey Pine Barrens for the creation of the data set; (a) before the burn; (b) after burn was initialized (photos courtesy of Dr. Robert Kremens, Chester F. Carlson Center for Imaging Science, Rochester Institute of Technology (RIT); credit: USDA Forest Service Northern Research Station).

Figure 4

Calibration graph for relating infrared output data to radiant temperature values from observations using a black box unit with the FLIR Lepton 1.5 camera.

Figure 5

A representive sample of $T_M$ matrix and a smoothed version used in SERF: (a) initial $T_M$ matrix with values sampled from the distribution for maximum temperatures; (b) $T_M$ matrix after smoothing.

Figure 6

Maximum, minimum, and threshold temperatures for each fire in degrees Celsius and the top and bottom of the threshold interval.

Figure 7

Recorded maximum temperatures for 355,200 cells from all fires in the data set; histogram and fitted kernel distribution (red line).

Figure 8

Rise (a) and fall (b) time value histograms and kernel distributions from the data set.

Figure 9

Heat coefficient histogram with kernel distribution; found largest temperature value in the maximum temperature matrix for each fire and the proportion of that maximum reached by each cell.

Figure 10

Initial conditions: (a) corner from $\left\{S_m\right\}$, (b) corner from $\left\{f_m\right\}$, (c) side from $\left\{S_m\right\}$, (d) side from $\left\{f_m\right\}$, (e) chunk from $\left\{S_m\right\}$, (f) chunk from $\left\{f_m\right\}$, (g) double chunk from $\left\{S_m\right\}$, and (h) double chunk from $\left\{f_m\right\}$.

Figure 11

Spotting initial condition added to the simulations to analyze fires beyond what was represented in the data set.

Figure 12

Histogram of the proportion of cells that did not burn in each fire from the data set ($U$). The exponential curve fitted to the histogram shown here in red has a mean of $\langle U\left(f_m\right)\rangle =0.0855$.

Figure 13

Percentage differences in stage transition probabilities for the SERF simulations versus the data set. The simulations reproduce the transition probabilities with an error of less than $3\%$ for all cases except the stage two to three transition where the error is $12\%$.

Figure 14

Box plot comparing the heat coefficients in the SERF simulations and the data set; the red line in the middle of the boxes indicates median values. Observe the relative similarity between $k$ in the data set and SERF simulations.

Figure 15

Box plot showing the unburnt proportion of land in the SERF simulations compared to the data set. Observe the relative similarity between $U$ in the data set and simulations.

Figure 16

Lingering embers in the simulations and fire data sets; (a) $f_8$, second 500 of 1100; (b) $f_{50}$, second 2550 of 2894; (c) $S_{71}$, second 2000 of 2310; (d) $S_{93}$, second 900 of 1241.

Figure 17

Successful representation of the lingering heat after the fireline moves through the area; images from SERF simulation number 30; (a) time step 30; (b) time step 50; (c) time step 100; (d) time step 200; (e) time step 400; and (f) time step 700.

Figure 18

The $300\times 300$ grid for a basic CA model with probability of spread weighted by wind; [(a)–(d)] northern winds at 15 mph; (a) time step 5; (b) time step 75; (c) time step 150; (d) time step 250; [(e)–(h)] no winds; (e) time step 5; (f) time step 20; (g) time step 80; and (h) time step 150.

Figure 19

Side ignition: Simulation 4; (a) time step 5; (b) time step 200; (c) time step 400; (d) time step 700; (e) time step 1000; and (f) time step 1300.

Figure 20

Side ignition: Dataset Fire 120; (a) time step 200; (b) time step 220; (c) time step 250; (d) time step 300; (e) time step 400; and(f) time step 500.

Figure 21

Corner ignition: Simulation 25; (a) time step 75; (b) time step 150; (c) time step 300; (d) time step 500; (e) time step 900; and (f) time step 1300.

Figure 22

Corner ignition: Dataset Fire 25; (a) time step 65; (b) time step 80; (c) time step 100; (d) time step 150; (e) time step 180; and (f) time step 250.

Figure 23

Chunk ignition: Simulation 45; (a) time step 30; (b) time step 70; (c) time step 200; (d) time step 300; (e) time step 500; and (f) time step 700.

Figure 24

Chunk ignition: Dataset Fire 145; (a) time step 5; (b) time step 15; (c) time step 30; (d) time step 60; (e) time step 100; and (f) time step 300.

Figure 25

Double Chunk ignition: Simulation 90; (a) time step 30; (b) time step 50; (c) time step 90; (d) time step 200; (e) time step 500; and (f) time step 800.

Figure 26

Double Chunk ignition: Dataset Fire 3; (a) time step 5; (b) time step 20; (c) time step 40; (d) time step 70; (e) time step 100; and (f) time step 160.

Figure 27

Spotting ignition: Simulation 63; (a) time step 10; (b) time step 20; (c) time step 50; (d) time step 100; (e) time step 300; and (f) time step 600.