not generally known, the methods were developed and tested by using artificial
data with a known, “ground truth" ignition point or fire arrival time.

For estimating the ignition point of a fire, an artificial fire arrival time
was created and artificial fire detections were placed on the surface of the
fire arrival cone. Using a grid search strategy, an ensemble of forecasts with
varying locations and times of ignition was made and the data likelihood of
each was computed. The estimated time and place of ignition was found from the
ignition point of the forecast with the highest data likelihood. This method
worked to identify the time and place of ignition for a test using a “ground
truth" artificial fire arrival time derived from the equation of a cone as
well as in a test where the “ground truth" was taken as the fire arrival time
output from a WRF-SFIRE simulation. A third test of the method was made using
data from a real wildfire. In this real-world example, the method was able to
identify an ignition time within an hour of that surmised by fire
investigators, but the estimated ignition location differed from that provided
by investigators by around 3 km.

For estimating the fire arrival time, the testing took place in two stages. In
the first stage, artificial fire detection data was created and the method for
estimating the fire arrival time was used to attempt to reconstruct the fire
arrival time from the sparse artificial data. Testing, using various
strategies and key parameters for computer functions used in the method, was a
key goal of this first step. Based on the results of the testing, a workable
method for producing accurate estimates of the fire arrival time was devised.
The testing also revealed some situations in which the method is likely to
produce poor results. The method is likely to fail when only a small amount of
observations are available for relatively small fires. The method also
produced poor results when there was more than one fire in the domain. This
shortcoming is more serious. During wildfire season, many fires can exist
concurrently in a geographic region. The method presented here will attempt to
treat these separate events as if they were a singular fire and the resulting
estimate of the fire arrival time can be expected to show fire spread in
regions where no data indicates such burning has occurred.

The second stage of this testing was to determine how well the established
method worked for more complicated “ground truth" fire arrival times, taken
from various forecasts produced by WRF-SFIRE. The goal was to use the method
developed in the first stage in exactly the same way to see if similar results
could be achieved, indicating the method can be generalized to fire scenarios
other than those in the first stage of the testing. The results of the
estimates in the second stage were a bit worse than those in the first stage.
In particular, the method tended to underestimate the size of the fire and
give a poorer estimate for the growth rate of the fire.

Finally, the method was applied to estimating the fire arrival time of real-
world fires. Because the actual fire arrival time of such fire is not known,
assessment of the method was made by comparison with infrared perimeter
observations. The method produced good results in terms of these comparisons
with both dimensions of the MOE and the Sørenson index around 0.9. These
scores are at least as good as those obtained in the hundreds of artificial
fires that were used to test and develop the method. Despite the high scores
for these real-world scenarios, it should be realized that the shortcomings
previously mentioned are still of concern. The method is likely to deliver
poor results during the early stage of a fire, when few satellite observations
are available, and the presence of more than one fire in the domain will cause
problems in the real-world situation just as it did in testing with artificial
data.

With a good estimate of the fire arrival time established, it is possible to
get an estimate of the rate of spread of the fire at all locations in the fire
domain. In this work, we used the known uncertainties in the satellite
observations to develop a sense of how reliable the estimates of the ROS are.
Although used sparingly in this work, the method for for finding the ROS from
satellite data has greater potential to impact wildfire modeling in a positive
way. At the heart of wildfire model are the spread models like the Rothermel
or Balbi models. Although widely used, other, improved models could be
devised. Possibly the method for determining the ROS established here could be
used in conjunction with the large amount of historical satellite data to
develop a new model using machine learning techniques.

####  6.1.3 Data Assimilation and Adjustment of the Fuel Moisture Content

Several different forecast strategies using data assimilation were discussed
in this work and comparisons of simulations using these strategies follow. The
Patch Springs Fire and Cougar Creek Fire are presented here. The Camp Fire
also served as an example of the data assimilation techniques but will not be
treated in the same way as the other two because during the simulation period
its mechanism of spread was largely due to winds carrying burning embers ahead
of the fire front. The WRF-SFIRE model does not currently model such behavior
and the concept of adjusting the FMC content makes little sense under such
circumstances. The foresting strategies to be compared follow. A single
forecast, without using data assimilation is included in this comparison as a
control. At a bare minimum, any forecast strategy using data assimilation
techniques should be able to produce better results than this single forecast
if it is to be worthy of consideration and further study.

  1. 1.

A single forecast, started from an ignition point

  2. 2.

A forecast using data assimilation cycling

  3. 3.

A forecast with data assimilation cycling and adjustment of FMC

  4. 4.

48-Hour Forecast strategy

Each forecast strategy has been evaluated by comparing a final forecast
perimeter with an infrared perimeter observation using the MOE and the
Sørenson index. For simplicity, a score for each strategy was computed from
the sum of these measures as

$\text{SCORE}=\text{MOE X}+\text{MOE Y}+S.$ (6.1.1)

where MOE X and MOE Y are the two components of the measure of effectiveness
describing decreasing false negatives and false positives, respectively, and
$S$ is the Sørenson index.

Table 6.1 gives the results of these scores for both the Patch Springs and
Cougar Creek fires. In both cases, the 48-hour forecast strategy produced the
best results, and the worst results were obtained by single forecasts from an
ignition point that made no attempt to assimilate satellite data. Use of data
assimilation and data assimilation with FMC adjustments gave mixed results,
with both strategies falling in the middle. Part of the reason for the success
of the 48-hour strategy is surely due to the extra perimeter data that was
used in the process of finding an estimate of the fire arrival time that was
used for initializing the model. Another potential advantage was that the data
assimilation performed was over a relatively show period and didn’t seek to
make large changes to the forecast. Further discussion of the particulars of
each fire and its simulations are given below.

Forecast Strategy | Patch Springs | Cougar Creek
---|---|---
Single Forecast | 1.8940 | 1.9927
Data Assimilation | 2.0217 | 2.1081
Data Assimilation and FMC | 2.0075 | 2.1563
48-Hour Strategy | 2.0970 | 2.3999
Table 6.1: Overall results of simulation strategies for the Patch Springs and
Cougar Creek Fire simulations. For both fires, the 48-hour forecast strategy
produced the best results. Using a single simulation produced the worst
results.

##### Patch Springs Fire Simulations

Comparison was made between four simulations of the Patch Springs Fire. The
simulations using a single run, data assimilation cycling, and data
assimilation with FMC adjustment were all started from an identical ignition
point and the 48-hour strategy simulation was started from an estimated fire
arrival time made using satellite and infrared perimeter data. The single
simulation represents 130 hours of forecast time and the other simulations
make 58 hours of forecast, each.

Table 6.2 summarizes the results using the MOE and Sørenson index, and Figure
H.38 shows a graphical representation of the results. The 48-hour forecast
strategy produced the best result for this simulation. It should be noted that
all forecast strategies failed to capture the rapid growth of the fire that
occurred during the fourth day. The large red areas of false negative in the
northeast section of the panels in Figure H.38 show the region where the
observed fire growth was explosive during this period. The reason the model
failed to predict this growth is unclear. Sudden changes in weather or an
inaccurate accounting of the fuel properties in the are could explain the
model’s shortcomings. The simulation using data assimilation showed more
burning in this region, but it also showed more burning in areas where no fire
was actually observed. The simulation using data assimilation with FMC
adjustment managed to control the size of the fire and produced a result
similar to that of the simulation using the 48-hour forecast strategy.

Forecast Strategy | MOE X | MOE Y | ||MOE|| | Sørenson
---|---|---|---|---
Single Forecast | 0.4920 | 0.7629 | 0.9078 | 0.5982
Data Assimilation | 0.7009 | 0.6476 | 0.9543 | 0.6732
Data Assimilation and FMC | 0.6247 | 0.7157 | 0.9500 | 0.6671
48-Hour Strategy | 0.6450 | 0.7559 | 0.9937 | 0.6961
Table 6.2: Results for the Patch Springs fire simulations. The 48-hour
forecast strategy produced the best results. The worst results were from a
single simulation without using any data assimilation.

##### Cougar Creek Fire

The four strategies were applied to the Cougar Creek Fire Simulation. The
single run, data assimilation cycling, and the data assimilation cycling with
FMC adjustments were all started from an identical ignition point. The
simulation using the 48-hour forecast strategy was started from an estimated
fire arrival time made using satellite data and infrared perimeter
observations. The single run simulation represents 105 hours of forecast time,
the two simulations with data assimilation have 57 hours of forecast time, and
the simulation using the 48-hour strategy has 57 hours of forecast time.

Table 6.3 summarizes the results using the MOE and Sørenson index and Figure
H.39 shows a graphical representation of these results. The 48-hour forecast
strategy produced the best result for this simulation. This strategy tended to
underestimate the fire size, but the perimeter was close to the observed
perimeter in many places. The worst result was obtained by running a single
simulation. The overall size of the fire was similar to the observed fire, but
the perimeter matched poorly. Using data assimilation made for a forecast that
had too large of an area. Using data assimilation with FMC adjustment improved
the forecast by slowing down the rate of spread and produced a forecast closer
to that of the 48-hour strategy.

Forecast Strategy | MOE X | MOE Y | ||MOE|| | Sørenson
---|---|---|---|---
Single Forecast | 0.6638 | 0.6647 | 0.9394 | 0.6642
Data Assimilation | 0.9873 | 0.4773 | 1.0966 | 0.6435
Data Assimilation and FMC | 0.7025 | 0.7353 | 1.0169 | 0.7185
48-Hour Strategy | 0.7305 | 0.8722 | 1.1377 | 0.7972
Table 6.3: Results for the Cougar Creek Fire simulations.

## References

  * Albini (1976) Albini FA (1976).  “Estimating wildfire behavior and effects.”  U. S. Forest Service. General Technical Report INT-30.  http://www.treesearch.fs.fed.us/pubs/29574.
  * Andrews _et al._ (2007) Andrews P, Finney M, Fischetti M (2007).  “Predicting Wildfires.”  _Scientific American_ , 297, 46–51, 54.  10.1038/scientificamerican0807-46.
  * Baker (2011) Baker N (2011).  “Joint Polar Satellite System (JPPS) VIIRS Geolocation Algorithm Theoretical Basis Document.”  Available at https://lpdaac.usgs.gov/sites/default/files/public/product_documentation/vnp03_v1_atbd.pdf, retrieved April 1, 2018.
  * Balbi _et al._ (2009) Balbi JH, Morandini F, Silvani X, Filippi JB, Rinieri F (2009).  “A physical model for wildland fires.”  _Combustion and Flame_ , 156(12), 2217–2230.  ISSN 0010-2180.  10.1016/j.combustflame.2009.07.010.
  * Benali _et al._ (2016) Benali A, Russo A, Sá ACL, Pinto RMS, Price O, Koutsias N, Pereira JMC (2016).  “Determining Fire Dates and Locating Ignition Points With Satellite Data.”  _Remote Sensing_ , 8(4), Article number 326.  ISSN 2072-4292.  10.3390/rs8040326.
  * Brewer and Clements (2020) Brewer MJ, Clements CB (2020).  “The 2018 Camp Fire: Meteorological Analysis Using In Situ Observations and Numerical Simulations.”  _Atmosphere_ , 11(1).  ISSN 2073-4433.  10.3390/atmos11010047.
  * Cal Fire (2018 (Accessed March 3, 2020) Cal Fire (2018 (Accessed March 3, 2020)).  _Green Sheet: Burn Injuries, Camp Incident_.  https://assets.documentcloud.org/documents/5628194/18-CA-BTU-016737-Camp-Green-Sheet.pdf.
  * Cardil _et al._ (2019a) Cardil A, Monedero S, Ramarez J, Silva CA (2019a).  “Assessing and reinitializing wildland fire simulations through satellite active fire data.”  _Journal of Environmental Management_ , 231, 996 – 1003\.  ISSN 0301-4797.  10.1016/j.jenvman.2018.10.115.
  * Cardil _et al._ (2019b) Cardil A, Monedero S, Silva CA, Ramirez J (2019b).  “Adjusting the rate of spread of fire simulations in real-time.”  _Ecological Modelling_ , 395, 39–44.  ISSN 0304-3800.  10.1016/j.ecolmodel.2019.01.017.
  * Clark _et al._ (1996) Clark TL, Jenkins MA, Coen J, Packham D (1996).  “A Coupled Atmospheric-Fire Model: Convective Feedback on Fire Line Dynamics.”  _J. Appl. Meteor_ , 35, 875–901.  10.1175/1520-0450(1996)035<0875:ACAMCF>2.0.CO;2.
  * Coen and Schroeder (2013) Coen JL, Schroeder W (2013).  “Use of spatially refined satellite remote sensing fire detection data to initialize and evaluate coupled weather-wildfire growth model simulations.”  _Geophysical Research Letters_ , 40, 1–6.  10.1002/2013GL057868.
  * Cunningham and Linn (2007) Cunningham P, Linn RR (2007).  “Numerical simulations of grass fires using a coupled atmosphere-fire model: Dynamics of fire spread.”  _Journal of Geophysical Research: Atmospheres_ , 112, Art. D05108, 17pp.  ISSN 2156-2202.  10.1029/2006JD007638.
  * Dahl _et al._ (2015) Dahl N, Xue H, Hu X, Xue M (2015).  “Coupled fire–atmosphere modeling of wildland fire spread using DEVS-FIRE and ARPS.”  _Natural Hazards_ , 77(2), 1013–1035.  ISSN 1573-0840.  10.1007/s11069-015-1640-y.
  * Daley (1991) Daley R (1991).  _Atmospheric data analysis_.  Cambridge ; New York : Cambridge University Press.  ISBN 0521382157.
  * Farguell _et al._ (2021) Farguell A, Mandel J, Haley J, Mallia DV, Kochanski A, Hilburn K (2021).  “Machine Learning Estimation of Fire Arrival Time from Level-2 Active Fires Satellite Data.”  _Remote Sensing_ , 13(11), 2203.  ISSN 2072-4292.  10.3390/rs13112203.
  * Ferguson (1967) Ferguson TS (1967).  _Mathematical statistics: a decision theoretic approach_.  Academic Press, London, England;New York, New York;.  ISBN 9781483221236;9781483182537;1483221237;1483182533;.
  * Filippi _et al._ (2011) Filippi JB, Bosseur F, Pialat X, Santoni P, Strada S, Mari C (2011).  “Simulation of coupled fire/atmosphere interaction with the MesoNH-ForeFire models.”  _Journal of Combustion_ , 2011, Article ID 540390.  10.1155/2011/540390.
  * Finney (1998) Finney MA (1998).  “FARSITE: Fire Area Simulator – model development and evaluation.”  Res. Pap. RMRS-RP-4 Revised 2004, Ogden, UT, USDA Forest Service, Rocky Mountain Research Station.  10.2737/RMRS-RP-4.
  * Finney (2006) Finney MA (2006).  “An overview of FlamMap fire modeling capabilities.”  In PL Andrews, BW Butler (eds.), _Fuels Management – How to Measure Success_ , pp. 213–220. USDA Forest Service.  Proceedings RMRS-P-41, available at http://www.treesearch.fs.fed.us/pubs/25948.
  * Gabbert (2019) Gabbert B (2019).  “Utah: Patch Springs Fire burns 13,000 acres southwest of Salt Lake City.”  https://wildfiretoday.com/2013/08/15/utah-patch-springs-fire-burns-13000-acres-southwest-of-salt-lake-city/.
  * Giglio (2015) Giglio L (2015).  “MODIS Collection 6 Active Fire Product User’s Guide Version 2.6.”  Department of Geographical Sciences, University of Maryland.  Available at http://modis-fire.umd.edu/files/MODIS_C6_Fire_User_Guide_A.pdf, accessed March 2015.
  * Giglio _et al._ (2016) Giglio L, Schroeder W, Justice CO (2016).  “The collection 6 MODIS active fire detection algorithm and fire products.”  _Remote Sensing of Environment_ , 178, 31–41.  ISSN 0034-4257.  10.1016/j.rse.2016.02.054.
  * Goss _et al._ (2020) Goss M, Swain DL, Abatzoglou JT, Sarhadi A, Kolden CA, Williams AP, Diffenbaugh NS (2020).  “Climate change is increasing the likelihood of extreme autumn wildfire conditions across California.”  _Environmental Research Letters_ , 15(9), 094016.  10.1088/1748-9326/ab83a7.
  * Haley _et al._ (2018) Haley J, Farguell Caus A, Mandel J, Kochanski AK, Schranz S (2018).  “Data Likelihood of Active Fires Satellite Detection and Applications to Ignition Estimation and Data Assimilation.”  In DX Viegas (ed.), _Advances in Forest Fire Research_. University of Coimbra Press.  Accepted. Available at https://arxiv.org/abs/1808.03318, July 2018\.
  * Jaffe _et al._ (2020) Jaffe DA, O’Neill SM, Larkin NK, Holder AL, Peterson DL, Halofsky JE, Rappold AG (2020).  “Wildfire and prescribed burning impacts on air quality in the United States.”  _Journal of the Air & Waste Management Association_, 70(6), 583–615.  10.1080/10962247.2020.1749731.  PMID: 32240055, https://doi.org/10.1080/10962247.2020.1749731.
  * Jahn _et al._ (2011) Jahn W, Rein G, Torero J (2011).  “Forecasting fire growth using an inverse zone modelling approach.”  _Fire Safety Journal_ , 46(3), 81 – 88.  ISSN 0379-7112.  https://doi.org/10.1016/j.firesaf.2010.10.001.
  * Jolly (2015) Jolly W (2015).  “Climate-induced variations in global wildfire danger from 1979 to 2013.”  _Nature Communications_ , 6, 7537.  10.1038/ncomms8537.
  * Lafore _et al._ (1998) Lafore JP, Stein J, Asencio N, Bougeault P, Ducrocq V, Duron J, Fischer C, Héreil P, Mascart P, Masson V, Pinty JP, Redelsperger JL, Richard E, Vilà-Guerau de Arellano J (1998).  “The Meso-NH Atmospheric Simulation System. Part I: adiabatic formulation and control simulations.”  _Annales Geophysicae_ , 16(1), 90–109.  10.1007/s00585-997-0090-6.
  * Linn _et al._ (2002) Linn R, Reisner J, Colman JJ, Winterkamp J (2002).  “Studying wildfire behavior using FIRETEC.”  _Int. J. of Wildland Fire_ , 11, 233–246.  10.1071/WF02007.
  * Lloyd (1982) Lloyd S (1982).  “Least squares quantization in PCM.”  _IEEE Transactions on Information Theory_ , 28(2), 129–137.  10.1109/TIT.1982.1056489.
  * Loboda and Csiszar (2007) Loboda T, Csiszar I (2007).  “Reconstruction of fire spread within wildland fire events in Northern Eurasia from the MODIS active fire product.”  _Global and Planetary Change_ , 56(3), 258 – 273.  ISSN 0921-8181.  https://doi.org/10.1016/j.gloplacha.2006.07.015.  Northern Eurasia Regional Climate and Environmental Change.
  * Mandel _et al._ (2014a) Mandel J, Amram S, Beezley JD, Kelman G, Kochanski AK, Kondratenko VY, Lynn BH, Regev B, Vejmelka M (2014a).  “Recent advances and applications of WRF-SFIRE.”  _Natural Hazards and Earth System Science_ , 14(10), 2829–2845.  10.5194/nhess-14-2829-2014.
  * Mandel _et al._ (2011) Mandel J, Beezley JD, Kochanski AK (2011).  “Coupled atmosphere-wildland fire modeling with WRF 3.3 and SFIRE 2011.”  _Geoscientific Model Development_ , 4, 591–610.  10.5194/gmd-4-591-2011.
  * Mandel _et al._ (2008) Mandel J, Bennethum LS, Beezley JD, Coen JL, Douglas CC, Kim M, Vodacek A (2008).  “A Wildland Fire Model with Data Assimilation.”  _Mathematics and Computers in Simulation_ , 79, 584–606.  10.1016/j.matcom.2008.03.015.
  * Mandel _et al._ (2016) Mandel J, Fournier A, Jenkins MA, Kochanski AK, Schranz S, Vejmelka M (2016).  “Assimilation of Satellite Active Fires Detection Into a Coupled Weather-Fire Model.”  In _Proceedings for the 5th International Fire Behavior and Fuels Conference April 11-15, 2016, Portland, Oregon, USA_ , pp. 17–22. International Association of Wildland Fire, Missoula, Montana, USA.  http://www.iawfonline.org/wp-content/uploads/2018/02/5th-Internatonal-Fire-Behavior-and-Fuel-Conference-Proceedings-Final-updated-1.9.2017-web.pdf,accessed March 3, 2020.
  * Mandel _et al._ (2014b) Mandel J, Kochanski AK, Vejmelka M, Beezley JD (2014b).  “Data Assimilation of Satellite Fire Detection in Coupled Atmosphere-Fire Simulations by WRF-SFIRE.”  In DX Viegas (ed.), _Advances in Forest Fire Research_ , pp. 716–724. Coimbra University Press.  10.14195/978-989-26-0884-6_80.
  * Mandel _et al._ (2019) Mandel J, Vejmelka M, Kochanski AK, Farguell A, Haley JD, Mallia DV, Hilburn K (2019).  “An Interactive Data-Driven HPC System for Forecasting Weather, Wildland Fire, and Smoke.”  In _2019 IEEE/ACM HPC for Urgent Decision Making (UrgentHPC), Denver, CO, USA_ , pp. 35–44. IEEE.  10.1109/UrgentHPC49580.2019.00010.
  * MathWorks (2020 (accessed October 10, 2020) MathWorks (2020 (accessed October 10, 2020)).  _Cubic smoothing spline_.  https://www.mathworks.com/help/curvefit/csaps.html.
  * MathWorks (2021 (accessed April 28, 2021) MathWorks (2021 (accessed April 28, 2021)).  _2-D Gaussian filtering of images - MATLAB imgaussfilt_.  https://www.mathworks.com/help/images/ref/imgaussfilt.html.
  * MathWorks (2021 (accessed February 5, 2021) MathWorks (2021 (accessed February 5, 2021)).  _Shortest path between two single nodes - MATLAB shortestpath_.  https://www.mathworks.com/help/matlab/ref/graph.shortestpath.html.
  * MathWorks (2021 (accessed March 10, 2021) MathWorks (2021 (accessed March 10, 2021)).  _Gradient, slope, and aspect of data grid - MATLAB gradientm_.  https://www.mathworks.com/help/map/ref/gradientm.html.
  * McGrattan _et al._ (2013) McGrattan K, McDermott R, Weinschenk C, Overholt K, Hostikka S, Floyd J (2013).  “Fire Dynamics Simulator User’s Guide.”  National Institute of Standards and Technology Special Publication 1019, 262 pages (April 2013).
  * Mell _et al._ (2007) Mell W, Jenkins MA, Gould J, Cheney P (2007).  “A physics-based approach to modelling grassland fires.”  _Intl. J. Wildland Fire_ , 16, 1–22.  10.1071/WF06002.
  * NASA (2021) NASA (2021).  “Earth Observation Data | Earthdata.”  https://earthdata.nasa.gov/earth-observation-data.
  * Nishihama (1997) Nishihama M (1997).  “MODIS Level 1A Earth Location: Algorithm Theoretical Basis Document Version 3.0.”  Available at https://modis.gsfc.nasa.gov/data/atbd/atbd_mod28_v3.pdf, retrieved April 1, 2018.
  * Ntaimo and Zeigler (2004) Ntaimo L, Zeigler BP (2004).  “Expression of a Forest Cell Model in Parallel DEVS and Timed Cell-DEVS Formalisms.”  In _Proceedings of the 2004 Summer Computer Simulation Conference_ , pp. 25–29. SCS.  Available at http://www.acims.arizona.edu/PUBLICATIONS/PDF/NtaimoForestCellPaper.pdf.
  * Parks (2014) Parks SA (2014).  “Mapping day-of-burning with coarse-resolution satellite fire-detection data.”  _International Journal of Wildland Fire_ , 23(2), 215–223.  10.1071/WF13138.
  * Pyne _et al._ (1996) Pyne S, Andrews PL, Laven RD (1996).  _Introduction to Wildland Fire_.  Wiley, New York.
  * Ramírez _et al._ (2011) Ramírez J, Monedero S, Buckley D (2011).  “New approaches in fire simulations analysis with Wildfire Analyst, Sun City, South Africa, May 9–13, 2011.”  In _7th International Conference on Forest Fire Research_.
  * Reisner _et al._ (2000) Reisner J, Wynne S, Margolin L, Linn R (2000).  “Coupled atmospheric-fire modeling employing the method of averages.”  _Monthly Weather Review_ , 128(10), 3683–3691.  10.1175/1520-0493(2001)129<3683:CAFMET>2.0.CO;2.
  * Rios _et al._ (2014) Rios O, Jahn W, Rein G (2014).  “Forecasting wind-driven wildfires using an inverse modelling approach.”  _Natural Hazards and Earth System Sciences_ , 14(6), 1491–1503.  10.5194/nhess-14-1491-2014.
  * Rochoux _et al._ (2013) Rochoux MC, Delmotte B, Cuenot B, Ricci S, Trouvé A (2013).  “Regional-scale simulations of wildland fire spread informed by real-time flame front observations.”  _Proceedings of the Combustion Institute_ , 34, 2641–2647.
  * Rochoux _et al._ (2014) Rochoux MC, Emery C, Ricci S, Cuenot B, Trouve A (2014).  “Towards predictive simulation of wildfire spread at regional scale using ensemble-based data assimilation to correct the fire front position.”  _Fire Safety Science_ , 11, 1443–1456.  10.3801/IAFSS.FSS.11-1443.
  * Rothermel (1972) Rothermel RC (1972).  “A Mathematical Model for Predicting Fire Spread in Wildland Fires.”  USDA Forest Service Research Paper INT-115.  https://www.fs.fed.us/rm/pubs_int/int_rp115.pdf, accessed March 2018.
  * Rothermel and Rinehart (1983) Rothermel RC, Rinehart GC (1983).  “Field Procedures for Verification and Adjustment of Fire Behavior Predicitions.”  U.S. Forest Service General Technical Report INT-142. Ogden, UT.  https://www.fs.fed.us/rm/pubs_int/int_gtr142.pdf.
  * Sá _et al._ (2017) Sá ACL, Benali A, Fernandes PM, S PRM, Trigo RM, Salis M, Russo A, Jerez S, Soares PMM, Schroeder W, Pereira JMC (2017).  “Evaluating fire growth simulations using satellite active fire data.”  _Remote Sensing of Environment_ , 190, 302–317.  ISSN 0034-4257.  10.1016/j.rse.2016.12.023.
  * Schoennagel _et al._ (2017) Schoennagel T, Balch JK, Brenkert-Smith H, Dennison PE, Harvey BJ, Krawchuk MA, Mietkiewicz N, Morgan P, Moritz MA, Rasker R, Turner MG, Whitlock C (2017).  “Adapt to more wildfire in western North American forests as climate changes.”  _Proceedings of the National Academy of Sciences_ , 114(18), 4582–4590.  ISSN 0027-8424.  10.1073/pnas.1617464114.  https://www.pnas.org/content/114/18/4582.full.pdf.
  * Schroeder and Giglio (2017) Schroeder W, Giglio L (2017).  “Visible Infrared Imaging Radiometer Suite (VIIRS) 750 m Active Fire Detection and Characterization Algorithm Theoretical Basis Document 1.0.”  Available at https://lpdaac.usgs.gov/sites/default/files/public/product_documentation/vnp14_atbd_v1.pdf, retrieved August 28, 2018.
  * Schroeder _et al._ (2008) Schroeder W, Prins E, Giglio L, Csiszar I, Schmidt C, Morisette J, Morton D (2008).  “Validation of GOES and MODIS active fire detection products using ASTER and ETM+ data.”  _Remote Sensing of Environment_ , 112(5), 2711–2726.  10.1016/j.rse.2008.01.005.
  * Skamarock _et al._ (2008) Skamarock WC, Klemp JB, Dudhia J, Gill DO, Liu Z, Berner J, Wang W, Powers JG, Duda MG, Barker DM, Huang XY (2008).  “A Description of the Advanced Research WRF Version 4.”  NCAR Technical Note 556.  10.5065/1dfh-6p97.
  * Sørensen (1948) Sørensen T (1948).  _A Method of Establishing Groups of Equal Amplitude in Plant Sociology_.  Biologiske skrifter. I kommission hos E. Munksgaard.
  * Srivas _et al._ (2016) Srivas T, Artés T, de Callafon RA, Altintas I (2016).  “Wildfire Spread Prediction and Assimilation for FARSITE Using Ensemble Kalman Filtering1.”  _Procedia Computer Science_ , 80, 897–908.  ISSN 1877-0509.  10.1016/j.procs.2016.05.328.  International Conference on Computational Science 2016, ICCS 2016, 6-8 June 2016, San Diego, California, USA.
  * Stuart (2010) Stuart AM (2010).  “Inverse problems: A Bayesian perspective.”  _Acta Numer._ , 19, 451–559.  10.1017/S0962492910000061.
  * Sullivan (2009a) Sullivan AL (2009a).  “A review of wildland fire spread modelling, 1990-present, 1: Physical and quasi-physical models.”  _International Journal of Wildland Fire_ , 18, 347–368.  10.1071/WF06143.
  * Sullivan (2009b) Sullivan AL (2009b).  “A review of wildland fire spread modelling, 1990-present, 1: Physical and quasi-physical models, 2: Empirical and quasi-empirical models, 3: Mathematical analogues and simulation models.”  _International Journal of Wildland Fire_ , 18, 1: 347–368, 2: 369–386, 3: 387–403.  10.1071/WF06143, 10.1071/WF06142, 10.1071/WF06144.
  * Sullivan (2009c) Sullivan AL (2009c).  “A review of wildland fire spread modelling, 1990-present 3: Mathematical analogues and simulation models.”  _International Journal of Wildland Fire_ , 18, 387–403.  10.1071/WF06144.
  * Syifa _et al._ (2020) Syifa M, Panahi M, Lee CW (2020).  “Mapping of Post-Wildfire Burned Area Using a Hybrid Algorithm and Satellite Data: The Case of the Camp Fire Wildfire in California, USA.”  _Remote Sensing_ , 12(4).  ISSN 2072-4292.  10.3390/rs12040623.
  * Trucchia _et al._ (2020) Trucchia A, D’Andrea M, Baghino F, Fiorucci P, Ferraris L, Negro D, Gollini A, Severino M (2020).  “PROPAGATOR: An Operational Cellular-Automata Based Wildfire Simulator.”  _Fire_ , 3(3).  ISSN 2571-6255.  10.3390/fire3030026.
  * USDA Forest Service and Management (2013 (accessed April 20, 2020) USDA Forest Service F, Management A (2013 (accessed April 20, 2020)).  _InciWeb the Incident Information System: Cougar Creek_.  https://web.archive.org/web/20170522031551/https://inciweb.nwcg.gov/incident/4484/.
  * USDA Forest Service and Management (2015 (accessed April 20, 2020) USDA Forest Service F, Management A (2015 (accessed April 20, 2020)).  _InciWeb the Incident Information System: Patch Springs Wildfire_.  https://web.archive.org/web/20130825074158/http://inciweb.nwcg.gov/incident/3665.
  * USDA Forest Service and Management (2018 (accessed April 20, 2020) USDA Forest Service F, Management A (2018 (accessed April 20, 2020)).  _Camp Fire Information - InciWeb the Incident Information System_.  https://web.archive.org/web/20190228180400/https://inciweb.nwcg.gov/incident/6250/.
  * Vejmelka _et al._ (2016) Vejmelka M, Kochanski AK, Mandel J (2016).  “Data assimilation of dead fuel moisture observations from remote automatic weather stations.”  _International Journal of Wildland Fire_ , 25, 558–568.  10.1071/WF14085.
  * Veraverbeke _et al._ (2014) Veraverbeke S, Sedano F, Hook SJ, Randerson JT, Jin Y, Rogers BM (2014).  “Mapping the daily progression of large wildland fires using MODIS active fire data.”  _International Journal of Wildland Fire_ , 23, 655–667.  10.1071/WF13015.
  * Wang _et al._ (2017) Wang W, Bruyère C, Duda M, Dudhia J, Gill D, Kavulich M, Keene K, Chen M, Lin HC, Michalakes J, Rizvi S, Zhang X, Berner J, Ha S, Fossell K, Beezley JD, Coen JL, Mandel J, Chuang HY, McKee N, Slovacek T, Wolff J, Fossell K (2017).  “ARW Version 3 Modeling System User’s Guide.”  Mesoscale & Miscroscale Meteorology Division, National Center for Atmospheric Research.  http://www2.mmm.ucar.edu/wrf/users/docs/user_guide_V3.8/ARWUsersGuideV3.8.pdf, retrieved February 2017.
  * Warner _et al._ (2004) Warner S, Platt N, Heagy J (2004).  “User-Oriented Two-Dimensional Measure of Effectiveness for the Evaluation of Transport and Dispersion Models.”  _Journal of Applied Meteorology - J APPL METEOROL_ , 43, 58–73.  10.1175/1520-0450(2004)043<0058:UTMOEF>2.0.CO;2.
  * WildfireAnalyst (2021 (accessed July 5, 2021) WildfireAnalyst (2021 (accessed July 5, 2021)).  “Homepage.”  https://www.wildfireanalyst.com/.
  * Xue _et al._ (2012) Xue H, Gu F, Hu X (2012).  “Data Assimilation Using Sequential Monte Carlo Methods in Wildfire Spread Simulation.”  _ACM Trans. Model. Comput. Simul._ , 22(4), 23:1–23:25.  ISSN 1049-3301.  10.1145/2379810.2379816.
  * Xue _et al._ (2001) Xue M, Droegemeier K, Wong V, Shapiro A, Brewster K, Carr FH, Weber D, Liu Y, Wang D (2001).  “The Advanced Regional Prediction System (ARPS) – A multi-scale nonhydrostatic atmospheric simulation and prediction tool. Part II: Model physics and applications.”  _Meteorology and Atmospheric Physics_ , 76, 143–165.

##  Chapter 7 WORKFLOW AND DETAILS ON THE FUNCTIONS

This section will add additional detail about the methods used and the
computer functions written for this research.

###  7.1 About the Code and Data

This appendix offers and overview of some of the Matlab functions used to run
the experiments performed during this research. Data is supplied and Matlab
scripts are provided.

####  7.1.1 Software Requirements and Dependencies

  * •

Operating system: The Matlab code make some system calls that need to be run
in a Linux environment.

  * •

The oldest version of Matlab used in this research was R2017a.

  * •

The following Matlab toolboxes are required: Curve Fitting, Mapping,
Statistics and Machine Learning, Image Processing Toolbox, and Control System
Toolbox.

Most of the the Matlab functions used for the task of data assimilation are
kept in a Github repository maintained at https://github.com/openwfm/wrf-fire-
matlab. The repository may be cloned and the functions needed exist in the
branch ’cycling.’ A list of the functions is available at
https://github.com/openwfm/wrf-fire-matlab/tree/master/cycling.

####  7.1.2 Data and Functions for Testing

Much of the data and the Matlab functions used in this research are available
for download. The download link contain one zip file that may be expanded into
a directory structure containing functions and scripts that perform various
tests or demonstrate some method developed in the thesis.

The data and functions have been added to the Auraria Institutional
Repository. The homepage for this repository is
https://digital.auraria.edu/air. The archive is hosted at:

http://digital.auraria.edu/IR00000295/00001

Search for ’James D. Haley’,’Assimilation of Satellite Active Fires Data’ for
possible additional uploads or in the case that the link provided fails.

The data is also mirrored at the following address:
https://figshare.com/articles/dataset/Assimilation_of_Satellite_Active_Fires_Data_-
_Data_and_Code/15044337

Within the compressed file are two directories.

  1. 1.

wrf-fire-matlab This directory contains the Matlab functions that can be found
in the ’cycling’ branch of the git repository referenced above. Running the
script startup.m within this directory will add the paths all sub-directories
to the Matlab environment.

  2. 2.

scripts This directory contains data and functions to perform some of the
tests that were part of this research. The artificial data sets used for a
large part of the testing have been included. These data sets in include
artificial fire arrival time and artificial fire detections. Another set
contains the fire arrival times taken, from WRF-SFIRE output, and the
artificial fire detections associated with them. The detection data and WRF-
SFIRE output from a simulation of the Patch Springs fire has been included.
This directory contains a set of many sub-directories containing individual
tests, detailed below. In some cases, Matlab code has been copied into these
sub-directories from the main code directory so that default values or
graphics options can be set. The testing functions should be run in their
respective sub-directories. The following subsections adds details about the
contents purpose of those those sub-directories.

##### artificial_data

The files in this directory run an example case creating an estimated fire
arrival time from artificial data that is also created here. The estimate is
then assessed and scores computed. This can be run slowly if the artificial
fire created is large and has many detection points.

##### data_assimilation

The files in this directory run an example case of the data assimilation
routine. This shows how adjustment of the forecast fire arrival time is made.
Matlab “versions" of satellite data and files from WRF-SFIRE containing only
necessary variables are included in this directory. This can be run quickly.

##### estimate_fire_arrival_time

This creates an estimate of the fire arrival time from satellite data. An
output file from WRF-SFIRE sets up the domain and a "Matlab Version" of
satellite data is included. Uses the single pass and the multigrid approach
for a comparison.

##### test_artificial

Testing artificial data files. The script in this directory steps through
testing the process for estimating the fire arrival time, using 260 artificial
fire arrival times. Plots of the MOE X, MOE Y, Sorenson, relative error are
produced. By default, the test loops through only the first 6 artificial fire
scenarios, but that can be changed to included all. This testing can take a
long time. Testing emulates that from Section 3.4.1, using a single pass
method.

##### test_p

Testing artificial data files. The script in this directory steps through
testing, using 260 artificial fire arrival times, the optimal value of $p$ to
use in interpolating additional points along the shortest paths. This can take
a long time. Only a few of the artificial data scenarios are tested by
default. The testing produces figures comparable to Figure 3.35 and Figure
H.12

##### test_wrf_output

Testing WRF-SFIRE output files used as “ground truth." The script in this
directory steps through testing the process for estimating the fire arrival
time, using 115 fire arrival times from WRF-SFIRE. Plots of the MOE X, MOE Y,
Sorenson, relative error are produced. By default, the test loops through only
the first 6 artificial fire scenarios, but that can be changed to included
all. This testing can take a long time. Emulates the testing in Section3.4.1.

###  7.2 Workflow

####  7.2.1 Data Assimilation with FMC Adjustment

The main function written for data assimilation with adjustment of the FMC is
new_cycles. The function is passed a string containing the relative path to an
output file from WRF-SFIRE and gives output by replacing the fire arrival time
and changing the FMC content in a rewrite file used by WRF-SFIRE during the
next forecast cycle. Figure G.1 shows the how the the function calls other
functions that are described in Section 7.2.2.

Figure G.1: Functions used for performing data assimilation with adjustment of
fuel moisture. The large box contains the function new_cycles and the boxes
inside are the functions called from within it. Figure G.2: Functions used for
clustering fire detection data and construction of the shortest paths. The
large box contains the function cluster_paths and the boxes inside are the
functions called from within it.

####  7.2.2 Functions used

  1. 1.

         choose_time_step(f)

Helps choose the frame of a wrfout file. The input ‘f’ is a string with path
to a wrfout file. Output is a character string with the time of the wrfout
frame.

  2. 2.

         cone_compare(ps,tign2)

Function compares the two fire arrival times. Used for adjusting the ROS in a
simulation. Input ’ps’ comes from ps = cluster_paths(w,1,250) and is a struct
with a forecast fire arrival time. Input ’tign2’ will be the analysis fire
arrival time obtained from tign2 = squish4(ps,gq,da). Typical use is
[r1,r2,adjr0,outer] = cone_compare(ps,tign2) where ’r1’ and ’r2’ are the
average ROS in the forecast and analysis, respectively. The variable ’adjr0’
is an experimental variable for use in adjusting the ROS in the model by the
namelist.fire input file. The variable ’outer’ is a struct with some
statistics about the forecast and the analysis fire arrival times.

  3. 3.

         cluster_paths(w,cull,grid_distance)

Main function for organizing detection data and creating path structure. Calls
many other functions in the process. Input ‘w’ is a Matlab struct from the
read_wrfout_tign function. The input ‘cull’ can be used to limit the number of
active fire detections used, cull = 1 uses all detections. The input
grid_distance sets the spacing on the grid used for the interpolation routine.
Output is a Matlab struct with fire detection data interpolated to a grid, a
directed graph with the detection data, and shortest paths from an assumed
ignition point to all other detection locations in the fire domain. Typical
use is ps = cluster_paths(w,1,250).

  4. 4.

         detection_probability(tign)

The function produces the curve describing the probability of a satellite
detecting a fire based on time difference between observation and fire arrival
time. Input ‘tign’ is a vector with times before and after fire arrival time.

  5. 5.

         estimate_tign(ps)

The function makes makes an estimated fire arrival time from satellite data by
drawing a succession of polygons around the active fire detections. Input ‘ps’
is from ps = cluster_paths(w,1,250). Output is a matrix storing the fire
arrival time. Typical usage is t = estimate_tign(ps).

  6. 6.

         filled\_contours(ps,tign_new)

Function plots contour maps of two fire arrival time. Input ’ps’ is a path
structure with forecast fire arrival time and input ’tign new’ is the analysis
fire arrival time in typical usage. no output.

  7. 7.

         fire_choice()

Selects from different fires simulated in the thesis. Sets up paths where
detection and perimeter data is stored. No input required. Output are strings
with with paths to fire data, fire name, and other particulars of the
simulation.

  8. 8.

        fire_gradients(lon,lat,tign,unit)

Function returns the partial derivatives of the firearrival time. Inputs
’lat,lon,tign’ can be taken as the latitude, longitiude, and fire arrival time
output by WRF-SFIRE, respectively. Input ’unit’ is an integer flag (unit =1
means yes) that returns partial derivatives as components of a unit vecotr.
Typical use is [dx,dy,nan_msk] = fire_gradients(lon,lat,tign,unit)

  9. 9.

         fixpoints2grid(red,pts)

Interpolates the active fire detection data onto the computational grid. Calls
function “fixpt" to find nearest grid location for a given latitude and
longitude location. Input ’red’ is from red = subset_domain(w). Input ‘pts’ is
an $n\times 2$ matrix with rows containing the latitude and longitude of fire
detections.

  10. 10.

        insert_analysis(w,ps,tn)

The function creates a new Matlab struct from input ‘w’ containing the
variable ’analysis’ which is the input ‘tn’ that comes from the data
assimilation function tn = squish4(ps,1,1). Input ‘ps’ is the path structure
from ps = cluster_paths(w,1,250).

  11. 11.

         interp_paths(ps,p_param)

Interpolates new points along the shortest paths. Input ‘ps’ is from ps =
cluster_paths(w,1,250). Input p_param is the smoothing parameter in the
interpolation routine. The default is p_param = 0.9

  12. 12.

          make_spline(time_bounds,num_pts)

The function produces splines used for making the data likelihood function and
its derivatives. Input time_bounds ,default value 72, is a scalar giving the
with of the time window to create the spline. Input num_pts gives the number
of points to use when making the spline.

  13. 13.

        make_tign(ps,alpha,p_param,grid_fraction)

The function makes an estimated fire arrival time using the iterative
interpolation technique from Chapter 3. Input ‘ps’ is from ps =
cluster_paths(w,1,250). Input ‘alpha’ controls blending between initial
estimate for the fire arrival time and the interpolated fire arrival time from
iterative interpolation. The default is alpha = 1, no weight is given to the
initial estimate. Input grid_fraction is used to interpolate data onto a
different sized grid.

  14. 14.

         new_cycles(f)

The function runs the cycling routine for data assimilation. Input ‘f’ is a
string with path to a wrfout file. Many functions are called. Output is
written into files needed to restart a simulation.

  15. 15.

         read_wrfout_tign(f,ts)

Reads in a wrfout file to collect variables about the grid, fire arrival time,
fuels, and other variables. The input ‘f’ is a string with path to a wrfout
file. The input ‘ts’ is optional and is a character string with the time of a
wrfout frame. Output is a Matlab struct file with variables describing the
domain of the fire. Typical use is w=read_wrfout_tign(f).

  16. 16.

         smooth_up(tign,a,b)

Function applies Gaussian smoothing to a fire arrival time, with more smoothin
applied for earlier times and decreasing linear with the fire arrival time.
Typical use is sm_up = smooth_up(tign,a,b). Input ’tign’ is a fire arrival
time. Input ’a’ controls how much smoothing is applied, it is the variance of
the Gaussian, default is 300. Input ’b’ is the proportion of the varaiance for
smoothing the the fire arrival time at the end of the simulation period and
the default is 1/3.

  17. 17.

          sort_rsac_files(prefix)

Reads a directory with satellite detection data and produces list of fire fire
and geolocation products organized by time of observation. Input ‘prefix’ is a
string with a path to satellite data products. Typical use is
p=sort_rsac_files(prefix).

  18. 18.

         squish4(ps,gq,da)

This functions performs the iterative interpolation. Output is the fire
arrival time. Input ’ps’ is from ps = cluster_paths(w,1,250). Input ’gq’ is an
integer flag (gq = 1 means yes) to determine if ground detections will be
used. Input ’da’ is an integer flag (da = 1 means yes) whether to use
likelihood to perform data assimilation. typical use is tign_new =
squish4(ps,gq,da).

  19. 19.

         subset_domain(w)

Can be used to select only the portion of the fire domain where the fire is
active. Converts the fire arrival time to datenum format. Input ‘w’ is from
w=read_wrfout_tign(f). Typical use is red = subset_domain(w).

  20. 20.

          subset_l2_detections(prefix,p,red,time_bounds,fig)

Compares the list of all detection data with start and end time of a
simulation and outputs a Matlab struct file with active fire detection data
for the granule within the fire domain. Input ‘prefix’ is a string with a path
to satellite data products. Input ‘p’ is from p=sort_rsac_files(prefix).Input
‘red’ is from red = subset_domain(w). Typical use is g =
subset_l2_detections(prefix,p,red,time_bounds,fig).

  21. 21.

         subset_small(red,n,m,full_set)

Interpolates the fire grid onto a different size mesh. Uses scattered
interpolant methods. Input ‘red’ comes from the subset_domain function. Inputs
‘m’ and ‘n’ are integers giving the size of the new grid to work on. Input
full_set is an integer indicating whether to interpolate all variables in the
struct ‘red’ if full_set = 1. Output is a Matlab struct like the input ‘red.’
Typical use is r = subset_small(red,n,m,full_set)

Figure G.3: Figures generated in the function cluster_paths. On the left is
figure 177, showing clustering of the active fire detection data. On the right
figure 178, showing the paths generated from the ignition to all other
detections in the domain.

Figure G.4: On the left is the figure showing the decrease in the relative
difference between successive iterations in the interpolation scheme
implemented in the squish4 function. On the right is the norm of the
difference of the time of active fire detections and and the estimated fire
arrival time at the detection locations. The figures are produced when running
the function squish4.

##  Chapter 8 ADDITIONAL FIGURES, TABLES, AND TESTING

Additional figures, tables, and testing to supplement the discussion and
summarize many of the tables of values found in the main text.

###  8.1 Figures and Tables

Figure H.1: Iterative interpolation. The sequence of panels shows the process
of iterative interpolation applied on a one-dimensional fire line when making
an estimated fire arrival time. At each detection location an estimate of the
fire arrival time is made by adjusting the fire arrival time in places where
detection data exists. A Gaussian smoothing is then applied to remove
discontinuities in the data and to avoid over-fitting of uncertain data. Each
row in the figure shows two iterations of the adjustment and smoothing steps.
The left plot of each pair shows the effect of adjusting the fire arrival time
at the location of a detection. The roughness introduced by the adjustment is
then reduced by the smoothing operation and the result is shown in the right
plot of the pair.

Figure H.2: Iterative interpolation. The sequence of panels shows the process
of iterative interpolation applied on a one-dimensional fire line when making
an estimated fire arrival time. Extra data points were added at the midpoint
between each of the original detections. Compare with the plots in Figure H.1.
The addition of more points helps the estimate resolve the gradient
information seen on the left side of the figures at approximately time
$t=5.5$.

Figure H.3: Iterative interpolation without adding additional points. The
sequence of panels shows the process of iterative interpolation applied on a
one-dimensional fire line when using detection data to adjust the fire arrival
time. Each row of of plots in the figure shows two iterations of the
adjustment and smoothing steps. The left plot of each pair shows the effect of
adjusting the fire arrival time at the location of a detection. The roughness
introduced by the adjustment is then reduced by the smoothing operation and
the result is shown in the right plot of the pair. Note that in the first
panel in the upper left that the data likelihood has allowed for large changes
downward in the fire arrival time but only small changes, if any, upwards.

Figure H.4: Iterative interpolation with adding additional points. The
sequence of panels shows the process of iterative interpolation applied on a
one-dimensional fire line when when using detection data to adjust the fire
arrival time. Extra data points were added at the midpoint between each of the
original detections. Compare with the plots in Figure H.3. The addition of
more points helps the estimate resolve the gradient information seen on the
left side of the figures at approximately time $t=5.5$.

Figure H.5: The sequence of plots illustrates the multigrid approach to estimating fire arrival time from satellite data. Each plot the figure shows an estimated fire arrival time and the satellite detection data interpolated onto a grid with 250 m spacing. In the upper left, the surface is an initial estimate of the fire arrival time made by drawing polygons around the detection active fire detections. The remaining figures show the estimates of the fire arrival time after being made on computational grids of decreasing grid spacing. The initial estimates are smooth and flat because interpolation of the satellite data onto a coarse grid causes the interpolation method to change the fire arrival time over as large geographic area around each detection. As the method decreases the working grid size, the fire arrival time in the area around the detections is moved closer to the time those detections were recorded.  Figure H.6: An example of a scenario for which the method cannot produce a satisfactory fire arrival time. In all testing scenarios, the estimated ROS for this configuration was the worst. In the case of real detections, the data would suggest there are in fact two fires in the domain. Scenrario | AGE | MRE | SRE | MOE X | MOE Y | ||MOE|| | Sorenson | Best | Worst
---|---|---|---|---|---|---|---|---|---
Multi - NP | 0.1024 | 0.0083 | 0.0059 | 0.9801 | 0.7960 | 1.2656 | 0.8741 | 198 | 88
Multi - 500 | 0.2341 | 0.0034 | 0.0019 | 0.5713 | 0.9764 | 1.1407 | 0.7065 | 145 | 155
Multi - 1000 | 0.1154 | 0.0043 | 0.0012 | 0.9610 | 0.8358 | 1.2755 | 0.8913 | 112 | 252
Multi - 2000 | 0.0045 | 0.0041 | 0.0019 | 0.9612 | 0.8421 | 1.2806 | 0.8938 | 70 | 220
Multi - 3000 | 0.1156 | 0.0044 | 0.0013 | 0.9601 | 0.8364 | 1.2755 | 0.8907 | 69 | 88
Multi - 4000 | 0.1971 | 0.0046 | 0.0013 | 0.9578 | 0.8362 | 1.2730 | 0.8907 | 54 | 88
Single - NP | 0.1407 | 0.0162 | 0.0105 | 0.9720 | 0.7642 | 1.2395 | 0.8511 | 190 | 159
Single - 1000 | 0.3598 | 0.0163 | 0.0105 | 0.9642 | 0.7750 | 1.2426 | 0.8552 | 204 | 159
Table H.1: Averages of the assessment scores made for the 280 estimated fire arrival times generated from artificial data taken to be “ground truth" for the purpose of comparison. The columns for best and worst indicate the specific artificial data scenarios for which each strategy produced the best or worst estimate. There is little agreement between strategies in terms of which scenarios produced the best or worst estimates. Scenario | MRD | SRD | MDD | SDD
---|---|---|---|---
Multi - NP | -0.0348 | 0.1785 | 0.00089 | 0.1551
Multi - 500 | -0.0236 | 0.1753 | 0.0015 | 0.1524
Multi - 1000 | 0.0340 | 0.1772 | 0.0025 | 0.1568
Multi - 2000 | -0.0187 | 0.1716 | -0.00024 | 0.1568
Multi - 3000 | 0.0373 | 0.1803 | 0.0021 | 0.1294
Multi - 4000 | 0.0374 | 0.1797 | 0.0026 | 0.1259
Single - NP | -0.0852 | 0.1579 | 0.0020 | 0.1750
Single - 1000 | -0.0840 | 0.1645 | 0.0035 | 0.1800
Table H.2: Results for the experiment computing the ROS and the direction of
the gradient using 280 artificial fire arrival times as the “ground truth"
fire arrival time. The multigrid approach using additional points with 2000
meter spacing had the best performance in matching the true ROS of the
simulated fire.

Figure H.7: Test results from estimating the fire arrival time using the
multigrid strategy with interpolation of extra points along the paths at a
spacing of 2000 meters. This strategy produced the best results among those
tested. The upper left shows how the average growth rate of the estimated fire
arrival time closely matched that of the “ground truth." The upper right shows
show the relative errors. The middle left and right panels show the MOE and
the Sørenson index scores, respectively. The lower right panels on the bottom
show histograms of the comparison of the difference in the average ROS and the
angle of the gradient for the simulations. Figure H.8: Scatter plot of the MOE
for 115 estimated fire arrival times generated from artificial detections
scattered on WRF-SFIRE simulation outputs. Most of the points have have a
first coordinate close to 1, indicating a tendency to overestimate the size of
the actual fire. Figure H.9: Histogram of the relative errors for 115
estimated fire arrival times generated from artificial detections scattered on
WRF-SFIRE simulation outputs. The mean of the errors was 0.56% and the
standard deviation was 0.15%.  Figure H.10: Histogram of the errors in
estimated ROS for 115 estimated fire arrival times generated from artificial
detections scattered on WRF-SFIRE simulation outputs.

Figure H.11: A gallery of some of the results from the test of estimating fire
arrival time using output from WRF-SFIRE simulations as “ground truth."
Assessment of plots in the top row show examples where the estimated fire
arrival time produced good scores, the middle row show examples with score
near the average, and the bottom row shows scores well below the average. The
method consistently underestimated the the actual fire area. The worst scores
were obtained for small fires with few satellite detections.

Figure H.12: Assessment of estimated fire arrival times of the Patch Springs
Fire using varied values of the interpolation parameter $p$. The figures
summarize the results in Table H.3. On the top row, rom left to right are the
plots of MOE X and MOE Y. On the bottom are the plots of ||MOE||, and the
Sørenson index. Scores generally increase with the value of $p$, but the drop
in MOE Y when $p=1.0$ suggests that using $p=0.9$ is optimal.

Figure H.13: Assessment of estimated fire arrival times of the Cougar Creek Fire using varied values of the interpolation parameter $p$. The figures summarize the results in Table H.3. On the top row, rom left to right are the plots of MOE X and MOE Y. On the bottom are the plots of ||MOE||, and the Sørenson index. Scores generally increase with the value of $p$, but the drop in MOE Y when $p=1.0$ suggests that using $p=0.9$ is optimal. p | MOE X | MOE Y | ||MOE|| | Sorenson
---|---|---|---|---
No Interpolation | 0.9095 | 0.8503 | 1.2451 | 0.8789
0.0 | 0.8095 | 0.8757 | 1.1926 | 0.8413
0.1 | 0.8244 | 0.8867 | 1.2107 | 0.8544
0.2 | 0.8339 | 0.8773 | 1.2104 | 0.8551
0.3 | 0.8446 | 0.8869 | 1.2247 | 0.8652
0.4 | 0.8554 | 0.8821 | 1.2287 | 0.8685
0.5 | 0.8774 | 0.8832 | 1.2449 | 0.8803
0.6 | 0.8905 | 0.8826 | 1.2538 | 0.8865
0.7 | 0.8911 | 0.8785 | 1.2513 | 0.8848
0.8 | 0.9048 | 0.8812 | 1.2629 | 0.8928
0.9 | 0.9226 | 0.8752 | 1.2717 | 0.8983
1.0 | 0.9250 | 0.8520 | 1.2576 | 0.8870
Table H.3: Results of varying parameter $p$ for estimates of the fire arrival time of the Patch Springs Fire. The first row shows the scores when no additional points are interpolated along the paths. The original path structure contained 305 active fire detections. Interpolation with a spacing of 2000 meters added an additional 62 points to the path structures. The scores were made by comparison to an infrared perimeter observation from August 16, 09:47 UTC. The results are summarized in Figure H.12. p | MOE X | MOE Y | ||MOE|| | Sorenson
---|---|---|---|---
No Interpolation | 0.8820 | 0.7893 | 1.1836 | 0.8331
0.0 | 0.7659 | 0.9516 | 1.2215 | 0.8487
0.1 | 0.7947 | 0.9497 | 1.2384 | 0.8653
0.2 | 0.7997 | 0.9375 | 1.2322 | 0.8631
0.3 | 0.8079 | 0.9415 | 1.2406 | 0.8696
0.4 | 0.8085 | 0.9293 | 1.2318 | 0.8647
0.5 | 0.8236 | 0.9378 | 1.2481 | 0.8770
0.6 | 0.8198 | 0.9416 | 1.2485 | 0.8765
0.7 | 0.8299 | 0.9303 | 1.2467 | 0.8772
0.8 | 0.8318 | 0.9311 | 1.2485 | 0.8786
0.9 | 0.8512 | 0.9326 | 1.2627 | 0.8901
1.0 | 0.9014 | 0.8964 | 1.2713 | 0.8989
Table H.4: Results of varying parameter $p$ for estimates of the fire arrival
time of the Cougar Creek Fire. The first row shows the scores when no
additional points are interpolated along the paths. The original path
structure contained 432 active fire detections. Interpolation with a spacing
of 2000 meters added an additional 24 points to the path structures. The
scores were made by comparison to an infrared perimeter observation from
August 15, 10:33 UTC.

Figure H.14: A sampling of some of the estimated fire arrival times generated
in the experiment estimating the fire arrival time using artificial data. on
each row, the plots show comparisons between the “ground truth" and estimated
fire arrival times. All plots of the estimates were derived using the
multigrid method with interpolation of additional points on the paths with
2000 meter spacing. The example on the bottom, simulation 227, had the worst
ROS error for all estimates made using the multigrid approach, regardless of
spacing of interpolated points on the paths.

Figure H.15: Path structures using varying values of the interpolation
parameter $p$ and assessment of the fire arrival times constructed from them.
Each row shows the path structure and the assessment for a particular value of
$p$. The top row has $p=0.1$ of extra points and the bottom row has $p=0.9$.

Figure H.16: Path structures using varying values of the interpolation
parameter $p$ and assessment of the fire arrival times constructed from them.
Each row shows the path structure and the assessment for a particular value of
$p$. The top row has $p=0.1$ of extra points and the bottom row has $p=0.9$.

Figure H.17: Assessing the estimated fire arrival time of the Cougar Creek
Fire using a one-pass method (left) and multigrid method (right) by comparison
with an infrared perimeter observation. The estimates are derived for the
available satellite data up to the perimeter time of August 15, 10:33:00 UTC.
Both methods tend to underestimate the size of the fire. The routine for
plotting the area within the infrared perimeter has failed, giving a larger
black region within the fire that results in lower scores than should be
assigned to these estimations of the fire arrival time.

Figure H.18: Assessing the estimated fire arrival time of the Cougar Creek Fire using a one-pass method (left) and multigrid method (right) by comparison with an infrared perimeter observation. The estimates are derived for the available satellite data up to the perimeter time of September 4, 02:38:00 UTC. Both methods tend to underestimate the size of the fire. This is the final perimeter observation available. Both methods have similar results, but the multigrid method gives less false negatives and more false positives. # | Perimeter Time | MOE_X | MOE_Y | |MOE| | S
---|---|---|---|---|---
1 | 12-Aug 07:00:00 | 0.4855 | 0.8138 | 0.9476 | 0.6082
2 | 14-Aug 05:56:00 | 0.7794 | 0.9759 | 1.2490 | 0.8667
3 | 14-Aug 07:00:00 | 0.8493 | 0.9151 | 1.2485 | 0.8810
4 | 15-Aug 07:00:00 | 0.7903 | 0.9588 | 1.2425 | 0.8664
5 | 15-Aug 10:33:00 | 0.7694 | 0.6912 | 1.0343 | 0.7282
6 | 16-Aug 03:42:00 | 0.8601 | 0.8985 | 1.2438 | 0.8789
7 | 16-Aug 07:00:00 | 0.8287 | 0.9239 | 1.2411 | 0.8737
8 | 16-Aug 19:00:00 | 0.8668 | 0.9209 | 1.2647 | 0.8930
9 | 17-Aug 04:13:00 | 0.8369 | 0.7308 | 1.1111 | 0.7803
10 | 18-Aug 17:00:00 | 0.8305 | 0.9168 | 1.2370 | 0.8715
11 | 19-Aug 09:55:00 | 0.9545 | 0.8844 | 1.3012 | 0.9181
12 | 20-Aug 04:48:00 | 0.9564 | 0.8817 | 1.3008 | 0.9175
13 | 20-Aug 17:00:00 | 0.9447 | 0.8794 | 1.2907 | 0.9109
14 | 22-Aug 02:00:00 | 0.9118 | 0.8678 | 1.2588 | 0.8893
15 | 22-Aug 18:30:00 | 0.8376 | 0.9473 | 1.2645 | 0.8891
16 | 23-Aug 08:16:00 | 0.9226 | 0.8718 | 1.2693 | 0.8965
17 | 24-Aug 04:42:00 | 0.7913 | 0.9192 | 1.2128 | 0.8504
18 | 25-Aug 07:47:00 | 0.7913 | 0.9522 | 1.2381 | 0.8643
19 | 26-Aug 03:58:00 | 0.7693 | 0.9488 | 1.2215 | 0.8497
20 | 27-Aug 04:00:00 | 0.7846 | 0.9520 | 1.2336 | 0.8602
21 | 28-Aug 09:25:00 | 0.8704 | 0.9379 | 1.2796 | 0.9029
22 | 28-Aug 10:00:00 | 0.8207 | 0.9369 | 1.2455 | 0.8749
23 | 29-Aug 19:00:00 | 0.8309 | 0.9305 | 1.2475 | 0.8779
24 | 31-Aug 10:25:00 | 0.7844 | 0.9506 | 1.2325 | 0.8595
25 | 02-Sep 08:00:00 | 0.8151 | 0.9493 | 1.2512 | 0.8771
26 | 03-Sep 09:53:00 | 0.8250 | 0.9487 | 1.2573 | 0.8825
27 | 04-Sep 02:38:00 | 0.8140 | 0.9340 | 1.2389 | 0.8699
Table H.5: Assessment of estimated fire arrival time for the Cougar Creek Fire. Estimates were made without using the multigrid strategy. Each estimate was made using all the available satellite data up to the the time of the infrared perimeter observation that is used to make the comparison. As can be seen by examining the area columns in the table, the fire experienced little to no growth after August 28. Figure 3.38 shows how the area of the fire changed with time. # | Perimeter Time | MOE_X | MOE_Y | |MOE| | S
---|---|---|---|---|---
1 | 12-Aug 07:00:00 | 0.5821 | 0.7902 | 0.9814 | 0.6704
2 | 14-Aug 05:56:00 | 0.9045 | 0.9126 | 1.2849 | 0.9086
3 | 14-Aug 07:00:00 | 0.8725 | 0.8841 | 1.2421 | 0.8783
4 | 15-Aug 07:00:00 | 0.8909 | 0.9193 | 1.2802 | 0.9049
5 | 15-Aug 10:33:00 | 0.8337 | 0.6671 | 1.0677 | 0.7411
6 | 16-Aug 03:42:00 | 0.9215 | 0.8629 | 1.2625 | 0.8913
7 | 16-Aug 07:00:00 | 0.9196 | 0.8635 | 1.2615 | 0.8907
8 | 16-Aug 19:00:00 | 0.8954 | 0.8619 | 1.2428 | 0.8783
9 | 17-Aug 04:13:00 | 0.9434 | 0.6603 | 1.1515 | 0.7769
10 | 18-Aug 17:00:00 | 0.9198 | 0.8142 | 1.2284 | 0.8638
11 | 19-Aug 09:55:00 | 0.9741 | 0.7835 | 1.2501 | 0.8685
12 | 20-Aug 04:48:00 | 0.9606 | 0.7906 | 1.2441 | 0.8674
13 | 20-Aug 17:00:00 | 0.9462 | 0.8038 | 1.2416 | 0.8692
14 | 22-Aug 02:00:00 | 0.9709 | 0.7951 | 1.2549 | 0.8743
15 | 22-Aug 18:30:00 | 0.9136 | 0.8141 | 1.2237 | 0.8610
16 | 23-Aug 08:16:00 | 0.9662 | 0.8287 | 1.2729 | 0.8922
17 | 24-Aug 04:42:00 | 0.8694 | 0.8557 | 1.2198 | 0.8625
18 | 25-Aug 07:47:00 | 0.8602 | 0.8828 | 1.2326 | 0.8714
19 | 26-Aug 03:58:00 | 0.8214 | 0.9198 | 1.2332 | 0.8678
20 | 27-Aug 04:00:00 | 0.8492 | 0.9098 | 1.2445 | 0.8785
21 | 28-Aug 09:25:00 | 0.8808 | 0.9137 | 1.2691 | 0.8969
22 | 28-Aug 10:00:00 | 0.8989 | 0.8756 | 1.2549 | 0.8871
23 | 29-Aug 19:00:00 | 0.8844 | 0.8824 | 1.2493 | 0.8834
24 | 31-Aug 10:25:00 | 0.8837 | 0.9128 | 1.2705 | 0.8980
25 | 02-Sep 08:00:00 | 0.8735 | 0.8717 | 1.2340 | 0.8726
26 | 03-Sep 09:53:00 | 0.8830 | 0.8866 | 1.2513 | 0.8848
27 | 04-Sep 02:38:00 | 0.9049 | 0.8724 | 1.2569 | 0.8883
Table H.6: Assessment of estimated fire arrival time for the Cougar Creek
Fire. Estimates were made without using the multigrid strategy. Each estimate
was made using all the available satellite data up to the the time of the
infrared perimeter observation that is used to make the comparison. As can be
seen by examining the area columns in the table, the fire experienced little
to no growth after August 28. Figure 3.38 shows how the area of the fire
changed with time. Figure H.19: Histogram of the ROS computed along the paths
in the directed graph of the Camp Fire. The mean rate of spread was 0.2524
m/s. This is a high number when compared with other fires studied in this
research.

Figure H.20: The uncertainty in the position and fire arrival time of active
fire detections produces uncertainty in the computed ROS between consecutive
detections in a path. The panel on the left shows 200 perturbations of the
time and locations of two fire detections connected in a path. The
perturbation of the spatial locations was made following a Gaussian
distribution to reflect the geolocation error. The perturbation of the points
in time was made using a uniform distribution. In the upper right is a
histogram of the ROS between two consecutive and randomly perturbed points
along a path used for an actual estimate of the fire arrival time of the Patch
Springs Fire. The QQ plot in the panel on the bottom shows the ROS is not
normally distributed. Figure H.21: The difference between the average ROS
along paths in the graphs and in the fire arrival time cone estimates for the
artificial “ground truth" experiment, using the multigrid approach and a
spacing between additional points interpolated along paths at a distance of
2000 meters. 280 estimated fire arrival times were compared with the “ground
truth." The ROS along paths was on average 0.0053 m/s faster than in the
estimate with a standard deviation of 0.4118 m/s. This figure gives a sense of
how well the ROS compares on average in each simulation, but has no
information about how the difference in the ROS can vary with location in
individual scenarios.

Figure H.22: Comparison of infrared perimeters and the perimeters of an
estimated fire arrival time for the Camp Fire. The progression of the fire
during the first several days was estimated from satellite data. The top row
shows the first two perimeter comparisons and the bottom row shows the third
and fourth. Note that all the estimated perimeters underestimate the size of
the fire.

Figure H.23: Assessment of the cycles of the Patch Fire simulation. The
graphics give a graphical representation of how the fire area of simulation
cycles match a perimeter observation made on August 16 at 09:47 UTC. The
panels from to to bottom and left to right cycles 0 through 4, with the lower
right figure being the perimeter comparison for a simulation initialized using
an estimated fire arrival time. The cycling method does produce better
estimates as data is assimilated, but the large black and red areas in the
figures indicate that model is not accurately predicting where the fire will
be burning.  Figure H.24: Schematic for several data assimilation cycles run
consecutively to simulate the Cougar Creek fire of 2015. Each simulation was
run until 09:00 UTC on August 15 for the sake of comparison. In typical
operational usage, simulations would not extend more than two days beyond the
end of the spin-up period of the previous cycle. Figure H.25: Schematic for
several data assimilation cycles run consecutively in order to simulate the
Camp fire of 2018.

Figure H.26: Assessment of the cycles of the Cougar Creek Fire simulation. The
panel in the lower right shows the result from a simulation initialized from
an estimate of the fire arrival time derived from satellite fire data.

Figure H.27: Assessment of the cycles of the Camp Fire simulation by
comparison with an infrared perimeter observation made on November 10, 07:00
UTC. The panel in the lower right shows the result from a simulation
initialized from an estimate of the fire arrival time derived from satellite
fire data. Except for the initial cycle, the model tended to overestimate the
fire size by expanding to the northwest and southeast more that was observed.
These graphics summarize tha data recorded in Table 4.3.

Figure H.28: Assessment of the Patch Springs Fire simulation using the 48-hour
forecast strategy. On the upper left and right are comparisons between the
infrared perimeter observation and the first and second forecasts,
respectively. On the bottom, the final perimeters of the first and second
forecasts are displayed together. As can be seen, the data assimilation of a
small number of satellite granules was able to slow the growth of the modeled
fire and make for a better forecast.

Figure H.29: Assessment of the Cougar Creek Fire simulation using the 48-hour
forecast strategy. At the left and center are comparisons between the infrared
perimeter observation and the first and second forecasts, respectively. On the
right, the final perimeters of the first and second forecasts are displayed
together. As can be seen, the data assimilation of a small number of satellite
granules was able to slow the growth of the modeled fire and make for a better
forecast.

Figure H.30: Cycle 1 of the Patch Fire simulation with adjustment of FMC. In
the upper left and right are contours of of the fire arrival time for the
forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain.In
this case the forecast area and the forecast ROS were higher than the estimate
from the data, indicating an increase of the FMC by 0.1967%

Figure H.31: Cycle 2 of the Patch Fire simulation with adjustment of FMC. In
the upper left and right are contours of of the fire arrival time for the
forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain.

Figure H.32: Cycle 3 of the Patch Fire simulation with adjustment of FMC. In
the upper left and right are contours of of the fire arrival time for the
forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain. No
changes to the FMC were made for the next simulation cycle.

Figure H.33: Cycle 4 of the Patch Fire simulation with adjustment of FMC. In
the upper left and right are contours of of the fire arrival time for the
forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain.

Figure H.34: Assesment of the cycles of the Patch Fire simulation using
adjustment of FMC. The panels show, from top to bottom and left to right, the
assessments of cycles 0 to 4. The simulations overestimated the size of the
fire, as was the case when no adjustments to the FMC had been made. The figure
on the lower right shows the assessment of the simulation initialized from
satellite data, the other figures show the cycles of a simulation started from
an ignition point.

Figure H.35: Cycle 2 of the Cougar Creek Fire simulation with adjustment of
FMC. In the upper left and right are contours of of the fire arrival time for
the forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain. The
forecast underestimated the size of the fire and overestimated the ROS so that
the FMC was not adjusted.

Figure H.36: Cycle 3 of the Cougar Creek Fire simulation with adjustment of
FMC. In the upper left and right are contours of of the fire arrival time for
the forecast and the analysis, respectively. On the bottom is the histogram
showing the difference between the ROS at mesh points in the fire domain. The
forecast underestimated the size of the fire and overestimated the ROS so that
the FMC was not adjusted.

Figure H.37: Assessment of the cycles of the Cougar Creek Fire simulation that
used adjustments of the FMC. TThe panels show, from top to bottom and left to
right, the assessments of cycles 0 to 4. The panel in the lower right shows
the result from a simulation initialized from an estimate of the fire arrival
time derived from satellite fire data. Compare with Figure H.26. The
adjustment of the FMC has resulted in a better simulation in cycle 4.

Figure H.38: Assessment of the cycles of the Patch Fire simulation using
various forecasting strategies. The graphics give a graphical representation
of how the fire area of simulation cycles match a perimeter observation made
on August 16 at 09:47 UTC.

Figure H.39: Assessment of the cycles of the Patch Fire simulation. Figure
H.40: Distribution of the difference of detection times. The distribution has
the familiar shape of a triangle resulting from the sum of two uniformly
distributed random variables. The peak is $t_{2}-t_{1}$, the difference of the
reported times of fire detections. The paramater $l$ gives the length of the
support of the uniform random variables. Figure H.41: Distributions of the
reciprocals of difference of detection times. As the time between detections
increases, the distribution becomes narrower. Wider distributions result from
closer detection times. In these cases, it was assumed that an individual
detection time was a uniform random variable over the period spanning the six
hours previous to the satellite overpass and detection. Figure H.42: Gradients
in the estimated fire arrival time with shortest paths from directed graph of
detection data. This is a detail of a small section in the fire domain to
illustrate how the paths align with the gradient of the fire arrival time
estimate.

Figure H.43: The difference in ROS between the “ground truth" and the estimate
made from data. On the upper left, the histogram shows computed differences
for all ROS in the fire domain. On the right, only the ROS differences less
than 2 m/s in magnitude have been retained. On the bottom, a QQ plot confirms
that the the differences in the ROS are not normally distributed.

###  8.2 Additional Testing

####  8.2.1 Experiment: Effect of Using Perimeter Data on the Estimate of the
Fire Arrival Time

When infrared perimeter observations are available, they may be used in the
same way as satellite fire detections to help derive an estimate of the fire
arrival time. In this test, a comparison was made between estimates of the
fire arrival time made from “ground truth" artificial fire times whose
surfaces had been scattered with artificial active fire detections. Two sets
of estimates were made. One set was made using only artificial detections and
the other was made using artificial perimeter observations as well. The
following experiment uses a limited number of cases to get a first impression
of whether using perimeter data could have a large effect on how well the
method for estimating the fire arrival time works. In general, the use of
perimeter data did result in better estimates, but the difference was not
large. If there had been a large difference, then further testing would have
been used to determine under what conditions and what strategies could be best
used to arrive at the best possible estimate of the fire arrival time.

Four artificial fire arrival times were made. Each represented a fire burning
for 6 days. An artificial perimeter of 100 points was made at the time
corresponding to midnight on each day of the simulation. Estimates of the fire
arrival time were made either using or not using the artificial perimeters.
The estimates were then assessed using the methods described in Section 3.3.
The results, in Table H.7 show, that use of perimeter observations produces
better estimates of the fire arrival time.

Figure H.44: Using perimeter data as an additional source of fire detections
in the method. The top row shows the path structure made from a “ground truth"
fire arrival time and artificial detections and a plot of how the fire arrival
time compared to the ground truth. The bottom row shows the path structure
made from the detection data used in the paths in the top row as well as more
data points created from artificial perimeter data. Several “rings of
detections" can be seen in the lower path structure. The plots on the right
side of the figure show that the use of perimeter data makes for a bestter
estimate of the fire arrival time. No Perimeters Used
---
Cone | MOE X | MORE Y | |MOE| | Sørenson | Relative Error
1 | 0.5255 | 0.9990 | 1.1288 | 0.6888 | 0.0085
2 | 0.5449 | 1.0000 | 1.1388 | 0.7054 | 0.0095
3 | 0.6766 | 0.9974 | 1.2052 | 0.8062 | 0.0064
4 | 0.7573 | 0.9939 | 1.2495 | 0.8596 | 0.0098
Average | 0.6261 | 0.9976 | 1.1806 | 0.7650 | 0.0085
Perimeters Used – 100 points in each
Cone | MOE X | MORE Y | |MOE| | Sorenson | Relative Error
1 | 0.6197 | 0.9986 | 1.1752 | 0.7648 | 0.0085
2 | 0.5317 | 1.0000 | 1.1326 | 0.6942 | 0.0083
3 | 0.7894 | 0.9595 | 1.2425 | 0.8662 | 0.0063
4 | 0.8626 | 0.9622 | 1.2923 | 0.9097 | 0.0064
Average | 0.7009 | 0.9801 | 1.2106 | 0.8087 | 0.0074
Table H.7: Comparison of estimates of fire arrival times made with or without
using perimeter information in the path structure. Using perimeter information
gives better spatial representations and has smaller relative errors when the
estimated fire arrival times are compared to the “ground truth" fire arrival
times.