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Published on February 28, 2014

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Urban fringe and transportation corridor convection-diffusion model for anthropogenically-initiated wildfire ignition prediction Ravi R Sadasivuni Department of Geosciences Mississippi State University Dr. Bill Cooke

Overview  Introduction  Background  Objective and Approach  Observational Data Analysis  Study Area & Wildfire Data  Correlation with urban fringe and transportation Corridors  Seasonal Analysis  Spatial Interaction Model  Road Density and Gravity models  Convective Diffusion Model (CDM) For Wildfire Ignition  Formulation and coefficient calibration  Validation of Convection-Diffusion Model  Conclusions

Background: Wildfires  Ignitions arising from humans.  Fires consume 2 to 10 million acres of forests every year (Johnson, and Govatski, 2013) .  Recent wildfire damage assessments  Yosemite National park in Sept 2013  Cause: to escape from illegal marijuana case  Colorado Fire in 2012 - displaced 30000 people with an economic loss of $3.2m damage.  Cause: industries nearby  Environmental agencies are concerned with the prevention of wildfires Colorado Fire, 2012 Source: (http://visibleearth.nasa.gov/view_rec.php?id=6884)

Background: Wildfires     Urban fringes Build up of fuels Careless smokers Camping and other recreational activities  Seasonal Frequency  High - late winter/early spring  Low – Summer  Both fire size and frequency show bi-modal nature  Fire as a management tool (Pyne, 2001) 2 2  Man used fire :  as a Suppressor of lightning fire,  as a Stoker of industrial fire, • Unfortunately he is a promoter of anthropogenic fire  How fire starts/spreads: 1 3 1. Human interaction on the ground causes 2. Fire movement from canopy to canopy 3. Causes from ground to canopy

Objective and Approach Objective: Develop and validate a robust spatial interaction model to predict anthropogenically-initiated accidental and incendiary wildfire probability Approach:  Wildfire prediction model is developed from fluid dynamics analogy of movement of people  Wildfire observation data analysis and model calibration  Validation against observational data for Southeast Mississippi Region, including comparison with Gravity model

Approach: Modeling Philosophy  Anthropogenically initiated wildfire is directly related to the movement of people  Movement of people are:  general guided by the cities  aligned with the transportation corridors  anisotropically aligned along high traffic volume  roads provide access points to the woods for people with incendiary motive  Influencing factors grouped as global and local variables.  Global variables are modeled using Gravity term  Local variables are parameters of transportation corridors modeled as convective/diffusive fluxes

Observational data ±        Study area - Southeastern Mississippi in Mississippi Primary roads - white lines (from MARIS) Railroads - black lines (from MARIS) Cities and its population (from MARIS) Wildfire incidences for years 1992-2009 (black symbols) (United States Forest Service ) Traffic volume in yellow symbols (gomdot.com) Black horizontal and vertical lines show the quadrats for the rail-road interaction analysis

Observation Data Analysis: Wildfire Cause and Frequency Analysis 3000 Arson Campfire Children Smoking RailRd Wildfire Frequency # of Wildfires 2500 2000 1500 1000 500 0 Years • 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Arson caused wildfire (64%) dominates than other fires, and they were very Years of Wildfire caused by Arson high in 1992-1996 and 2000 – 2007, whereas fires due to campfire (0.2%), Children (0.5%), Smoking (0.69%) and railroad (0.5%) are small. • Unintentional (fires caused due to negligence) fires are around 2% of total. • Wildfires due to natural causes is < 1%.

Observation Data Analysis: Wildfire Area by Arson • Fire size distribution shows a log-normal distribution with a mean fire size is 18.2 acre • Wildfires caused due to arson are clustered around the populated areas • Arson fires with 10-50 acres size are dominant ±

Observation Data Analysis: Cyclic Nature of Wildfires and its Size and Frequency  Cyclical nature of fires was not the same all years.  Sometimes summer fires are more numerous, but that is rare.  Dec. 2005 is an very obvious case where summer and fall fires increased due to Katrina

Observation Data Analysis: Annual Trends (Ppt and Freq) Herein, we have categorized the entire year into summer and winter of 6 months duration, i.e., • • Summer: April through September and Winter: October through March.  Fire frequency is highest when precipitation is greatest in late winter (Grala and Cooke, 2010) .  A second period of high fire frequency occurs in early winter.

Observation Data Analysis: Normalized Wildfire Risk Distribution • • More clustered in the urban fringes of southern Mississippi • ± ± Area weighted historic wildfire risk Winter fires - around cities and along the road  Shows sharp distinction in high and low risk regions • Low Risk Annual High Risk Winter Summer Summer fires are more evenly distributed • These are used to test with the seasonal risk predictions made by the models

Observational Data Analysis : Fires vs Roads • Wildfire decreases with the increase of the distance from the roads • Historic wildfire events across the road buffers helped evaluate the ignition potential and calibration of ν (nu) which is 1/1250 through the curve fit of the observational data

Observational Data Analysis : Fires vs Intermodal Transportation  Roads and Rails run in parallel, so rail buffers alone cannot be analyzed.  Wildfire events per unit length of the rail roads were computed in the study region for the years 1992-2009.  Quadrats with Inter-modal transportation corridors show 30% higher wildfire frequency

Observational data Analysis: Fires With Cities   Analysis is performed using the cities Hattiesburg, Laurel and Ellisville.  Wildfire events increase along the city radius  (Units: km / Sq. Km) Road density at the fire locations along with distance from the city center. Peak frequency at the medium density road, consistent with Gilreath 2006.

Previous Prediction Models  United States Forest Service models use correlations between the historical observational and geographical data, climatic and vegetation components to obtain fire risk potential indices  There are few models which account both fuel loads and ignition sources to predict wildfire potential  Road Density and road buffers tells about the activity along corridors but not the activities (from traffic vol) and its origin from the cities (Cooke and Grala, 2010; Gilreath, 2006)  Gravity based model gives a GLOBAL measure of propulsiveness and a measure of destination attractiveness as the flow of activity between different zones, but does not consider the transportation corridors (Sadasivuni et al., 2013).  Most wildfire ignition distribution models fail to define the diffusion direction, while diffusion seldom occurs across the Euclidean distance, but along the transportation corridors (Ayeni 1979)

Gravity Model  Spatial interaction - The flow of activity between different zones and the summation of various flows or interactions gives rise to the location of activities  A Large city is more likely to attract an individual than a smaller city  Newton‟s formula is modified with physical mass for population size PiPj and a friction (cost) is inverse power function of distance f(cij)=dij-λ Pij = PiPj / dij-λ where λ is a parameter of the function dij is the distance between i and j (Sadasivuni et al. 2013, “Ecological Modeling”)

Comparison of Gravity and Road Density Models in Wildfire Risk Assessment ± • The models are tested with the normalized obs. Data • Gravity model shows good interaction among cities, somewhat aligned along the roads • Performs poorly than Road density model in Medium risk zones (urban fringes), and low risk zones • Road Density Road density model shows poor correlation with R2 = 0.23 • Gravity model shows modest agreement R2 = 0.75 0.8 Normalized Historic Fire Risk Area Weighted Historic Wildfire Risk y = 0.4758x + 0.2515 R² = 0.2321 0.6 0.4 0.2 Fire potential Linear Regression 0 0 0.2 0.4 0.6 0.8 Road Density Model Fire Potential y = 0.8917x + 0.0637 R² = 0.7316 Normalized Historic Fire Risk 0.8 0.6 0.4 0.2 Fire Potential Linear (Fire Potential) 0 0 0.2 0.4 0.6 Gravity-Model Fire Potential Gravity model based Wildfire Risk 0.8

Wildfire Ignition: CDM Approach  Anthopogenic factors influencing wildfire ignition are grouped as “global” and “local variables”  Global variable (Population) modeled from Gravity model  “Local variables” as convection and diffusion a. Diffusion from Inter-model transportation corridors b. Convection from Traffic Volume  Calibration & Validation a. Calibrating model coefficients using observational data b. Preliminary validation for Hattiesburg area

Wildfire Ignition Flow Chart: CDM Modeling Details Wildfire Risk Anthropogenic Factors Fuel P-E Climate Ignition Local Global Population Intermodal Transportation Vegetation Gravity (P/d2) Seasons Damping ( ) Roads Rails Additive Multiplicative Diffusion (√ ) Diffusion (√ ) Traffic Vol Convection V Vt Lro

Wildfire Ignition: CDM Formulation Occurrence of fire ( ) depends on fuel ( f) and ignition potentials ( ( x, y , t ) f ( x, y , t ) i ( x, i ) y) varies in space (vegetative characteristics) and time (variation of the seasons) f i assumed to be function of space only and depends on,     proximity (D) to city or population area (P); proximity (dro/ra) to railroads (ra) and roads (ro); traffic volume (Vt)  Is a function of time, but not considered herein; length or density of the corridors (Lro/ra)

Wildfire Ignition: CDM Formulation 2 1 LB i B Vt Lro V     Convection along Roads d ro / ra 2 d    P D2   Diffusion along Corridors Gravity from Cities where, V is the convection velocity, is the diffusivity coefficients and is a gravity model damping term inside the city. (Sadasivuni et al., submitted to Ecological Modelling)  Model couples the multi-criteria behavioral pattern in a single dynamic equation  Unknown coefficients to be calibrated using observational data

CDM coefficient Calibration: Fires vs Road Density  Analysis is performed using 3 large cities in the central region i.e. Hattiesburg, Laurel and Ellisville.  Fire frequency plotted vs distance from city to obtain damping of potential inside the city Gravity Model

CDM coefficient Calibration: Fires vs Roads • Wildfire decreases with the increase of the distance from the roads • Historic wildfire events across the road buffers helped evaluate the ignition potential and calibration of ν (nu) which is 1/1250 through the curve fit of the observational data

CDM coefficient Calibration Fires vs Traffic Volume per Road Density • The convection plays an important role in generating an anisotropic behavior of the city gravity potential in angular direction ( c). • This is along the high traffic volume

Analytic Model and Calibration City Potential P D2   City Interaction is modeled following Gravity Model Damping function is derived from an exponential curve fit over the data

Analytic Model and Calibration: Transportation Corridors  The diffusive coefficient ν (nu), which is 1/1250 computed through the curve fit of the observational data is applied to transportation corridors.  Ignition potentials due to the road and cities are somewhat independent of each other, thus can be treated separately.

Analytic Model and Calibration: Traffic Volume Traffic volume generates an anisotropic behavior of the city potential along the angular direction ( c), 1 LB c B V Vt Lro Convection P D2 1 VTr ( c ) Gravity VTr ( c ) e ( c) 2 P D2 / 45 VTr ~ 1- 15 is traffic volume per road density Gaussian distribution along the traffic volume direction c

Analytic Model and Calibration: Total Potential   Ignition potentials due to the road and cities are somewhat independent of each other, thus can be treated separately, therefore: Spatial distribution of the combined Road and City ignition potential for two different city and road connection patterns.

Depiction in Fortran Code (a) (b)  The combined wildfire ignition potential is tested using an in-house Fortran code  Test Study region around Hattiesburg area, 80 km x 50 km  Depiction of the study region for the Fortran simulations.  The cities are represented as filled circular regions.  Roads (Black) and Rails (Brown) with straight line segments.  Domain discretized using 1001x1001 points, i.e., 85m x51m resolution.

Intermodal Transportation Corridors and City Interaction  High fire ignition potential distribution showing anisotropy conditions of traffic volume  High fire ignition potential distribution coincident with more fires in broken ellipses  The high spikes signify the high activity areas

Quantile analysis of Fire Distribution Across Risk Zones  Observed fires (or fire frequency) distributed in the quantile bins  From the figure roads have high number of fires in the high risk zone and almost equal number in Medium and very high risk zones  The city potential shows a decrease in wildfire frequency from medium to high risk zones, whereas the road potential shows almost uniform frequency in medium to very high risk zones. Combined model i.e. „total‟ (Black dotted) performs better for wildfire frequency predictions than the city and road models alone

Using Convection-Diffusion Model (CDM) Prediction of Wildfire Risk ± ± • The model is applied to southeastern Fire district Mississippi. • The gravity is distributed everywhere whereas the CDM model is portraying more localized risks. Quitman Hattiesburg Poplarville Wiggins Gravity model Area Weighted Historic Wildfire Risk (Winter) 1 0 CDM Model

t-test Analysis: CDM and Gravity model prediction in the risk zones H0: CDM – Gravity =0 < • This suggests that both the models agree in the prediction of the shaded zone.

Comparison of CDM and Gravity models for number of Fires in Different Risk Zones • Gravity model shows equal frequency of fires in medium, high and very highrisk zones. • CDM model predicts that the frequency of fires increases with the severity of the risk, and most fires lie in high and very high-risk zones. • Overall, CDM model performs better than Gravity model for the prediction of wildfire frequency. 1400 1200 CDM Actual Number of Fires Gravity 1000 800 600 400 200 0 V. Low Low Medium Risk Zone High V. High

Comparison of CDM and Gravity models for risk area in Different Risk Zones • Gravity model predicts almost 20% higher area for the very high risk region compared to the CDM model. • Almost uniform area distribution in Gravity model is expected as it depends only on the distance from the city Gravity 35 CDM 30 % Risk Area CDM model predicts that the risk area decreases as the severity of risk increases. • 40 Observation 25 20 15 10 5 0 V. Low Low Medium High V. High Overall, CDM wildfire area predictions agree with the expected trend in the region, however the area is significantly over-predicted in very low-risk zone.

Annual Regression Analysis of the models y = 0.8917x + 0.0637 R² = 0.7316 0.6 0.4 0.2 Annual 0.8 Normalized Historic Fire Risk Normalized Historic Fire Risk 0.8 y = 0.9237x + 0.0468 R² = 0.7966 0.6 0.4 0.2 Fire Potential Linear (Fire Potential) 0 Fire Potential Linear Regression 0 0 0.2 0.4 0.6 Gravity-Model Fire Potential 0.8 0 0.2 0.4 0.6 0.8 CDM Fire Potential • Results showed Gravity and CDM models perform quite well with an R2 = 0.731 and R2=0.80 respectively. • CDM model performs slightly better than the gravity model for the annual analysis.

Seasonal Regression Analysis of the Gravity model y = 0.5978x + 0.0792 R² = 0.6192 0.6 0.4 0.2 y = 0.8145x + 0.0836 R² = 0.7543 0.8 Normalized Historic Fire Risk Normalized Historic Fire Risk 0.8 0.6 0.4 0.2 Fire Potential Linear (Fire Potential) 0 0 0 • • • Fire Potential Linear (Fire Potential) 0.2 0.4 0.6 Gravity Model Potential (Summer) 0.8 0 0.2 0.4 0.6 Gravity Model Potential (Winter) 0.8 In summer, the figure shows slope of 0.597, intercept = 0.0792, and R2 = 0.619. In winter, the figure shows slope of 0.8145, intercept = 0.0836, and R2 = 0.7543. Overall, model performance is better in winter than in summer. This is expected as winter fires are more anthropogenically related than summer fires.

Seasonal Regression Analysis of the CDM model y = 0.6669x + 0.1313 R² = 0.6057 0.6 0.4 0.2 0.8 Normalized Historic Fire Risk Normalized Historic Fire Risk 0.8 y = 0.9889x + 0.0212 R² = 0.8725 0.6 0.4 0.2 Fire Potential Linear Regression Fire Potential Linear (Fire Potential) 0 0 0 • • • 0.2 0.4 0.6 (a) CDM Model Potential (Summer) 0.8 0 0.2 0.4 0.6 (b) CDM Potential (Winter) 0.8 In summer, the figure shows slope of 0.667, intercept = 0.1313, and R2 = 0.6057. In winter, the figure shows slope of 0.99, intercept = 0.0212, and R2 = 0.8725. CDM model also shows better agreement with observation in winter compared to Gravity model.

Observational Data: Conclusions  Over 65% of the wildfires in the region are due to arson, and most burn an area of 10-50 acres  About 2/3rd of the wildfires occur in winter season and shows peak in the late and early winter  Up to 60-70% of the wildfires lie within 1.5 kilometer buffer of the designated highways  Winter wildfires are clustered near the populated regions and roads connecting them, whereas summers fires are more-or-less evenly distributed. In CDM: Anthropogenic factors influencing wildfire ignition are grouped as “global” and “local variables” Global variable (Population) modeled from Gravity model with damping inside the city Local variables as convection and diffusion  Diffusion and Convection fluxes from Inter-model transportation corridors and traffic volume respectively Calibration of unknown model coefficients – convection, diffusion and damping  using observational data and implemented in GIS

Conclusions  An analytic model is developed assuming that the transportation corridor and city potential are uncorrelated;  the traffic volume and population influences the city potential along the circumferential and radial directions, respectively  Wildfire ignition potential correlates best with medium road density , i.e., peaks in the suburban area, and are aligned along the busy roads  CDM model predicts an increase in wildfire frequency whereas the Gravity model shows peak frequency in medium risk zone.  Gravity and CDM model predictions compare well with each other for highrisk zone, but disagree in very high-, medium- and low-risk zones  Averaged wildfire area predicted by CDM model decreases with the increase in severity of the risk while Gravity model predicts almost uniform wildfire area in all the risk zones.

Conclusions  Wildfire risk distribution predicted by both the models perform better in winter than in summer  In the winter season, CDM model outperforms the Gravity model, in the wildfire predictions  Overall, CDM model preforms better than the Gravity model both for the prediction of wildfire frequency, risk area and potential distribution.  The wildfire ignition model developed herein can:  provide a static ignition layer, which can be combined with dynamic meteorological conditions and fuel layers within GIS framework to refine the locations and seasonal variations of the wildfire risks.  helps fire managers better plan wildfire mitigation (fuel reduction) and stage equipment geographically  even if they can't reduce fuels, the fire managers can stage equipment in the areas of drought with high ignition probability.  be used for land use planning and development, and to predict initiation of wildfires.

References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. Ayeni, M.A.O., 1979. Concepts and Techniques in Urban Analysis. London, Croom Helm Books. Ayeni, B., 1992. A Place for everything and everything in its Place, An Inaugural Lecture, University of Ibadan. Batty, M., 1976. Urban Modelling: Algorithms, Calibrations, Predictions, Cambridge, UK: Cambridge University Press. BBC, 2012. http://www.bbc.co.uk/news/world-us-canada-18632545 Brewer, J.S. and Rogers C.H., 2006. Relationships between prescribed burning and wildfire occurrence and intensity in pine–hardwood forests in north Mississippi, USA. International Journal of Wildland Fire, 15, 203–211. Cooke, W.H., Grala, K., Evans, D.L. and Collins, C., 2007a. Assessment of Pre- and Post-Katrina Fuel Conditions as a Component of Fire Potential Modeling for Southern Mississippi. Journal of Forestry. Society of American Foresters. 105(8), 389-397. Cooke, W.H., Anantharaj, V., Wax L.C., Choi, J., Grala, K., Jolly, M., Dixon, P.G., Dyer, J., Evans, D.L. and Goodrich, G.B., 2007b. Integrating climatic and fuels information into National Fire Risk Decision Support Tools. In Proceedings of the Fire environmentinnovations, management, and policy. Fort Collins, CO: USDA Forest Service, Rocky Mountain Research Station. Destin, FL. Disney, M., Lewis, P., & Saich, P. (2006). 3D modelling of forest canopy structure for remote sensing simulations in the optical and microwave domains. Remote Sensing of Environment, 100(1), 114-132. Gilreath, J.M., 2006. Validation of variables for the creation of a descriptive fire potential model for the Southeastern Fire District of Mississippi (Thesis), Starkville: Mississippi State University. Grala, K. and Cooke, W.H., 2010, Spatial and temporal characteristics of wildfires in Mississippi, USA, International Journal of Wildland Fire, 19(1), 14–28. Johnson, C., and Govatski, D. (2013). Forests for the People: The Story of America's Eastern National Forests. Island Press USDA Forest Service, Rocky Mountain Research Service Proceedings, Eds. P.N. Omi and L.A. Joyce, pp 379–385. Fort Collins, CO. National Interagency Fire Center (NIFC). Wildland Fire Statistics. Accessed April 20, 2006, Boise, Idaho. http://www.nifc.gov/stats/wildlandfire.html. ORNL, 2011. Freight Management and Operations, Federal Highway Administration, http://faf.ornl.gov/fafweb/Data/Freight_Traffic_Analysis/chap5.htm Pyne, S.J., Andrews, P.L and Laven, R.D. 1996. Introduction to wildland fire. New York: Wiley. Rein, G. (2009) Smouldering combustion phenomena in science and technology. International Review of Chemical Engineering 1: 3–18. Sadasivuni, R.R., 2007. Gravity Model to Detect Forest Fire–Prone Areas in the Southeast Fire District of Mississippi (MS Thesis), Mississippi State University: Department of Geosciences, Mississippi State University. Sadasivuni, R. R., O'Hara, C. G., Nobrega, R. and Dumas, J., 2009. A Transportation Corridor Case Study For Multi-Criteria Decision Analysis. In proceedings American Society of Photogrammetry and Remote Sensing Conference, Baltimore, MD,. Sadasivuni, R., Cooke, W.H. and Bhushan, S., 2013. Wildfire Risk Prediction in Southeastern Mississippi Using Population Interaction. Ecological Modeling. Shields, R., 1997. Flow as a new paradigm. Space and Culture, 1, 1-7. Fire Triangle, (2013) http://www.sc.edu/ehs/modules/Fire/01_triangle.htm

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