Convection–Diffusion Model for the Prediction of Anthropogenically-Initiated Wildfire Ignition

Abstract

A spatial interaction model to predict anthropogenically-initiated accidental and incendiary wildfire ignition probability is developed using fluid flow analogies for human movement patterns. Urban areas with large populations are identified as the sites of global influencing factors, and are modeled as the gravity term. The transportation corridors are identified as local influencing factors, and are modeled using fluid flow analogy as diffusion and convection terms. The model is implemented in ArcGIS, and applied for the prediction of wildfire hazard distribution in southeastern Mississippi. The model shows 87 % correlation with historic data in the winter season, whereas the previously developed gravity model shows only 75 % correlation. The normalized error for convection–diffusion model predictions is about 5 % in the winter season, whereas the gravity model shows an error of 7 %. The proposed model is robust as it couples a multi-criteria behavioral pattern within a single dynamic equation to enhance predictive capability. At the same time, the proposed model is more costly than the gravity model as it requires evaluation of distance from intermodal transportation corridors, transportation corridor density, and traffic volume maps. Nonetheless, the model is developed in a modular fashion, such that either global or local terms can be neglected if required.

Keywords

Anthropogenic-fire / Convection–diffusion model / Fire ignition potential / Mississippi / Wildfire hazard

References

[1] Ashworth A, Evans D, Cooke W, Londo A, Collins C, Neuenschwander A. Predicting southeastern forest canopy heights and fire fuel models using GLAS data. Photogrammetric Engineering and Remote Sensing, 2010, 76(8): 915-922 10.14358/PERS.76.8.915

[2] Ayeni MAO. Concepts and techniques in urban analysis, 1979, London: Croom Helm Books

[3] Brewer JS, Rogers CH. Relationships between prescribed burning and wildfire occurrence and intensity in pine-hardwood forests in north Mississippi, USA. International Journal of Wildland Fire, 2006, 15: 203-211 10.1071/WF05068

[4] Burgan RE, Klaver RW, Klaver JM. Fuel models and fire potential from satellite and surface observations. International Journal of Wildland Fire, 1998, 8(3): 159-170 10.1071/WF9980159

[5] Cardille JA, Ventura SJ, Turner MG. Environmental and social factors influencing wildfires in the upper Midwest. United States. Ecological Applications, 2001, 11(1): 111-127 10.1890/1051-0761(2001)011[0111:EASFIW]2.0.CO;2

[6] Catry FX, Rego FC, Bação FL, Moreira F. Modeling and mapping wildfire ignition risk in Portugal. International Journal of Wildland Fire, 2009, 18(8): 921-931 10.1071/WF07123

[7] Chan Y. Location theory and decision analysis, 2011 2 Berlin: Springer 10.1007/978-3-642-15663-2

[8] Cooke WH, Grala K, Evans DL, Collins C. Assessment of pre- and post-Katrina fuel conditions as a component of fire potential modeling for southern Mississippi. Journal of Forestry, 2007, 105(8): 389-397.

[9] Dickson BG, Prather JW, Xu Y, Hampton HM, Aumack EN, Sisk TD. Mapping the probability of large fire occurrence in northern Arizona, USA. Landscape Ecology, 2006, 21(5): 747-761 10.1007/s10980-005-5475-x

[10] Dutta, S. 2010. Spatio-temporal characteristics of Mississippi wildfires. Thesis, Mississippi State University, Starkville, MS.

[11] EC (European Commission). 2012. The European Forest Fire Information System: New fire causes classification scheme adopted for the European Fire Database. European Commission—Joint Research Centre Report, Version 1, April 2012.

[12] Eccleston CH. Environmental impact assessment: A guide to best professional practices, 2011, Boca Raton, Fl: CRC Press 10.1201/b10717

[13] Faghri, A.J., A.J. Lang, and H.E. Henck. 2001. An AL-based hybrid system for locating of park-and-ride facilities. Transportation Research Board, 80th Annual Meeting, Washington, DC.

[14] Faivre N, Jin Y, Goulden ML, Randerson JT. Controls on the spatial pattern of wildfire ignitions in Southern California. International Journal of Wildland Fire, 2014, 23(6): 799-811 10.1071/WF13136

[15] Fotheringham AS, O’Kelly ME. Spatial interaction models: Formulations and applications, 1989, Dordrecht: Kluwer Academic Publishers

[16] Fowler C, Konopik E. The history of fire in the southern United States. Human Ecology Review, 2007, 14(2): 165-176.

[17] Gilreath, J.M. 2006. Validation of variables for the creation of a descriptive fire potential model for the Southeastern Fire District of Mississippi. Thesis, Mississippi State University, Starkville, MS.

[18] Grala K, Cooke WH. Spatial and temporal characteristics of wildfires in Mississippi, USA. International Journal of Wildland Fire, 2010, 19(1): 14-28 10.1071/WF08104

[19] Haight RG, Cleland DT, Hammer RB, Radeloff VC, Rupp TS. Assessing fire risk in the wildland-urban interface. Journal of Forestry, 2004, 102(7): 41-48.

[20] Heyerdahl EK, Brubaker LB, Agee JK. Spatial controls of historical fire regimes: A multiscale example from the interior west, USA. Ecology, 2001, 82(3): 660-678 10.1890/0012-9658(2001)082[0660:SCOHFR]2.0.CO;2

[21] Holmes E, Lewis M, Banks J, Veit R. Partial differential equations in ecology: Spatial interactions and population dynamics. Ecology, 1994, 75(1): 17-29 10.2307/1939378

[22] Huff DL. A probabilistic analysis of shopping center trade areas. Land Economics, 1963, 39(1): 81-90 10.2307/3144521

[23] Kathrin F. Eiselt HA, Frederick HS, Camille PC, Marianov V. Central places: The theories of von Thünen. Foundations of location analysis, International Series in Operations Research & Management Science, 155, 2011, New York: Springer 471-505.

[24] Kraskey R. Incendiary wildfires: Minnesota gets tough on arsonists. Fire Management Notes, 1985, 46(1): 16-18.

[25] Kuhlken R. Setting the woods on fire: Rural incendiarism as protest. Geographical Review, 1999, 89(3): 343-363 10.2307/216155

[26] McCormack E. Using a GIS to enhance the value of travel diaries. Institute of Transportation Engineers Journal, 1999, 69(1): 38-43.

[27] Miller, C. 2003. Wildland fire use: A wilderness perspective on fuel management. Fire, fuel treatments, and ecological restoration. In USDA Forest Service, Rocky Mountain Research Service Proceedings, ed. P.N. Omi and L.A. Joyce, 379–385. Fort Collins, CO.

[28] Narayanaraj G, Wimberly MC. Influences of forest roads on the spatial pattern of human- and lightning-caused wildfire ignitions. Applied Geography, 2012, 32(2): 878-888 10.1016/j.apgeog.2011.09.004

[29] Oldham, K.T.S. 2008. The doctrine of description: Gustav Kirchhoff, classical physics, and the “purpose of all science” in 19th-century Germany. Ph.D. Thesis, University of California, Berkeley.

[30] Openshaw S. Neural network, genetic, and fuzzy logic models of spatial interaction. Environment & Planning A, 1998, 30(10): 1857-1872 10.1068/a301857

[31] ORNL (Oak Ridge National Laboratory). 2011. Freight management and operations. Federal Highway Administration, http://faf.ornl.gov/fafweb/Data/Freight_Traffic_Analysis/chap5.htm. Accessed 6 Nov 2014.

[32] Parsons, D.J. 2000. The challenge of restoring natural fire to wilderness. In Wilderness science in a time of change conference: Wilderness ecosystems, threats, and management. Proceedings RMRS-P-15, Vol 15, U.S. Department of Agriculture Forest Service, Missoula, Montana, ed. D.N. Cole, S.F. McCool, W.T. Borrie, and J. O’Laughlin, 276–282.

[33] Petrakis M, Psiloglou B, Lianou M, Keramitsoglou I, Cartalis C. Evaluation of forest fire risk and fire extinction difficulty at the mountainous park of Vikos–Aoos, Northern Greece: Use of remote sensing and GIS techniques. International Journal of Risk Assessment and Management, 2005, 5(1): 50-65 10.1504/IJRAM.2005.006612

[34] Pew, K.L., and C.P.S. Larsen. 2001. GIS analysis of spatial and temporal patterns of humancaused wildfires in the temperate rain forest of Vancouver Island, Canada. Forest Ecology and Management 140: 1–18.

[35] Porojan A. Trade flows and spatial effects: The gravity model revisited. Open Economies Review, 2001, 12(3): 265-280 10.1023/A:1011129422190

[36] Pyne SJ, Andrews PL, Laven RD. Introduction to wildland fire, 1996, New York: Wiley

[37] Rietveld P, Nijkamp MP. Hall R. Spatial interaction models. Handbook of transportation science, 2002, Norwell: Kluwer Academic Publishers 279-320.

[38] Romero-Calcerrada R, Novillo CJ, Millington JDA, Gomez-Jimenez I. GIS analysis of spatial patterns of human-caused wildfire ignition risk in the SW of Madrid (Central Spain). Landscape Ecology, 2008, 23(3): 341-354 10.1007/s10980-008-9190-2

[39] Sadasivuni, R. 2013. Urban fringe, transportation corridor convection-diffusion model for anthropogenically-initiated wildfire ignition prediction. Ph.D. dissertation, Mississippi State University.

[40] Sadasivuni, R.R., O’Hara, C.G., Nobrega, R., 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.

[41] Sadasivuni R, Cooke WH, Bhushan S. Wildfire risk prediction in southeastern Mississippi using population interaction. Ecological Modeling, 2013, 251: 297-306 10.1016/j.ecolmodel.2012.12.024

[42] Shields R. Flow as a new paradigm. Space and Culture, 1997, 1(1): 1-7 10.1177/120633129700100101

[43] Stephens SL. Forest fire causes and extent on United States Forest Service lands. International Journal of Wildland Fire, 2005, 14(3): 213-222 10.1071/WF04006

[44] Stillwell J, Duke OW, Dennett A. Technologies for migration and commuting analysis: Spatial interaction data applications, 2010, Hershey, PA: Business Science Reference (IGI Global) 10.4018/978-1-61520-755-8

[45] Stouffer SA. Intervening opportunities: A theory relating mobility and distance. American Sociological Review, 1940, 5(6): 845-867 10.2307/2084520

[46] Syphard A, Radeloff V, Keeley J, Hawbaker T, Clayton M, Stewart S, Hammer R. Human influence on California fire regimes. Ecological Applications, 2007, 17(5): 1388-1402 10.1890/06-1128.1

[47] Tobler WR. Spatial interaction patterns. Journal of Environmental Systems, 1976, 6(4): 271-301 10.2190/VAKC-3GRF-3XUG-WY4W

[48] USDA (U.S. Department of Agriculture) and USDI (U.S. Department of the Interior) Wildland fire and prescribed fire management policy: Implementation procedures reference guide, 1998, Boise: National Interagency Fire Center

[49] Vasconcelos MJP, Silva S, Tome M, Alvim M, Pereira JC. Spatial prediction of fire ignition probabilities: Comparing logistic regression and neural networks. Photogrammetric Engineering and Remote Sensing, 2001, 67(1): 73-81.

[50] Wilson JP, Burrough PA. GIS, dynamic modeling, geostatistics, and fuzzy classification: New sneakers for a new geography?. Annals of the Association of American Geographers, 1999, 89(4): 736-746 10.1111/0004-5608.00173

[51] Yang J, He HS, Shifley SR, Gustafson EJ. Spatial patterns of modern period human-caused fire occurrence in the Missouri Ozark Highlands. Forest Science, 2007, 53(1): 1-15.

[52] Zhai YS, Munn IA, Evans DL. Modeling forest fire probabilities in the South Central United States using FIA data. Southern Journal of Applied Forestry, 2003, 27(1): 11-17.