1 Applications of point process modeling, separability testing, & estimation to wildfire hazard assessment 1. Background 2. Problems with existing models (BI) 3. A separable point process model 4. Testing separability 5. Alarm rates & other basic assessment techniq Earthquak es: next lecture.
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Background Problems with existing models (BI) A separable point process model Testing separability
Applications of point process modeling, separability testing, & estimation to wildfire hazard assessment. Background Problems with existing models (BI) A separable point process model Testing separability Alarm rates & other basic assessment techniques. Earthquakes: next lecture. - PowerPoint PPT Presentation
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Applications of point process modeling, separability testing, & estimation to wildfire hazard assessment
1. Background2. Problems with existing models (BI)3. A separable point process model4. Testing separability5. Alarm rates & other basic assessment techniques
Earthquakes: next lecture.
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Los Angeles County wildfires, 1960-2000
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Background Brief History.
• 1907: LA County Fire Dept.• 1953: Serious wildfire suppression.• 1972/1978: National Fire Danger Rating System.
(Deeming et al. 1972, Rothermel 1972, Bradshaw et al. 1983)• 1976: Remote Access Weather Stations (RAWS).
Wind factors: w = CUB (/op)-E. C = 7.47 exp(-0.133 0.55). B = 0.02526 0.54. E = 0.715 exp(-3.59 x 10-4 ).
Net fuel loading: wn = w0 (1 - ST). Heat of preignition: Qig = 250 + 1116 Mf.
Slope factor: s = 5.275 -0.3 (tan 2. Packing ratio: = b / p.
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On the Predictive Value of Fire Danger Indices:
From Day 1 (05/24/05) of Toronto workshop:• Robert McAlpine: “[DFOSS] works very well.”• David Martell: “To me, they work like a charm.”• Mike Wotton: “The Indices are well-correlated with fuel moisture and fire
activity over a wide variety of fuel types.”• Larry Bradshaw: “[BI is a] good characterization of fire season.”
Evidence?
• FPI: Haines et al. 1983 Simard 1987 Preisler 2005Mandallaz and Ye 1997 (Eur/Can), Viegas et al. 1999 (Eur/Can), Garcia Diez et al. 1999 (DFR), Cruz et al. 2003 (Can).
• Spread: Rothermel (1991), Turner and Romme (1994), and others.
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Some obvious problems with BI:• Too additive: too low when all variables are med/high
risk.
• Low correlation with wildfire. Corr(BI, area burned) = 0.09 Corr(BI, # of fires) = 0.13 Corr(BI, area per fire) = 0.076! Corr(date, area burned) = 0.06! Corr(windspeed, area burned) = 0.159
• Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)
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Some obvious problems with BI:• Too additive: too high for low wind/medium RH,
Misses high RH/medium wind. (same for temp/wind).
• Low correlation with wildfire. Corr(BI, area burned) = 0.09 Corr(BI, # of fires) = 0.13 Corr(BI, area per fire) = 0.076! Corr(date, area burned) = 0.06! Corr(windspeed, area burned) = 0.159
• Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)
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More problems with BI:
• Low correlation with wildfire. Corr(BI, area burned) = 0.09 Corr(BI, # of fires) = 0.13 Corr(BI, area per fire) = 0.076! Corr(date, area burned) = 0.06! Corr(windspeed, area burned) = 0.159
• Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)
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r = 0.16(s
q m
)
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More problems with BI:
• Low correlation with wildfire. Corr(BI, area burned) = 0.09 Corr(BI, # of fires) = 0.13 Corr(BI, area per fire) = 0.076! Corr(date, area burned) = 0.06! Corr(windspeed, area burned) = 0.159
• Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)
… More on the fit of this model later. First, how can we test whether a separable model like this is
appropriate for this dataset?
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Testing separability in marked point processes:
Construct non-separable and separable kernel estimates of by smoothing over all coordinates simultaneously or separately. Then compare these two estimates: (Schoenberg 2004)
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Testing separability in marked point processes:
May also consider:
S5 = mean absolute difference at the observed points.
S6 = maximum absolute difference at observed points.
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S3 seems to be most powerful for large-scale non-separability:
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However, S3 may not be ideal for Hawkes processes, and all these statistics are terrible for inhibition processes:
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For Hawkes & inhibition processes, rescaling according to the separable estimate and then looking at the L-function seems much more powerful:
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Testing Separability for Los Angeles County Wildfires:
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Statistics like S3 indicate separability, but the L-function after rescaling shows some clustering of size and date: