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 techniques Earthquakes: next lecture.

2 Los Angeles County wildfires,

3 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).  Damages. 2003: 738,000 acres; 3600 homes; 26 lives. (Oct 24 - Nov 2: 700,000 acres; 3300 homes; 20 lives) Bel Air 1961: 6,000 acres; $30 million. Clampitt 1970: 107,000 acres; $7.4 million.

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6 NFDRS’s Burning Index (BI): Uses daily weather variables, drought index, and vegetation info. Human interactions excluded.

7 Some BI equations : (From Pyne et al., 1996:) Rate of spread: R = I R  (1 +  w  +  s ) / (  b  Q ig ).Oven-dry bulk density:  b = w 0 / . Reaction Intensity: I R =  ’ w n h  M  s.Effective heating number:  = exp(-138/  ). Optimum reaction velocity:  ’ =  ’ max (  /  op ) A exp[A(1-  /  op )]. Maximum reaction velocity:  ’ max =  1.5 (  1.5 ) -1. Optimum packing ratios:  op =  A = 133  Moisture damping coef.:  M = M f /M x (M f /M x ) (M f /M x ) 3. Mineral damping coef.:  s = S e (max = 1.0). Propagating flux ratio:  = (  ) -1 exp[(  0.5 )(  + 0.1)]. Wind factors:  w = CU B (  /  op ) -E. C = 7.47 exp(  0.55 ). B =  E = exp(-3.59 x  ). Net fuel loading: w n = w 0 (1 - S T ).Heat of preignition: Q ig = M f. Slope factor:  s =  -0.3 (tan  2.Packing ratio:  =  b /  p.

8 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 Simard 1987 Preisler 2005 Mandallaz and Ye 1997 (Eur/Can), Viegas et al (Eur/Can), Garcia Diez et al (DFR), Cruz et al (Can). Spread: Rothermel (1991), Turner and Romme (1994), and others.

9 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) = !Corr(date, area burned) = 0.06 !Corr(windspeed, area burned) = Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)

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14 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) = !Corr(date, area burned) = 0.06 !Corr(windspeed, area burned) = Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)

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16 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) = !Corr(date, area burned) = 0.06 !Corr(windspeed, area burned) = Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)

17 r = 0.16 (sq m)

18 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) = !Corr(date, area burned) = 0.06 !Corr(windspeed, area burned) = Too high in Winter (esp Dec and Jan) Too low in Fall (esp Sept and Oct)

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21 Model Construction Relative Humidity, Windspeed, Precipitation, Aggregated rainfall over previous 60 days, Temperature, Date. Tapered Pareto size distribution f, smooth spatial background . (t,x,a) =  1 exp{  2 R(t) +  3 W(t) +  4 P(t)+  5 A(t;60) +  6 T(t) +  7 [  8 - D(t)] 2 }  (x) g(a). … More on the fit of this model later. First, how can we test whether a separable model like this is appropriate for this dataset?

22 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)

23 Testing separability in marked point processes: May also consider: S 5 = mean absolute difference at the observed points. S 6 = maximum absolute difference at observed points.

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25 S 3 seems to be most powerful for large-scale non-separability:

26 However, S 3 may not be ideal for Hawkes processes, and all these statistics are terrible for inhibition processes:

27 For Hawkes & inhibition processes, rescaling according to the separable estimate and then looking at the L-function seems much more powerful:

28 Testing Separability for Los Angeles County Wildfires:

29 Statistics like S 3 indicate separability, but the L-function after rescaling shows some clustering of size and date:

30 r = 0.16 (sq m)

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35 Model Construction Wildfire incidence seems roughly separable. (only area/date significant in separability test) Tapered Pareto size distribution f, smooth spatial background .  (t,x,a) =  1 exp{  2 R(t) +  3 W(t) +  4 P(t)+  5 A(t;60) +  6 T(t) +  7 [  8 - D(t)] 2 }  (x) g(a). Compare with:  (t,x,a) =  1 exp{  2 B(t)}  (x) g(a), where B = RH or BI. Relative AICs (Poisson - Model, so higher is better): PoissonRHBIModel 

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39 Comparison of Predictive Efficacy False alarms per year % of fires correctly alarmed BI 150: Model  : BI 200:138.2 Model  :1315.1

40 One possible problem: human interactions. …. but BI has been justified for decades based on its correlation with observed large wildfires (Mees & Chase, 1993; Andrews and Bradshaw, 1997). Towards improved modeling Time-since-fire (fuel age)

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42 Towards improved modeling Time-since-fire (fuel age) Wind direction

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44 Towards improved modeling Time-since-fire (fuel age) Wind direction Land use, greenness, vegetation

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46 Greenness (UCLA IoE)

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48 Towards improved modeling Time-since-fire (fuel age) Wind direction Land use, greenness, vegetation Precip over previous 40+ days, lagged variables

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52 Conclusions: (For Los Angeles County data, Jan Dec 2000:) BI is positively associated with fire incidence and burn area, though its predictive value seems limited. Windspeed has a higher correlation with burn area, and a simple model using RH, windspeed, precipitation, aggregated rainfall over previous 60 days, temperature, & date outperforms BI. For multiplicative models (and sometimes for additive models), can estimate parameters separately. Separability testing: S 3 seems quite powerful. Next lecture: earthquakes: Ogata’s residual analysis, prototypes, and non-simple point process models.