Background Problems with existing models (BI) A separable point process model Testing separability

1. 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.

2. Los Angeles County wildfires, 1960-2000

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.

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 = IRx (1 + fw+ fs) / (rbe Qig). Oven-dry bulk density: rb = w0/d. Reaction Intensity: IR = G’ wn h hMhs. Effective heating number: e = exp(-138/s). Optimum reaction velocity: G’ = G’max (b/ bop)A exp[A(1- b / bop)]. Maximum reaction velocity: G’max = s1.5 (495 + 0.0594 s1.5) -1. Optimum packing ratios: bop = 3.348 s -0.8189. A = 133 s -0.7913. Moisture damping coef.: hM = 1 - 259 Mf /Mx + 5.11 (Mf /Mx)2 - 3.52 (Mf /Mx)3. Mineral damping coef.: hs = 0.174 Se-0.19 (max = 1.0). Propagating flux ratio: x = (192 + 0.2595 s)-1 exp[(0.792 + 0.681 s0.5)(b + 0.1)]. Wind factors: sw = CUB (b/bop)-E. C = 7.47 exp(-0.133 s0.55). B = 0.02526 s0.54. E = 0.715 exp(-3.59 x 10-4 s). Net fuel loading: wn = w0 (1 - ST). Heat of preignition: Qig = 250 + 1116 Mf. Slope factor: fs = 5.275 b -0.3(tan f)2. Packing ratio: b = rb / rp.

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. 1983 Simard 1987 Preisler 2005 Mandallaz 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.

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) = 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)

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) = 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)

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) = 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)

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) = 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)

21. Model Construction • Relative Humidity, Windspeed, Precipitation, Aggregated rainfall • over previous 60 days, Temperature, Date. • Tapered Pareto size distribution f, smooth spatial background m. l(t,x,a) = b1exp{b2R(t) + b3W(t) + b4P(t)+ b5A(t;60) + b6T(t) + b7[b8 - D(t)]2} m(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 l 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: S5 = mean absolute difference at the observed points. S6 = maximum absolute difference at observed points.

25. S3 seems to be most powerful for large-scale non-separability:

26. However, S3 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 S3 indicate separability, but the L-function after rescaling shows some clustering of size and date:

30. r = 0.16 (sq m)

32. (sq m) (F)

35. Model Construction • Wildfire incidence seems roughly separable. (only area/date significant in separability test) • Tapered Pareto size distribution f, smooth spatial background m. [*] l(t,x,a) = b1exp{b2R(t) + b3W(t) + b4P(t)+ b5A(t;60) + b6T(t) + b7[b8 - D(t)]2} m(x) g(a). Compare with: [**] l(t,x,a) = b1exp{b2B(t)} m(x) g(a), where B = RH or BI. Relative AICs (Poisson - Model, so higher is better):

39. Comparison of Predictive Efficacy

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)

41. (years)

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

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

46. Greenness (UCLA IoE)

47. (IoE)

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

49. (cm)