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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).

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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NFDRS’s Burning Index (BI): Uses daily weather variables, drought index, and

vegetation info. Human interactions excluded.

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Some BI equations: (From Pyne et al., 1996:)

Rate of spread: R = IR (1 + w+ s) / (b Qig). Oven-dry bulk density: b = w0/.

Reaction Intensity: IR = ’ wn h Ms. Effective heating number: = exp(-138/).

Optimum reaction velocity: ’ = ’max ( / op)A exp[A(1- / op)].

Maximum reaction velocity: ’max = 1.5 (495 + 0.0594 1.5) -1.

Optimum packing ratios: op = 3.348 -0.8189. A = 133 -0.7913.

Moisture damping coef.: M = 1 - 259 Mf /Mx + 5.11 (Mf /Mx)2 - 3.52 (Mf /Mx)3.

Mineral damping coef.: s = 0.174 Se-0.19

(max = 1.0).

Propagating flux ratio: = (192 + 0.2595 )-1 exp[(0.792 + 0.681 0.5)( + 0.1)].

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)

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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) = 1exp{2R(t) + 3W(t) + 4P(t)+ 5A(t;60) + 6T(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?

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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:

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r = 0.16(s

q m

)

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32(F)

(sq

m)

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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) = 1exp{2R(t) + 3W(t) + 4P(t)+ 5A(t;60)

+ 6T(t) + 7[8 - D(t)]2} (x) g(a).Compare with:

(t,x,a) = 1exp{2B(t)} (x) g(a), where B = RH or BI.

Relative AICs (Poisson - Model, so higher is better):

Poisson RH BI Model

0 262.9 302.7 601.1

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Comparison of Predictive Efficacy

False alarms

per year

% of fires correctly alarmed

BI 150: 32 22.3

Model : 32 34.1

BI 200: 13 8.2

Model : 13 15.1

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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)

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Towards improved modeling

• Time-since-fire (fuel age)• Wind direction

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Towards improved modeling

• Time-since-fire (fuel age)• Wind direction• Land use, greenness, vegetation

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Greenness (UCLA IoE)

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(IoE)

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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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(cm

)

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Conclusions:(For Los Angeles County data, Jan 1976- 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: S3 seems quite powerful.

Next lecture: earthquakes: Ogata’s residual analysis, prototypes, and non-simple point process models.