Forecasting occurrences of wildfires

1
Forecasting occurrences of wildfires
earthquakes using point processes with
directional covariates
Frederic Paik Schoenberg, UCLA
Statistics Collaborators Haiyong Xu, Ka Wong.
Also thanks to Yan Kagan, James Woods, USGS,
SCEC, NCEC, Harvard catalogs.
2

1. Background
2. Existing point process models for wildfires
   earthquakes
3. Problems, esp. wind moment tensors
4. Directional kernel direction wind
5. Using focal mechanisms in ETAS

3
Los Angeles County wildfire centroids,
1960-2000
4

• 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)
• 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.

5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8

• Global Earthquake Data
• Local e.q. catalogs tend to have problems, esp.
  missing data.
• 1977 Harvard (global) catalog created.
• Considered the most complete. Errors best
  understood.
• Harvard Catalog, 1/1/84 to 4/1/07
• Shallow events only (depth lt 70km)
• Mw 3.0
• Only focal mechanism estimates of high or medium
  quality

9
(No Transcript)
10
(No Transcript)
11
2. Existing models for forecasting eqs
fires NFDRSs Burning Index (BI) Uses daily
weather variables, drought index, and
vegetation info. Human interactions excluded.
12
Some BI equations (From Pyne et al.,
1996) Rate of spread R IR x (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 Gmax (b /
bop)A expA(1- b / bop). Maximum reaction
velocity Gmax 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.
13
1
14

• Point Process Models
• Conditional rate l(t, x1, , xk q) e.g.
  x1location, x2 area.
• a non-neg. predictable process such that ? (dN
  -ldm) is a martingale.
• Wildfire incidence seems roughly multiplicative.
• (only marginally significant in separability
  test)
• Roughly exponential in relative humidity (RH),
  windspeed (W), precipitation (P), avg precip over
  prior 60 days (A), temperature (T), and date (D).
• Tapered Pareto size distribution f, smooth
  spatial background m.
• l(t,x,a) f(a) m(x)
• b1expb2R(t) b3W(t) b4P(t) b5A(t) b6T(t)
  b7b8 - D(t)2
• Or, split by season
• l(t,x,a) f(a) m(x)
• B1,i expb2,i R(t) b3,i W(t) b4,i P(t) b5,i
  A(t) b6,i T(t)

15
(No Transcript)
16
(No Transcript)
17

• Aftershock activity described by modified Omori
  Law K/(tc)p

18
(No Transcript)
19

• 3. Some problems with existing models
• BI has low correlation with wildfire.
• Corr(BI, area burned) 0.09
• 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)

20
(No Transcript)
21
(No Transcript)
22
(No Transcript)
23

• 3. Some problems with existing models, continued
• Wildfires no use of wind direction.
• Santa Ana winds (from NE) typically hot dry.
• ETAS no use of focal mechanisms.
• Summary of principal direction of motion in an
  earthquake, as well as resulting stress changes
  and tension/pressure axes.

24
4. Directional kernel regression and wind ?i
yi gk(q - qi) / ? gk(q - qi), using a circular
kernel g, such as the von-Mises density gk(q)
expk cos(q)/2p I0(k).
25
4. Directional kernel regression and wind f(q)
estimated via ?i yi gk(q - qi) / ? gk(q -
qi), using a circular kernel g, such as the
von-Mises density gk(q) expk cos(q)/2p I0(k).
26
RHlt 15 15 lt RH lt 30
27
Improvement in forecasting
28
5. Using focal mechanisms in ETAS
29
Distance to next event, in relation to nodal
plane of prior event
30
In ETAS (Ogata 1998), l(t,x,m) f(m)m(x) ?i
g(t-ti, x-xi, mi), where f(m) is exponential,
m(x) is estimated by kernel smoothing,
and
i.e. the spatial triggering component, in polar
coordinates, has the form g(r, q) (r2 d)q
. Looking at inter-event distances in Southern
California, as a function of the direction qi of
the principal axis of the prior event, suggests
g(r, q qi) g1(r) g2(q - qi r), where g1 is
the tapered Pareto distribution, and g2 is the
wrapped exponential.
31
(No Transcript)
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
tapered Pareto / wrapped exp. ? biv.
normal (Ogata 1998) ? Cauchy/ ellipsoidal (Kagan
1996) ?
37
Thinned residuals
Data ? tapered Pareto / wrapped exp. ?
Cauchy/ ellipsoidal (Kagan 1996) ? biv.
normal (Ogata 1998) ?
38
Tapered pareto / wrapped exp.
Cauchy / ellipsoidal
39
Cauchy/ ellipsoidal (Kagan 1996)
biv. normal (Ogata 1998)
tapered pareto / wrapped exp.
40

• Conclusions
• The impact of directional variables on a scalar
  response can readily be summarized using
  directional kernel regression.
• The resulting function can then be incorporated
  into point process models, to improve forecasting
  of the response variable.
• Wildfires wind direction is very significant,
  and models incorporating wind direction and other
  weather variables forecast about twice as well as
  the BI (which uses these same variables).
• Earthquakes focal mechanism estimates should be
  used to improve triggering functions in ETAS
  models.

41
(No Transcript)
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
Greenness (UCLA IoE)
46
(IoE)
47
(No Transcript)
48
(No Transcript)
49

• On the Predictive Value of Fire Danger Indices
• From Day 1 of Toronto workshop (05/24/05)
• Robert McAlpine It 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.

50
(No Transcript)
51
(No Transcript)
52
(No Transcript)