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.
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Forecasting occurrences of wildfires & earthquakes using point processes with directional covariates
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. Background - PowerPoint PPT Presentation
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Forecasting occurrences of wildfires & earthquakes using point processes with directional covariates
Frederic Paik Schoenberg, UCLA StatisticsCollaborators: Haiyong Xu, Ka Wong. Also thanks to: Yan Kagan, James Woods, USGS, SCEC, NCEC, & Harvard catalogs.
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
Los Angeles County wildfire centroids, 1960-2000
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)
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 < 70km)• Mw 3.0+• Only focal mechanism estimates of high or medium quality
2. Existing models for forecasting eqs & fires
NFDRS’s Burning Index (BI): Uses daily weather variables, drought index, and
vegetation info. Human interactions excluded.
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/).
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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Point Process Models Conditional rate (t, x1, …, xk; ): [e.g. x1=location, x2 = area.]a non-neg. predictable process such that ∫ (dN -d) is a martingale.
Aftershock activity described by modified Omori Law: K/(t+c)p
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)
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.
4. Directional kernel regression and wind:∑i yi g( - i) / ∑ g( - i),
using a circular kernel g, such as the von-Mises densityg() = exp{ cos()}/2 I0().
4. Directional kernel regression and wind:f() estimated via ∑i yi g( - i) / ∑ g( - i),
using a circular kernel g, such as the von-Mises densityg() = exp{ cos()}/2 I0().
RH< 15% 15% < RH < 30%
Improvement in forecasting
5. Using focal mechanisms in ETAS
Distance to next event, in relation to nodal plane of prior event
In ETAS (Ogata 1998), (t,x,m) = f(m)[(x) + ∑i g(t-ti, x-xi, mi)],where f(m) is exponential, (x) is estimated by kernel smoothing,
i.e. the spatial triggering component, in polar coordinates, has the form:
g(r, ) = (r2 + d)q .
Looking at inter-event distances in Southern California, as a
function of the direction of the principal axis of the prior event,
• 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.
Greenness (UCLA IoE)
(IoE)
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 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.